stability and lability in student conceptions: · web viewalthough the details of his stage theory...

Stability and lability in student conceptions:some evidence from a case study.

Presentation at BERA, Liverpool, 1993


Keith S. Taber

Paper presented at the British Educational Research Association Annual Conference, University of Liverpool,

September1993

Abstract.

Educational research from recent years (constructivism,

stage theories, and ‘alternative conceptions’ work) inform

us that the classroom teacher needs to be able to answer

key questions before embarking on the teaching of a topic:

“What do the students already ‘know’ about this topic?”

“How consistent is the ‘prior knowledge’ with what I wish to

teach?”

“What level of sophistication of ideas are the students

ready to deal with in this topic?”

“How difficult will it be to overcome resistance due to any

“students’ knowledge” that is inconsistent with the “expert

knowledge” I am trying to teach?”

These questions are compounded by the individual

differences that make each learner unique. The teacher

needs tested methodology to answer these questions

effectively, and the time to apply it! Failing this, the teacher

needs the results of research that looks at the likely range

of answers to these questions in the topic area and level of

class being taught. The present research is focussed on a

particular topic area (chemical bonding) and a specific level

(GCE A level), and is attempting to find out what general

answers can be obtained from working closely with

Keith S. Taber – [email protected] 1

mailto:[email protected]



individual students. The present paper concerns one

individual student I worked with during the pilot stage of my

research, and treats the data obtained as a case study. I will

be focussing on the questions of how readily basic learning

develops into more sophisticated understanding, and how

readily “misconceptions” may be displaced. Although the

data from one student in one topic area is no basis for

generalisation I believe the case study will be of interest to

all teachers and researchers who are concerned with

answering the key questions (above) in their own areas of

work.





Introduction: Purposes of this paper.

There are two main purposes to the present paper - both implied to some extent in my title. I wish to discuss the extent to which a young person’s ideas in a particular science topic area change, or remain static, over a period of time, and interweaved with this I would like to explore the strengths - and limitations - of a case study approach in such an enquiry.

I intend to achieve these purposes through the following stages. First I wish to make explicit some of the assumptions that underpin my research and explain why I believe it is important that such work is carried out. Then I will outline the methodology being developed. Next I will introduce the topic area that forms the focus of my enquiry. With this foundation in place I will then discuss my interpretations of an individual student’s developing conceptual framework in this area of science.

Theoretical stance underpinning this research.

The following principles form part of the researcher’s own belief systems, and are implicit in the current research:

1. Meaningful student learning involves construction of knowledge in the mind of the learner, and is not a simple process of transmission from the book/teacher/instructor/lecturer.

2. Construction of meaning by the learner is a process that does not occur in isolation, but in the context of existing knowledge and beliefs.

3. Each individual learner is unique, and different learners’ conceptual frameworks will not be identical.

4. Conceptual change does not usually involve the sudden acquisition of complex new conceptual frameworks, and the complete abandonment or forgetting of previously existing knowledge, but tends to proceed over time, and usually in a step-wise manner.

5. It is in the interests of the teacher who wishes to promote effective learning to know her students, and (as far as possible) their existing





frameworks of ideas.

6. The learner is not always explicitly aware of their own knowledge and beliefs, but is likely to hold tacit beliefs that may have significance for new learning.

7. The attainment of a particular concept or framework, as demonstrated by its application in a particular context, does not exclude the co-existence of other concepts or frameworks that may be inconsistent, and may be applied in another context, or even in the same context at another time.

None of these ideas are novel, and most are widely supported amongst researchers into learning in science. This stance places my own work within the rather catholic church of ‘constructivism’ (e.g. Pope & Watts, 1988; Watts & Bentley, 1987.) In addition the emphasis on the uniqueness and importance of individual learners leads to a research enquiry which leans towards what has been called ‘paradigm 2’ research (Gilbert & Pope, 1986, pp.22) - a more naturalistic form of enquiry (Guba, 1978) with an emphasis on qualitative data analysis. The present paper has no statistical content, but deals with the case study of a single learner.

Research has suggested that many teachers undertake their professional work as though they implicitly believe that teaching is about the transmission of ideas from the teacher’s mind to the pupil’s mind (Fox, 1983). Although there is much talk of teachers and lecturers being ‘facilitators’ this does not necessarily suggest a fundamentally different philosophy: rather that the source of the information passed into the student’s mind is some resource other than the teacher herself.

Any idea that learners have empty minds waiting to be filled with knowledge neatly packaged through education is untenable in view of our current understanding of human learning. It is important for teachers to understand this point, as a tacit belief in a ‘transmission’ model of teaching leads to a certain set of reasons that may be logically blamed for ‘learning failures’: the teacher did not explain properly, or the student was not paying attention, or there is some fault in the transmission line (the teacher could not be heard, or perhaps the student could not read the board.) Practising teachers will know of instances when they gave an excellent presentation, the class were quiet and attentive, a full set of clear notes were transmitted to Keith S. Taber – [email protected] 4




exercise books; but later work suggested that the teacher’s knowledge and understanding were not transmitted to the class. It is important therefore for teachers to learn more about the way their students learn, so that they may plan and act accordingly.

The seminal work of Jean Piaget made clear - what parents have known down the ages - that there is an element of biological maturation involved in determining what children of different ages are capable of understanding and learning. Although the details of his stage theory have been much criticised, Piaget’s genetic epistemology (Miller, 1986, Chapter 7) has been of immense value. Work on cognitive acceleration based at Kings College London (Adey, 1992) has grown out of this field, and many researchers still draw inspiration from Piagetian ideas (e.g. Case, 1989; Castro & Fernández, 1987). Aside from his own theoretical construction of the way children’s style of thinking develops as they grow, Piaget established the use of the clinical interview as a key technique in such studies (Posner & Gertzog, 1982). The value of this methodology seems apparent to anyone who reads the interview data: transcripts that make it very clear that young children think very differently to adults about many aspects of the natural world. Perhaps just as important is the way in which much of this undulate thinking appears to be untutored: children spontaneously develop ideas about parts of their environment, and the relationships between such phenomena.

The work of George Kelly is also of importance in understanding how people learn, and why sometimes - in the view of their teachers at least - they don’t. Kelly saw people-as-scientists, a metaphor that suggests that people try to make sense of the environment by a constant process of forming conjectures and hypotheses that are open to testing and change (Pope, 1982; Pope & Watts, 1988; Watts & Pope, 1989). Kelly uses the idea of polar ‘constructs’ by which people evaluate phenomena, and although his work was primarily developed in the context of social relations rather than conceptual learning, it has lent itself to the evaluation of learners’ conceptual structures (Swift et al, 1983). The most important lesson of Kelly’s work for science education though is the principle that learning is an active process: and students actively try to make ‘sense’ of their environment, and impose (‘build’) structure upon it.

Although the work of Piaget warns teachers that they are unlikely to be able to teach certain concepts to young people until their thinking has reached certain levels of maturity (e.g. Shayer & Adey, 1981), Keith S. Taber – [email protected] 5




Kelly’s legacy seems at first sight much more promising: people tend to actively make sense of what is attended to in their surroundings. So surely all the teacher has to do is make sure the learner’s attention is focussed in the right place. Unfortunately not!

For one thing it has been suggested that the human brain is a product of evolution such that it is predisposed to a certain kind of sense, and this ‘common sense’ is not the same as scientific sense (Wolpert, 1992.)

Science teachers meet their students after they have already spent some years actively making sense of the world, based on limited data, and using their ‘common sense’. By the time of formal teaching the young people already have a network of interrelating ideas about many of the natural phenomena that the science teacher wants them to learn about (Driver & Erickson, 1983; Gilbert & Watts, 1983; Driver, Guesne & Tiberghien, 1985; Osborne & Freyberg, 1985.) Or rather to re-learn about. And perhaps this will require a certain amount of unlearning.

This last point is one of the central interests of constructivist teachers and researchers. If learning involves making sense of the world, then the teacher should try to relate new ideas to existing ones. But if the existing ideas are not only wrong from the scientific viewpoint, but are inconsistent or even contradictory to the ideas the teacher wishes the student to learn, then how should teaching proceed?

One premise of the constructivist school is that it is important to find out what the learner knows, to make explicit the current ‘knowledge’. This provides the teacher with information about how to link new ideas to existing knowledge. It also makes any alternative conceptions explicit to the learners so that they may be challenged. Such challenges are unlikely to succeed based purely on the authority of the teacher, and it is common to suggest that counter examples are presented to ‘disprove’ the misconceptions, and that students are allowed to explore the logical consequences of their ideas, where these consequences may well be in conflict with new evidence or other beliefs they hold. The Children’s Learning in Science project (CLiSP) has published exemplar material illustrating such an approach (e.g. Wightman, Green & Scott, 1986; see also Scott, Dyson & Gater, 1987.)

There has been much research into the nature of student Keith S. Taber – [email protected] 6




misconceptions / alternative conceptions / naïve theories / alternative frameworks / intuitive theories in science, although these have not been evenly distributed across the whole science curriculum. Some of this material is of the “before and after” school looking at how the ideas present in a group of learners differ following an intervention (i.e. teaching.) Much of the research is based on statistical analysis of paper-and-pencil tests {e.g. Andersson & Kärrqvist, 1983 (light); Bliss et al, 1988 (physics); Shipstone et al, 1988 (electricity); Sumfleth, 1988 (chemistry); and Viennot, 1979 (forces)}, rather than in-depth investigation of individuals, although the CLiSP team have used a much more imaginative approach: following up such statistical research with “naturalistic” case studies of classes experiencing current practice, and action research introducing constructivist teaching schemes (e.g in particle theory: Brook, Briggs & Driver, 1984; Wightman, Green & Scott, 1986; and Johnston & Driver, 1991 respectively). Also, as Black has pointed out (1989, pp.3-4.) there has been little attempt to undertake genuinely longitudinal studies following students over significant period of time. In practice little is known about the way students’ conceptual structures develop, and in particular how a students’ alternative framework may come to be replaced by the ‘orthodox’ scientific idea. How much of an impediment to new learning are misconceptions? Are the alternative ideas completely replaced and forgotten? Or does the (successful) student only acquire a second set of ideas, and the strategy of applying the new set in the context of science classes and tests? Do some leaners integrate new (scientific) and existing (alternative) ideas, even when they are logically inconsistent? Is the adoption of a new framework a simple case of applying logic and choosing the set of ideas which best explains the available data, and if so is the alternative framework discarded as soon as it is refuted (a Popperian model, if we make comparisons between individual learning and the progress of science); or does a revolution in thinking come as a gestalt-like paradigm-shift when the evidence is overwhelming and one’s emotional commitment to the previous framework will no longer suffice (a Kuhnian interpretation); or is maturation of a learner’s science knowledge like a progressive Lakatosian research programme (Watts & Pope, 1982); or does the learner subconsciously undertake a complex comparison, selecting the framework with greatest explanatory coherence (Thagard, 1992)? Only detailed examination of individual student ideas, over an extended period of time, is likely to suggest the most appropriate model, which could then inform teachers, curriculum developers and perhaps learners themselves.





Methodology.

I am in the process of developing methodology to explore the development of A level students’ understanding of chemical bonding. The work being reported today forms part of pilot study, and uses one research technique - a clinical interview where the student talks to a single researcher (myself) with a series of prepared diagrams as foci for the discussion. The interviews are recorded onto audio tape.In my ongoing work I am supplementing this technique with other means of collecting data, but in the present case study the data presented were obtained from a series of four interviews.

The interviews took place at three stages during the student’s study of A level chemistry. The first interview was undertaken at the start of the second term of the course (before the topic of concern had been explicitly studied.) The second interview took place at the end of the first year, and the third interview was conducted a few weeks before the final examination. This latter interview did not allow discussion of as much material as had been hoped, and it revealed that the student had serious misconceptions about some of the fundamental chemical ideas being considered. A short ‘tutorial’ was undertaken at the end of this interview, and the a follow-up interview took place two weeks later. As the interviews took place over an extended period of time (from January 1991 to May 1992) they provided data giving insights into changes in the students’ understanding of chemical bonding.

It has been suggested that educational enquiry can be related to a continuum of research styles that at one end (exemplified as so called paradigm 1) follows conventional scientific method, using control of variables and statistical inference. Such an approach could be typified by teaching two equivalent classes the same topic, but one subject to an intervention treatment, and the other being a control - taught in exactly the same way in terms of all relevant variables except that being studied. Statistical comparison of pre- and post- test scores in both groups leads to inferences about the effectiveness of the intervention. The procedural difficulties of controlling all relevant variables make such an approach exceedingly difficult. Research at the other end of the continuum, so-called paradigm 2 enquiry, takes a more naturalistic approach. Rather than plan an intervention, one tries to learn as much as possible by an in-depth examination of the behaviour of the individual or group being studied. To some extent this Keith S. Taber – [email protected] 8




“anthropological” approach is more suited to social research than cognitive studies - if only because some form of ‘intervention’ is likely to be needed to provoke our subjects into thinking about an abstract topic like chemical bonding.

So my own research occupies an intermediate position on the research continuum. My main method of data collection involves clinical interviews, in a quiet room away from the normal class context, with a tape recorder running. As I have a dual relationship to the student subjects, both researcher and teacher, I have a responsibility to intervene at some stage when they have misconceptions, rather than just observe and note their thinking. (This does not necessarily have to be done ‘on tape’.) However, I would view my basic stance as a researcher as naturalistic : I wish to explore the students’ ideas in depth, and ‘get inside their heads’. I am therefore trying to work with a limited sample of students, over an extended period of time, rather than using large scale survey techniques. One important aspect of my stance is that the people I am working with are known to me as human beings, and are not just experimental subjects. My research could be construed as action-research as I ultimately hope to learn how to teach ‘better’, and that is a concern that effects my students. It has been suggested that in action research the people with whom the teacher-researcher works in the enquiry should be called co-researchers. I do not think this term is meant to imply that the co-researchers are actively undertaking their own research, rather that they share an interest in the research, but nevertheless it seems a misleading term. I would prefer to call the students that I have been working with co-learners. We get together so that we can learn: they primarily wish to learn more about science, and I wish to learn more about their understanding of science, and we both consider that time spent discussing chemistry will be beneficial in meeting these goals. In Black’s terms my interviews may be “seen as a piece of learning and as a conversation between researcher and pupil” (1989, p.3.)

My interviews are respondent interviews (Powney & Watts, 1987, pp.17-18) in that the agenda of issues for discussion is primarily determined by the researcher . The interviews are semi-structured around a series of foci diagrams intended to be related to the topic area. In the first interview the opening questions tend to be of the form “what does this diagram show?” and “do you think there is any bonding represented in the diagram?” The co-learner’s responses suggest follow-up questions. Reflection on the interview tapes suggests a list of questions to be asked in the next interview - as is Keith S. Taber – [email protected] 9




discussed below. Although the diagrams are drawn especially for this research, the procedure draws heavily on the ‘interview about instances’ approach described by previous workers (e.g. Osborne & Freyberg, 1985, pp.6., Watts, Harrison & Gilbert, 1982.)

The data analysis is considered further below, but at this point it seems appropriate to mention that the term “journalistic” has been used to describe paradigm 2 research. In the case study described in this paper I have tended to follow a journalistic approach to quoting my co-learner Annie. Although all quotations are given verbatim from the transcripts, they have been edited for readability. Parts of utterances have been selected and spliced together to provide narrative, in the same way that a journalist might edit an interview for broadcast news. As authenticity in published work is often ensured by the quotation of lengthy passages to give the full context of an utterance, a deliberate decision to edit in this way places a responsibility on the researcher to ensure that increased readability is not attained at the cost of misrepresenting the full data. This responsibility is accepted in the belief that repeated listening to the recordings and reading of the transcripts before and during the compiling of the case study paper allows the researcher to integrate a greater amount of evidence than could ever be publicly presented in a verbatim transcript . All citations from transcripts, short of publishing full texts, involve some degree of editing, and lose some of the information in the original tapes (which can themselves perhaps not be made available without compromising confidentiality.) Even the audio-recording itself does not hold all of the information about mood and facial expression that the researcher may pick up during the interview, let alone what may be known of the co-learner outside of the clinical sessions. This approach may sound rather subjective, and even mystical, but the ability of the human brain to integrate data in a holistic way has been described by scientific Nobel laureate Barbara McClintock (Keller, 1983, pp.102-104, 115-117.)

As an example of the type of editing undertaken, consider the following extract from the case study,

“The absence of evidence of bonding (by Annie’s criteria) was compounded by confusion over the meaning of the plus and minus signs used to indicate positive and negative charges. The cations in fig. 5 were identified as sodium “atom”s (A1.250) despite the plus signs “representing the charges” (A1.246). The chloride anion was called a “chlorine atom” (A1.252). These





errors could have been ‘slips of the tongue’, were A not consistent in confusing the meaning of the signs. This becomes apparent when she explains that the structure is held together by “the attraction from the plus to the minus because like chlorine’s minus an electron and sodium is over an electron.” (A1.260) For A the “plus and minus signs on them representing the charge” (A1.246) do not mean an overall electrical charge, but a deviation from noble gas electronic structures: “sodium has like one extra electron in its outer shell, and chlorine has seven electrons in its outer shell so it’s minus an electron” (A1.262). What is given at GCSE level as the cause of electron transfer to form ions has become confused with the signification of the products of such a transfer: a ‘+’ sign meant to indicate one less negative electron in the atom than positive charge in the nucleus is seen as meaning one more electron than a stable configuration. The formation of ions by electron transfer explains the origin of the electrostatic forces that hold an ionic lattice together. A’s alternative conception of the ‘+’ and ‘-’ species means she must find an alternative mechanism to hold the substance together: “so by sort of exchanging, the sodium combining with the chlorine just by force pulls they would hold together” (A1.262). What does A mean by exchanging? “..by, well just the attraction in them.” (A1.264) From a conventional viewpoint A’s conception of figure 5 makes little sense: the structure is held together, but without any bonding; there are charges on neutral atoms; atoms are combining without overlapping; and the atoms are exchanging not electrons but force pulls related to the electronic configuration. However A’s comments seem to be more that just a make-shift argument put together on the spur of the moment. Indeed the misidentification of ions as neutral, although not entirely consistent throughout the interview, certainly pervaded A’s comments. This misunderstanding was abetted by an interpretation of diagrams that only recognised bonding between species represented as circles (or similar) if there was overlap.” (From section 5.2)

The extract was written after due reflection on all four interviews, but the quotations are based on the following extract from the first interview,

A1243 I: . . .Erm, so if you look at these, I mean you said they were Keith S. Taber – [email protected] 11




sodium and chlorineA: yesI: because presumably you recognise the Na and the Cl,A: yeah,I: but only two of them are labelled with ‘Na’ and ‘Cl’.

244 A: Yes.245 I: What about the others - what do you think they are?246 A: They’re probably sodium and chlorine, or else they could be, because of the signs, you’ve got plus and minus signs on them representing the charge, or else it could be similar elements going down the groups.247 I: Okay so you recognise that these, these things represent charges, and you probably guess it’s just me being lazy that I haven’t labelled them all,

A: {laughs}I: so I’ve just labelled the first couple, erm, so these are

what, so you reckon this little one will be, what will that be do you reckon?248 A: Sodium.249 I: That will be a sodium, molecule?250 A: Atom.251 I: Sodium atom, what about this one here?252 A: Chlorine atom.253 I: That’ll be an atom. But these have got charges on,

A: yeah,I: okay, but unlike 2, 3 and 4 we’ve seen previously they’ve

had bonds in, A: yeah,I: chemical bonds, whereas this, we don’t have chemical

bonds? 254 A: No.255 I: Do you think this thing would fall apart? Or would it hold together?256 A: • • • • • • • • • If you heated it, or reacted it in some way, it would hold together, and it would probably get held together by just forces.257 I: By forces. Any idea what kind of forces would hold it together?258 A: Probably just the attraction.259 I: Uh hm.260 A: The attraction from the plus to the minus because like chlorine’s minus an electron and sodium is over an electron. So they could just like hold them together, but not actually combine.Keith S. Taber – [email protected] 12




261 I: Right, chlorine’s, so sodium’s, say that about the electrons again.262 A: Sodium has like one extra electron, ‘cause it has like an extra electron in its outer shell,

I: uh huh,A: and chlorine has seven electrons in its outer shell so it’s

minus an electron so by sort of exchanging,I: huh hm,A: the sodium combining with the chlorine just by force pulls

they would hold together.263 I: You say by exchanging, did you say?264 A: Yeah by, well just the attraction in them.

Whilst reading interview extracts - such as the one just quoted - purveys a sense of discourse and dynamism that is necessarily lacking from the case study with its engineered narrative, it is the researcher’s task to make sense of the co-learner’s comments, and to marshal the evidence in a way that supports the interpretation suggested, to provide the reader with an overview of the co-learner’s ideas that would not be gleaned from a single reading of the transcripts themselves. Close study of the primary data allows the researcher to juxtapose comments that were separated by many lines of text in the original transcripts,

“By contrast, at the time of the second interview, A was certainly aware of the existence of van der Waals forces, and knew they were relatively weak forces that were readily disrupted. A now reported that such forces occurred in iodine (figure 17), but she also suggested a wider range of examples. The atom (e.g. sodium, fig. 1) was held together by “van der Waals forces ... weak forces, which pull towards the nucleus. Which are readily disrupted” (A2.2). In metallic iron (figure 6) “it’s probably van der Waals forces, holding it together” (A2.93), although these forces are not the same as metallic bonding “‘cause you can get van der Waals forces in, covalent things as well” (A2.107). Indeed lithium iodide (figure 8) is “ionically bonded, but the forces holding it together will be, (pause, 5s approx.) van der Waals I suppose” (A2.125).” (from section 12.2: note that the quotations are from utterances 2, 93, 107 and 125 of the transcript.)





Chemical bonding.

Chemical bonding is a major theoretical topic that underpins the science of chemistry at all levels. Despite this children’s and students’ understandings of bonding have not been extensively studied. Researchers have preferred to consider topics such as energy, motion, plant nutrition or the Earth, where it is known that children develop intuitive theories before formal teaching. Chemical bonding is a topic that can only be studied in the context of atomic theory, and unless children develop intuitive ideas about atoms, they are not able to develop these ideas to form naïve views of how atoms bond together. This might seem to imply that alternative conceptions in this area are unlikely, but in fact my research suggests this is not so. For although children are unlikely to develop alternative chemical bonding theories before formal instruction about atoms, and how they join together, they will build these ideas into their existing conceptual frameworks, forging links with apparently related ideas that they previously acquired. In order to ‘construct’ ‘sensible’ consistent knowledge of the world, the learner will have to interpret what the teacher tells her in the light of her existing understanding of the natural world. The meaning the learner constructs may not be that similar to the meaning the teacher ‘had in mind’. For example the teacher may implicitly use her tacit framework of knowledge for energy, forces and electrical charge, but the learner’s alternative conceptual framework in these areas may be quite different (Watts, 1983a, 1983b; Gilbert & Watts, 1983, Brook & Driver, 1984, pp.106-108, Brook et al, 1986, pp.150-156, Shipstone et al, 1988.) and perhaps even incommensurable. As Feyerabend (1988) suggests,

“there are frameworks of thought (action, perception) which are incommensurable” (p.218) and “the development of perception and thought in the individual also passes through stages which are mutually incommensurable” (p.219),

or as Kuhn (1977) has it:“Proponents of different theories (or different paradigms, in the broader sense of the term) speak different languages - languages expressing different cognitive commitments, suitable for different worlds. Their abilities to grasp each other’s viewpoints are therefore inevitability limited by the imperfections of the processes of translation and of reference determination” (pp.xxii-xxiii, c.f. Watts & Gilbert, 1983.)

The fascinating aspect to chemical bonding as a topic (rather than say Newton’s laws of motion, or plant nutrition) is the manner in which the Keith S. Taber – [email protected] 14




learner is required to develop the concepts as she studies chemistry at a higher level. The difference between chemical bonding as a topic at GCSE, or at A level, or at degree level, is not merely a matter of increasing detail, or increasing the scope of application of the ideas. At GCSE chemical bonding is already an abstract topic. At A level more sophisticated ideas are needed: ideas that require the student to hold a plurality of models and interpolate between them. GCSE ideas are extended and developed, but also supplanted. (I have used the metaphor of students’ acquiring a toolbox of bonding ideas to apply on a range of chemical problems: Taber, 1993: The Toolbox Analogy.) Chemical bonding is therefore a potentially fertile topic area for studying the development of student ideas.

Some insights from A case study.

In this section I wish to discuss some of the data obtained from my case study co-learner, who I will refer to as Annie. Annie was born in 1974, and attended an F.E. College from September 1990 to July 1992. On entry she nine GCSE grades: one A, four Bs and four Cs. She had obtained a B in Chemistry. She studied A levels in biology, chemistry and government & politics. At the end of the course she obtained 2Cs and a D - the D in chemistry - and went on to University to read a degree in the humanities.

The questions I wish to address here are:

1. Did the methodology described enable an evaluation of Annie’s ideas about chemical bonding?

2. Was it possible to follow the development of Annie’s ideas by virtue of the longitudinal nature of the study, and if so what does this case study suggest about the way learners’ ideas develop in sophistication?

3. Was there any evidence that Annie had any ‘alternative conceptions’ related to chemical bonding, and if so how readily were these ideas replaced after exposure to formal instruction?

Does the case study allow an evaluation of Annie’s ideas about bonding?Keith S. Taber – [email protected] 15




All four interviews were transcribed (the compiled transcript runs to over forty one thousand words) and an analysis was undertaken thematically, i.e. in terms of the various aspects and categories of chemical bonding. This process produced the case study paper (at ‘only’ thirty seven thousand words) which will be used as the data source for this present discussion.

It can be seen that the clinical interview approach is very powerful for uncovering a co-learner’s ideas. The interactive nature allows the use of specific follow-up questions during an interview to clarify the co-learner’s comments, allowing a form of validation that is not available when pen-and-paper testing is used. (The CLiSP team have used a mixture of written test-items, and follow-up interviews. However if there is a delay of several days between the pupil answering a written test item and being interviewed then the pupil may not readily bring the previous train of thought to mind. This would lead to additional complications if the stability of the learner’s thinking is being investigated.) By using substantial interviews (typically 30 minutes to an hour ) as the main research technique there is scope for considerable ‘internal validation’ of the interviewer’s interpretations of the co-learners comments during a single interview. Such validation takes several forms:

1) confirming responses by repeating or rephrasing questions,

e.g. 1 - confirming that Annie did not class intra-atomic binding as a form of bonding:

A117 I: . . . What I would like to know: is there any bonding going on there?19 A: Erm. No.

. . .

48 I: . . . Er, so we’ve got a nucleus, and we’ve got electrons, and they are being held in, and you wouldn't identify any kind of bonding in that diagram?49 A: No.50 I: No. So there’s no, no chemical bonds there?51 A: No.





e.g. 2 - confirming that Annie did not consider a diagram of a K+ - F- ion pair to exhibit bonding:

A1349 I: So in that diagram, have we got any kind of chemical bond?350 A: No.351 I: Did we have a chemical bond in the previous two diagrams, the lithium iodide, and the hydrogen?352 A: Yeah.353 I: Yeah. But there is no chemical bond here?354 A: No,

I: okay,A: because they’re not combined.

2) clarifying ideas by asking follow-up questions:

e.g. 3 - clarifying whether Annie was suggesting all electrons shown in a tetrachloromethane molecule were moving around, or just some:

A1197 I: . . .. Do you think the electrons actually stay in one place here? Or do you think they move around?198 A: No, I think they move around.199 I: All electrons?200 A: No I think the ones that are fixed to the carbon would stay,

I: so you’re pointing at...,A: more or less.

201 I: You are pointing to these ones involved,A: yeah,I: in the bonding?

202 A: Yeah, the ones that are involved in that, they can’t really move around, like all the way around the shell.203 I So these ones would be able to,

A: yeah,I: but these ones would be fairly fixed, because of the

bonding.204 A: Yeah.





e.g. 4 - clarifying what Annie understood by the term ‘electron rich’:

A1461 I: Now do you know what compound that is? Any idea?462 A: • • • Looks like a benzene ring. 463 I: Yeah, that’s right. Any idea what this, er, strange looking circle in the middle is?

A: > It’s... >I: < Or < what it’s meant to represent?

464 A: Shows where the electrons are, because it’s electron rich.. . . 475 I: Okay, so why do you say it’s electron rich, what does that mean exactly?476 A: Erm, not really sure, but I wrote it down yesterday. {Both laugh.}

3) paraphrasing what one believes to be the co-learner’s argument, and seeking confirmation:

e.g. 5 - paraphrasing Annie’s comments about the meaning of ‘plus’ and ‘minus’ symbols:

A1280 I: So the plus means one electron more than an outer, the full shell,

A: yeahI: and the minus means one electronA: minusI: less than an outer shell,A: yeah,I: and that’s what holds them together.

281 A: Yeah.

e.g. 6 - paraphrasing Annie’s comments about the forces between lithium and iodine in a molecule of lithium iodide:

A1Keith S. Taber – [email protected] 18




321 A: It’s the same sort of thing again - the lithium combines with the iodine - to make a stable outer shell between the two, by sharing electrons,

I: uh hm,A: but the lithium has a smaller charge, or smaller pull than

the iodine, so the actual shape of it goes in towards. It sort of goes inwards because its attracting the lithium, whereas if the lithium was attracting it, it would be like a reverse picture.322 I: So, so the iodine’s attracting what, sorry?323 A: The lithium.324 I: The iodine’s attracting the lithium, and the lithium is not attracting the iodine?325 A: Yeah, they’re both attracting each other but because this one’s got a larger force,

I: uh huh,A: then it will pull to.., towards the lithium more.

327 I: The iodine’s got a larger force,A: yeah,I: so it will pull towards the lithium more?

328 A: Yeah.

e.g. 7 - paraphrasing Annie’s ideas about how successful counter ions with different valencies are in forming compounds:

A1400 A: Yeah, they’re sort of attracting there [indicating on diagram], they’re sort of like matched up, elements which they have been chosen to join with.401 I: Uh hm.402 A: But none of them have actually reached that far. And it seems like aluminium is being more successful, than the potassium.403 I: Yeah, why do you say that, yeah?404 A: Because the cone, cone shape on it, sort of goes further over, to all but reach it, whereas the potassium one sort of like stops quite a bit shorter.405 I: That’s true, yes, it’s certainly drawn that way, isn’t it. The aluminium one is nearly getting there, and the potassium’s not making much

A: noI: headway really. Any ideas why that might be?

406 A: • • • • • • • • • • • Is it something to do with the charges, sort of aluminium’s got three plus charge, so if it did combine, then it Keith S. Taber – [email protected] 19




would still have one electron over, but it would complete the outer shell. But potassium would still leave it with one electron less. So the pull isn’t so great.407 I: Right, so the potassium could only provide it with one electron, and it needs two,

A: yeah,I: is that what you’re saying? Aluminium could provide it with

three and it only needs two,A: yeah,I: so that’s going to be more successful. Okay, if I had one in

the middle here then which I haven’t got, let’s say I had calcium,A: hm,I: which would be two plus,A: yeah,

that could provide two electrons. 408 A: Yeah.409 I: So do you think that would be somewhere in between these two diagrams, or because it can provide the right number of electrons do you think it would be more successful than the aluminium?410 A: Yeah, the shape would be like the bottom one of the two, but the calcium circle would actually be inside sort of the nose, the cone.411 I: So, they’d actually coalesce?412 A: Yeah.

4) returning to the same point in the same context later in the interview, to see if a consistent response is given by the co-learner:

e.g. 8 - checking to see if Annie genuinely classed bonds in benzene as ionic, or had become confused:

A1447 I: Well what about picture twelve then? Can we see any bonds there?448 A: Yes.449 I: Right, what kinds of bonds have we got there do you think?450 A: • • • Ionic.451 I: These are ionic bonds. How many bonds do you think are in there?452 A: • • • • • • • • • Twelve.Keith S. Taber – [email protected] 20




453 I: Twelve, okay. Are all the bonds the same?454 A: Well they’re sort of two types.455 I: Uh hm.456 A: There’s C to H bonds or C to C bonds.457 I: Right, do you think they’re both ionic bonds, both those types?458 A: Yeah.

then later:

499 I: What about in the previous diagram, when we looked at number twelve. You said what, there were twelve ionic bonds there?500 A: Mm.501 I: Any covalent bonds?502 A: I’ve got it the wrong way round. Should have been covalent bonds, not ionic.

e.g. 9 - confirming that Annie had learnt to distinguish between the sodium atom and the Na+ species:

A242 I: . . . you’ve told me what you think the electronic configuration of

A: yeahI: sodium is, which I think is 2.8.1 you said, yeah?

A: Uh hm, yeah I: chlorine 2.8.7, this, this here, this Na+, A: yes I: can you tell me what the electronic configuration you think of that is, Na+?43 A: Erm, 2.844 I: 2.8. What about the chlorine, sorry this Cl-?45 A: 2.8.8.46 I: 2.8.8. So they’re different to the actual atoms?47 A: Yes.

and later

A2179 I: Can we just focus back to, this one, sodium chloride?Keith S. Taber – [email protected] 21




180 A: Yeah.181 I: What did you tell me was the electronic configuration of the sodium atom?182 A: 2.8.1183 I: What about the sodium ion shown there?184 A: It’s 2.8185 I: What about the chlorine atom?186 A: It’s 2.8.7187 I: And what about the chloride ion?188 A: It’s 2.8.8

5) approaching the same point through a different context later in the interview, to see if the co-learner gives a consistent response in the different contexts:-

e.g. 10 - finding if Annie’s ideas about the degree of localisation of bonding and non-bonding electrons in the aluminium chloride dimer were consistent with her ideas about tetrachloromethane:

A1197 I: . . . Do you think the electrons actually stay in one place here? Or do you think they move around?198 A: No, I think they move around.199 I: All electrons?200 A: No I think the ones that are fixed to the carbon would stay,

I: so you’re pointing at...,A: more or less.

201 I: You are pointing to these ones involved,A: yeah,I: in the bonding?

202 A: Yeah, the ones that are involved in that, they can’t really move around, like all the way around the shell.203 I So these ones would be able to,

A: yeah,I: but these ones would be fairly fixed, because of the

bonding.204 A: Yeah.

and later





A1593 I: Right, can any of those electrons move around?594 A: Yes.595 I: Which ones?596 A: The ones in the chlorine. ‘Cause the aluminium ones are sort of fixed to the chlorine bonds that they’re sharing.597 I: Right, so these six here, these belong to the chlorine?598 Yeah.599 I: And they can move around?600 A: Yeah.601 I: But the eight in the central circles, they all belong to the aluminium?602 A: Yeah.603 I: And they can’t move?604 A: Yeah, they’re more stable, more fixed.

e.g. 11 - to find if Annie’s interpretation of the ‘+’ symbol in Na+ was also applied in K+ and Al3+:

A1260 A: The attraction from the plus to the minus because like chlorine’s minus an electron and sodium is over an electron. So they could just like hold them together, but not actually combine.261 I: Right, chlorine’s, so sodium’s, say that about the electrons again.262 A: Sodium has like one extra electron, ‘cause it has like an extra electron in its outer shell,

I: uh huh,A: and chlorine has seven electrons in its outer shell so its

minus an electron so by sort of exchanging,I: huh hm,A: the sodium combining with the chlorine just by force pulls

they would hold together.

and later

333 I: Right, okay, so this one here where it’s got a K and a plus, what does that represent?334 A: Potassium. 335 I: Right, is that,

A: That’s just a,





I: a potassium molecule, or?336 A: An atom that has an extra electron.337 I: Potassium atom, and it’s got one extra electron over a full shell

A: yeahI: and that’s what the plus means, one more electron than it

wants? 338 A: Yeah.

and later still

361 I: So just look at potassium, that’s K+ again, isn’t it?362 A: Yeah.363 I: So, you’ve told me that the plus means?364 A: One electron in the outer shell, that’s over.365 I: Over what it would like to have?366 A: Yeah, yeah.367 I: What about this aluminium three plus? Al3+? What do you think about that?368 A: That has three electrons in its outer shell more than it needs,

I: Now in itA: three over.

The availability of these different modes of validation also create a burden of analysis for the researcher. A teacher who held a epistemic stance of learning based on the ‘transmission’ of knowledge model would be testing a pupil to she if she had acquired particular knowledge, or had a sufficient understanding of a particular principle to apply it successfully in a given context. Once it was established whether the appropriate ‘right’ answers could be given to a question, it would be sensible to move on to the next ‘element’ of knowledge to be tested. Such assessment could generally be adequately undertaken through standard written tests. The constructivist accepts that the co-learner’s knowledge is not a series of discrete items learnt as a sub-set of independent knowledge elements offered through the curriculum. Indeed constructivists do not see knowledge as structured through a static series of ‘kind’ and ‘part’ hierarchies added to in piece-meal fashion: rather than the co-learner’s conceptual structure is a complex network of interrelated facts and theories, examples and counter-





examples, weighted beliefs and doubts, and that this complex is fluid, both in terms of being open to learning, and indeed in terms of the parts of the structure activated (i.e. brought to consciousness) being dependent on factors such as emotional mood, external context (i.e. ‘question context’) and even internal context - that is what the co-learner has recently been thinking about that is connected in any way to the current focus of attention. Human beings can hold several conflicting ideas, and the reasons why they choose to apply with one rather than the other at a particular time are not always well understood. De Bono has set out a general model of such brain processes (1969), and Thagard and coworkers have developed a computer simulation, ECHO, that models the way competing scientific theories may be compared in terms of their explanatory coherence (Thagard, 1992), but so little detail is known about the physical processes that provide the basis for human mind (Rose, 1992) that such valiant efforts should be seen as no more than useful starting points in studying the complexity of human mental functioning.

Given such a constructivist stance the researcher has to ‘make sense’ of one’s interview data. Ignoring the problems of transcription, and assuming one has tapes and transcripts which are representative of the research interaction itself, one has to work with one’s understanding of the utterances made by the co-learner, made in response to her understanding of the questions the interviewer thought to ask at the time . Perhaps the best model for the analysis is that of a Baconian-Popperian scientist, if there be such a thing. The researcher sifts through the interviews, reading and re-reading, checking the tapes for inflection or to confirm the transcripts, seeking patterns and categorising responses. In the present work such categories have been of two types. I had a series of classes of conceptual nature: covalent bonding, ionic bonding, atomic structure, delocalisation and so forth, and I set out to index all the utterances related to each category so that may be read together and compared. I also looked for examples of utterances relating to a totally different set of categories such as examples of anthropomorphism, use of metaphor and analogy and so forth. (At the same time I was also looking for a third series of categories - examples related to methodology: where I had not listened to an answer, or had unintentionally asked too leading a question, or not followed up an interesting point: both because these points can effect the confidence placed on one’s own interpretations of co-learner utterances, and to make explicit my own faults and limitations in interviewing so that I will learn to perform more effectively during future interview sessions.) The Popperian nature of Keith S. Taber – [email protected] 25




this work is in the formation of conjectures during analysis: conjectures that are open to refutation by re-reading the script, or comparing with other utterances at other points in the interview. Categories are flexible, and new ones may be taken-up, and examples deleted, or moved to other categories. Reflection on later transcripts, and data from other co-learners , allows one to revisit and re-assess the material being analysed. The work is Popperian in that all my hypotheses are falsifiable, but as it is accepted that a co-learner can hold contrary views and inconsistent schemes it is not a naïve version of Popper whereby a single apparent counter-example with lead to the rejection of an interpretation based on much exemplar material. Indeed according to Kelly’s fragmentation corollary it is the existence of such pluralism that enables effective hypothesis testing (Watts & Pope, 1985, p.7), and this will apply both to the teacher-researcher and the co-learners.

The development of Annie’s bonding ideas - some examples of the lability of student frameworks.

The longitudinal nature of the work reported herein allows the development of the co-learners ideas to be followed. In the case study paper Annie’s comments are reported in some detail, and what follows will, for the sake of brevity, be little more than vignettes. The interested reader/listener is strongly recommended to read the full case study report.

e.g. 12 - covalent bonding.

During the first interview Annie saw covalent bonding as being the type of bonding between two non-metallic atoms (see section 4.2 of the case study), whereas she seemed to consider that sharing electrons (or overlap or combining of atoms) was a more general criterion for any form of bonding (section 2.2) By the second interview her idea of covalent bonding was related to the sharing of electrons between similar atoms (section 4.3), although she had little appreciation of the electrostatic nature of the bond. At the start of the fourth interview however Annie was also able to explain how the atomic nuclei attract the bonding electrons due to electrostatic force (section 4.4).





e.g. 13 - metallic bonding.

During the first interview Annie did not believe metals needed any bonding to hold together, as the atoms involved were of the same element (section 7.1). By the second interview she agreed there was a form of bonding, but as this did not involve atoms combining she seemed to rate this as a lower form of bonding than covalent (section 7.3). In the final interview, although Annie still did not consider iron had “actual bonds” she was able to give a good description of the “delocalised” electrons which were “like a sea” (section 7.6).

e.g. 14 - canonical forms.

Although in the second interview Annie though that the canonical forms meant to represent molecular resonance implied discrete molecular structures (section 9.4), by the third interview she realised that they were just pictures that were meant to imply delocalisation, and only existed in the minds of scientists (section 9.5).

e.g. 15 - dative (co-ordinate) bonding.

In the first interview Annie demonstrated no concept of dative bonding (section 10.1), but in the second interview her ideas of bonding had become sophisticated enough for her to suggest that in some bonds both electrons come from the same atom, even though she used her own nomenclature for this rather than the term dative, or coordinate (section 10.2).

e.g. 16 - hydrogen bonding.

Annie’s comments about a diagram showing a chain of hydrogen fluoride molecules show how her ideas on bonding became increasingly sophisticated during her A level course. At the time of the first interview she did not recognise the existence of any bonding between the molecules (section 11.1). In the second interview A was able to identify and locate the bond, and comment that it was a lot weaker than a proper bond! (section 11.2) It should be pointed out that Annie also wished to locate hydrogen bonds in several inappropriate contexts. This latter tendency seemed to have been overcome by the Keith S. Taber – [email protected] 27




third interview as she was clear that hydrogen bonding could not occur in materials that did not contain hydrogen. In addition she was able to explain that this type of bonding was an interaction between a hydrogen atom and a lone-pair of electrons on another atom (section 11.3)

e.g. 17 - van der Waals forces.

In the first interview Annie seemed to have no concept of van der Waals forces, and instead invoked alternative, apparently ad hoc, reasons for molecular solids to hold together (section 12.1). By the later interviews she was was clear that van der Waals forces existed, and that they were weak interactions that were readily disrupted - although she imbued them with an ubiquitous nature and seemed to feel this was a ‘catch-all’ category that could be applied in a range of contexts (sections 12.2 and 12.3).

Stability in Annie’s ideas of chemical bonding.

The examples given above all show how Annie made significant advances in understanding aspects of chemical bonding during the sixteen months of the case study. In this section I wish to turn to two examples where Annie’s ideas did not developed to the extent that would be expected during an A level course.

Stability in Annie’s ideas of chemical bonding - an example of how GCSE knowledge can interfere with A level learning.

e.g. 18 - bond polarity.

At GCSE students are taught that elements may be conveniently classed as metals or non-metals (with a few semi-metals perhaps mentioned), and this dichotomy amongst elements leads to a dichotomous classification of bonding - covalent between non-metallic elements, and ionic between a metal and a non-metal. At A level both dichotomies give way to continua. The elements may be categorised Keith S. Taber – [email protected] 28




on an electronegativity scale, and bonding may be polar. Essentially covalent compounds may exhibit some degree of ionic behaviour when there is a difference in electronegativity between the elements. Ions may be polarised and essentially ionic substances can show some degree of covalent character.

Annie had clearly learnt that bonding between non-metals is covalent, and between a metal and non-metal is ionic (sections 4.2, 5.1, 6.1). During her course Annie acquired a concept of bond polarity, which she correctly related to electronegativity (section 6.9), and she was also able to discuss the use of the ‘∂+’ and ‘∂-’ symbols to indicate bond polarity (section 6.8), although she did not relate this to ‘partial charges’.

Despite this Annie continued to classify bonding as covalent or ionic, rather than polar (section 6.9).

Stability in Annie’s ideas of chemical bonding - an example of how an alternative conception can lead to a framework of ideas that interferes with orthodox understanding.

e.g. 19 - ‘deviation’ charges.

In the first interview it became clear that Annie’s interpretation of the symbols ‘+’ and ‘-’ which are extensively used to show ions in chemistry was different to the conventional interpretation. The orthodox meaning is of electrostatic charges, so that any species shown as ‘+’ or ‘-’ is not neutral. Annie however had a totally different interpretation: that the symbols represented deviations from noble gas electronic configurations (section 5.2).

Her interpretation led to her not recognising the presence of bonding in a diagram of sodium chloride, as the charge symbols implied to her that the species still had their atomic electronic configurations (section 5.1, see also section 5.10). One consequence of this was that Annie interpreted the force between the sodium and chloride species as due to an attraction between opposite charges, but for her this meant oppositely signed deviations from noble gas electronic configurations: Na+ being one electron in excess, and Cl- being one electron deficient.





As Annie had opposite charges, and they still attracted, she was presumably able to make sense within her own alternative framework of much that she heard and read. However, such an alternative conception did have consequences for her understanding of aspects of her course. One example is that although Annie acquired a reasonably orthodox understanding of the ∂+ and ∂- symbols used to show bond polarity, she did not associate the term ‘partial charge’ with this symbolism, apparently unable to relate this to electronic configurations (section 6.8). Annie was able to balance equations using her deviation charges, but as she was seeking full shells rather than neutrality the results could be quite different to the usual answers: in the case of aluminium sulphate her stoichiometry was (Al3+)4(SO42-)2 (section 5.7). Another consequence was that Annie was unsure whether Na+Cl- represented a compound or a mixture of elements, and confused the properties of sodium chloride, with those of its constituent elements (sections 5.10 and 5.11).

It is not possible from the case study to suggest the origin of Annie’s alternative conception of charge. However it is clear that the alternative ‘deviation’ interpretation was present in the first interview, whereas there was no evidence of the conventional ‘non-neutral’ interpretation. By the second interview (after formal teaching of the bonding topic) Annie had acquired the conventional interpretation, but this did not lead to the elimination of the ‘deviation’ meaning. Indeed her alternative framework appeared to be applied spontaneously, whereas the conventional interpretation was used when questioning was targeted specifically at the electron configuration of ions compared to the atoms. Such cuing appeared to ‘switch’ Annie into applying her new conventional interpretation, although later she would resort to the alternative meaning. Annie had presumably made sense of much that had been presented to her at GCSE and the start of her A level course using her alternative framework. Revisiting ionic bonding at A level and being taught contradictory ideas must have been confusing, so perhaps it is not surprising that some of Annie’s utterances seemed to contain strands of both interpretations (sections 5.5 and 5.10). By the fourth interview (after a ‘tutorial’ intervention: section 5.14) Annie was able to give a good account of ionic bonding in conventional terms, and to apply the conventional application of change symbols. However, even at this stage there are vestiges of her earlier framework apparent in the language used, such as referring to a chlorine atom as being “sort of minus an electron” and sodium being a “sort of positively charged, ion because of the, the extra electron”





(section 5.15).

At this point it may be appropriate to refer to Pope & Denicolo’s comments on ‘multiple frameworks’ as a warning against over-interpretation of data. They suggest that ‘framework spotting’ may not be “sufficient to do justice to the data”, and ask the question “what is the operative intuitive theory held by the pupil? Is it several component intuitive theories or is it the system of necessary inter-relationships which is the intuitive theory?” (1986, p.158.) They refer to transcript utterances where “one could disaggregate a quotation into component parts which would ‘fit’ one of these conceptual categorisations but the sense of the ideas being expressed indicated an explanation which embraced more than one of these seemingly discrete and mutually exclusive categories” (p.159.) If I were still working with Annie I would want to investigate her multiple frameworks: to try and determine whether her use of aspects of the ‘deviation’ framework after having apparently adopted the ‘non-neutral’ framework for charge was purely habitual, or due to an inability to fully apply her new framework, or just confusion; or whether indeed she was operating from a specific “system of interrelationships” “which embraced more than one of these seemingly discrete and mutually exclusive categories”. My own interpretation would be that I was privy to a process of change: that the ‘deviation charge’ construct was stable enough to resist complete replacement during her A level course, but labile enough to allow the ‘non-neutral charge’ construct to partially supplant it. My choice of the word ‘lability’ is a pun - it is used as a chemical term referring to the ease of replacement of one species by another in a chemical system . In Kelly’s constructivism the term used would be ‘permeability’ , the degree of openness of construct systems to change (Watts & Pope, 1985, p4.) As Watts and Pope describe:

“In some cases students create new conceptions quite separate and distinct from ones they have used previously, perhaps only a moment or two beforehand. They will amend on-going ones to cater for new or changing situations and will in many cases persist with theories for as long as they can. In some situations they effectively override complicating factors and argue a simplified case, in others they introduce seemingly unnecessary developments and argue an expansive and elaborate construction.” (pp.14-15.)

This permeability in learners may be contrasted to Kelly’s “‘hardening of the categories’, a common affliction amongst scientists” (quoted by Watts & Pope, p.20) as recognised by Einstein in most of his Keith S. Taber – [email protected] 31




colleagues who:“do not look from the facts to the theory but from the theory to the facts; they cannot extricate themselves from a once accepted conceptual net, but only flop about in it in a grotesque way”

These two examples of stability - unhelpful stability from the point of view of on-going learning - were not the only ones that could have been drawn from the case study. Another theme that could be explored was her interpretation of diagrams meant to represent electron clouds showing where electron density is significant in bonds (sections 4.5, 5.6, 5.16 and 6.2). Annie’s understanding - or misunderstanding here - is related to her thinking in other areas. Because Annie did not understand what the diagrams were meant to show, they did not help her appreciate polar bonding when it was illustrated through such representations. The reason Annie could maintain an alternative interpretation of the electron clouds as being a type of force-field was related to her ignorance of basic electrostatic ideas (she did not study A level physics) that had her confuse the effects of charge - distorted electron clouds - with the fields themselves. This same ignorance of fundamental physics enabled her to believe that neutral atoms would attract if their had opposite ‘deviation’ charges, whilst remaining skeptical of the attraction between species with orthodox charges. In order to analyse a co-leaner’s framework of ideas it is necessary for the researcher to behave in a reductionist manner: classifying, separating, collecting together pieces of evidence. However it is important to remember that the co-learner actually has a complex network of inter-related concepts and constructs, as may be seen from the way Annie’s ‘deviation’ charge concept effected her understanding of partial charges, stoichiometry and compound properties.

Summary.

In this paper I have discussed the reason why I favour the use of interviews as a main enquiry technique, and why I prefer to work closely with a small number of co-learners and try to obtain an in-depth feel for their ideas. I have illustrated my approach with evidence from a case study based on four interviews with Annie during her A level chemistry course. I believe the insights I have obtained would not have been possible from survey techniques, asking a relatively rigid Keith S. Taber – [email protected] 32




and limited number of questions to a large sample of students. I have demonstrated how this approach enables one to follow the development of the co-learner’s ideas, and to diagnose possible blocks to further learning. In Annie’s case I have considered two particular ‘blocks’. One of these is the failure to pass from a dichotomous classification system appropriate to an earlier stage of study, to the continuum approach needed for a good understanding at A level. This block could be understood almost in terms of a stage theory: maybe Annie had not developed the mental maturity to handle such operations? Perhaps some aspects of A level chemistry need the co-learner to acquire the “fifth stage” proposed by some stage-theorists? (Arlin, 1975; Kramer, 1983). Such ‘post-formal’ operational thinking has the characteristics that:

“(a) Knowledge has a relativistic, non-absolute nature;(b) contradiction is accepted as part of reality; and(c) the integrative approach to thinking is a central feature” (Castro & Fernández, 1987, p.443.)

However the second example - an alternative interpretation of common chemical nomenclature, which was built into an alternative explanatory framework - does not support a neoPiagetian interpretation. Annie’s deviation charges are no less abstract than the physicists’ electrostatic charges, and her application of her ideas showed considerable ingenuity. Annie’s framework was not an intrinsically inferior one, just an alternative she had constructed. Although the case study does not shed light on its origins, it did allow diagnosis, and an opportunity to intervene, and make explicit to Annie where her ideas differed from those that would be acceptable in her A level examination. As with all case studies little can be generalised to a wider population: perhaps no other A level student will ever develop a ‘deviation’ interpretation of charges. However, I believe the methodology I am developing can be generalised, and with other co-learners I am finding other misconceptions, other confusions, other alternative constructions of chemistry. Perhaps classroom teachers cannot be expected to undertake extensive case studies with all their students, but the message of my research for those involved in teacher education to pass on is:

1. commitment to a constructivist view of teaching means a commitment of the teacher to be a learner, a learner about students’ ideas;

2. alternative frameworks are idiosyncratic, so it is important to talk to Keith S. Taber – [email protected] 33




your co-learners as individuals;

3. above you, listen to what your co-learners are saying, and try and to perceive it through their frameworks as much as your own.

Acknowledgements: I would like to thank: Merton College, Oxford, for awarding a study visit that allowed an initial literature search to be carried out; Havering College for support in various ways; and Mike Watts (at Roehampton) for much stimulating discussion. And, of course, to ‘Annie’ for talking with me.

References.

Adey, P., The CASE results: implications for science teaching, International Journal of Science Education, 14 (2), 1992, pp.137-146.

Andersson, B. & Kärrqvist, C., How Swedish pupils, aged 12-15 years, understand light and its properties, European Journal of Science Education, 5 (4), 1983, pp.387-402.

Arlin, P. K., Cognitive development in adulthood: a fifth stage?, Developmental Psychology, 11 (5), 1975, pp.602-606.

Black, P., Introduction to Adey, P., with Bliss, J., Head, J., & Shayer, M., (eds.), Adolescent Development and School Science, Lewes (East Sussex): The Falmer Press, 1989, pp.1-4.

Bliss, J., Morrison, I. & Ogborn, J., A longitudinal study of dynamics concepts, International Journal of Science Education, 10 (1), 1988, pp.99-110.

Brook, A., Briggs, H. & Driver, R., Aspects of secondary students’ understanding of the particulate nature of matter, Children’s Learning in Science Project, Leeds: Centre for Studies in Science and Mathematics Education, University of Leeds, January 1984.

Brook, A. & Driver, R., Aspects of Secondary Students’ Understanding of Energy: Full Report, Children’s Learning in Science Project, Leeds: Centre for Studies in Science and Mathematics Education, University of Leeds, November 1984.

Brook, A., Driver R., Anderson, M. & Davidson, J., The Construction of Meaning and Conceptual Change in Classroom Settings: Case Studies on Energy, Children’s Learning in Science Project, Leeds: Centre for Studies in Science and Mathematics Education, University of Leeds, July 1986.

Case, R., Science teaching from a developmental perspective: the importance of central conceptual skills, in Adey et al (eds.), Adolescent Development and School Science, Lewes (East Sussex): The Falmer Press, 1989, pp.125-152.





Castro, E. A. & Fernández, F. M., Intellectual development beyond formal operations, International Journal of Science Education, 9 (4), 1987, pp.441-447.

de Bono, Edward, The Mechanism of Mind, London: Penguin Books (first published by Jonathan Cape), 1969.

Driver, Rosalind and Gaalen Erickson, Theories-in-action: some theoretical and empirical issues in the study of students’ conceptual frameworks in science, Studies in Science Education, 10, 1983, pp.37-60.

Driver, R., Guesne, E. & Tiberghien, A., Children’s Ideas in Science, Milton Keynes: Open University Press, 1985.

Feyerabend, P., Against Method (Revised edition), London: Verso, 1988.

Fox, D., Personal theories of teaching, Studies in Higher Education, 8 (2), 1983, pp.151-163.

Gilbert, John K., and D. M. Watts, Concepts, misconceptions and alternative conceptions: changing perspectives in science education, Studies in Science Education, 10, 1983, pp.61-98.

Gilbert, J. & Pope, M., Making Use of Reported Enquiry in Science Education (Module R2 Study Guide, M.Sc. in the Practice of Science Education), University of Surrey and Roehampton Institute, 1986.

Guba, E. G., Towards a Methodology of Naturalistic Inquiry in Educational Evaluation, Los Angeles: Centre for the Study of Evaluation, UCLA, 1978.

Johnston, Kate, & Driver, Rosalind, A Case Study of Teaching and Learning about Particle Theory: a constructivist teaching scheme in action, Children’s Learning in Science Project, Leeds: Centre for Studies in Science and Mathematics Education, University of Leeds, 1991.

Keller, Evelyn Fox, A Feeling for the Organism: The Life and Work of Barbara McClintock, New York: W. H. Freeman and Company, 1983.

Kuhn, Thomas S., The Essential Tension: selected studies in scientific tradition and change, Chicago: University of Chicago Press, 1977.

Kramer, D. A., Post-formal operations? A need for further conceptualization, Human Development, 26, 1983, pp.91-105.

Miller, A. I., Imagery in Scientific Thought, Cambridge (Massachusetts): MIT Press, 1986.

Moore, W., Schrödinger: Life and Thought, Cambridge: Cambridge University Press, 1989.

Osborne, R. & Freyberg, P., Learning in Science: The implications of children’s science, Auckland: Heinemann, 1985.

Pope, M. L., Personal construction of formal knowledge, Interchange, 13 (4), 1982, pp.5-7.

Pope, Maureen & Pam Denicolo, Intuitive theories - a researcher’s dilemma: some practical methodological implications, British Educational Research Journal, 12 (2), 1986, pp.153-166.

Pope, Maureen & Mike Watts, Constructivist goggles: implications for process in teaching and





learning physics, European Journal of Physics, 9, 1988, pp.101-109.

Posner, G. J. & Gertzog, W. A., The clinical interview and the measurement of conceptual change, Science Education, 66 (2), 1982, pp.195-209.

Powney, J. & Watts, M., Interviewing in Educational Research, London: Routledge & Kegan Paul, 1987.

Rose, S., The making of memory: from molecules to mind, London: Bantam Press, 1992.

Scott, Philip, in association with Tony Dyson & Steven Gater, A constructivist view of learning and teaching in science, Leeds: Centre for Studies in Science and Mathematics Education - Children’s learning in science project, June 1987.

Shayer, M. & Adey, P., Towards a Science of Science Teaching: Cognitive development and curriculum demand, Oxford: Heinemann Educational Books, 1981.

Shipstone, D. M, Rhöneck, C.v., Jung, W., Kärrqvist, C., Dupin, J.-J., Joshua, S. & Licht, L., A study of students’ understanding of electricity in five European countries, International Journal of Science Education, 10 (3), 1988, pp.303-316.

Sumfleth, E., Knowledge of terms and problem-solving in chemistry, International Journal of Science Education, 10 (1), 1988, pp.45-60.

Swift, D. J., D. M. Watts & M. L. Pope, Methodological pluralism and personal construct psychology: a case for pictorial methods of eliciting personal constructions, paper presented to the 5th International Conference on Personal Construct Psychology, Boston, Massachusetts, July 1983.

Taber, Keith S., Developing understanding of chemical bonding: the toolbox analogy, unpublished working paper (available from the author), January 1993.

Taber, K.S., Student conceptions of chemical bonding: using interviews to follow the development of A level students’ thinking, paper presented to the Conference on On-going Research, ‘Facets of Education - Dimensions of Research’, Institute of Educational Research and Development, 24.6.93, University of Surrey.

Taber, K. S., Annie: Case study of an A level student’s understanding of chemical bonding, paper to the symposium ‘Science Education - Teacher Education’, British Educational Research Association Annual Conference, Liverpool, September 1993.

Taber, Keith S., Understanding the ionic bond: student misconceptions and implications for further learning, paper to be presented to the symposium ‘Research and Assessment in Chemical Education’ (22.09.93) at the Royal Society of Chemistry Autumn Meeting, Warwick, 21-23.09.93

Thagard, P., Conceptual Revolutions, Oxford: Princeton University Press, 1992.

Viennot, L., Spontaneous reasoning in elementary dynamics, European Journal of Science Education, 1 (2), 1979, pp.205-222.

Watts, D. M., Harrison, G. & Gilbert, J. K., Maximising research data in the analysis of unstructured interviews, paper to the British Educational Research Association Annual Conference, St. Andrew’s, September, 1992.

Watts, D. M. & Pope, M. L., A Lakatosian view of the young personal scientist, paper to the British Conference on Personal Construct Psychology, Manchester (UMIST), September





1982.

Watts, D. M. & Gilbert, J., Enigmas in school science: students’ conceptions for scientifically associated words, Research in Science and Technological Education, 1 (2), 1983, pp.161-171.

Watts, M., A study of schoolchildren’s alternative frameworks of the concept of force, European Journal of Science Education, 5 (2), 1983, pp.217-230.

Watts, M., Some alternative views of energy, Physics Education, 18, 1983, pp.213-217.

Watts, Mike, & Di Bentley, Constructivism in the classroom: enabling conceptual change by words and deeds, British Educational Research Journal, 13 (2), 1987, pp.121-135.

Watts, Mike, & Maureen Pope, Thinking about thinking, learning about learning: constructivism in physics education, Physics Education, 24, 1989, pp.326-331.

Watts, D. M. & M. L. Pope, Modulation and fragmentation: some cases from science education, paper presented at the 6th International Congress on Personal Construct Psychology, 198?

Wightman, Thelma, in collaboration with Peter Green and Phil Scott, The Construction of Meaning and Conceptual Change in Classroom Settings: Case Studies on the Particulate Nature of Matter, Leeds: Centre for Studies in Science and Mathematics Education - Children’s learning in science project, February 1986.

Wolpert, L., The Unnatural Nature of Science, London: Faber & Faber, 1992.




Appendix: Case study of an A level student’s understanding of chemical bonding

Case study of an A level student’s understanding of chemical bonding

Preface:

This working paper describes the ideas of an A level student in relation to chemical bonding. The data from which this case study is drawn were obtained during a series of tape recorded interviews with the student. ‘Annie’ (as she is signified) had given permission for the recordings, which were later transcribed by KT for analysis. The first interview (signified A1) took place during the second term of the A level course, at which stage the topic of bonding had not been formally taught (although GCSE knowledge was assumed, and the subject was not avoided in teaching other topics, including electronegativity.) The second interview (A2) was undertaken at the very end of the first year of the course, and a third interview (A3) shortly before the final A level examination. The presence of uncertainties and misconceptions during this interview led to a brief ‘tutorial’ on bonding and a follow-up interview (A4) about a week later.

The existence of data from a sequence of interview allows one to consider the stability and/or development of Annie’s ideas. The study takes the form of action-research in that the interviewer was one of the chemistry lecturers teaching Annie throughout her two years of A level chemistry. There are therefore methodological issues of to what extent a clinical interview is an intervention, and this should be born in mind when reading the paper. Annie’s responses may at times may reflect a train of thought that would not have been set in operation in the absence of the stimulus question.

The focus for the interviews was a sequence of diagrams drawn to represent atoms, molecules, and so forth. Each quotation or statement about Annie’s expressed views is indexed in terms of the transcripts made from the tapes: A2.46 would represent the 46th utterance as enumerated on the transcript prepared from the recording of Annie’s second interview.

The structure of the case-study is largely thematic: i.e. a series of sub-headings have been selected, and Annie’s comments on these themes have been abstracted. (Including comments about figures that Annie Keith S. Taber – [email protected] A1




does not consider relate to a theme if the ‘expert’ view differs.) There is a certain amount of repetition inherent in using such a thematic narrative approach, as the reader may notice.

It should be noted that this is a working paper, in that it is likely to be updated in the light of further study of the original interviews, and reflections on the recordings of interviews from other students. The views in this paper reflect my interpretations, and have not yet been subjected to any independent tests of validity.

Keith S. Taber – [email protected] A2




Contents:-

0. Introduction: Annie’s style of talk.

1. Atomic structure (and molecular reality!)1.1 Forces holding atoms together.1.2 Representation of electrons.1.3 Electron orbitals and shells.1.4 Atomic structure and the periodic table.1.5 Three dimensional structures.1.6 Confusing macroscopic and microscopic entities.1.7 Penetration and overlap.1.8 Core charge and shielding.

2. Chemical bonding.2.1 Inter-atomic binding.2.2 Bonding is more than just forces, and is represented by overlap.2.3 Heating and bonds.

3. Rationale and mechanism for bonding.3.1 Stable electronic structures.3.2 Electronegativity, energy and entropy considerations.3.3 Forces.3.4 Stability as a psuedo-explanation.

4. Covalent Bonding.4.1 First interview: Annie recognises a class of bonding called ‘covalent’.4.2 Covalent bonding is between non-metals.4.3 Second interview: electrons shared between the same sort of things.4.4 Final position: equally shared electrons held in position by electrostatic force.4.5 Electron clouds on the horizon?

5. Ionic Bonding.5.1 Ionic bonds are found between metal atoms and non-metal atoms that overlap.5.2 The alternative ‘deviation’ interpretation of charge symbols.Keith S. Taber – [email protected] A3




5.3 Electron density cloud interpreted as a force field.5.4 Summary of Annie’s ideas about ionic species.5.5 The second interview: competing interpretations of charge symbols.5.6 Bonding electron density remains confused with forces.5.7 The need for overall neutrality in ionic species.5.8 Ionic or covalent bonding?5.9 Multiple ionic bonds?5.10 Third interview: continued uncertainty over whether Na+ is bonded to Cl-.5.11 The effect of heat on sodium chloride.5.12 Synthesis of sodium chloride.5.13 Annie’s understanding of ionic bonding at the end of her course.5.14 The tutorial.5.15 The fourth interview: electron transfer and forces between charges.5.16 Electron clouds, forces and causality.5.17 Stoichiometric ratios and neutral ionic compounds.5.18 Annie’s final understanding of charge.

6. Polar bonding.6.1 First interview:

Annie displays a ‘dichotomy’ approach to classing bonding types.6.2 Electron clouds misinterpreted as force fields.6.3 Second interview: bonding by “like almost a force field”.6.4 A constructivist interpretation of Annie’s ‘pseudo-argument’.6.5 Annie retains a dichotomy classification of bonding. 6.6 The third interview: polar and non-polar solvents.6.7 Electronegativity.6.8 Partial charges: ∂+, ∂-.6.9 The fourth interview:

Annie recognises bond polarity, but still classes bonds as covalent or ionic.

7. Metallic Bonding.7.1 First interview: no bonding in metals.7.2 Second interview: uncertainty over the presence and type of bonding in metals.





7.3 Third interview: metallic bonding,but atoms don’t combine as they do in covalent/ionic

bonding.7.4 Coordination number.7.5 The tutorial.7.6 Fourth interview: a less definite form of bonding

- delocalised electrons allow atoms to take turns in having full outer shells.

8. Multiple Bonding.8.1 First interview: double bonds occur in organic structures.8.2 The second interview: mainly covalent bonds, that are fixed and can’t twist.

9. Delocalisation and resonance.9.1 First interview: benzene - electron-rich with single bonds.9.2 Resonance not appreciated from canonnical forms.9.3 Second interview: benzene - some awareness of delocalisation.9.4 Canonical forms considered as representing discrete molecular structures.9.5 The third interview: benzene - electron delocalisation through the complex,

and canonical forms do not really exist.

10. Dative bonding.10.1 First interview: no concept of dative bonding.10.2 Second Interview: Annie suggests bonds with two electrons from the same atom.

11. Hydrogen bonding.11.1 First interview: no bonds between HF molecules.11.2 The second interview: ubiquitous bonds weaker than proper bonds.11.3 The third interview:

attractions between lone pairs and hydrogen hold molecules together.

12. Van der Waals forces.12.1 First interview: integrity of molecular solids due to forces stabling-up.12.2 The second interview: ubiquitous weak bonds, readily Keith S. Taber – [email protected] A5




disrupted. 12.3 The third interview: Annie still does not discriminate

examples and non-examples of van der Waals forces.





0. Introduction: Annie’s style of talk.

Annie’s speech often contained apparent qualifications which might be associated with uncertainty or timidity. It is interesting to note how this is especially true in the third interview when Annie was only a few weeks from her ‘A level’ examinations. It is quite possible that this style of speech may have been associated with a general lack of confidence in her knowledge and understanding. However I do not believe it is possible to read too much into the specific uses of “sort of” and “like” as they seem to be habitual and are sometimes used in circumstances where it is most unlikely Annie is unsure of her utterance. So whilst atoms “sort of share an electron each” (A1.65) , “sort of combine” (A1.65), are “sort of like unstable” (A1.77) and one might “have to react them in some sort of way” (A1.91) suggest uncertainty, and the nucleus being “just sort of like, there” (A2.6) does not imply great confidence, there are other instances of usage which seem purely habitaul. For example figure 5 “shows circles with sort of plus and minus signs in” (A3.30) and figure 1 has “sort of, got eleven” (A3.66) electrons shown. On other occasions the “sort of”s are redundant in showing that Annie is not sure of an answer, as the following extract indicates, (from A3)

910 A: The electrons are held in, erm, in sort of levels, so, it’s to do with sort of bonding, like you can only get two electrons in the first quantum shell. So that they are held in these shells. Why they don’t quite fall into the nucleus, I’m not quite sure, but obviously you are going to get sort of very minute particles, of the element, which is going to sort of stop them. Again you can’t really say, you’ve got a slab of, sort of, say, erm, sodium or something, you can’t really say, right in the middle of there, there’s the nucleus, because sort of, or, of them if you gave me like a block of sulphur, or sodium sorry, and you sort of put a pin into half the middle, you couldn’t say right that’s the nucleus because it’s sort of held all together, because it’s made up of atoms, although you assume

I: mmA: the nucleus is in the centre because that’s the obvious

place to be, so obviously it’s going to be in the centre, so it gets sort of the elec.., erm the sort of forces are distributed evenly around, its er, you can’t, you couldn’t detect it in a classroom, well you could with erm, goodness all these gadgets they have these days. Er, so, they’re Keith S. Taber – [email protected] A7




they’re all held in quantum shells which are different energy levels, and you can sort of promote electrons should you need to in bonding, so, so if for example you need a bond to have, I don’t know, an extra electron in a p orbital, you can donote an s, s electron across, to give you hybrids, things. But why they fall into the nucleus, I’m, not quite sure. I don’t think I could describe that.

Annie also had a tendency to use the word “obvious”, although not always in obviously appropriate contexts! For example “an actual piece” (A1.182) of “carbon tetrachloride” (tetrachlormethane, A1.116) “would obviously be, it could be like a crystal shape, or something.” (A1.182)

“Or something” was another qualification used by Annie. The circle in the benzene ring meant “unsaturated, aromatic, or something” (A2.287) and two canonical forms of the ethanoate ion were “Superimposable or something.” (A1.299) In a similar way Coulomb’s law has “something to do with er, size, spin, and all that.” (A4.527)

Annie’s use of “obviously” included things that were anything but obvious, “obviously the sodium block is made up of like millions and millions of little atoms of sodium” (A3.16), and “the nucleus is in the centre because that’s the obvious place to be, so obviously it’s going to be in the centre” (A3.10) so “you assume the nucleus is in the middle which it obviously is.” (A3.14) For Annie ‘obviously’ could mean ‘because I’ve been told by reliable authority’ or ‘by definition’. However this usage means that little weight can be given to literal interpretations of the word in statements such as “obviously, the more you heat something into a gas, the less fruitful collisions you are going to get” (A3.198)

Annie also tended to be unnecessarily self-deferent, as when she judged her own comments as a “daft way of thinking” (A3.468) and “just rambling, I suppose” (A2.113).

Another interesting finding was the way in which Annie used the word ‘because’. This word implies causality, and also the direction: this effect is because of that cause. Yet Annie also used the word ‘because’ when she did not seem to be describing such a causal relationship. In order to discuss this with her I suggested an example from sport (knowing that Annie was interested in sports). She agreed that on a Saturday morning in Liverpool a lot of people would be wearing red, Keith S. Taber – [email protected] A8




and a lot wearing blue. It was suggested that in the afternoon those wearing red would tend to move to one place, and those wearing blue to another. Annie agreed with this example, so it was put:

A4:95 I: And we could say therefore, that the reason that some people go towards the Liverpool ground, is because they’re wearing red, and the reason some people go towards the Everton ground, is because they’re wearing blue. Now would that be a fair description? 96 A: Yeah.97 I: And do you agree with the sense of cause and effect there - that people go to watch Liverpool because they’re wearing red hats and red scarves? And people go to look at Everton because they’re wearing blue hats and blue scarves?98 A: Yes.99 I: So would you say the cause of which football team you go to see, the cause of that, is what clothes you happen to be wearing?100 A: • • • • Unless you’re a rambler. {Laughs}101 I: Ah, is it, but is it not...102 A: No, no, well yes if you’re wearing, you’re obviously supporting that colour, so,

I: But does that mean...?A: that team, so...

I: So that’s cause?A: so you’d assume, that they were going to watch, the team

they favoured. 103 I: Right, okay, erm, I’ll think of a different example, I think.

The comment about the rambler suggested that Annie could not see the point I was making: the use of ‘because’ in this context was acceptable to her. My new example was that of swimmers at a pool.

A4:105 I: Erm, • • if you go to the swimming pool, and watch people swimming, you’ll find out that some people when they’re swimming at a swimming pool, tend to wear a swimming costume that only covers, the hips basically,

A: rightI: and other people either a swimming costume that covers

most of the trunk, or two separate parts to it. And if you observe them very closely, which is always a bit suspicious at a swimming pool,

A: {laughs}Keith S. Taber – [email protected] A9




I: you’ll notice that when they get out of the pool, they’re attracted towards different rooms, these changing rooms I think they’re called. But all the people who just have, the one part of the erm, costume, are attracted towards one room, and the others are attracted towards the other room, the ones with sort of either very long costumes or two part costumes. So is it fair to say that it’s caused by what clothes they are wearing, that determine which room they go and get changed in?106 A: Yes.107 I: It is? 108 A: • • • • Yes.109 I: That’s the cause of it?110 A: • • • • • Yeah. It’s also conventional as well.

Assuming that Annie, who was a sensible and intelligent young woman, did not really believe that people supported football teams, or entered male/female changing areas because of the clothing they happened to be wearing, it is fair to assume that Annie’s understanding of the usage of the word ‘because’ was not orthodox. Annie used the word ‘because’ a lot: consider these examples from the same interview at which the discussion above occurred:

“Sodium’s sort of positively charged, ion because of the, the extra electron, so the chlorine attracts, attracts the, the, attracts the electron initially, which, ‘cause it’s being sort of pulled towards, the, the what was the negative nucleus, then they’re just sort of, • • • just sort of held, erm, just by charges, sort of, because you’ve got conflicting charges, they’re being pulled, pulled inwards by the nucleus, and the nucleus will contain, will sort, will contain the force to full, to pull, the electrons towards it. So there will, because you’ve still got this electron which has been chucked into another shell, then that electron’s being pulled towards the chlorine.” (A4.26)

“No, it hasn’t still got it, but because, in a way it’s lost, but it’s gained. ‘Cause by losing it, it’s sort of not got an extra electron, it’s minus the electron it would have had originally, but it’s gained a stable shell. Because of the next, next shell down” (A4.46)

“Yeah, there’s still bonds, but, not in the sense of like covalent or ionic bond, you’re not getting electrons completely





transferred or shared, between the two. It’s not as definite. ’Cause if, if they, if it was definite, then you’d get, you wouldn’t be able to like conduct your electricity, because you’ve got, sort of free electrons moving around, in metals, and that’s why they can can conduct electricity, really. Because they’re sort of delocalised and move about freely, then the electrical current can pass through” (A4.90).

It is therefore wise to show some caution in interpreting Annie’s own use of “because”, and “‘cause” as perhaps sometimes she only intends ‘is related to’ or ‘is associated with’.

1. Atomic structure (and molecular reality!)

1.1 Forces holding atoms together.

When Annie was first asked how protons and neutrons were held together in the nucleus she suggested that “forces from the outer ring” (A1.27) were “pushing them” (A1.29). Annie was not sure what held the electrons in place, but she thought it could be “connected” to the “set pattern of how many can go in each shell” (A1.33), or it was “to do with the structure of it” (A1.35). The electrons don’t fall out as “forces hold them together” (A1.41), that is “the attraction from the nucleus, from the protons” (A1.43). At the start of the second interview A was again shown figure 1 and asked what forces hold the atom together. She reported “van der Waal forces...the atoms [electrons?] are held in by weak forces which pull towards the nucleus” (A2.2). Annie didn’t know what held the nucleus together, it was “just sort of like, there” (A2.6). For a moment she suggested, but immediately withdrew, “hydrogen bonds” (A2.6), before settling on “just forces within, the atom that push it together” (A2.6). Annie suggests there could be some kind of symmetry with the forces holding the electrons in place: “I don’t know if it’s something to do with , ‘cause the nucleus pulls in the electrons, so if the electron forces actually help bind the nucleus, in any way” (A2.8). These comments have a common strand in that if Annie fully understood the nature of the phenomena she was suggesting she should not seriously have entertained them as possibilities. Wan der Waals forces are only appropriate to explain Keith S. Taber – [email protected] A11




attraction between non-polar neutral species, which would not attract on a simple static electrostatic model - unlike electrons and nuclei. Hydrogen bonds are a form of interatomic (usually intermolecular) linking involving hydrogen, and not appropriate to intra-atomic attractions in sodium. Both of these comments show that Annie was not successfully distinguishing between the molecular and sub-atomic scales. Annie’s final suggestion ignores the direction of the electrostatic attractions on the nucleus due to the electrons, which individually would pull protons out of the nucleus (although almost cancelling overall). This could be classed as an example of a Newton’s third law error, type b (i.e. wrong direction assigned to the ‘reaction’ force.)

In the third interview Annie reported that the electrons in the atom are “held together by, erm, sort of, oh, electrostatic forces coming out from the a.., nucleus of the atom, which pulls the electrons in. So although they’re sort of, in their own orbitals and can move freely, they don’t sort of whizz off.” “Obviously the larger the atom you are going to get the less, less power the nucleus has on the electrons so the closer they are to the nucleus, the more power, the more force is holding them in, making a, a sort of, a denser, sort of compact molecule, atoms” (A3.6). The force originates “from the nucleus, erm neutrons, protons in the nucleus, make up a plus charge, which would draw the electrons in, by elec.., electrostatic forces” (A3.8).

At the end of the third interview Annie was asked if the atomic nucleus was attracted by the atomic electrons. Annie thought “no, but, saying that I’ll probably go home and somebody’s probably discovered that it is. So, erm, • • • • obviously the, the electrons, in a, may sort of control what’s actually happening in the nucleus. Sort of, sort of, holding the neutrons and the protons together” (A3.491). Unfortunately the cassette tape ‘ran-out’ at this point before Annie could expand on her ideas.

When discussing figure 7 (meant to represent a hydrogen molecule) during the fourth interview, Annie was asked whether there was any charge anywhere in a hydrogen atom “they’ll have been a charge, within the nucleus” (A4.183). “So you’d have had neutrons, which would have given you, a charge” (A4.185). Although when it was queried whether neutrons have a charge she replied “no they don’t” (A4.187), “protons and electrons” (A4.189) had charge. The nucleus of a hydrogen atom contained “one proton, and two neutrons” (A4.191). Keith S. Taber – [email protected] A12




The atom also contained an “electron” (A4.199), and there was attraction between the electron and nucleus (A4.201.) In the hydrogen molecule the “pull on the electron from the nucleus” (A4.243) was greater than the pull on the nucleus of the electron “because, you’ve got, you’ve got a positive charge, inside, which is gonna attract the negative electron. Erm, which, should be, if you look at other elements then that’s just generally much more, although they they’re of similar charge, it seems to be convention that that’s the way that, that the, the force goes” (A4.245). [By way of an analogy the - presumed more familiar - Earth-Sun system was introduced into the discussion. However it transpired that Annie was “not really very up on, astronomy” (A4.255). Annie “suppose[d] there must be” (A4.261) a force from the Sun to the Earth, although she had “never really thought about it” (A4.263), and does “not really” (A4.267) think that the Earth attracts the sun “due to size. If you look at the size of the earth compared to the sun, it’s such a dot, there’s not really any way that the earth’s going to attract, the sun” (A4.267). Annie thought that the force of “the Sun on the Earth” (A4.271) is larger than that of the earth on the sun. When I shook my head she then proposed that the force of “the Earth on the Sun” (A4.271) is greater. When she was told this was also incorrect she suggests “I know the earth has sort of like a neutral, sort of attraction from both. Sort of held, holds them there” (A4.276), “I really don’t know” (A4.278). After being told that the force on the Earth and the force on the Sun are the same size she was able to suggest {somewhat tautologically} that the attraction of the proton for the electron, and the attraction of the electron for the proton were “both equal” (A4.280).]

During the fourth interview Annie was shown figure 32a, meant to represent a potassium atom adjacent to a bromine atom , and “in the diagram, potassium” (A4.355) is the larger of the two, “because you’ve got, less electrons, overall, so the actual, the attraction for the nucleus is less, than, because you don’t need, you don’t need as much energy to pull all the electrons in as you do in the, the bromine one. Because, because you’ve got more electrons then you need a lot more, more energy to keep them all combine.., sort of like confined. So it is, because you’re pulling all these electrons in more, then you result in a smaller atom” (A4.356). “You’ve got one outer electron, so the actual pull from the nucleus to the outer electron and all of the other electrons, won’t be needed, well you won’t need as much energy as you will with the bromine, where you’ve got to have all these, you’ve got well six extra electrons to be pulled in. So you’re going to need Keith S. Taber – [email protected] A13




more energy, there to con.., {sound of finger stabbing at diagram} to keep the molecule togeth.., the atom together, so then because you’ve got forces which have to sort of keep, keep, the electrons in more, then, you know if you sort of, got to pull something in more then it’s going to be smaller, than the potassium one” (A4.358). I paraphrased my understanding of Annie’s argument to see if she would confirm my version. It’s harder to pull in seven electrons than it is to pull in one electron, {“Yeah” (A4.360)}, and because it’s harder to pull in seven electrons than one, you have to use more energy, {“yes” (A4.311)}, and because you’ve got use more energy, you pull it in further, {“Yeah” (A4.362).} This answer appears to show that Annie has some difficulty in separating the effects of different variables in her mind. She also appears to invoke an argument that is either anthropomorphic or teleological: if more energy (force?) is needed to attract seven electrons than one, then more energy (force?) will be used. Cause and effect are confused here - the number of electrons present is seen as a sufficient cause for increased forces being applied to them. The potassium atom gets smaller when its outermost electron is transferred “because you’ve, now got, you’ve got rid of, what was one electron in a outer shell, you’ve got rid of that so you don’t need, in effect you don’t need as much energy, to hold one sort of stray, stray end so you’ve got, ‘cause you’ve got a full outer shell, underneath you still need a lot of energy but you don’t need as much, as was needed on the other and also, there’s less there to control” (A4.379). When asked to focus on the third shell and compare between the parts of the diagram showing the potassium before and after transfer Annie first suggests “it’s reduced” (A4.387), and only when asked by how much concedes “well the actual, the inner shell, the actual inner, sort of section hasn’t changed at all” (A4.389). The bromine “atom’s got larger sort of so quantum shell number four has increased in size. Due to the addition of an electron” (A395), but Annie was “not really sure” (A4.397) why.

The idea of the nucleus’ force being ‘used up’ on the core electrons recurred later in the interview when I was attempting to find out if Annie understood the idea of shielding, in terms of diagram 32. Would the core electrons have any influence on the outermost electron? “• • Yeah they’ll, they’ll cut down the amount that it’s being pulled towards the nucleus because it’s being sort of, they’re being pulled in before. So, the actual pull on the outer electron will be less than what’s in between” (A4.511). Paraphrasing, the nucleus has a certain ‘pulling power’, “yeah” (A4.514), and that because it’s using some of that up, Keith S. Taber – [email protected] A14




pulling in those first electrons in this first shell, and in the second shell, and in the third shell, that by the time it gets to the fourth shell, it hasn’t got much left for that? “Yeah” (A4.516)

1.2 Representation of electrons.

When Annie pointed out that the chlorine electrons and carbon electrons were represented differently in figure 3 (A1.134), she was asked what difference there was between these electrons. Annie suggested they might “actually contain some of the element in the electron” (A1.138), suggesting she had not fully come to terms with the ‘fundamental nature’ of sub-atomic particles. When asked about the size and charge of the electrons Annie suggested that these would be different for the different elements (A1.144, 146 and A1.148, 150 respectively). If electrons had a colour they would “pick out the colour from the element” (A1.156). If these ideas were firmly held (rather than a panic response to the questioning) they had disappeared by the second interview. Now chlorine and carbon electrons were the same size (A2.19), and had “the same charge” (A2.21). Annie did not think an electron had colour (A2.27) being “just a charged particle” (A2.29).

1.3 Electron orbitals and shells.

The circles in figure 3 represent the “quantum shells, on what the electrons sit” (A1.186) which would be spherical in three-dimensions (A1.194). When discussing the similar representation (of an aluminium chloride dimer) in figure 15 Annie reported that “the [electrons] in the chlorine [can move about] ‘cause the aluminium ones are sort of fixed to the chlorine bonds that they’re sharing” (A1.596). “The ones in the chlorine” referred to the electrons that were not involved in bonding, which Annie thought belonged to the chlorine (A1.598, 606), and which Annie thought were “more stable, more fixed” (A1.604), rather than the electrons involved in bonding and being “shared” (A1.610) between the aluminium and chlorine. Two observations may be made about these comments. Firstly that it is more appropriate to refer to the stability of the overall system (molecule versus atoms) rather than of the individual electrons. Secondly Annie seems to associate the areas of overlap on diagrams such as fig 15. with the actual location of the electrons - i.e. bonding electrons are restricted to the overlap area, whereas non-bonding electrons are free to move around the whole Keith S. Taber – [email protected] A15




‘quantum shells’. Similarly, in tetrachloromethane (figure 3), electrons “move around”, but “the ones that are fixed to carbon would stay” (A1.200): “they can’t really move around, like all the way around the shell” (A1.202). The target interpretation would be different: that all the electrons are located in orbitals, but that the molecular orbitals in which bonding electrons are to be found are located between the two atomic centres. The atomic orbitals in which the ‘lone pair’ electrons are to be found are restrictive to a similar extent, but are located in relation to only one atomic centre.

Annie’s ideas did not seem to have developed far by the second interview, when again referring to figure 15 she reported “the electrons they don’t stay in a fixed state there, they go round, like in orbitals, or in spherical, things” (A2.378). Despite using the word ‘orbital’ it is not clear that Annie distinguishes it from ‘shell’ as in the same utterance she reports that the electrons are all “held in and going round and making up the, the shells” (A2.378). In the third interview she reports “The black circles indicate electrons and sort of where they’re moved within the orbitals, except that they wouldn’t be fixed, they’d sort of be whizzing around within the energy levels [i.e. shells]” (A3.4). The electrons in the atom are “held together by, erm, sort of, oh, electrostatic forces coming out from the a.., nucleus of the atom, which pulls the electrons in. So although they’re sort of, in their own orbitals and can move freely, they don’t sort of whizz off.” The electrons don’t fall into the nucleus as they “are held in, erm, in sort of levels, so, it’s to do with sort of bonding, like you can only get two electrons in the first quantum shell. So that they are held in these shells” (A3.10). “...they’re all held in quantum shells which are different energy levels, and you can sort of promote electrons should you need to in bonding, so, so if for example you need a bonds to have, I don’t know, an extra electron in a p-orbital, you can donate an s, s-electron across, to give you hybrid, things” (A3.10).

1.4 Atomic structure and the periodic table.

In the second interview Annie was asked about the normal electronic configuration of aluminium, atomic number 13, and she worked out this was “2.8.3” (A2.350). This would locate the element “in the transition, bit, and it’s group three” (A2.352). When shown figure 32a (i.e. the top third of the figure)during the fourth interview Annie was able to recognise the atom “potassium” (A4.334) “because you’ve got, Keith S. Taber – [email protected] A16




an outer electron on its own, so I would say that was, obviously a group one metal, and then counting up the number of shells inside, if my arithmetic and memory is, functioning, which is probably highly unlikely, {laughing} I deduce that to be potassium” (A4.338), with the electronic configuration of “2.8.8.1” (A4.340). The atom is in period “Three. No two. No three” (A4.346). But it has “four” (A4.348) shells of electrons, so it will be in period “four” (A4.350).

1.5 Three dimensional structures.

When Annie was asked about the shape of tetrachloromethane she seem to be confused between the molecule (“the way the electron shells conform”) and “an actual piece” which “wouldn’t have to be flat and laid out” but could “be like a crystal shape” (A1.182)

Annie recognised that real chemical species could be three-dimensional, for example the ethanoate ion in figure 13 (A1.556), where the four bonds around the methyl carbon would “go off at about hundred and nine degrees” (A1.558). However she thought the structure in figure 12 (representing the benzene molecule) “would three dimensional” (A1.562) and not flat (A1.564).

1.6 Confusing macroscopic and microscopic entities.

In chemistry the macroscopic phenomena experienced in the laboratory are explained in a series of models which different ranges of application. One aspect of this is that of scale. It was commented above (section 1.1) that Annie would attempt to explain sub-atomic phenomena in terms of intermolecular interactions. Annie seemed to have difficulty in distinguishing between the scales at which particular terms and ideas could be used. When she was asked what holds iodine together as a solid (looking at figure 17) Annie gave an answer which was appropriate to the question of what held the discrete molecules together: “it shares electrons between, between itself, well not itself but it’s same sort of, things like” (A2.401), rather than what caused the molecules to stay together.

At the start of the third interview Annie was shown figure 1 (a sodium atom) and asked to describe the structure of the atom. Her response, Keith S. Taber – [email protected] A17




and the dialogue that developed, is remarkable in that whilst able to answer quite sensibly about an individual atom, Annie also showed a considerable degree of confusion between molecular (microscopic) and molar (macroscopic) entities. For the purposes of this analysis I will first present her comments regarding the atomic scale, and then move on to her more quizzical comments.

“it’s obviously a group one element. Erm, due to the fact that it’s got one outer electron. Or else it could have been, sort of had electrons removed from another group but that’s probably highly unlikely” (A3.2). “The black circles indicate electrons and sort of where they’re moved within the orbitals, except that they wouldn’t be fixed, they’d sort of be whizzing around within the energy levels [i.e. shells]” (A3.4). The electrons in the atom are “held together by, erm, sort of, oh, electrostatic forces coming out from the a.., nucleus of the atom, which pulls the electrons in. So although they’re sort of, in their own orbitals and can move freely, they don’t sort of whizz off.” “Obviously the larger the atom you are going to get the less, less power the nucleus has on the electrons so the closer they are to the nucleus, the more power, the more force is holding them in, making a, a sort of, a denser, sort of compact molecule, atoms” (A3.6). The force originates “from the nucleus, erm neutrons, protons in the nucleus, make up a plus charge, which would draw the electrons in, by elec.., electrostatic forces” (A3.8). The electrons don’t fall into the nucleus as they “are held in, erm, in sort of levels, so, it’s to do with sort of bonding, like you can only get two electrons in the first quantum shell. So that they are held in these shells” (A3.10). “...they’re all held in quantum shells which are different energy levels, and you can sort of promote electrons should you need to in bonding, so, so if for example you need a bonds to have, I don’t know, an extra electron in a p-orbital, you can donate an s, s-electron across, to give you hybrid, things. But why they fall into the nucleus [sic] I’m, not quite sure. I don’t think I could describe that” (A3.10).

Taken together these comments give a considerable amount of information about atomic structure: the electrons are in orbitals, which are associated with energy levels, and they move around, although they cannot leave the atom, as there are electrostatic forces acting on them, due to the positive nucleus. Electrons closest to the nucleus are most strongly held, and in some circumstances electrons can move between orbitals. Annie is not sure why electrons do not fall into the nucleus, but knows that it is something to do with the quantum shells.Keith S. Taber – [email protected] A18




However, in the midst of this quite competent description of her understanding of atomic structure Annie interjects two “asides” which refer to phenomena outside the scope of the figure. On the first occasion the reference is to the metallic lattice which Annie feels the atom would be part of, and she acknowledges this was “from background knowledge”. The second, longer, aside is more remarkable, as it seems to show serious confusion between macroscopic and microscopic phenomena. It almost appears to have been provoked by a question of the form ‘how do you know there is an atomic nucleus at the centre of a piece of material?’ although no such question was asked by the interviewer. In both of the utterances it is interesting that Annie returns to her main theme after the ‘intermezzo’:

“The structure of it. Right, the structure’s held, it’s obviously a group one element. Erm, due to the fact that it’s got one outer electron. Or else it could have been, sort of had electrons removed from another group but that’s probably highly unlikely. Er, it’s held together by ionic bonds, within the lattice, er, er, it’s a meta.., metallic structure. You can’t see that from the diagram, but sort of know that from background knowledge. A metallic structure. Looking at the arrangement it would be sodium” (A3.2).

“The electrons are held in, erm, in sort of levels, so, it’s to do with sort of bonding, like you can only get two electrons in the first quantum shell. So that they are held in these shells. Why they don’t quite fall into the nucleus, I’m not quite sure, but obviously you are going to get sort of very minute particles, of the element, which is going to sort of stop them. Again you can’t really say, you’ve got a slab of, sort of, say, erm, sodium or something, you can’t really say, right in the middle of there, there’s the nucleus, because sort of, or, of them if you gave me like a block of sulphur, or sodium sorry, and you sort of put a pin into half the middle, you couldn’t say right that’s the nucleus because it’s sort of held all together, because it’s made up of atoms, although you assume the nucleus is in the centre because that’s the obvious place to be, so obviously it’s going to be in the centre, so it gets sort of the elec.., erm the sort of forces are distributed evenly around, its er, you can’t, you couldn’t detect it in a classroom, well you could with erm,





goodness all these gadgets they have these days. Er, so, they’re they’re all held in quantum shells which are different energy levels, and you can sort of promote electrons should you need to in bonding, so, so if for example you need a bond to have, I don’t know, an extra electron in a p orbital, you can donote an s, s electron across, to give you hybrids, things. But why they fall into the nucleus {sic} I’m, not quite sure. I don’t think I could describe that” (A3.10).

It is interesting the just before Annie starts to question the ‘straw man’ in the second extract, she suggests that “very minute particles, of the element” are “going to stop” electrons fall into the nucleus. Although Annie is capable of competently discussing atomic phenomena she does not seem to have fully separated molecular and molar ideas in her own mind. The nucleus is defined to be at the centre (of an atom) and the electrons (of that atom) surround the nucleus - but Annie is confusing an atom with a sample of material,

“Well it’s just you assume the nucleus is in the middle which it obviously is. But if you were to say right, then you’ve got a like a say a cube, and you say ‘right that is’ for example ‘a cube of sodium’, and you imagine all the electrons to be all the way round, if you stuck a pin in the middle it wouldn’t mean that was the nucleus, because it’s made up of atoms. So I think I’m just confusing matters here really” (A3.14)

So if one pointed at the very centre of a cubic centimetre of sodium, would one be pointing at a nucleus?

“The chance, it could be 50:50 because the atom may lay sort of that side, of the point, ‘cause obviously [sic] the sodium block is made up of like millions and millions of little atoms of sodium, so within each atom you are going to get a nucleus, and this arrangement of electrons. So the chances are of you hitting the nucleus are probably quite high due to the fact they are so small, but it also could be quite slim” (A3.16)

Although this response is hardly definitive it shows that when Annie focusses on this question she can successfully distinguish the atomic and macroscopic realms. Perhaps Annie’s understanding in this area is ‘firm’ enough to withstand direct questioning, but requires deliberate consideration, so that Annie’s answers show some confusion when the Keith S. Taber – [email protected] A20




distinction is peripheral to the main focus of the question being asked.

1.7 Penetration and overlap.

Later in the interview Annie is asked why in sodium chloride (figure 5) the ions do not move any closer if they are attracted together. Annie suggests “they could only get so, so close, because of the size of the atoms” (A3.202). She seems to be suggesting that the atoms are impenetrable, although when discussing covalent bonds Annie has described how atoms “combine” (A1.65) and “join” (A1.540). In the case of figure 5 the atoms do not coalesce as “they could only get so close due to the fact that sodium’s a fairly, well it’s a, a small atom compared to chlorine, due to the fact that, the nucleus is pulling the electrons in on the sodium more, so, due to the fact that it’s got less electrons there, so the charge, or the amount of electrons, in the chlorine aren’t being held quite as tightly together. And also the on.., ionic radius has increased” (A3.204). This ‘answer’ does not explain any more than the previous statement - it still implies a tacit belief that the atoms (ions actually) are impenetrable - but gives some further information that the sodium cation is smaller than a sodium atom, whilst the chloride anion is larger than the chlorine atom. This could be classed a psuedo-argument: it has the form of an explanation, but does not address the question asked. It is not clear if Annie actually realises this, or just assumes at a deep level that the ions are unable to intermingle, and therefore misunderstands what would literally be a meaningless question form her perspective.

1.8 Core charge and shielding.

During the fourth interview Annie was asked to compare figures 33 and 32. In figure 33 “it looks as though, you’ve basically just put in the outermost shell, rather than all the, the inner, inner shells as well” (A4.462). The core charge was also represented, but Annie interpreted these numbers as “you’ve put in the number of electrons, that are in the outermost shell. For the first two at least. And I don’t know what’s happened for the last four, completely confused” (A4.466). Despite having refuted herown conjecture, and having this confirmed by being explicitly told ‘that’s not meant to be the number of electrons’, Annie still hypothesised that “at a guess I’d say that it was, • • • trying to show the number of electrons in the outer shell” (A4.474). Agreeing Keith S. Taber – [email protected] A21




this was not so Annie was “completely confused” (A478).

Annie could calculate nuclear charge as the “number of protons [is] normally equal to the number of neu.., erm electrons” (A4.488). A considerable amount of leading questioning was required to induce Annie to refer to any shielding effects. Would the electron experience the pull of all the protons pulling it in towards the centre? “Er, • • • • • • • • • • yes” (A4.498) Is there anything that might prevent the effect of those protons being as potent as it might be? (No response: pause of approximately twelve seconds.) Would it experience the full effect of the protons tugging at it, trying to pull it in towards the centre? “• • • • Mm • • yes and no, I think” (A4.501). Is there anything else that might effect that electron apart from those protons? “I’d say what sort of state it’s in (A4.503). Any thing else on the diagram? “Oh in the diagram, sorry. • • The, the, the, the attraction of the other atom” (A4.506). And if that’s far enough away not to be an influence is there anything else effecting it? “• • No” (A4.507). Annie did not seem to be going to suggest that the core electrons could have an influence. What else is present in that part of the diagram? • • Apart from the nucleus and the outermost electron? “You’ve got the electrons on, in the shells, in between, on the, second, third, fourth” (A4.509). Would they have any influence on the outermost electron? “• • Yeah they’ll, they’ll cut down the amount that it’s being pulled towards the nucleus because it’s being sort of, they’re being pulled in before. So, the actual pull on the outer electron will be less than what’s in between” (A4.511). Paraphrasing, the nucleus has a certain ‘pulling power’, “yeah” (A4.514), and that because it’s using some of that up, pulling in those first electrons in this first shell, and in the second shell, and in the third shell, that by the time it gets to the fourth shell, it hasn’t got much left for that? “Yeah” (A4.516) So (very closed question!) did Annie think they’ll be any direct influence between those electrons? The outer shell electrons and the other electrons? “• • • Er, yes in a way, because they’re not going to be able, I mean they’re not going to be able to get too close, be-cause they’re erm, as they’re similar charges, then obviously they are going to repel, to a certain extent” (A4.517) Annie’s background in electrostatics was rather limited, she had heard of Coulomb’s law (A4.525) which had “something to do with er, size, spin, and all that” (A4.527).

2. Chemical bonding.Keith S. Taber – [email protected] A22




2.1 Inter-atomic binding.

Annie did not use the term chemical bonding to apply to the atomic binding itself - there is no bonding holding the atom together (A1.49, 51).

2.2 Bonding is more than just forces, and is represented by overlap.

During the first interview Annie explained that (in tetrachloromethane, figure 3) bonds are represented “by the circles that overlap” (A1.134). Annie recognised bonding in figure 7 (hydrogen molecule) and figure 8 (lithium iodide) (A1.352), but not in figure 9 (potassium fluoride) “because they’re not combined” (A1.354). If no overlap was shown, the diagram was not considered to represent bonding, so in figure 11 (a chain of hydrogen fluoride molecules) “there is [bonding] within the, within the sort of shape of the H-F, but when it meets up to like the H-F on the corners of the other shapes, they don’t actually bond” (A1.426). So there is no bonding in figure 10 between the sulphate anion and either the potassium cation (A1.436) or the aluminium cation (A1.438). Figure 16 (aluminium chloride dimer) has connections between aluminium atoms and chlorine atoms made by lines, and Annie is not sure if there is any bonding shown in this diagram (A1.702, 708). In figure 17 the iodine molecules are held together (A1.728), though not by chemical bonds (A1.738) but by “probably just the forces of pressure and, the, like the charges from each thing they would be stable” (A1.730). Is Annie referring to the intramolecular bonds? “There should be from the forces, the forces from each iodine should have combined to stable-up. But, there’s probably other forces, which, erm, hold it together, in a solid or, so it wouldn’t break off or anything” (A1.736). Annie seems content to refer to ‘other forces’ as an explanatory device.

According to Annie’s interpretation there is no bonding (A1.283) shown in figure 5 (sodium chloride) as “no electrons are shown and they don’t actually overlap or anything they just go in rows” (A1.242). Bonding is not needed to hold the structure together as “it would probably get held together by just forces” (A1.256). Annie was asked if the ions calcium-two-plus and oxygen-two-minus would form a double ionic bond. Annie thought they “wouldn’t need to” (A1.754), as they “would Keith S. Taber – [email protected] A23




just combine” (A1.758) but not form a bond (A1.762).

Similarly there is no bonding in iron (figure 6), (A1.301) although the atoms will hold together (A1.295) as the atoms are “all the same sort” (A1.297), and therefore “they don’t need to be bonded” (A1.301). However two hydrogen atoms in a molecule would be held together by forces due to “their electrons...lack of them and abundance of them” (A1.307) - forces that appear to be needed despite the atoms being of the same sort.

So it would seem that by the first interview Annie had undertaken learning experiences related to chemical bonding, and had also been exposed to some consideration of the role of forces in (atomic and molecular) structures, but had not integrated these two ideas. Bonding was a quite specific phenomenon with (or represented by) definite characteristics, but an absence of bonding did not exclude the presence of forces holding atoms, molecules and other structures together. The two common ways of representing covalent bonding in introductory chemistry courses are the overlapping of circles symbolising the atoms, and lines drawn between the chemical elemental symbols. Annie seemed to only recognise the former symbolism. Some of these themes were explored further in the second interview.

At the time of the second interview Annie still seemed not to have integrated the concepts of chemical bonding and interatomic forces. For example figure 8 represents something that is “ionically bonded, but the forces holding it together will be • • • • • van der Waals I suppose?” (A2.125). In addition to this lack of integration, Annie was still limited to a criterion of atomic overlap representing bonding. Figure 8 (lithium iodide ‘molecule’) was considered to show bonding, but when Annie was asked (about the ion pair shown in figure 9) could the K+ and F- combine to form a compound, she replied “No. Not looking at this diagram” (A2.127). It would be expected that after one year of an A level course a student would know that potassium fluoride was a stable compound, but it seems Annie’s reponse was determined by her own interpretation of the diagram, which showed the ions apart. Annie certainly seemed to understand what the term compound means, although she found it difficult to define without tautology: “a compound is two, two elements that combine to form a new compound, or a new, new sort of substance, and they’re actually





physically like interlocked. But if you had a mixture, then you’d have, say, bits of potassium and bits of fluorine and you could be able to separate them, by some means, but the compound they’re actually fixed, so you get a new thing produced” (A2.129). Annie confirms that her judgment was based on the lack of overlap, with the electron density envelope drawn only around the anion “to show that the, the force on this wouldn’t combine whereas on, on the, the previous thing [fig. 8, LiI] it’s got the, the pull towards either of them, whereas this one the, the pull is not combining the potassium” (A2.149). It seems Annie interprets the electron density envelope as the extent of some finite force field that attracts atoms or ions together: “it [F+] could pull it [K+] towards it slightly, but not enough to actually combine” (A2.152). In figure 10 the electron density around a sulphate anion is being distorted (polarised) towards an aluminium cation, and Annie was asked if these species could form a compound. This “could be probable, because it’s reaching out more the shape of the, the direction of this nose bit is, sort of shaping more towards it” (A2.214) - more that is than a companion diagram with a potassium cation. A consistent application of these ideas would suggest that the sulphate/aluminium combination was closer to forming a compound than the sulphate/potassium combination (an answer that is also consistent with Annie’s recognition of bonding represented by overlap - the sulphate/aluminium bond having more covalent character). Annie thought “they’d probably be about equal[ly successful in forming a compound], but I think the aluminium would probably have a better chance as it’s got, it’s a smaller atom, but then you’d end up with one electron over, so, the potassium probably would” (A2.218). This response seems to suggest that Annie is calling upon a number of criteria which she has not fully reconciled.

In the third interview Annie reported that there was “no” (A3.96) chemical bonding in figure 5. She also thought there was “no” (A3.139) bonding inside the iodine molecule, “it’s not bonding. But there’s sort of van der Waals forces” (A3.140). “There must be some sort of attraction, between them both, erm, to basically hold the atoms together, because they’re minus an electron, to make them slightly more stable” (A3.150).

In the fourth interview, just prior to her examination, Annie was asked to say what she thought a chemical bond was. For Annie “it’s a link between two atoms, which can be of various, various types. But





basically links two things together, by either combination, or just charge” (A4.2), “well, like exchange. Through like reactions. To sort of combine fully, or just by force they’re held there. Actual forces on the atoms” (A4.4). This answer contains references to some of the major aspects of chemical bonding: a chemical bond as a “link between two atoms” formed through chemical “reaction” enabling new chemical “combinations”, with the atoms involved held in their new positions by “forces on the atoms” due to “charge”. However, a more critical reading suggests that although Annie acknowledges “various types” of bond, she demonstrates evidence of a dichotomous classification, probably left over from GCSE level work: bonds hold things together “by either combination, or just charge”, “to combine fully, or just by force”. The archetypes that may be suggested for this classification are the pure covalent bond model, where atoms overlap to “combine fully”, and the pure ionic bond model, where ions are held together “just by force” by “just charge” - apparently a lesser form of bond!

2.3 Heating and bonds.

Whilst discussing the intermolecular and intramolecular bonds in iodine during the third interview Annie made a general statement about the way heating affect bonds: “if you apply heat to something then you are breaking down, you’re causing the bonds, in between, most bonds have sort of, er, sort of er, er, a level whereby they can go up to a certain heat and then they’ll be broken down. So, I don’t know what it is for iodine” (A3.162).

3. Rationale and mechanism for bonding.

3.1 Stable electronic structures.

When first interviewed Annie used the ideas of ‘stable’ electronic shells to explain bonding phenomena. The two atoms in the hydrogen molecule (fig. 2) “joined because they only have one electron in their first shell so they combine to form a stable first shell” (A1.59). In figure 4 “each oxygen [atom] is giving two electrons to match-up to the other two, so they can form a shell of eight” (A1.230) In figure 8 “lithium combines with the iodine - to make a stable outer shell between the Keith S. Taber – [email protected] A26




two, by sharing electrons...” (A1.321).

In figure 10 the aluminium cation appears (on Annie’s interpretation) to have been “more successful” (A1.402) in joining with the sulphate anion than the potassium cation. This is explained in terms of aluminium having sufficient surplus electrons to “complete the [sulphate] outer shell. But potassium would still leave it with one electron less. So the pull isn’t so great” (A1.406). The aluminium chloride dimer in figure 15 is also explained using this approach: “[aluminium]’s got the amount that it needs, to stabilise” (A1.608).

The same ideas are used in the second interview. For example the tetrachloromethane molecule (fig. 3) “they all share an electron, so the electron circuit is made up by one of each to give them all full outer shells” (A2.12). The tendency to complete outer shells could be used to explain why both elements and compounds can form molecules. “A molecule could be of an atom [element?], which has got like two of itself, like a hydrogen molecule’s got two hydrogen. To give an outer shell,” (A2.135) “but a compound has got like two or more different elements, in it to make up the full stable shell” (A2.137).

In the fourth interview we discussed the formation of sodium chloride, where a sodium atom can be understood to have transferred an electron to chlorine and “by losing it, it’s sort of not got an extra electron, it’s minus the electron it would have had originally, but it’s gained a stable shell. Because of the next, next shell down” (A4.46), “it would become more stable, because it’s gone into a, sort of a molecule anyway” (A4.48). Although “you have to put energy in, to remove the electron, to start with” (A4.66) “because you’ve removed this electron, you’ve got, er a late, eight in your next quantum shell down, so that’s more stable than having one electron on its own, because it’s more likely to combine with something if you’ve got one all on its own” (A4.76).

3.2 Electronegativity, energy and entropy considerations.

Annie appeared to be quite comfortable with this somewhat qualitative approach to explaining bonding, whereas the more quantitative ideas seemed to confuse her. She felt it was possible to find out if enough attraction exists between ions (e.g. potassium cation and fluoride anion in figure 9) for them to “actually combine” (A2.152) by using Keith S. Taber – [email protected] A27




“values found out by Pauling for the electronegativity of elements. I think if you combine them, if you add two together and they become negative it won’t happen. Is that right, could be muddled up with something else?” (A2.156).

In the third interview there was a discussion of polar and non-polar solvents. Annie reported that from entropy considerations dissolving was more favourable than crystallisation, “ ‘cause of well, the sort of the kinetic energy in between, and erm, into like whatever you are going to dissolve it into. Erm, the sort of the readiness to form new bonds, should, should what you’re sort of dissolving the stuff into, be of, either a different charge, or, sort of a higher, higher electronegativity than itself. Or if its more reactive then you are going to get displacement” (A3.245).

3.3 Forces.

In iodine: “there must be some sort of attraction, between them both [the two atoms in a molecule], erm, to basically hold the atoms together, because they’re minus a, an electron, to make them slightly more stable” (A3.150).

After discussing the structure of the hydrogen atom, and the atttraction between the nucleus and the electron, Annie was asked about interactions between two hydrogen atoms that might collide, when “the proton from each atom, could attract the, sort of the electron from the other atom” (A4.205) and “the two protons and the electrons would repel each other” (A4.207) Annie accepted that when two hydrogen atoms collide the attractions would be greater than the repulsions “ ‘cause if they sort of bumped into each other, and the electron from one was, say for example, over the far side, then they’d move to get as far away apart as each other as possible anyway, so, if they collided that way then they would have combined” (A4.211). Annie seems here to be ignoring nuclear repulsions, and just focussing on electron repulsion in suggesting the electrons need to have maximum separation, “to join together. Well they’d sort, one would be, maybe, over far onto the left, maybe onto the left of each atom, so that they’re getting pulled towards, well the one on the second atom would be pulled towards the, proton, but the electron would be sort of in a way, sort of horizontal to it, over the, ‘cross the other side. ‘Cause that would be sort of the furthest away it could move. From that Keith S. Taber – [email protected] A28




electron” (A4.215) so in Annie’s model of the hydrogen atom, only one of the electrons has a bonding role, and the other is as far removed from it as possible. The atoms don’t just bounce apart as “once they have combined, then you’ve got, er, • • • • got two, tut oh, got the electrons are sort of shared between the two, which will hold them together” (A4.219), i.e. two electrons in a bonding role? The electrons are “not going to be in one fixed position, they’re going to be sort of, moving around anyway” (A4.223) but it’s “more likely that they’re going to be, farther apart” (A4.225) “Because they’re trying to get away from each other. But then if that happened, then, the actual, the two, two nuclei would repel each other, anyway so you’d, go back to sort of square one. So I think in a way you’d have to have like one in between, and sort of one on an outside post” (A4.227). Annie does not believe the two electrons could both be between the nuclei, as the electrons repel, but if they were repelled to opposite ends of the molecule the nuclei would repel and the molecule would dissociate, so Annie pictures one electron between the nuclei, and one at one end. As the electrons are moving around presumably the two electrons both spend some time at the centre of the molecule. Although an orthodox approach would put both bonding electrons between the nuclei as the most probable position, Annie has produced a ‘solution’ to the problem that is arguably just as acceptable based on qualitative considerations.

3.4 Stability as a psuedo-explanation.

It was noted above (section 3.1) that the two atoms in the hydrogen molecule (fig. 2) “joined because they only have one electron in their first shell so they combine to form a stable first shell” (A1.59). Without some independent definition of stability (other than stable systems are those that tend to be formed, and not to change) this is not an explanation of why the atoms joined, but a form of definition or example of a “stable first shell” (i.e. the type of first shell formed when two hydrogen atoms join to make a molecule.) Annie’s response becomes little more than a tautology in this analysis. “They only have one electron in their first shell so they combine to form a stable first shell” (A1.59) How does this happen? “It combines, the two atoms combine and they sort of share an electron each, so they sort of combine, so they’ve got two electrons between them, and they’ve each contributed, contributed one to the shell” (A1.65). The atom knows it’s only got one electron in its outer shell and it would be better off with two “because they’re sort of like unstable because they’ve Keith S. Taber – [email protected] A29




only got one, and hydrogen’s only got like one electron anyway, so it needs to combine so it can be more stable because they tend to not float around in ones” (A1.77). This is a pseudo-argument , or low level explanation, still at the level of tautology (it does this to become more stable, and I know it must become more stable because otherwise it wouldn’t do it.) Answers at this (low) level of explanation do not clearly distinguish cause and effect: are the atoms unstable because they tend not to “float around in ones”, or vice versa? (Note the comments on Annie’s use of “because” in the introduction.) So could the atoms seek one another out? “You know I think they’ll just combine, but I don’t know if you’d have to react them in some sort of way to get them to combine” (A1.91), “If there was enough of them in a box and there was like a even number of them I’d have thought that they’d have just attracted each other” (A1.93). In her consecutive utterances Annie’s position shifts. Rather than the atoms “just combin”ing , which may require human intervention to “react them” - possible evidence of confusion between macroscopic (e.g. samples of substances being mixed and heated) and microscopic(e.g. collisions between atoms) phenomena - the atoms “just attract” (A1.93). Following this Annie agrees there is some sort of force between the atoms (A1.96), but cannot suggest what form this takes (A1.97).

Later in the interview Annie informed me that Ca2+ and O2- “wouldn’t need to” (A1.754) form a double bond “Because one’s lacking two electrons, and one’s got two, so, they would just combine” (A1.758). Annie seems to feel that certain processes naturally (“just”) occur, and do not require mechanistic explanations.

4. Covalent Bonding.

4.1 First interview: Annie recognises a class of bonding called ‘covalent’.

When first shown figure 2 Annie identified it as representing a “hydrogen molecule” (A1.57) (To an ‘expert’ the term ‘molecule’ implies covalent bonding, bit such an association cannot be assumed with students: at one point in the third interview Annie uses the term “molecules in the ionic state” (A3.100).) Unlike figure 1 (which showed an atom) “these are joined because they only have one electron in





their first shell so they combine to form a stable first shell”. (A1.59) Annie did recognise the presence of a chemical bond (A1.67), and when asked if she had a name for that kind of bond she tentatively classified it, “Erm • • • • • • • • is it covalent?” (A1.69)

Annie also recognised the existence of the covalent bond in a number of other diagrams. Figure 3 showed covalent bonds (A1.222), the figure representing oxygen (fig. 4) also showed a covalent bond (A1.226), and figure 11 represented “five” (A1.430) “covalent” (A1.432) bonds. The bond between the two carbon atoms in fig. 13 was covalent (A1.540) as was the bonding “between the two iodines in each molecule” (A1.718) shown in figure 17.

However Annie was not entirely clear about using this category. When asked about figure 12 (benzene) she first described the bonding as “ionic” (A1.450), and only later corrected “I’ve got it the wrong way round. Should have been covalent bonds, not ionic” (A1.502).

4.2 Covalent bonding is between non-metals.

Annie was aware that bonds she described as covalent involved sharing of electrons. For example she described the bond in the hydrogen molecule (figure 2) in the following terms: “the two atoms combine and they sort of share one electron each, so they sort of combine, so they’ve got two electrons between them, and they’ve each contributed, contributed one to the shell.” (A1.65) When later during the same interview Annie was asked where the electrons came from, Annie responded that “they just like both pull together” (A1.616) and that “one came from one hydrogen, and one came from the other one.” (A1.618) In a similar way she described the carbon-chlorine bonds in figure 3: “one [electron] comes from the carbon, and one comes from the chlorine” (A1.630). However when she was asked to define a covalent bond Annie did not refer to sharing of electrons, but rather as “a bond that is formed between non-metals” (A1.71) She repeated this criterion later in the interview: “covalent are non-metallic bonds, so when you get a single bond from chem.., er, carbon to hydrogen that’s, they’re both non-metals, so that would count as a covalent bond” (A1.744). When describing the carbon-oxygen double bond represented in figure 13 (the ethanoate ion) she explicitly used this criterion: “that’s covalent in that case because it’s two non-metals joining” (A1.540).Keith S. Taber – [email protected] A31




It can be shown that Annie was not also using sharing as a criterion by her comments about figure 15 (which represented a dimer of aluminium chloride, drawn to show atomic overlap and sharing of electrons.) Annie recognised that aluminium “shared [electrons] with the chlorine” (A1.610) but categorised the bonding as “ionic” (A1.574) “because it’s a metal and a non-metal combining” (A1.578).

To summarise, when Annie was first interviewed her comments indicate that she was aware of a category of chemical bonding which she labelled ‘covalent’. The main criteria used to determine whether bonding fitted this category was that covalent bonding was between non-metallic elements, whereas ionic bonding would be between metals and non-metals. This classification system appeared to take priority over any ideas about sharing of electrons (as opposed to their transfer.) Although representations of atomic overlap seemed to be an important cue for Annie, this criteria seemed to relate to bonding per se rather than covalent bonding in particular.

4.3 Second interview: electrons shared between the same sort of things.

In the second interview Annie was asked about the electrons shown in figure 3 (meant to represent a molecule of tetrachloromethane), and the extent to which the ‘carbon electrons’ and the ‘chlorine electrons’ are similar, and/or different. Annie believed that “they all share an electron, so the electron circuit is made up by one of each to give them all full outer shells” (A2.12), showing that at this stage in her course the idea of electron sharing was part of her understanding of this type of bond. However her response to figure 7 (meant to represent a hydrogen molecule, in terms of the symmetrical distribution of electron density) did not refer to equal sharing of electrons, but to the atoms being held together by “their polar densities” (A2.63).

Later in the interview Annie was asked about the type of bonding in figure 17 (representing iodine molecules in a regular arrangement), she immediately replied “they’re covalent bonds. Between, iodine, and itself. Well just to form like iodine molecules, that’s repeated all over the place” (A2.397). Each iodine molecule had “one” bond and “it shares electrons between, between itself, well not itself but it’s same sort of, things, like” (A2.401).Keith S. Taber – [email protected] A32




In the second interview Annie demonstrated that she had a category of bonding called covalent, which involved the sharing of electrons. She was able to apply thing in the orthodox manner, and was seen to do so in the context of one diagram where the overlap of atomic electron shells was explicitly shown (tetrachloromethane) and another where molecules were shown as ‘figure of eight’ shapes (iodine), but when presented with a representation of the hydrogen molecule as having a roughly cylindrical electron cloud (figure 7), she presented an explanation in terms of “polar densities”, charges, and hydrogen bonding, before referring to covalent bonding (see below), and no mention of sharing of electrons was made.

In the third interview (and despite her orthodox comments in the second interview almost one year earlier) Annie reported that there were “Van der Waals forces” (A3.130) “between iodine atoms” (A3.132) in figure 17. There were interactions between the atoms in the molecules (A3.138), but “it’s not bonding. But there’s sort of van der Waals forces” (A3.140). However in the vapour state iodine “still exists in a molecule” (A3.146) so “there must be some sort of attraction, between them both, erm, to basically hold the atoms together, because they’re minus a, an electron, to make them slightly more stable” (A3.150). Her introduction of van der Waals forces into the discussion (appropriate for the intermolecular interactions) appears to have interfered with her understanding of the intramolecular interactions. This confusion did not interfere with her basic understanding of covalent bonding as when “they share electrons” (A3.412).

4.4 Final position: equally shared electrons held in position by electrostatic force.

In the final interview Annie described how in a covalent bond “each atom contributes, er an electron, well the electrons are shared equally between the atoms involved, so you haven’t got dominance from one atom with the bonds, or of the electrons sorry” (A4.8). Annie has been asked how the bond holds the atoms together, but this answer seemed rather to address what made a bond covalent. The atoms do not just fall apart “‘Cause the electrons are sort of held in circuits, orbitals, because when they sort of combine together, they’re sort of going around freely, so you’ve got all the forces, sort of just like they’re Keith S. Taber – [email protected] A33




being pulled in by the nucleus. Electrons are being pulled in, so you’re, you’ve got sort of the nucleus pulling in, the electrons from the other, atom. So it helps them stay together” (A4.10). The forces are “electrostatic” (A4.12).

4.5 Electron clouds on the horizon?

The section presented above seems to provide some evidence of a development of Annie’s ideas about covalent bonding: it occurs between non-metallic elements, where electrons are shared between similar atoms, with the electrons equally shared, and electrostatic forces holding the atoms together. Selective reading of the interview transcripts would provide view of Annie’s understanding of covalent bonding that is fairly consistent, but shows increased sophistication. The ‘loss’ of covalent bonding in iodine, could be explained as a ‘blip’, perhaps due to the stress of approaching examinations. However, it was also mentioned above that when asked about figure 7 (the hydrogen molecule, with the bonding electrons represented as an envelope around the two nuclei) Annie’s responses were not consistent with this picture. Indeed this diagram acted as a focus for demonstrating some of Annie’s uncertainties and confusions.

Figure 7 was intended to represent the symmetrical nature of the bonding orbital in hydrogen. At the time of the first interview Annie understood what was intended as an electron density envelope as a representation of force, “attraction of two hydrogen atoms...” (A1.305) and her comments show this force was in some way related to electronic configuration, “these are joined because they only have one electron in their first shell so they combine to form a stable first shell”. (A1.59) and “...you’ve got two electrons, two atoms, and it’s the way that the, the force pulls them together.” (A1.305) What type of force was this? “Their electrons, the lack of, lack of them and abundance of them” (A1.307), in the case of the hydrogen molecule the “lack of them” (A1.309).

In the second interview Annie did not refer to the electrons, but to the atoms being held together by “their polar densities” (A2.63), “they’re both polar, like one’s plus and one’s minus, so the, the polarity of them cancel. To hold them together, and also to give them a, an even shape, constant shape” (A2.67). It was not clear in what sense “one’s plus and one’s minus”: or whether this figure was understood to be like the Keith S. Taber – [email protected] A34




figure seen previously showing the Na+ and the Cl-, “No, because, they, they both, yes it would because they’ve got the same charge. No” (A2.69). This charge on the hydrogen is “one plus” (A2.71), so both hydrogen atoms were H+ (A2.73, 75), giving an overall charge of “two-plus” (A2.77): i.e. the species shown was H22+ (A2.79). However, this was wrong as hydrogen should be “H21+” (A2.81). These references to polarity and charges are inappropriate for a neutral molecule comprising of two equivalent (and therefore equally electronegative) atoms, but this confusion would appear to be related to Annie’s alternative interpretation of the meaning of symbols ‘+’ and ‘-’ in these contexts, and this is examined in more detail in the next section, discussing ionic bonding. Annie’s conclusion from her deliberations (and answer to my original question) was that “they’re held together by hydrogen bonds” (A2.81). So was this similar to iron where Annie had earlier suggested hydrogen bonding? “No because, that’s [figure 7], looks like it’s forming a molecule, and they’re [figure 6] just a, an arrangement” (A2.83), “it’s a, covalent bond” (A2.89).

In the third interview Annie introduces the idea of electron density, but still seems confused about how this relates to charge and force: figure 7 “represents the, sort of the way the electron density is, in the hydrogen molecule. Er, ‘cause they’ve both got similar charges, you’re not going to get any sort of like polarisation around the two, so you’re getting even distribution” (A3.481). The two atoms are “being pulled, but they’re not sort of like really, really close, they’re in a way, they’re sort of being confined. Sort of, ‘cause they are, sort of similar, erm, they’re not repelling, tremendously, but they’re sort of being attract, they are being attracted I suppose. Erm, but, because neither is sort of more negative than the other, neither of them are being, attracted more than, each other so they’re sort of a fair distance apart, although they are together in effect” (A3.485).

The fourth interview occured two weeks after the third interview and a ‘tutorial’ going over some of the ideas that Annie seemed confused about. Despite this ‘intervention’ Annie still found this figure to be difficult to explain in orthodox terms. She was clear that figure 7 showed “a hydrogen molecule” (A4.154) which had “no” (A4.158) charge. However there was an attraction between the atoms (A4.160) as “originally they, would have both had, plus charges, most of, because of the fact that they’ve both got like one electron in their outer shell. So they’ve sort of, been joined together. As you can see Keith S. Taber – [email protected] A35




from the diagram, the sort of distribution, of the, the charge, because they were both of similar electronegativities, and similar charges, then the actual, the actual sort of sh.., shape, sort of use that description, the actual way that the, the charge has been sort of distributed, around the molecule is fairly, fairly symmetrical” (A4.162). Note that Annie is still applying her alternative‘devaition’ model of atomic charge: hydrogen atoms “had, plus charges ... because of the fact that they’ve both got like one electron in their outer shell”. She did mean that they were charged before joining together (A4.168). But when asked to explain why she thought so, she decided “they haven’t, although they’ve got, erm, I think I might have put that the wrong way, in effect. They’re, they’re positively charged ions, but, when they would have combined they wouldn’t have, I mean you have a charge if you add or take away an electron, so that wasn’t happened so they just sort of got, characteristic sort of like tending to go towards, one way or another” (A4.169). They weren’t ions before joining (A4.171) “they were just atoms” (A4.171), “so that they wouldn't have had a charge, although they would have, had, had a f.., er, force, they had sort of some sort of characteristic which made them, sort of attract the way they did, although it wasn’t like a, a posit.., or some definite charge there was, some hint of something there. To get them to come together” (A4.173). The two atoms were neutral (A4.175), and the molecule was neutral (A4.177) with two electrons (A4.179) and two protons (A4.181). The electrons in the molecule are “not going to be in one fixed position, they’re going to be sort of, moving around anyway” (A4.223) and it is “more likely that they’re going to be, farther apart” (A4.225) “because they’re trying to get away from each other. But then if that happened, then, the actual, the two, two nuclei would repel each other, anyway so you’d, go back to sort of square one. So I think in a way you’d have to have like one in between, and sort of one on an outside post” (A4.227). This model suggests a polar molecule, with a roughly linear arrangement (electron-proton-electron-polar), but the diagram suggests that “you haven’t really got any, polarisation” (A4.231) “because if you did, then, the char.., all the forces, the pull on one nucle.., nucleus would be much more, so the sort of electron density would be pulled towards one pole rather than the other. Which you haven’t really got” (A4.231). The atoms cannot move closer together as “there’s only really a distance, you can have because, you are still gonna get repulsion between, the nuclei, and, the electrons so they can’t go too close. Without they’re being sort of pushed away, they’ll sort of go, like with magnets, if you take them, you can push them so far, but there is a point where, they will start repelling” Keith S. Taber – [email protected] A36




(A4.233). Both nuclei are equally attracted to the electrons (A4.239). Despite completing her A level chemistry course Annie’s understanding of basic electrostatic ideas (charge, force) appears to offer little support in explaining covalent bonding, even to the extent of having to invoke “some hint of something” to attract the atoms together.

5. Ionic Bonding.

5.1 Ionic bonds are found between metal atoms and non-metal atoms that overlap.

In the first interview Annie was certainly aware that there was a class of bonding called ionic. Figure 12 (benzene) was thought to contain “twelve” (A1.452) “ionic” (A1.450) bonds (A1.480). There were “two types” (A1.454) of bond “C to H bonds or C to C bonds” (A1.456), but both were ionic (A1.458.) However later when comparing the types of bonds represented in the different figures she changed her mind, “I’ve got it the wrong way round. Should have been covalent bonds, not ionic.” (A1.502)

Figure 15 (aluminium chloride dimer) was thought to represent “eight” (A1.574) bonds “which are all ionic” (A1.574). The bonds were all the same (A1.586), all ionic (A1.588). The reason that Annie thought figure 15 (which was drawn as if the aluminium-chloride bonds were due to shared electrons) showed an ionic substance was “because it’s a metal and a non-metal combining.” (A1.578)

Figure 5 which was intended to illustrate an ionic substance (sodium chloride) was not interpreted as such, even though it did show a metal and non-metal, as Annie did not interpret the diagram as showing the species combining, and therefore did not think any bonding was represented (A1.240). For Annie figure 5 showed “just sodium and chlorine atoms” (A1.238), with “no” bonding (A1.240) as no electrons were shown, and “they don’t actually overlap or anything, they just go in rows.” (A1.242.)

5.2 The alternative ‘deviation’ interpretation of charge symbols.





The absence of evidence of bonding (by Annie’s criteria) was compounded by confusion over the meaning of the plus and minus signs used to indicate positive and negative charges. The cations in fig. 5 were identified as sodium “atom”s (A1.250) despite the plus signs “representing the charges” (A1.246). The chloride anion was called a “chlorine atom” (A1.252). These errors could have been ‘slips of the tongue’, were Annie not consistent in confusing the meaning of the signs. This becomes apparent when she explains that the structure is held together by “the attraction from the plus to the minus because like chlorine’s minus an electron and sodium is over an electron.” (A1.260) For Annie the “plus and minus signs on them representing the charge” (A1.246) do not mean an overall electrical charge, but a deviation from noble gas electronic structures: “sodium has like one extra electron in its outer shell, and chlorine has seven electrons in its outer shell so it’s minus an electron” (A1.262). What is given at GCSE level as the cause of electron transfer to form ions has become confused with the signification of the products of such a transfer: a ‘+’ sign meant to indicate one less negative electron than positive charge in the nucleus is seen as meaning one more electron than a stable configuration. The formation of ions by electron transfer explains the origin of the electrostatic forces that hold an ionic lattice together. Annie’s alternative conception of the ‘+’ and ‘-’ species means she must find an alternative mechanism to hold the substance together: “so by sort of exchanging, the sodium combining with the chlorine just by force pulls they would hold together” (A1.262). What does Annie mean by exchanging? “..by, well just the attraction in them.” (A1.264) From a conventional viewpoint Annie’s conception of figure 5 makes little sense: the structure is held together, but without any bonding; there are charges on neutral atoms; atoms are combining without overlapping; and the atoms are exchanging not electrons but force pulls related to the electronic configuration. However Annie’s comments seem to be more that just a make-shift argument put together on the spur of the moment. Indeed the mis-identification of ions as neutral, although not entirely consistent throughout the interview, certainly pervaded Annie’s comments. This misunderstanding was abetted by an interpretation of diagrams that only recognised bonding between species represented as circles (or similar) if there was overlap.

Annie identified the electronic configurations of the species Na+ and Cl- as “2.8.1” (A1.272) and “2.8.7” (A1.277) respectively, and





reiterated that being “one over, and that one’s one short” (A1.279) holds them together without bonding (A1.283). Later she described K+ as “an atom that has got an extra electron” (A1.336), and described F- as having “an outer shell of seven which has one less electron” (A1.340). In the discussion that follows it will be appropriate to distinguish between the conventional significance of the ‘+’ and ‘-’ symbols, and Annie’s alternative understanding. One could refer to the orthodox meaning as the ‘overall charge’ interpretation, but Annie seems to also use the term ‘charge’ for her understanding of these symbols (A1.246, see above), so the clumsy-sounding term ‘non-neutral’ is used instead. As Annie’s own interpretation is concerned with symbols showing deviations from noble gas electron structures the shorthand term ‘deviation’ interpretation will be used.

In figure 15 (aluminium chloride dimer) Annie suggests “the aluminium must have been a three-plus. So it needed, sort of, three extra.” This does not seem to be consistent with Annie’s explanation of other examples - three plus should mean three electrons over a noble gas electronic configuration - but neither does it seem to fit with a standard (‘non-neutral’) interpretation, where a three-plus species would presumably not “need” to be neutralised, else it would not have become charged.

Later in the interview Annie is asked if it is possible to have a double ionic bond. She is “not really sure” (A1.752) and the example of calcium-two-plus and oxygen-two-minus is suggested to her. Annie felt this combination “wouldn’t need to” (A1.754) form a bond “because one’s lacking two electrons, and one’s got two, so, they would just combine without needing to worry about other, other erm element” (A1.758) “sort of joining on to make up full shells” (A1.760) but this would not be a chemical bond (A1.762). The term “one’s lacking two electrons” could be taken to mean the cation, “and one’s got two” could refer to the anion, but this is unlikely as their “joining” would not be required to “make up full shells”. It seems that most likely Annie again implies that ‘2-’ means “lacking two electrons” compared with a noble gas structure, and ‘2+’ implies the calcium which has “got two” electrons in its outer shell: she appears to be using the ‘deviation’ interpretation.

5.3 Electron density cloud interpreted as a force field.





Annie suggested that the circle shown in figure 9 (meant to show that the electron density associated with the bond was entirely around the anion, i.e. complete electron transfer) “is that the, the force just around the fluorine, but the K hasn’t been combined with it?” (A1.342).

5.4 Summary of Annie’s ideas about ionic species.

Although Annie does recognise a category of ionic bonding she defines this in terms of bonding between metals and non-metals rather than in terms of electron transfer. This means that ionic bonds will be reported when a (weak) metal is shown sharing electrons with a non-metal. As Annie expects bonding to be represented by overlap or a drawn linkage she does not recognise ionic (or other) bonding in figure 5. She also tends to misunderstand the use of symbols meant to signify charged species, and has her own alternative interpretation for the ‘+’ and ‘-’ signs, as showing deviations from noble gas electronic structure.

5.5 The second interview: competing interpretations of charge symbols.

The first interview took place before bonding as a specific topic was studied at A level. By the time of the second interview, at the end of the first year of the course, the topic had been formerly tackled. The question that must be examined is the extent to which Annie’s conceptions of ionic bonding changes over this period.

Figure 5 was intended as a standard diagram of ionic bonding (in sodium chloride), but to Annie “the circles represent atoms of sodium and chlorine, in an arrangement” (A2.33) rather than ions. This response is consistent with her earlier responses. However semi-structured interviewing allows one to use different lines of questioning, and it was decided to see if Annie’s interpretation of the ‘ + ’ and ‘ - ’ symbols had changed. Annie was asked the electronic configuration of ‘sodium’ and gave the answer “2.8.1” (A2.37) - correct for the atom. When asked to give the electronic configuration of the ‘Na+ entity’ Annie also gives the correct answer, “2.8” (A2.43), suggesting she does appreciate a distinction. However this response is not immediate:





I: “Do you know what the electronic configuration of the Na+ entity is? This bit here, this Na+?”A “Yeah, erm. [pause, 7s approx.] Could you repeat the question please?” (A2.41)

Possibly the reaction suggests that Annie was identifying Na+ with ‘sodium’ (i.e. atom) and did not understand why she was being asked the same question twice. Only when the interviewer pushed the distinction (“you’ve told me what you think the electronic configuration of sodium is,...this here, this Na+ can you tell what the electronic configuration you think of that is, Na+?”) does Annie give her answer indicating that the ion is different to the atom. She then confirms that these species are different (A2.47) and is able to label the species shown as “ions” (A2.49). It is possible to interpret this sequence as A misunderstanding a question, or not concentrating, or being momentarily confused. It would also be possible to suggest a more specific, although tentative, interpretation: that Annie had learnt (i.e. memorised) the expert ‘non-neutral’ interpretation, but that it had not displaced her own alternative ‘deviation’ interpretions as uncovered in the first interview. This alternative interpretation had presumably been acquired during GCSE (or earlier) and tended to be used spontaneously, but when she realised that the question did not seem to make sense in these terms (i.e. she had already used the answer this interpretation required!) she was able, after a pause, to access the more recently acquired interpretation. The sequence discussed does not by itself present unequivocal evidence for such an interpretation, but later comments do seem to support such a proposal.

Some ambiguity appears when after she has identified Na+ and Cl- as ions Annie is asked what the ‘ + ’ symbolises: “it represents the electron that’s been lost. So giving it a positive charge. Because it would have been positive. And the chlorine, like an electron has been added, to give it, to make it up to the full shell. So like it’s minus an electron really” (A2.53). This interesting statement is worthy of deconstruction. Parts of it may be understood on the conventional interpretation that symbols such as ‘ + ’ represent an overall electrical charge, whilst other comments seem to revert to the earlier meaning of deviation from noble gas electronic configuration.

“[ + ] represents the electron that’s been lost. So giving it a positive charge”

This is totally consistent with the conventional ‘overall charge’ meaning.





“Because it would have been positive”When? This seems to imply before the electron was lost when it was actually neutral. However this extract makes sense in the ‘deviation’ interpretation: previously the atom was “positive” in that is had one electron more than a noble gas configuration.

“And the chlorine, like an electron has been added, to give it, to make it up to the full shell.”

This is the conventional ‘non-neutral’ understanding of the ‘ - ’ symbol.

“So like it’s minus an electron really”It is hard to understand how the chloride ion is “minus an electron”, but this comment is consistent with the ‘deviation’ interpretation of the ‘ - ’ symbol as representing a species with one electron less than a noble gas configuration, a description which would apply to the atom not the anion.

This utterance appears to be part-way to the accepted understanding of a diagram such as figure 5, but Annie’s previous alternative conceptions seem to interfere with any consistent understanding. It is possible to examine Annie’s comments about other figures later during the interview to see whether they suggest she is using the ‘non-neutral’ or ‘deviation’ interpretation of the positive and negative signs.

In referring to figure 8 (lithium iodide ‘molecule’) Annie reports “the iodine, molecule [sic], has got, erm a configuration like chlorine, so it’s got seven, electrons, in it’s outer shell, so it’s got a negative charge” (A2.109), which implies the ‘deviation’ interpretation: iodine is negative as it is deficient of one electron compared to the noble gas structure. However in the next figure (9) K+ is a “potassium atom, which has lost an electron” (A2.141) which would be called an “ion” (A2.143), and F- is a “fluorine [sic] ion” (A2.147).

Figure 10 included representations of the sulphate anion, which being a more complex ion and having a double negative charge, provides a useful focus for questioning Annie. The ‘2-’ “represents the, that when , the, the sulphur and the oxygen combined, it produced a full outer shell, but two electrons just missing off it, so by like erm, by adding up the electrons to provide this full outer shell of all the, like the sulphur and the four oxygen rings, coming of it, two, two electrons had to be added, to form this, these outer rings, so that donates there, there are





actually two electrons missing” (A2.170). This is a complicated answer, where the term “rings” seems to mean the circles that could be drawn to show the outer shells of the individual atoms. Again the utterance may be deconstructed into segments:

“when , the, the sulphur and the oxygen combined, it produced a full outer shell, but two electrons just missing off it,”

This can be understood in terms of the ‘deviation’ interpretation, i.e. when a sulphur atom and four oxygen atoms combine the resultant electronic configurations are two electrons deficient of full shells and so the symbol ‘ 2- ’ is suffixed.

“so by like erm, by adding up the electrons to provide this full outer shell of all the, like the sulphur and the four oxygen rings, coming of it, two, two electrons had to be added, to form this, these outer rings,”

This comment seems to follow from the previous segment, as the species was two electrons ‘deficient’, two electrons have been added. This would be consistent, except that the ‘2-’ would no longer be appropriate as the deficiency would have been ‘made good’. However on the conventional ‘non-neutral’ interpretation the ‘2-’ is appropriate as two electrons have been added.

“so that donates there”It is not clear from the transcript alone which species is implied to be donating to which.

“there are actually two electrons missing”This comment seems to return to the ‘deviation’ meaing implied in the first segment, i.e. the sulphate ion has “two electrons missing” so this is signified by ‘2-’.

At the time of interview I was not sure which of these interpretations was being implied by this seemingly contradictory statement, and asked Annie to specify whether the ‘2-’ meant the species had two extra electrons (‘non-neutral’) or was two electrons short (‘deviation’ from noble gas structure): “It’s two electrons short” (A2.176). Annie had returned to the interpretation of such symbols that she had demonstrated in the first interview, despite her earlier orthodox comments about Na+ and Cl-.

As a response to this ‘regression’ figure 5 was again presented and Annie was asked the electronic configuration of the sodium atom,





“2.8.1” (A2.182); the sodium ion shown, “2.8” (A2.184); the chlorine atom, “2.8.7” (A2.186); and the chloride ion, “2.8.8” (A2.188). In this particular context Annie’s answers followed the ‘non-neutral’ interpretation. So what did the minus sign mean on the chloride ion? “That one electron was added” (A2.190). The plus, in sodium-plus, meant “that one was taken away” (A2.192) again consistent with the ‘non-neutral’ understanding. So if something had two minuses is should imply “it’s had two added” (A2.198), and SO42- had “ had two electrons added” (A2.200). Again when the questioning focussed on the difference between atoms and ions Annie was able to use a consistent and logical interpretation based on a ‘non-neutral’ meaning for charge symbols, when a direct question about the meaning of ‘+’ and ‘-’ symbols elicited a reponse based on the ‘deviation’ understanding.

5.6 Bonding electron density remains confused with forces.

‘Pure’ ionic bonding involves complete transfer of electrons, and therefore a representation of the electron density associated with the bond would reflect the concentration around the anion. Figure 9 (potassium and fluoride ions) would be an example of this, whereas figure 8 (lithium iodide) shows some electron density around the metal atom to indicate a polar bond. However Annie interpreted the electron density envelopes (electron clouds) as “the shape of the bond...or the shape of the field of the bond that’s, being produced” (A2.151). Consequently Annie considered that the species in figure 9 (K+ and F-) could not combine to form a compound (A2.126) as “the pull is not combining the potassium” (A2.149), whereas in the lithium iodide case (fig. 8) “it’s got the, the pull towards either of them” (A2.149).

5.7 The need for overall neutrality in ionic species.

In the second interview Annie was asked about the possibility of forming compounds from counter ions. She showed an awareness of the need for neutrality: for example when asked about the case of K+ and SO42- “it’s probable, but you’d probably need two of them, because to make up that to nought, and to get rid of the K+, sign, you’d need two of them, where-else if you just added that, if you





added the K to the SO42-, then you’d take it down to KSO4-. So you’d still need like another potassium, ion to hold it” (A2.206), “so if you used two, then it would build it all up and it would be equal and things” (A2.220). The interviewer did not introduce the complication that in real crystals an enormous number of ions would be involved, but focussed on the appropriate ratio in terms of the species considered. So in this case one anion and two cations could combine. The Al3+ / SO42- case is more complex and several of each ion are needed for neutrality. Annie thought that with one of each species “you’d end up with one electron over” (A2.218) - a comment consistent with her ‘deviation’ interpretation of charge symbols: Al3+ had (on this view) three electrons over a full shell, whereas SO42- was two deficient leading to a surplus of one electron in the combination. (On the ‘expert’, i.e. ‘non-neutral’, interpretation the combination was one electron deficient - although all atoms involved had noble gas type electronic structures, the formation of aluminium cation involved the donation of three electrons, of which only two were accepted by the sulphate species.) Although Annie recognised that one of each ion would not balance, she found it more difficult to suggest an appropriate combination. To get neutral overall “you could use, erm, one sulphate and two aluminiums...you’d have to have two of two, of each” (A2.224). I pointed out that two aluminiums made six plus (at least on the ‘non-neutral’ interpretation - but perhaps it equalled two minus for Annie?), and “so you’d have to use, erm, [pause, 15s approx.]...you have to use, quite a lot of each. Something like, erm, [pause, 3s approx.] you’d have to use, say four aluminiums, and, two, sulphates” (A2.226). Despite earlier discussion about the meaning of charge symbols the interviewer had not realised how Annie’s ‘deviation’ interpretation could be applied to stoichiometry. I clarified Annie’s answer, and both interviewer and subject agreed that we had twelve plus, and four minus. Was that what we wanted? “That’d make eight. It would make eight, so it would be neutral. Anyway it would give you eight, eight plus” (A2.230). From the conventional (‘non-neutral’) interpretation, and the interviewer’s perspective this statement is self-contradictory: either the combination would be eight plus, or neutral - options that were mutually exclusive.) So it was put to Annie: eight plus?: “mm” (A2.232); would that be neutral?: “a neutral charge” (A2.234); (one more attempt!) would eight-plus be neutral?: “[pause, 4s approx.] No it, because it would become nought” (A2.236). What would become nought?: “Well the charge, if, if you had eight, if you





had eight plus it’s like having seven minus or eight minus, you don’t really have that because you have your shell with all your electrons in it, which could be eight” (A2.238). From the ‘deviation’ interpretation Annie’s answer is quite consistent: each Al3+ has three electrons over a full shell, so four cations gives twelve electrons over - but eight of these electrons make a new ‘full shell’ so only four surplus electrons have to be considered, and these may be absorbed by two sulphate anions - each with a configuration deficient in two electrons. Had the interviewer followed this logic in situ it would have been interesting to ask Annie about where the eight surplus electrons that formed “your shell with all your electrons in it” were located amongst the four aluminium and two sulphate species. From the interviewer’s (‘non-neutral’) perspective the combination of four triply-positive cations and two doubly-negative anions did not lead to neutrality. By neutral Annie meant “it’s like in the middle, really” (A2.240) “in the middle of erm, it’s not negative or positive” (A2.242). Having established this meaning of neutral the interviewer asks if the combination “aluminium-4-sulphate-2, which is eight plus” is neutral, and Annie concedes “no, it wouldn’t be” (A2.246), as to be neutral the overall charge has “to be nought really” (A2.248). This established Annie is then able to suggest another possible combination: “two aluminium and three of them” (A2.250) “three sulphates” (A2.252). This segment of the interview is particularly interesting in that Annie seems to demonstrate once more that she is aware of, and capable of applying, the conventional interpretation of charge symbols, but that she retains and tends to use instead her earlier alternative interpretation.

5.8 Ionic or covalent bonding?

Annie seems unsure what type of bonding would be present in aluminium sulphate (figure 10): it would be “covalent” (A2.254) “or it could be ionic” (A2.256). This is despite the prolonged discussion of the formation of this combination from the species Al3+ and SO42-. However in potassium sulphate there would be “ionic” (A2.258) bonding.

In figure 15 (the aluminium chloride dimer shown with overlapping atoms and electrons sharing) “they’re ionic bonds, between aluminium and chlorine, atoms” (A2.338) (not ions note!), even though Annie later uses the term “sharing”: “it’s bonded in, like it’s got, it’s sharing in





fours. It’s got like four chlorines attached to it” (A2.364). Figure 16 showed the same species (Al2Cl6) but with bonds shown as lines (with one Al-Cl ‘bond’ for each Al having an arrowhead to indicate dative bonding). Annie recognised that “it’s the same as before” (A2.383). Lines drawn between atoms (as diagrams of overlapping atoms) are conventionally used when signifying bonds that are essentially covalent, but Annie percieved the (non-dative) connections as “the ionic bonds, between the, the three chlorines and an aluminium” (A2.386). Annie thus remained consistent in interpreting the bonding character in the two diagrams, as well as reiterating her view on first seeing figure 15 in the first interview.

5.9 Multiple ionic bonds?

When Annie was asked about the type of double bonds possible she thought that it was probable that double “ionic” (A2.336) existed. This suggests a naive conception of ionic bonding. If a covalent bond is a pair of electrons shared between two atoms, then it may readily be seen how multiple bonding could be extrapolated from this definition. If an ionic bond is due to the force between two oppositely charged ions that are adjacent, then the meaning of ‘double ionic bond’ is not clear. The force between ions will depend on the separations of the centres of charge as well as the ionic charges, so any simple definition of multiple bonding in terms of the product of ionic charges would be of limited usefulness. However if the student focussed on the transfer of electrons (to form ions) rather than the ionic bonds themselves) a simple definition would be available, and might seem significant.

5.10 Third interview: continued uncertainty over whether Na+ is bonded to Cl-.

During the third interview Annie described ionic bonding in terms of “one of them donates, an electron” (A3.414). However, her earlier confusion over this type of bonding - seen in the previous interviews - was apparent in the more detailed discussions of figure 5, which showed “sodium and chlorine molecules, or atoms. Probably making sodium chloride, I would hazard a guess at” (A3.28). So Annie was not sure if the diagram did represent a compound. “In the structure represented it shows circles with sort of plus and minus signs in. So it’s





really showing sort of the sodium and chlorine ions and not actually showing any way they're bonding, because if they were bonded, then there would an overall sort of neutral charge, because of the donation of electrons, neither would have a plus or a minus charge, so, I would say that that hasn’t got any bonding in it, because they’ve still got their original charge, or the ionic charge on them. If you get a molecule of sodium chloride, the overall charge is neutral, due to the fact that the sodium’s donated an electron, and the chlorine’s accepted, an electron” (A3.30). Although Annie was using the terms “ion” and “ionic charge” she is using the ‘deviation’ interpretation: the symbols show the original electronic configurations so no electron transfer can have taken place - had bonding occurred these ‘charges’ (deviations) would have been neutralised. Although not in a compound the ions “are probably held together, because it, because you’ve still got the ionic sort of charges of them both erm, I would say that basically, it’s almost like they’ve been sort of, well they can’t be sort of chucked in a beaker, but it’s almost like they’re mixed but they haven’t combined. I think they’re, they’re sort of held together just by the attraction of their forces in effect” (A3.40). Annie is aware the the symbols suggest attraction. Alternatively, perhaps the diagram is representing the compound, but still showing the earlier ‘deviations’: “although. I mean they, they may well have combined. You might be showing on this diagram just the charges of the chlorine and the sodium to just say ‘this is sort of how they combine’ like sort of sodium’s a one plus, so matching up with a one minus will combine to give a sodium chloride molecule, whereby they would be joined, but I would say they’re joined, or they’ve just attracted, together, obviously if you had lots and lots of negatives, and lots of positives then they wouldn’t attract, they’d repel because of the similar charge. Whereas these are opposites - so they will attract” (A3.42). Annie is aware that figure 5 shows a “solid” (A3.48) as “the atoms are all very close together, they’re all in a uniform sort of structure, lined-up” (A3.50) “sort of close-packed” (A3.52) and held together, not by bonding, but by a “sort of attraction between the charges, so it would probably be held together by sort of van der Waals forces, between the, between the atoms” (A3.56).

It appears that Annie is still confused about the meaning of ‘+’ and ‘-’ signs, Na+ and Cl- have “still got their original charge” whereas if bonded “neither would have a plus or a minus charge”, “because of the donation of electrons”. She makes the ‘deviation’ interpretation





explicit: the symbols indicate “that would be an electron. Sort of that signifies that there’s, the atom is sort of, has one extra electron in it, so it’s got a plus charge, so it’s got an extra electron, whereas this one is deficient of an electron” (A3.60). And yet in almost the ‘next breath’ Annie suggests that in the Na+ species “to give it a stable structure the electron has been sort of somehow removed” (A3.64). Her confusion between the two interpretations becomes more apparent if the rest of this last utterance is quoted:

“to give it a stable structure the electron has been sort of somehow removed, so theoretically the electron is present which, it’s sort of present, but it’s not, they’ve sort of taken the electron away, but it sort of still belongs to the sodium, so it still has, sort of a, a noble gas structure, so the electron which has sort of, been removed means it has got a bonding power of one plus, ‘cause one electron is sort of in the outer quantum shell, whereas the chlorine, say if you took this as a chlorine molecule you’d have sort of I don’t know, seven electron in the outer shell, so its in effect, erm sort of adopted an electron from somewhere, to give it the noble gas structure, so it’s really one minus an electron” (A3.64).

However, when asked to focus on species and discuss their sub-atomic composition Annie’s responses become clearer. The sodium atom in figure 1 had “eleven” (A3.66) electrons and “eleven” (A3.38) protons, whereas the Na+ species in figure 5 have “eleven” (A3.70) protons, but only “ten” (A3.72) electrons, as “they’ve lost an electron” (A3.78). The Cl- species “have one more electron than proton” (A3.74) as “they’ve gained an electron” (A3.80). This analysis is in full accord with the standard (what I have referred to as ‘non-neutral’) interpretation of the ‘+’ and ‘-’ symbols, rather than the ‘deviation (from noble gas electronic structure)’ interpretation that Annie often seemed to apply. (However later during this third interview Annie described the neutral iodine atoms (in molecular iodine) in figure 17 as being “minus an electron” (A3.150).)

After this clarification of the charges on the Na+ and Cl- species Annie was asked again whether they would fall off of a sample of the material from figure 5. The particles “would be held together. I think it’s partly due to the attraction of the opposite charges ... probably, van der Waals forces” (A3.82). The attractions between charges, and van der Waals forces are “separate, but they’re sort of related in a way, because they are both involved in sort of holding molec.., or atoms





together without sort of committing, total electrons” (A3.94) For Annie there is still no bonding in figure 5 (A3.96), which - had it shown molecules - “would be sodium chloride, but as we’ve got the molecules in the ionic state, it would be sodium mol.., atoms and chlorine atoms” (A3.100). Once again Annie uses the term ‘atom’ for the species signified ‘+’ and ‘-’. Atoms?, “ions” (A3.102). Annie has seen sodium chloride (A3.108) “crystals. Salt” (A3.115), which exists as “molecules” (A3.110), “sodium and chlorine atoms joined to form the sodium chloride molecule” (A3.120), “by van der Waals forces” (A3.122), whereas figure 5 shows “just sodium and chlorine” (A3.172). As sodium and chlorine exist in different states at room temperature does the diagram show a solid? “If it was to be sodium and chlorine, or sodium chloride it would be solid. If it was just the sodium and chlorine ions, then sodium would be a solid and chlorine would be, a, a gas” (A3.174). The figure “shows a solid, really, because if you had, if they were ions then all the chlorines would be, sort of very scattered about, all the minus charges would be sort of all over the place. And all the sodiums would be sort of like uniformly lined up” (A3.176) So it is a solid shown (A3.178), and “it’s got to be sodium chloride” (A3.180), and Annie now believes there will be chemical bonding between the sodium and the chlorine (A3.182), and that it will be “ionic bonding” (A3.184). It is of interest that Annie was a second year A level student only a month from her final A level examinations, but it was only as a result of a lengthy discussion that she was able to identify figure 5 as representing ionic bonding despite the figure being fairly typical of such diagrams, and sodium chloride being the very archetype of an ionic compound used in GCSE and A level work!

5.11 The effect of heat on sodium chloride.

Annie thought that a molecule of sodium chloride would contain “two” (A3.34) atoms, but figure 5 does not show any molecules (A3.40). Annie was asked whether molecules of NaCl would be given off if sodium chloride was heated enough: she replied in the affirmative (A3.46), but her comments show she was thinking not of boiling, but of thermal decomposition: “Yeah. I think they’d dissociate, so you’d get molecules of chlorine given off. ‘Cause chlorine’s sort of not as, well neither of them are, well they’re both fairly stable I suppose, but because sodium is a solid, and erm if you break, if you melts, er sort of sodium chloride out, it’s got a very high melting point. Erm, no I don’t think it would go in a vapour phase, I think you would get, sort of Keith S. Taber – [email protected] A50




chlorine given off, and sort of sodium left” (A3.46). Although she was asked about a compound, Annie refers in her answer to the properties of the elements from which it is comprised.

Later the same point was returned to. On heating the sodium chloride “would melt” (A3.186), and “when they melt, when, when sort of anything’s in a solid all the, sort of atoms or molecules all sort of, lined up very well. When they melt they sort of slightly dissociate, and because the bonds have been broken in between, sort of the chlorine and the sodium, you tend to get, maybe sort of chlorine, chlorine gas formed, as you’re sort of getting to the end of your liquid, to go off to form a gas. I don’t think you could form a sodium gas” (A3.188), “if you kept on heating it some chlorine, chlorine gas would be given off” (A3.192). “You get chlorine gas. But I think due to the fact that chlorine, is sort of a gas at room temperature anyway, and sodium’s a solid that you’d, if you are looking at them separately, and when you combine them I still reckon that, that’s what you’d get sodium, it won’t be in a solid state, I don’t know how it would, remain” (A3.194), “you wouldn’t get much [chlorine] I don’t think, I think you’d get a small amount” (A3.196).

In the liquid state the ions would “still attract, but it would be a sort of much great.., er, less sort of attraction due to the fact because they’ve all sort of been, heated up and broken down. Sort of the particles been given more energy so they’re going to move more. So the actual chances of them, sort of colliding with an opposite charge is, is less, but is, and also if they were to turn into a gas. If you were to get a compound which you turned into a gas. Then, obviously, the more you heat something into a gas, the less fruitful collisions you are going to get” (A3.198). Annie’s answer again implies that any bonding has been “broken down”, and it seems it will only be re-established by “fruitful collisions” between oppositely charged entities.

5.12 Synthesis of sodium chloride.

As Annie seemed to have difficulty associating figure 5 with ionic bonding, so an attempt was made to approach the topic from a different starting point. Annie was asked what would happen if sodium was heated in chlorine. She quite confidently predicted that “sodium would probably catch fire” (A3.209), “it would burn in chlorine” (A3.211) “so, sodium chloride, would be evolved” (A3.211). Annie Keith S. Taber – [email protected] A51




agreed that you would produce what was represented in figure 5 (A3.213), the kind of material which was “ionically bonded” (A3.219) and so had “fairly high melting points. Er, dissolving in non-polar {sic} solvents” (A3.219). (This last point was later clarified when Annie reported that she thought “water” (A3.374) and not benzene would dissolve sodium chloride “ ‘cause it’s polar” (A3.376).)

5.13 Annie’s understanding of ionic bonding at the end of her course.

The third interview was held in May 1992, in the month before Annie’s final examination. At this point Annie does not spontaneously recognise figure 5 as showing ionic bonding, although recognising the existence of some form of forces (van der Waals, and/or forces between charges) giving the structure its integrity. Annie still shows confusion between two competing ways of interpreting charge symbols, one of which implies that some elements may be attracted by their (oppositely ‘charged’) deviations from stable electronic structures. Perhaps related to this is a confusion between the properties of a compound, and of its constituent elements - even though this distinction is one of the most fundamental in chemistry.

5.14 The tutorial.

The recognition during the third interview that Annie was still far from the othordox understanding of some areas of the work, and especially ionic bonding, led to a short ‘tutorial’ at the end of the interview where I went over some of the basic points. Part of this conversation is reported for information:

A3494 I: When I get to number 5, I would say that diagram was meant to represent bonding • •

A: Uh huhI: but meant to represent ionic bonding rather than covalent

bonding,A: yesI: but ionic bonding is just as important. But because in a

pure ionic bond, we assume there is a complete transfer of an electron, from one to another, we don’t tend to show an overlap.’Cause when Keith S. Taber – [email protected] A52




we show an overlap what we’re usually talking about is where the bonding electrons go. So in diagram • • (where am I) • • 7 for instance, this envelope’s meant to show where the electrons are, and there’s two of them, and they move around both atoms, and we show an envelope. But when we are doing ionic bonding, like in this sodium chloride, if we assume sodium chloride is a pure ionic bond, which, you know, is an approximation,

A: yeahI: then we’re assuming there’s been complete electron

transfer, and therefore the electron that was, the electrons that make up the bond really are only in one of the species.

A: uh huh.I: Now sometimes I think you get a little bit confused about

what the positive and negative signs mean. Not always. And I think we agreed in the end that this was ionic bonding, didn’t we?495 A: Yeah.496 I: And these were ions. But there was talk about “well it’s plus because that means it’s got electron over, er an inert gas configuration.” So if we looked at the sodium it’s got one electron more than it would like to have, in a sense, so that makes it plus. That’s what you seemed to be saying at the start?497 A: Yeah.498 I: But that’s, that’s not sodium plus is it, that’s just sodium atoms.499 A: Just sodium.500 I: So this is something different, sodium plus, that’s lost an electron.501 A: Uh hm.502 I: And that was what you said at the end I think, when we were talking about ionic bonding. But that wasn’t really what you were saying at the start, I don’t think.503 A: No.504 I: Erm, so the plus means it’s lost an electron, and minus means it’s gained an electron, and because it has had this electron transfer, there is an ionic bond. And all the ionic bond is is the attraction between a positive and a negative. But then, that’s all chemical bonding ever is. Certainly at the level we study it.

5.15 The fourth interview: electron transfer and forces between charges.





An ionic bond “involves, one of the atoms donating all of the electrons, to the other one, to the other atom which is sort of deficient, in electrons so, making it up to the, number it needs, to like have a full stable outer shell which is what all sort of compounds are aiming for. Erm, so you’ve got, sort of complete transfer of electrons. Rather than sharing” (A4.14). The transfer of electrons is “from one, one of the elements, sort of in their outer orbital, the electron is transferred, to the outer orbital, of the other element, so you’ve got sort of partially, well you’ve got fully, fully filled outer shells, but partially shared” (A4.20) (partially as not all the atom’s electrons are involved?). An example would be “sodium chloride” (A4.16) where “the er, sodium atom, gives up its outer electron to the chlorine atom which is sort of minus an electron” (note that Annie still uses the term “minus an electron” thus equating ‘deficiency’ compared to a noble gas electronic configuration with a word associated with negative (‘minus’) charge.) Although the sodium atom “gives up its outer electron” “the electron isn’t removed, it’s erm, the sodium atom still, sort of contains that electron, but it’s combined with the chlorine, so in effect, it’s still got its own electron, but it’s sort of donated it to the chlorine, so the chlorine’s now got a full outer shell. And erm, because you’ve got, sort of the one going into the seven, the sodium in effect has got eight as well. Because it’s, ‘cause it’s donated one, it hasn’t got any in the outermost shell, but the next shell down, is full. So it’s making it all stable” (A4.24). The first part of this explanation seems to suggest that the sodium atom can both give its valence electron and keep it, but “it hasn’t still got it, but because, in a way it’s lost, but it’s gained. ‘Cause by losing it, it’s sort of not got an extra electron, it’s minus the electron it would have had originally, but it’s gained a stable shell. Because of the next, next shell down” (A4.46). So perhaps Annie simply means to suggest that as the sodium ion is part of a compound including the chloride ion it retains an interest in this electron by being part of the same system. This seems to be a mature and holistic approach to the compound . Alternatively perhaps she just means that a gain in stability justifies a loss of electron. Certainly Annie seems to understand the process of electron transfer, and its relationship with electronic configuration. However, previously she has seen the cause of attraction between these elements as due to deviations from noble gas electronic structure, rather than due to charges resulting from electron transfer. So it is interesting to examine how Annie explained ionic bonding two weeks later. For her the sodium and chlorine (chloride) remain together as “sodium’s sort of positively charged, ion because of the, the extra electron, so the chlorine attracts, attracts Keith S. Taber – [email protected] A54




the, the, attracts the electron initially, which, ‘cause it’s being sort of pulled towards, the, the what was the negative nucleus, then they’re just sort of, • • • just sort of held, erm, just by charges, sort of, because you’ve got conflicting charges, they’re being pulled, pulled inwards by the nucleus, and the nucleus will contain, will sort, will contain the force to full, to pull, the electrons towards it. So there will, because you’ve still got this electron which has been chucked into another shell, then that electron’s being pulled towards the chlorine” (A4.26) by “sort of, just a force which is on the, the electron” (A4.28) “because the nucleus has the power to draw these electrons in, then the force I suppose you could say is, either held by the, nucleus and is sort of dragging electrons towards it or is held by the, the nuc.., well the atoms, well the electrons always being centred towards the nucleus” (A4.30). Annie’s explanation seems to lack coherence and clarity, and it could be suggested that this reflects confusion in her own mind. There are still vestiges of her ‘deviation’ approach: “sodium’s sort of positively charged, ion” not because it has lost an electron, but “because of the, the extra electron”, extra presumably to a noble gas electronic structure. And “the chlorine attracts, attracts the, the, attracts the electron initially, which, ‘cause it’s being sort of pulled towards, the, the what was the negative nucleus” - or rather the chlorine atom(?) which was negative because it had a deficiency of an electron compared to a noble gas electronic structure”, so Annie seems quite clear about what attracts the atoms, but after electron transfer “then they’re just sort of, • • • just sort of held, erm, just by charges, sort of, because you’ve got conflicting charges”. These charges are apparently the conventional ‘non-neutral’ rather than ‘deviation’ charges, but Annie does not seem to be as confident in the action of these types of charge.

Figure 32 was intended to represent the process of electron transfer and ion formation. It had three sections meant to represent neutral atoms, electron transfer and the resultant ions. In the first part Annie identified atoms of “potassium” (A4.334) and “bromine” (A4.330). The second part of the figure “shows, the transfer of one electron, to the bromine atom, so, you know you’re going to end up with, erm, a 2.8.8.8 configuration for what was the bromine. And you’re going to end up with a, 2.8.8 for what was the potassium. So it’s, showing transfer of one electron” (A4.364). In the third part “you’ve got a smaller circle which, unless you’re trying to fool me here, is, which was, was the potassium, but obviously now it hasn’t got one of the outer electrons, so, it is no more. And you’ve got an increased, • • • an Keith S. Taber – [email protected] A55




increased atom which was the bromine, which has now got the, the sort of the complete outer shell, configuration. So both by bromine gaining an electron, and sort of potassium losing an electron you’ve now got sort of full outer shells. But now the atoms, one’s sort of larger than the other. Sort of shape, or the sizes have sort of changed places” (A4.375). (The potassium species has got smaller “because you’ve, now got, you’ve got rid of, what was one electron in a outer shell, you’ve got rid of that so you don’t need, in effect you don’t need as much energy, to hold one sort of stray, stray end so you’ve got, ‘cause you’ve got a full outer shell, underneath you still need a lot of energy but you don’t need as much, as was needed on the other and also, there’s less there to control” (A4.379). Annie did “not really” (A4.399) expect any force between the two ions as “they’ve now changed to, sort of, it’s changed to noble gases” (A4.401), “if you’re, if you’re going to go just by configuration then they are noble gases. But, you know, if they were, if they’re still, potassium in bro.., potassium and bromine, • • then • • • • ‘cause you’ve got like a potassium plus ion there now” (A4.403) “because you’ve got rid of an electron” (A4.405), so there is a potassium “ion and a bromine minus ion from gaining an electron and you are going to get attractions” (A4.407) “because you’ve got positive-negative, and they’re going to attract” (A4.409). Here, after a slight mental detour involving tansmutation of the ions into noble gases, Annie does display evidence that she is able to answer within the conventional scheme of attractions between charged ions. Her confusion with noble gases seems dissonant as she had previously identified the same species as the results of electron transfer between potassium and bromine atoms. It is possible to suggest that her alternative model of charged species being those which had non-noble gas electronic structures was again interfering with the conventional scheme for understanding ionic bonding, but such an interpretation must remain speculative.

5.16 Electron clouds, forces and causality.

When Annie is asked about figure 8 (representing a polar molecule of lithium iodide) Annie reports “That’ll be, er, ionic. Probably” (A4.284) because “for a start you’ve got, er metal and a non-metal. And you’re going to get complete transfer, of electrons from the lithium to the, iodine atom, and also, you can see there’s more of a pole, on the, on the atom” (A4.286). Annie refers to the “polarisation within the, the molecule. ‘Cause, ‘cause one is, sort of attracting more more than the, Keith S. Taber – [email protected] A56




more so than the other” (A4.288), but still classes the species as ionic (A4.292), because “of just the, the metals that you’ve got there. Of a metal and a non-metal. That’s the way that they normally combine” (A4.302).

In figure 9 (representing a potassium ion separated a short distance from a fluoride ion, with a circle representing the electron cloud around the fluoride) “you’ve got ions here, so obviously that’s why they’re charged, accordingly. If they were just atoms then they wouldn’t have had any sort of charge at all. I think you’re trying to show, • • • I think you’re trying to show where the sort of electron density lies, around such a, or the strong, sort of most electronegative, atom of, of fluorine. ‘Cause obviously all the electrons are centred around, that ion” (A4.306). There “there could be” (A4.308) a bond, and it would be “a ionic bond” (A4.312). “The fluorine” (A4.314) is shown as the larger part “‘cause you’ve got sort of the electron density going all the way, sort of almost like complete, sort of dominance” (A4.314). There will be an “electrostatic” (A4.318) force from the potassium ion onto the fluoride ion (A4.316) and also a force from the fluoride ion onto the potassium ion (A4.320) which would “be electrostatic as well” (A4.322). Annie thought “the strength from the fluorine to the potassium will be far greater, than the other . Than like from the potassium to the fluorine. ‘Cause obviously, if, if they were equal, then you wouldn’t get, you wouldn’t get all this, polarisation of sort of electrons. They would just sort of be distributed evenly, rather than being centred around one, one of the atoms rather than the other” (A4.324). The first part of this answer seems to fit well with earlier comments that (i) an atomic nucleus attracts an electron more than vice versa (A4.245) and (ii) the Sun’s attractions for the Earth is greater than vice versa (A4.277) ; but her justification suggests that although she was asked about the forces between the ions Annie’s response is more concerned with the forces between the atomic cores and the bonding electrons. As in discussing diagram 5 above Annie seems to focus on the act of electron transfer, as if this was the bond, rather than the resulting attraction between opposite charge. Annie’s understanding of mechanics principles is seen to be lacking in two areas here. She seems ignorant of, or unable to apply, Newton’s third law, in the case of a cation-anion pair, electron-nuclei system, or the Earth-Sun system. She also seems to imply that in figure 9 the bonding electrons are being pulled more towards the anion core than the cation core, and thus experience an overall applied force. Whilst this would be true for two approaching neutral atoms - one of potassium, one of Keith S. Taber – [email protected] A57




fluorine - once the electron transfer had occurred it would be better to assume an equilibrium situation had been reached. Annie seems to confuse the effect (transfer of electron) with its cause (greater attraction from the fluorine atomic core).

When discussing figure 32c, Annie was asked which force would be greater (the force on the potassium ion due to the bromide ion, or the force on the bromide ion due to potassium ion), and she thought “the force on the, bromide ion, to the potassium. So like potassium’s going to shift towards the bromine, or the bromide ion” (A4.415) “because, just literally the fact you’ve got less to move, from the sort of the potassium, to the bromine than moving the bromine to the potassium” (A4.417). Annie is apparently using an understanding of inertia to predict that there will be a greater effect of the interaction on the smaller ion, rather than answering the question asked: again she does not clearly distinguish between a cause (attraction between oppositely charged ions) and the likely effect (in the absence of any other forces, and if the ions were not close enough for repulsion between electron shells to balance the overall attraction of their net charges, the two ions would move closer, with the smaller {mass} ion moving faster and further.)

5.17 Stoichiometric ratios and neutral ionic compounds.

At the end of this final interview of the sequence Annie was asked again about figure 10 (representing polarisation of anions). It was in this context that she had previously suggested that a neutral aluminium sulphate would have a stoichiometric ratio of four aluminiums to two sulphates {which conventionally would give Al4(SO4)28+}, but now she thinks “you’d need, (let’s see,) two aluminiums and three sulphates” (A4.602), which would give the orthodox version of neutrality. Taken with other comments Annie made during this interview it would seem that although she had not completely stopped applying her alternative ‘deviation’ definition of charge, Annie was demonstrating the standard meaning of charge in chemical species more regularly.

5.18 Annie’s final understanding of charge.





Taken as a whole the fourth interview provides evidence that Annie had acquired a reasonably conventional approach to explaining ionic bonding, and in particular could use the orthodox interpretation of charge symbols on ions, as well as talk about the attraction between the charged ions that resulted from electron transfer. In addition there is also sufficient evidence to suggest that Annie had not completely abandoned her alternative framework of ‘deviation’ charges that seemed to interfere with so much of her understanding of this form of bonding. Annie did not study physics, and with a limited knowledge of electrostatic fields, the attraction between two opposite ‘non-neutral’ charges did not seem to be have any more explanatory value for her than the attraction she believed to exist between two atoms with opposite ‘deviation’ charge.

6. Polar bonding.

6.1 First interview: Annie displays a ‘dichotomy’ approach to classing bonding types.

During the first interview Annie did not seem to use a category of ‘polar bonding’, despite having formally studied the topic of electronegativity, where polar bonding was introduced. She describes the bonds in figure 3 (CCl4) as covalent although chlorine is a significantly more electronegative element than carbon. Figure 8 (lithium iodide) was meant to represent a polar molecule, but was judged by Annie to be “ionic” (A1.574) “because it’s a metal and a non-metal combining” (A1.578).

6.2 Electron clouds misinterpreted as force fields.

In figures 7 through 9 electron density envelopes are used to show the degree of bond polarity. In figure 7 (H2 - non-polar bond) this envelope is interpreted “you’ve got two electrons, two atoms, and it’s the way that the, the force pulls them together. And the sizes of them.” (A1.305) The shape “represents sort of the pull between if you had, if you drew the outer shell of electrons in, it represents the pull of them





together when they combine, and the forces.” (A1.319) Annie seems to be identifying the electron density envelope with the electrostatic forces that are the cause of bond polarity, rather than being the effect of such causes. However it is not clear whether the forces Annie refers to are those between the atomic cores and the bonding electrons (which will determine the bond polarity) or forces between the atoms themselves. This latter would be rather difficult to conceptualise. In a pure covalent bond (figure 7) the bonding electrons are attracted to the atomic cores on either side (and this is the primary interaction considered), whilst in a purely ionic interaction (figure 9) the ions are considered as integral species, rather than considering the valence electrons separately from the atomic cores. Figure 8 represents an intermediate situation - the polar bond: “lithium has a smaller charge, or smaller pull than the iodine, so the actual shape of it goes in towards. It sort of goes in towards because it’s attracting the lithium, whereas if the lithium were attracting it, it would be like the reverse picture.” (A1.321) What does Annie mean by “lithium has a ... smaller pull”? Lithium certainly has a smaller pull on the bonding electron pair than the more electronegative iodine, and thus the bond in polar. But if this is what Annie means, her subsequent comments are less clear: “it’s attracting the lithium, whereas if the lithium were attracting it” seems to be an example of what I have classed a N3a type error (Newton’s third law error, type a: no paired {‘reaction’} force recognised.) Annie seems to have shifted her focus from forces between the bonding electron pair and the atomic cores, and forces directly between the atoms. When asked to clarify her comments Annie’s new response shows a N3c type error (the paired (‘action’ and ‘reaction’) forces are of different magnitudes), “they’re both attracting each other but because this one’s got a larger force then it will pull ... towards the lithium more.” (A1.325)

It seems that when faced with an example of bonding that cannot be explained in terms of the simple models used at GCSE Annie has partially assimilated the new ideas met at A level, and has ‘patched’ the framework with her own ideas about what diagrams represent, “if you drew in the shells again, then it’s the way they sort of combine together. The forces.” (A1.330) Annie does appreciate that the electron density envelope represents (what the ‘expert’ might call) the molecular orbital obtained by the overlap of atomic orbitals, but at the same time she also feels that forces can be represented directly, rather than indirectly through the effects they have. This is emphasised when Annie describes the electron density in figure 9 Keith S. Taber – [email protected] A60




(entirely round the anion to show electron transfer, i.e. ionic bonding) “the force just around the fluorine” (A1.342) Figure 9 is not thought to represent bonding (A1.350, 354) “because they’re not combined” (A1.354). It has been previously been pointed out that this case study suggested that from an orthodox viewpoint Annie does not fully distinguish cause and effect in the context of atomic scale forces.

Figure 10 looks at polarisation in materials that are primarily ionic. Two sulphate ions are shown being polarised by a potassium cation and an aluminium cation respectively. The ionic separations are the same and the degree of polarisation is greater in the case of the three-plus aluminium. As the effect is purely electrostatic a calcium two-plus cation should have an intermediate effect. However Annie predicts “the calcium circle would actually be inside sort of the nose, the cone” (A1.410) i.e. the polarisation would be greater than either of the examples shown, so “it’d look like [figure] 8” (A1.414). Annie’s interpretation of the polarisation of the electron cloud around the cation is “they’re sort of attracting there, they’re sort of like matched-up elements which they have been chosen to join with” (A1.400) “but none of them have actually reached that far. And it seems like aluminium is being more successful, than the potassium.” (A1.402) “because the cone, cone shape on it, sort of goes further over, to all but reach it, whereas the potassium one sort of like stops quite a bit shorter.” (A1.404) As was seen for figure 9 Annie has ‘combination’ as a criterion for bonding (A1.354). In figure 10 “it’s getting pulled towards them. Towards the smaller atoms but it’s not actually, doing, as much as it needs to, to actually combine.” (A1.358)

It would seem that at the time of the first interview Annie did not recognise the category ‘polar bond’ and interpreted diagrams showing electron density envelopes as shapes representing forces rather than the effect of forces. Substances that might be classed as polar were instead categorised as covalent (tetrachloromethane) or ionic (lithium iodide).

6.3 Second interview: bonding by “like almost a force field”.

By the time of the second interview bonding had been studied as a topic in its own right within the lecture course. Annie felt she could explain the shape of the species shown in figure 8 (A2.109) and attempted to do so in the following terms: “the iodine, molecule [sic], Keith S. Taber – [email protected] A61




has got, erm, a configuration like chlorine, so it’s got seven, electrons in its outer shell, so it’s got a negative charge, so by pulling, the group one metal towards it, lithium, it gives it, a like almost a force field which pulls it towards it so, it gives it a, a bigger sort of shape at this end” (A2.109). It is not easy to understand this statement. Annie seems to picture neither a covalent lithium-iodine bond polarised by the greater iodine core charge, nor an iodine anion polarised by the high lithium cation charge density. Although Annie assigns a “negative charge” to iodine, she seems to be referring to the atom (with its “seven, electrons in its outer shell”), and is presumably using her ‘deviation’ meaning of charge (i.e. one electron less than a full shell - see the section 5 on ionic bonding.) It is not clear what the cause of the “force field” like phenomenon is, or why this should lead to the shape. So did the envelope represent something like a force field?: “No, it’s not but it’s like the, the pull from the iodine molecule [sic] on the lithium, is greater than the lithium pull on the iodine, to make a full outer shell, because it’s got more electrons there, whereas that one’s only got one, so it’s, less likely to be pulled by, the iodine molecule. And also the iodine molecule’s bigger, than the lithium molecule, so it’s got, the electrons have got a, a bigger force on the nucleus, and the nucleus has got a bigger pull on the electrons” (A2.111). This complex utterance is an example of what might be called a ‘pseudo-argument’ - it is structured like an argument, “...to...because...whereas...so...And...so...”, but the chain of reasoning cannot be readily followed, at least from an orthodox perspective. I commented that I was “getting a bit lost” as there was “too much there for me to take in at one go”, but Annie retorted that she was “just rambling, I suppose” (A2.113). Had Annie merely have been rambling she would not have been able to develop her argument in a consistent way. She was asked to explain her comments relating to the electronic configuration (“it’s got more electrons there, whereas that one’s only got one, so it’s, less likely to be pulled by, the iodine molecule”): “well, this is, 2.8.8.8.8.7 or something, it’s got seven in its last shell anyway. And lithium has only got one” (A2.117), so “...it’s going to need a lot of energy to pull seven electrons over towards it, like the whole molecule, so it’s more likely that iodine would pull the lithium over, as it has” (A2.119). Not only that, but “in fact it’s got more need for the, well they’ve both got need , but as it only needs like one electron, then it’s more likely to bring that towards it, so giving this, this like, triangle shape” (A2.119).

It would be possible to interpret some of Annie’s comments within a Keith S. Taber – [email protected] A62




conventional framework, “the pull from the iodine [core]... on the lithium [valence electrons], is greater than the lithium [core’s] pull on the iodine [valence electrons]...And also the iodine ... [core charge]’s bigger, than the lithium ... [core charge]...”, whereas without such an interpretation “it’s like the, the pull from the iodine molecule [sic] on the lithium, is greater than the lithium pull on the iodine” appears to be another example of an error using Newton’s third law (a N3c-type error). However the later segments of Annie’s argument seem to be less easily interpreted in this light: she seems to be arguing that iodine is one electron short of a noble gas configuration, whereas lithium is seven electrons short; it requires less energy to move one electron than seven, so the transfer will occur from lithium to iodine. This is consistent and logical, but ignores the mechanism by which electrons ‘move’, seeming to rely on final cause. This interpretation is also consistent with Annie referring to the bonding not as polar, but as “ionic” (A2.121).

6.4 A constructivist interpretation of Annie’s ‘pseudo-argument’.

There seem two ways of approaching what I have labelled pseudo-arguments. One approach is to accept that Annie was indeed “just rambling”, and being an intelligent young woman, is able to construct grammar of appropriate syntax, which some relevant-sounding words inserted between the conjunctions, without too much concern for the semantic content. The motivation for doing this may be that in an interview situation a student may feel pressured to respond, and perhaps an appropriate-sounding response will suffice. It is quite likely that (with teachers and lecturers asking closed questions in class, where they have expectations of the meaning of the students’ responses) such a tactic might be successful often enough for the student to consider it worthwhile. I expect this does happen, and it would be a worthy area for further research. Alternatively one may cynically suggest that a conceptually sophisticated subject such as chemistry makes so little sense to some students that they compose answers more as poets than logicians! Perhaps this is also true on some occasions. Neither of these approaches are helpful in analysing student utterances, except as a warning to the researcher not to ‘over-analyse’. From my own theoretical stance I must reject these interpretations as likely to have less validity (and utility) that a more constructivist position. Students - like all human beings - tend to try Keith S. Taber – [email protected] A63




and make sense of their world. For A level chemistry students their world includes atoms and electrons and bonds, and the strange questions asked by their teachers. My stance in this case study is that Annie is an intelligent young person, and her comments make sense to her, from her own mental constructions and frameworks, even though they may not make sense from my own. Of course, this does not imply that Annie has at any time a unitary, complete and totally self-consistent framework of constructs about bonding. Indeed, like all human beings, her conceptual frameworks will be partial, plural, fragmented, and fluid. In this sense my own framework for chemical bonding will differ from Annie’s only in a manner of degree: it will (presumably) be more complete, less fragmented, and more consistent. (In a similar way, my own conceptual framework for chemical bonding is almost certainly less complete, and more inconsistent than Nobel laureate Linus C. Pauling.) A pseudo-argument may be reconceptualised as a genuine logical argument if one can approach it from the other person’s framework. A constructivist approach informs me that I will also be trying to make sense of my world, which includes the transcripts of my discussions with Annie, and this should warn me against over-interpretation. Nevertheless I tentatively suggest my interpretation of Annie’s comments.

The lithium atom has a ‘deviation’ charge of +1 (i.e. one electron over a full shell) which means it gives rise a force, or need, which tends to donate its excess electron. (Alternatively the need could be satisfied by accepting seven electrons, but that would require more energy than donating one.) It is a small atom, with only a small number of electrons, and therefore only a relatively small force is needed from the nucleus to attract its electrons. Therefore the lithium nucleus attracts electrons weakly. The iodine atoms has a deviation charge of -1 (i.e. one electron deficient from a full shell.) It is a relatively large atom, with a large number of electrons, and therefore the nucleus is required to exert a large force to maintain them all in the atom. Therefore the nucleus has a large attraction for electrons. When the two atoms are adjacent the deviation charges cause an interaction between them, that would be satisfied by the transfer of one electron from lithium to iodine, or seven electrons from iodine to lithium. As the iodine nucleus attracts electrons more strongly than the lithium nucleus, and less energy is needed to transfer one electron than seven, the electron transfer will take place accordingly. The figure





represents this by showing how the force field type effect is larger at the iodine end of the diagram.

From an orthodox point of view such ideas are wrong in a number of particulars, discussed elsewhere in this paper. ‘Deviation’ charges (see section 5.2) are not recognised as such by physicists, and do not cause atomic interactions. The force fields outside atomic cores are the result of the core charge (i.e. nuclear proton charge minus shielding electronic charge), and not from some teleological mechanism that provides the nucleus with a larger force if it has more electrons (see section 1.1). However, for a student who has little understanding of basic electrostatic ideas, Annie’s alternative version of charges and their effects may have as much explanatory coherence as the orthodox electrostatics.

6.5 Annie retains a dichotomy classification of bonding.

As well as describing the bonding in figure 8 as ionic, Annie also fails to suggest that aluminium sulphate might be polar, even though she is not sure of the bonding: it could be “covalent” (A2.254) or “it could be ionic” (A2.256).

6.6 The third interview: polar and non-polar solvents.

In the third interview, when discussing figure 5 (meant to represent sodium chloride) Annie commented that it is a property of ionic substances to dissolve in non-polar solvents (A3.219). In order to find out if this was merely a slip-of-the-tongue, she was asked what a non-polar solvent was, and Annie replied that “it’s got an overall neutral charge” (A3.221) (which of course is true of polar solvents as well) so that whereas with a polar solvent “you’re going to get the plus, plus ions going to one, one part, and sort of the minuses to another” (A3.221), this would not occur in a non-polar solvent. This was a reasonable comment, suggesting that Annie knew which types of solvent were polar, and which non-polar, but when asked to give examples Annie suggested “benzene” (A3.223) as polar and “something like water” (A3.225) as non-polar. These examples did not match to the idea of polar solvents interacting with ions. Water was non-polar as it has “got, er, a two minus charge off the oxygen, so that combines with two hydrogens so that has an overall charge of two Keith S. Taber – [email protected] A65




plus, so when they combine you get an overall negative, well just neutral charge, because the, oxygen is sort of bonded either way it’s not going to get, it hasn’t got an overall, charge. The whole atom {molecule?} is sort of got a charge of nothing, because the hydrogens have accepted an electron from the oxygen, and sort of the oxygen, they, because they’ve sort of exchanged electrons everything’s, all the quantum shells...” (A3.227, unfortunately the tape ‘ran-out’ at this point before Annie could explain her ideas further.) Instead of considering the polarity of the O-H bond, and how this leads to a dipole which could give rise to dipole-ion interactions, Annie seems to give a quite detailed justification of the overall neutrality of the water molecule - which is her own stated criterion for non-polarity. A simpler argument for neutrality would be that the water molecule is composed of three neutral atoms! However we have seen elsewhere that Annie has an alternative approach to charge: for her an oxygen atom is indeed “two minus”, i.e. two electrons deficient of a noble gas electronic structure, and two hydrogen atoms could be considered to have an “overall charge of two plus”, although the electrons are not in excess of an actual noble gas structure, Annie is presumably considering an empty K shell as equivalent to a ‘full shell’. Annie’s confusion between valency and charge - so prevalent in her discussions of ionic bonding - is also interfering with her understanding of a fundamentally covalent molecule.

Annie’s ideas were challenged by considering the apparent logical corollary to her criterion of non-polarity, i.e. that polar solvents (benzene being her example) would presumably not be “overall neutral”,

“No it’s, it’s neutral, but it’s got, erm, it’s got hydrogen atoms which can be, can be bonded to, they’re easily displaced. ‘Cause you’ve got delocalised electrons in an benzene, benzene molecule, er, the electrons aren’t, they’re sort of distributing throughout the, throughout the sort of complex, rather than, sort of in, in water they just sort of go towards the oxygen. Possibly meet between the hydrogens. It could, because you’ve got such a, a, such a structure with benzene whereby you haven’t got single bonds all the way around, you’ve got to have three double bonds out of six, they sort of delocalise so that everything’s sort of, equal in the end” (A3.231). This “doesn’t make it polar but it means that some of the hydrogens at times haven’t got sort of the full, full attraction or the full charge. For example if, if you’ve got the benzene ring, erm, with the double





bond and the single bond and then, I don’t know somehow, a simplistic way of looking at it, and the bond moves, then you’ve got a hydrogen which is sort of, or you’ve got a chlorine, no, a carbon sorry, which has got a minus charge, on it then so the hydrogen can be displaced so it can sort of go off, with something else. For example if you’re going to put a sodium chloride in benzene then the hydrogen could join up with the chlorine molecule {ion?}” (A3.233).

Although these ideas are wrong from a conventional viewpoint, Annie has certainly built up a complex understanding of how benzene can dissolve ionic substances, with the idea of resonance (rather than delocalisation: “the bond moves”) allowing “easily displaced” hydrogens to interact with the anions (or electronegative/basic species - does Annie think that dissolving sodium chloride will give molecular chlorine, or was this a slip?) and presumably the “carbon ... which has got a minus charge” interacting with the cations from the solute. In the most common depiction of resonance in benzene the two Kekulé forms have alternating single and double carbon-carbon bonds around the ring, and if a mechanism is drawn for the resonance it would show a carbon atom losing the double bond to one neighbouring carbon, but simultaneously acquiring a double bond the other side. If one visualises the double bond “moving” away, but not being replaced, then the carbon atom should become a carbocation: however using Annie’s alternative construct of ‘deviation’ charges this carbon would be one electron deficient of a full L shell, and would be signified as a “carbon ... which has got a minus charge”: a carbanion. Later in the interview when Annie was asked about the charge on carbon atoms she reported that “they are sort of neutral all the time, due to the fact that they’ve got a plus four charge anyway [four electrons surplus to noble gas electonic structure], but they’re being bonded to ... four things, well they’re sort of like using up four of their electrons” (A3.273). On reflection Annie seemed to realise that the resonance in benzene would not change the overall bonding situation for the carbon atoms as “they should remain the same really because they’re, sort of held in this way, the actual charges, I mean whatever side of the carbon, it sort of lies on the right or the left side of the carbon then, it doesn’t really matter because they’re still being held, in that way” (A3.279). Despite reporting this novel, but not irrational, framework Annie then somewhat contradicted her comments about benzene as “water will dissolve sodium chloride” (A3.235), because the sodium chloride “just sort of dissociates” (A3.237) in water, whereas “I don’t know if it would dissolve in benzene. I know it would dissolve in water” Keith S. Taber – [email protected] A67




(A3.239). When chemists say something has a pole they mean “it’s attracted one way or the other” (A3.255) and “polar means that it’s going to attract the opposite charge to what it has” (A3.257). Benzene could be polar (A3.259).

6.7 Electronegativity.

Annie was asked about electronegativity, to see how she related this to polarity of bonds. She knew that an atom which has a large tendency to pull the electrons in bonds towards itself has “normally got like a high electronegativity, like fluorine” (A3.281), and something with a low tendency to attract electrons towards it was “fairly ... electropositive” (A3.283) such as “sodium” (A3.285). Other suggested examples of electronegative elements were “most of the group seven” (A3.287), “silicon” (A3.289), and as such elements were found in the “right hand side” (A3.291) of the periodic table, “in the p-block” (A3.291) “top half” (A3.293), then also “oxygen, carbon, nitrogen, sulphur”. Carbon was actually in group “four” (A3.297) so “it would be ... probably amphoteric, sort of can be either way” (A3.299). (Of course amphoteric is a term used by chemists to describe oxides and hydroxides, not elements; but the ‘nature’ of the oxide is a common criterion for distinguishing metals (low electronegativity) and non-metals (high electronegativity) at an elementary level, so this was not such an inappropriate comment.) One might expect hydrogen to be similarly considered, but “that sort of behaves in a different way, if you stick it with something that’s, something like chlorine then it’s going to pull, it’s going to be pulled towards the chlorine molecule. But then if you stick it with something like sodium, then that’s going to sort of pull the chl.., sodium. It’s sort of like a sort of like a separate. Although it, because it can act, can exist sort of as a plus or a minus, in a compounds, it’s sort of, although it influences the bonds it doesn’t, erm, it hasn’t got like a set rule, although it’s, don’t think it’s, don’t think it’s that electronegative, but it’s sort of in the middle again, although it can influence normal carbon” (A3.303). Annie seems to be commenting that although hydrogen’s electronegativity is, like carbon, of intermediate value; hydrogen is more likely than carbon to be involved in compounds that are primarily ionic in nature. If this is indeed the point being made it shows a sophisticated awareness that electronegativity value difference is not the only factor in the polarity of bonds: however Annie’s comments are not clear enough to support such an interpretation with great confidence.





Annie was aware that the electrons in a O-H bond “would be pulled towards the oxygen more than the hydrogen” (A3.306) whereas, apparently thinking in terms of electron-cloud diagrams “if you joined hydrogen and carbon the distribution of the pull would be equal” (A3.308) “so you’d sort of get, well just like an oval shape, ... if you were going to take the out.., sort of outer shells just to show the force . If you have carbon it would be sort of like an oval with hydrogen; but if you had sort of like hydrogen and chlorine then the charge would be much more around the chlorine, and if it was sodium it would be sort of reverse” (A3.310). A bond between two carbon atoms “would be equal as well. ‘Cause you’ve got the same, same sort of electronegativity, or positivity” (A3.318), “neither” (A3.322) of the carbons would be more electronegative.

6.8 Partial charges: ∂+, ∂-.

The questioning then turned to the distribution of charge in polar molecules. Given that the electrons in a O-H bond “would be pulled towards the oxygen more than the hydrogen” (A3.306), would the oxygen or the hydrogen be charged at all? The question was intended to see if Annie could apply the conventional scheme of assigning partial charges (usually designated ∂+, ∂-). “The hydrogen wouldn’t be charged, because it would be already bonded to part of the oxygen. Erm, obviously if the oxygen’s bonded to something else, then that’s not going to have a charge, an overall charge, but if it’s not, then it’s going to have a, still going to have a negative charge” (A3.330). I.e. a hydrogen atoms that has bonded to an oxygen atom has obtained a noble gas electronic structure, and so is now uncharged, but an oxygen atom has a ‘deviation charge’ of -2 (a deficiency of 2 electrons compared to a noble gas electronic structure), and if it is only forming one bond it still has a ‘deviation charge’ of -1 (a deficiency of 1 electron compared to a noble gas electronic structure).

(Unfortunately the interviewer was asking questions from a conventional framework of ideas about charge and valency, whereas Annie was largely responding from her alternative framework, and I was not aware of this at the time. From within my own paradigm I made little sense of some of Annie’s responses at the time of the discussions, and was only able to understand them as part of a consistent interpretation following retrospective analysis and reflection. The interpretation of A3.330 given above was not clear to Keith S. Taber – [email protected] A69




me at the time, and I asked for clarification: ‘So, sorry, if you’ve got oxygen-hydrogen, you say there is a bit of a charge?’ With the advantage of hind-sight this is an unfair question: Annie cannot be expected to discuss charges at either end of a bond without knowing whether the divalent atom was also bonded to anything else. Her response to this unfair question was a compromise “a slight overall charge, I would say” (A3.332) “to a negative” (A3.334). This answer did not do justice to either the researcher or co-learner’s framework of ideas.)

To the interviewer atoms are neutral (and Annie ‘knew’ this, although it did not fit with her interpretation of charge symbols), and so a molecule made of neutral atoms must also be neutral. But for Annie if one started off with a hydrogen atom, that would be “positive” (A3.338). An atom? “Oh no, an atom would be sort of no overall charge” (A3.340). Similarly an oxygen atom “would be neutral” (A3.344). So if one made a molecule, just of hydrogen atoms and just of oxygen atoms, and you didn’t add any electrons, and you didn’t take any electrons away, the overall molecule “would be neutral overall” (A3.344). Again we see that although Annie spontaneously used the ‘deviation’ charge interpretation, she was able to switch to the conventional ‘non-neutral’ interpretation of charges in answering some questions.

Having established - through somewhat leading questioning - the overall neutrality of molecules, another attempt was made - also through a leading question, see below - to focus on bond polarity:

I: Now if we’ve got an oxygen-hydogen bond, electrons tend to be more towards the oxygen end, so does the oxygen end of the bond have any charge - even a partial charge?

“No” (A2.346). Although Annie responded negatively to mention of partial charge, a follow up reference to ∂+ and ∂- induced a different response: “Hydrogen would be, ∂+” and “oxygen would be ∂-” (A3.347). The reference to the ‘delta’s appeared to facilitate a shift to a different perspective. In carbon-carbon bonds the atoms would not be ∂+ or ∂- (A3.350). Asked whether the atoms in carbon-hydrogen bonds were significantly ∂+ or ∂- Annie responded the “carbon would probably be ∂-” (A3.352), but when challenged (“it would?” - as carbon is only slightly more electronegative than hydrogen) qualified her response, “oh no, with atoms it would be neutral” (A3.355). The reference to atoms was not clear, and was not latched onto by the interviewer. Instead an even more leading question (although intended Keith S. Taber – [email protected] A70




to be confirmatory, as Annie’s response was understood through I’s framework) was asked - was Annie suggesting that in a molecule just with carbon and hydrogen which had similar electronegativities, then the bonds will be fairly symmetrical, and the charge would be fairly evenly smeared over the molecule? It wouldn’t be concentrated on certain atoms? I commented that Annie did not look convinced. She said she thought was confusing herself (A3.356), and laughed. Annie then explained in her own words that the “sort of the basic pull on, between the sort of the carbon and the hydrogen would be, roughly the same throughout the, the molecule ... although it would be sort of fairly the same, sort of like the attraction would be similar” (A3.355) and concluded “I don’t think there probably would be a charge overall” (A3.355).

It is possible to suggest a tentative interpretation of Annie’s comments. Annie is able to visualise degree of bond polarity through the shape of bonding electron clouds (as had been taught in the first term of her A level course) - although she interpreted the diagrams in terms of something akin a force field. This polarity is related to the electronegativity differences between the atoms. Annie is also aware of the use of the ∂+ and ∂- symbolism, and is aware of its use in O-H and C-H bonds (although it is not clear whether she relates this to the electron-cloud shapes, or has simply learnt it separately.) However Annie does not seem to relate unsymmetrical electron clouds, or ∂+/∂- symbols, with partial charge on atoms - as charge for Annie is related to the number of electrons in a quantum shell, and presumably she does not conceive of partial electrons, or electrons partially in a shell!. Although atoms are neutral, they can be + or - (contradictory on the conventional interpretation, but not for Annie using a ‘deviation’ interpretation of charge) if they do not have a noble gas electronic structure. An oxygen atom (electronic configuration: 2.6) would be 2-, but if it formed a bond with a hydrogen atom it would become overall 1- (electronic configuration: 2.7), and if it bonded to two hydrogen atoms it would become neutral overall (electronic configuration: 2.8). In this scheme questions about bond polarity, and those about charges within molecules, are distinct.

Annie was asked to suggest a molecule that only contained oxygen and hydrogen, and she suggested “water” (A3.358), which contained “two” (A3.360) bonds, both oxygen-hydrogen bonds (A3.362). She agreed that her previous comment (A3.306) about the electrons being more to one end applied to both the bonds in this molecule (A3.364), Keith S. Taber – [email protected] A71




but did not agree that the oxygen would have more share of the electrons “because the sort of the electrons, although sort of the, the oxygen would attract both, erm, it wouldn’t, it wouldn’t dominate the share of electrons. Erm, obviously if its, if you’re going to have oxygen and hydrogen bonded, erm, you’re getting the two sort of electrons you need for sort of like the full outer quantum shell from the hydrogens, although, sort of they’re going to be joined together, I don’t think in effect the hydrogens aren’t being robbed, of their electrons because they’re sort of being shared between the two” (A3.366). Despite this water would dissolve sodium chloride “ “Cause it’s polar” (A3.376) and “you’re going to get the positive charge will attract the negative. And vice versa” (A3.378).

It is possible that hydrogen provides a special problem for Annie’s conceptual scheme, as if it were to donate its electron it would not have a noble gas electronic structure, even though H+ implies one electron over a full shell. However, the themes in Annie’s comments about water are familiar from the previous examples discussed. To paraphrase my intepretation of Annie’s understanding of polar bonding during the third interview:-

Annie retains a primarily dichotomous classification of bonding so water must be either covalent or ionic. In either case bonding is caused by the ‘deviation’ charges on atoms with non-noble gas electronic structures. As a result of bonding atoms have full shells. In covalent materials this is a result of sharing electrons so thay are part of both atoms’ quantum shells, and count as part of the electronic structures of both. Because some atoms are more electronegative than others (related to, if not due to, position in the periodic table) some shared electron pairs are unsymmetrically placed along the bond axis, but still remain in the quantum shell of both atoms. Water is an example of this: the bonding electrons are nearer the oxygen, (which we might signify by showing the shape of the pull on the electrons, or by using ∂ symbols), but the electrons are still part of the hydrogen shell, which is therefore full, and so no (partial or otherwsie) charge exists on the atoms.

6.9 The fourth interview: Annie recognises bond polarity, but still classes bonds as covalent or ionic.





When discussing figure 7, a “hydrogen molecule”, Annie described “the sort of distribution, of the, the charge, because they were both of similar electronegativities, and similar charges, then the actual, the actual sort of sh.., shape, sort of use that description, the actual way that the, the charge has been sort of distributed, around the molecule is fairly, fairly symmetrical, hasn’t been polarised” (A4.162.) This was an appropriate description, although Annie considered that as electrons repel when two hydrogen atoms form a molecule the particles are arranged linearly, electron-proton-electron-proton (A4.211, 215, 227.)

Annie recognises bonding (A4.282) in figure 8 (which shows a molecule of lithium iodide), and classes it as “ionic. Probably” (A4.284) because “you’ve got, er metal and a non-metal. And you’re going to get complete transfer, of electrons from the lithium to the, iodine atom, and also, you can see there’s more of a pole, on the, on the atom” (A4.286). Although Annie refers to the diagram, and even uses the term “pole” she appears to base her classification on the recognition of a metallic element (lithium) and a non-metal (iodine), and the GCSE level knowledge that a metal-to-non-metal bond will be ionic. “The shape shows that, that the lithium atom, is going to attract, (let’s get this the right way round, * * * * * , erm, • • yeah,) yeah the, the, the iodine atom is, attracting the lithium atom. Er, or the lithium electrons I should say. It’s obviously showing that the, there’s polarisation within the, the molecule. ‘Cause, ‘cause one is, sort of attracting more more than the, more so than the other” (A4.288). This is a rather confusing comment, with the electron cloud shape (an effect of forces operating in the system) once again seemingly identified with the magnitude of the forces that would be acting on the bonding electrons if they were placed centrally between the two atoms (the cause). Although Annie uses the terms “polarisation” and “molecule” she feels the species is “ionic” (A4.292), not covalent (A4.294). It “could be” (A4.296) something in between covalent and ionic, but Annie “wouldn’t have said it was” (A4.296). Her classification was based on both the diagram itself and her background knowledge: “Something I think I know” (A4.300), “the fact that, sort of just the, the metals [elements?] that you’ve got there. Of a metal and a non-metal. That’s the way that they normally combine. Annie was asked if she though lithium was a strong metal, and iodine a strong non-metal, and she affirmed both of these proposals (A4.303, 304.) Even though figure 8 showed the most electronegative alkali metal (commonly known at A level to have significant covalent character in its compounds) and the most Keith S. Taber – [email protected] A73




electropositive of the halogen elements; and although the electron cloud was shown as being shared between the two atoms - a point explicitly noted by Annie - she still felt it more appropriate to classify a compound between a metal and non-metal as having ionic bonding. I would suggest that this demonstrates how previous learning about bonding as a dichotomy of ionic and covalent can limit learning of a continuum of bonding types, with many examples of significantly polar bonding. However it should be caustioned that one should not generalise from one case study - Annie’s framework of understanding is built upon the ‘deviation’ charges, and I have no evidence to suggest this is a common alternative conception.

7. Metallic Bonding.

7.1 First interview: no bonding in metals.

At the time of the first interview Annie did not seem to have a category of metallic bonding. When she was shown figure 6 she reported that the circles shown were “iron atoms within an element” (A1.285) “all lined together. They are all close together” (A1.289) They hold together (A1.295) but not because they are bonded but because “they’re all the same sort” (A1.297) so “they’re all the same and don’t need to be bonded” (A1.301)

7.2 Second interview: uncertainty over the presence and type of bonding in metals.

When Annie was shown figure 6, “ a piece of iron” (A2.57), during the second interview she again first thought there was “no” (A2.55) bonding, although the atoms were held together by “hydrogen bonds, between the, between the atoms. To give it a structure” (A2.59). In the absence of any hydrogen this was an unexpected response, and a little later during the interview when Annie suggested that the atoms in a hydrogen molecule were “held together by hydrogen bonds” (A2.81), she was asked whether the bonding in hydrogen was similar to that in iron. Annie’s response seemed to reflect her earlier opinion that there was no bonding present in iron: “no because, that[hydrogen]’s, looks like it’s forming a molecule, and they[iron]’re just an arrangement” Keith S. Taber – [email protected] A74




(A2.83). So did Annie think there was a hydrogen bond in iron? “Yeah, it’s probably van der Waals forces, holding it together” (A2.93), which was “different” (A2.95) to hydrogen bonding. In view of such self-contradiction Annie was asked again what kind of bonding was present, and this time she reported “that’s metallic bonding” (A2.97): not hydrogen bonds (A2.101), not covalent bonds (A2.103). So were there any van der Waals forces?: “yeah” (A2.105). So are van der Waals forces the same as metallic bonding? “no. ‘Cause you can get van der Waals forces in, covalent things as well” (A2.107). Over the course of a few minutes the iron had no bonding, had hydrogen bonding, was just an arrangement, had hydrogen bonding which was van der Waals forces, had van der Waals forces which were different to hydrogen bonds, had metallic bonding, and had van der Waals forces which were not the same as metallic bonding! At this time Annie seemed to have no stable ideas about the bonding - if any - in iron, and in these circumstances her later comment that “you can probably get like metallic ... double bonds” (A2.336) gives little insight into her understanding of metallic bonding.

7.3 Third interview: metallic bonding, but atoms don’t combine as they do in covalent/ionic bonding.

During the third interview when Annie was shown the figure representing the sodium atom (figure 1) she commented that “it’s held together by ionic bonds, within the lattice, er, er, it’s a metallic structure” (A3.2), a statement seemingly self-contradictory from the orthodox viewpoint.

Figure 6 (a close-packed arrangement of iron atoms) had “no bonding shown” (A3.388) according to Annie. The substance shown was “an iron molecule” (A3.390), or rather “an iron atom” (A3.392). Annie would “assume it was a solid, made up of iron atoms, looking at the arrangement” (A3.394). This kind of material would be a “solid metal” (A3.398). Normally in metals there was “metallic bonding, which basically holds the atoms sort of above and below, together” (A3.402), “it holds them together by, sort of, the, the, the attraction - although, although they’re all similarly charged, erm, they don’t. They don’t in effect, sort of repel each other. If you’re in a solid then everything’s going to be fairly densely, sort of packed anyway” (A3.404), “they’re, they’re sort of held there. The molecules, sorry the atoms, are sort of held by metallic bonds, although, the, the basically the bonds are just Keith S. Taber – [email protected] A75




sort of held, holding them altogether rather than, rather than combining them to form, something” (A3.408). Annie seems to be suggesting that although bonds, metallic bonds, are present, these bonds are in some sense of a different (less important?) class than some other types of bond - perhaps those which combine different elements to form compounds? Metallic bonds are “sort of like ionic in a way, ‘cause one metal sort of donates to another, but it occurs in metals and it won’t occur between, I don’t know, er, a p-block [element] and an s-block [element]” (A3.416). It involves electrons “‘cause you’ve got to have the, the electrons there to attract, the other atoms” (A3.418). The electrons are “in the shell” (A3.420), “if you’re going to take maybe the outer shell, as, sort of like the, the highest quantum shell then, you’d say that like the electrons to bond would be in the outer, in the outer shell, outer circle that you’ve drawn” (A3.422). “They’re not, they’re not really being, they’re not sort of really sharing. And they’re not really combining, because you’re not making sort of a separate molecule, so although they are sort of like all held together, there is something going on, although, it’s not really, you can’t really class it as ionic bonding or, covalent” (A3.426). This last comment seems to emphasise how Annie’s framework for understanding bonding is built on the covalent-ionic dichotomy.

7.4 Coordination number.

Annie was aware of the term co-ordination number, and thought it was the “number of electrons in the outer shell, that it could [form] bond[s] with” (A3.430), a definition which seemed more appropriate for a different concept (valency). From the diagram (which only showed one layer of atoms) Annie suggested that the coordination number of iron was “six” (A3.434) as “basically, if you take, your central iron, iron atom, then it’s got six other atoms near it” (A3.436) “sort of directly next to” (A3.438) it. Annie appeared to be describing the number of nearest neighbours: “yes, so in that case it would have, six there, and (one, two,) six there as well, because if you were going to stack them up you’d get, oh this is going to get confusing now, erm, if you, if you took that as maybe the bottom, or the middle layer, then you’d have electrons below, and electrons above” (A3.440) “No, atoms, sorry” (A3.442). In all “you’d have • • • • • I seem to make fourteen, but that can’t be right” (A3.446). There followed some discussion of exactly how the atoms might pack, and Annie seemed to have some difficulty in visualising how many atoms could fit immediately above or below Keith S. Taber – [email protected] A76




the atomic layer shown (A3.450). Following the discussion (and some ‘walking’ of fingers around the diagram) Annie decided “we’d have a co-ordination of 12” (A3.46) as “you’d have the six in the same plane, there’s the iron, you’d have its six, sort of like nearest neighbours, in effect, and then, in the upper plane you’d have, erm, you’d have sort of three because of the size of them, they can’t all go, right close together, because you are going to get overlap, so if you put six there, if you draw out six in there, sort of in your mind, then you get them, and then below is going to be the same as above” (A3.462).

7.5 The tutorial.

Near the beginning of the final interview in the series Annie was asked what holds a metal together. From her comments in previous interviews (see above) it seems clear (i) that Annie did not rate metals as having bonding in as full a sense as covalent and ionically bonded materials, and (ii) that Annie had a confused notion of what metallic bonding is. During the ‘debriefing’ at the end of the third interview I commented that in metals

A3504 I ...there’s got to be some sort of attraction, and again it’s got an electrostatic basis. So with the metal here, what we assume is, that some of the outer shell electrons, dissipate throughout the lattice, they get transferred to the lattice. So I suppose when we draw this, these circles are now meant to represent something a bit different. They’re meant to represent an iron atom, minus the outermost electrons that are now wandering around the lattice. Just as in the ionic model here, these circles on number 5 with the positive signs, are meant to represent sodium atoms, that have lost an electron. But this has gone to the minus.505 A: Uh hm.506 I: So in the iron, or any metal, they represent the metal atom that’s lost a few outer electrons that have gone to the lattice.507 A: All right.

When, at the end of this session, we arranged to meet again for a fourth interview I suggested that,

526 I: ...maybe the first thing we’ll do, we’ll just have a quick clarification of the differences between ionic, covalent and metallic Keith S. Taber – [email protected] A77




bonding,A: uh hmI: based on the idea that in every case, what you’ve really

got is an attraction between positive and negative.

7.6 Fourth interview: a less definite form of bonding - delocalised electrons allow atoms to take turns in having full outer shells.

Two weeks after the ‘tutorial’ Annie told me “you haven’t got like actual bonds in metallic bonding, like you haven’t got anything, literally going in or out of a, a, a metal, but you’ve got delocalised electrons going round, the metallic atoms. In a sort of like a sea. So they’re, they’re all sort of freely flowing around” (A4.82) which holds the structure together “because, sort of, erm, metals haven’t got full, full outer shells, then by electrons moving around, they’re, they’re getting, er a full outer shell, but then they’re sort of losing it, but then like the next one along will be receiving a full outer shell. So, you’ve also got charges, that are forces from the nucleus pulling, just attracting, atoms from out, or electrons from outside in. Erm, • • • but mainly due to, like delocalised electrons they can move about, so, then you’ve got forces keeping, keeping it all together” (A4.84). Annie still did not acknowledge there were any “actual bonds” but rather it was “just attract”ions. She agreed that if there were no bonding of any type the atoms would not stick together (A4.86, 88), and that there was something called metallic bonding, which was a type of bonding (A4.89), and so “there’s still bonds, but, not in the sense of like covalent or ionic bond, you’re not getting electrons completely transferred or shared, between the two. It’s not as definite. ’Cause if, if they, if it was definite, then you’d get, you wouldn’t be able to like conduct your electricity, because you’ve got, sort of free electrons moving around, in metals, and that’s why they can can conduct electricity, really. Because they’re sort of delocalised and move about freely, then the electrical current can pass through” (A4.90). So despite completing a full A level course Annie retains a view that metallic bonding was “not as definite” as ionic or covalent bonding - which one might almost paraphrase for her as being ‘proper bonding’ or ‘real bonding’. Despite giving metallic bonding such a low status, there is definite progress over the sequence of interviews. In the first interview Annie did not admit metallic bonding, and subsequently (in the second interview) it became interchangeable with hydrogen bonds Keith S. Taber – [email protected] A78




(a difficult suggestion to rationalise), no bonding again, and van der Waals forces (perhaps not such a poor model); and then (in the third interview) ionic bonding (in some ways quite a good comparison.) Finally, in the fourth interview, “delocalised electrons going round, the metallic atoms. In a sort of like a sea. So they’re, they’re all sort of freely flowing around” and “you’ve got forces keeping, keeping it all together”.

8. Multiple Bonding.

8.1 First interview: double bonds occur in organic structures.

Annie was aware of multiple bonding during the first interview. She described figure 4 (oxygen molecule) as having a covalent bond (A1.226) which was quite similar to that in figures 2 and 3 (hydrogen and tetrachloromethane molecules) (A1.228) but was different in that “they’re sharing more electrons, like each bond, each oxygen is giving two electrons to match up with the other two, so they can each form a shell of eight.” (A1.230) However at that time Annie was not able to suggest what this type of bond may be called to differentiate it from those in the previous two diagrams.

However when she was later asked about figure 13 (ethanoate ion shown by structural formula) she reported “the oxygen is joined on the carbon with double bonds” (A1.488) which are “different” (A1.490) to covalent bonds. Not only does Annie produce the appropriate label, but she seems to have changed her mind about the relationship of double bonds and covalent bonds.

Indeed Annie seems to be confused by the terms ‘single’ and ‘double’ bonds on the one hand, and ‘ionic’ and ‘covalent’ on the other. “Single bonds are different” (A1.514) to covalent or ionic bonds, but “you probably get covalent bonds which are single bonds” (A1.518). Annie’s further comments suggest how this uncertainty arose: “they can probably occur in different, things, like in organic you talk about single bonds more than you talk about covalent, and then in inorganic you talk about covalent bond, more than you talk about single bonding or double bonding.” (A1.520) So “you’ve got different terminology, like Keith S. Taber – [email protected] A79




you could probably use single bonds to refer to something in inorganic, but when you talk about the structures and that, it’s easier to talk about single bonds and double bonds rather than saying that’s got a covalent bond or that’s got an ... ionic bond” (A1.528). So it is just a different name (A1.536) for the same type of bond.

When asked to look again at the double bond in figure 13 Annie now labels this as “covalent” (A1.540). Although aware that double or single bonds “can both be covalent” (A1.774) Annie explains “if I use ionic or covalent I’m talking about, sort of like a general, bond, but if I use double or single bonds that’s mainly organic, because sort of it represents, sort of the sharing, ‘cause it’s like you drawed all the molecules out more” (A1.770) The source of confusion appeared to be that “we tend to get taught them in separate contexts ... single and double bonds for organic and the other two for inorganic” (A1.777) so that Annie would not “combine them ... [and] say ‘ah this is covalent, and it’s got two single bonds and three double bonds’ ” (A1.777).

Annie’s failure to label the bond in figure 4 as double bonding may be partly related to this confusion about usage in he different branches of chemistry, and compounded by the way the bond was represented. The “covalent” bond in figure 4 was represented by atomic overlap, whereas the “double” bond in figure 13 was shown as a double line.

Annie is “not really sure” if it possible to have a double ionic bond (A1.752), although she later said that double and single bonds “can both be covalent” (A1.774) “but they’re not ionic” (A1.777).

The diagram of benzene (figure 12) with the pi-system symbolised by a circle was not recognised as having any multiple bonding: “they’re all single bonds” (A1.504).

8.2 The second interview: mainly covalent bonds, that are fixed and can’t twist.

When Annie was shown figure 12 during the second interview she thought the bonds were “covalent” (A2.275) and “single” (A2.277), at least “the carbon to hydrogen bonds are single, but the, [pause, 3s approx.] sort of one, one carbon to carbon bond would be a double bond” (A2.279). As all the carbon to carbon linkages are shown the same Annie was asked to identify the double bond, but “they’re all Keith S. Taber – [email protected] A80




single bonds” (A2.281), there were “no” (A2.285) double bonds.

In figure 13 however there was a “double-bonded O” (A2.316). A double bond is “just a bond ... the oxygen just gets double bonded on ... It’s just a bond that it it can’t be rotated” (A2.330). This reference to rotation was possibly provoked by the discussion of rotation about the carbon-carbon bond adjacent to the carbon-oxygen bond being discussed: “well a double bond can’t [twist around]. A single bond could” (A2.320); when moving between the two canonical forms the double bond “can’t break, and they can’t twist either” (A2.328), “if you twisted it you just can’t do that. It it won’t move, it’s like a, fixed feature” (A2.330). Double bonds would “mainly be covalent” (A2.332), but “you could probably get like metallic, ionic and covalent, but you couldn’t get like hydrogen double bonds” (A2.336).

(There was no time to discuss multiple bonding in any depth during the third or fourth interviews.)

9. Delocalisation and resonance.

9.1 First interview: benzene - electron-rich with single bonds.

When Annie first saw figure 12 in the first interview she recognised that it “looks like a benzene ring” (A1.462) although she thought that there were no double bonds (A1.586), as “they’re all single bonds” (A1.504). The circle “shows where the electrons are, because it’s electron rich” (A1.464) and “they’re denser in the circle” (A1.466) - not all the electrons - “just the ones from the carbon” (A1.472). Annie seems to accept (although not completely grasp) the ‘electron rich’ nature of benzene without having to consider multiple bonding and resonance. The diagram did not show canonical forms, and Annie does not appear to be tied to a valence bond approach, even though other comments (reported in other sections) suggest she does use the ‘full outer shell’ criterion for stable species.

9.2 Resonance not appreciated from canonnical forms.

Figures 13 (ethanoate ion) and 14 (boron trifluoride) were shown as valence bond type structures. Figure 13 (“one’s an inversion of the Keith S. Taber – [email protected] A81




other” (A1.484)) showed the delocalisation of the negative charge across the COO- group, whilst figure 14 (“seems to be different arrangements” (A1.508)) was intended to imply the polarity of the B-F bond by showing three canonical forms, each with a different B-F bond as an ionic link (the other two being covalent: a difference that way have caused Annie to stumble and identify different arrangements “of the three, or two elements” (A1.508).) Annie did not use the terms ‘resonance’ or ‘canonical form’ and in figure 13 referred to the two structures as separate compounds (A1.484, 486). Annie suggested that in figure 13 the double headed arrow meant “that if you turned either of the, the O-minus, or the o that’s double bonded around then you’d get the other compound? And it’s exactly the same for that one if you turn that around, ... so it’s like a reversible {pause} thing” (A1.486). And in figure 14 “is it like before they show how the F-minus can be changed around so you get like a mirror copy, of it, and then here it’s got a completely different structure? But altogether, it’s just the like the F’s been moved, round the three points of the triangle” (A1.550). Annie was not able to suggest a mechanism by which this might occur (A1.554).

9.3 Second interview: benzene - some awareness of delocalisation.

Annie has not yet reached a consistent clear interpretation of figure 12 (benzene) which has “single” (A2.277) “covalent bonds” (A2.275), although “one carbon to carbon bond would be a double bond” (A2.279), yet “they’re all single bonds” (A2.281). The circle could indicate “an unsaturated, aromatic or something?” (A2.287) - aromatic meaning “that it smells” (A2.289). When asked about how this relates to electrons Annie shows an awareness delocalisation, describing how the electrons “go around in the ring, so they sort of charge around and, they they don’t really belong to, they’re, they’re, they’re, they’re not fixed anyway, they don’t belong to anything in particular, so they’re, they’re free-flowing” (A2.295). Annie was asked if she know about the carbon atom hybridization, and after some thought suggested “sp3”, although she immediately added that “it can’t be”, and after a further pause said she was “not sure” (A2.297).

9.4 Canonical forms considered as representing discrete





molecular structures.

Figure 13 showed two canonical forms of an ethanoate anion, meant to represent a resonance structure. Annie’s comments suggest she interpreted the figure as showing two possible optical isomers, with the arrow symbolising “it’s a reversible reaction? Well it can be either. It’s er, I think it’s an optical, oh God, it can be a optical ima.., image of each other, it’s, could be either, it looks like it’s superimposable or something” (A2.299). The two structures represent “the same thing, but it can be either or, you know, the erm, it makes a difference where the double-bonded O is” (A2.302). This form of representation symbolises a single molecular structure which cannot be readily shown in a single (Lewis) diagram, so it was important to ask Annie to clarify if she thought there were two types of molecule (microscopic entities) present in this substance (macroscopic entity), but Annie does not seem to distinguish these two levels in her answer “it’s all the same sort of erm, molecule, substance” (A2.304), but would “reflect [sic] the light in different directions” (A2.304) if put through a “polarised, light meter thing” (A2.304), “but it would actually, look the same, really unless you studied it” (A2.304). This answer suggests two types of structure are present, so the light would “pick up say the double-bonded O in one, one direction, and it would pick it up on the other side” (A2.304) but is rather ambiguous as to whether they are just in a different orientation or distinct species. So are they the same molecule? “Well sort of yes and no, they’re actually the same thing, but the arrangement is a bit different, but they’d have the same properties” (A2.306), and they cannot be separated (A2.312). It is still not clear exactly what Annie thinks, perhaps because she is not clear in her own mind. Her comments seem to imply isomerism (“the arrangement is a bit different”), but could be interpreted as simply referring to the orientation of the species in the diagram (“they’re actually the same thing”). Annie is asked if it is possible for one “molecule” (actually a molecular ion), to change into the other, or whether “it’s fixed in one type”: “they probably do around the carbon” (A2.314), “the oxygens. The O-. And the, and the double-bonded O. So they would, they would rotate” (A2.316), i.e. the two structures interchange by rotation about the carbon-carbon single bond. At normal temperatures this would be expected to happen at a high frequency, but this is not what the canonical forms are meant to suggest. In the ethanoate anion movement between the two forms by rotation or electron movement would be indistinguishable. In the case





of rotation the oxygen atoms would swap position, whereas the formalism of Lewis-type resonance structures requires the atomic positions to be unchanged; but the diagram would not distinguish these possibilities. It is suggested that one of the oxygens is a heavier isotope, and Annie confirms that the isotopes swap position (A2.326), confirming that she understands the figure to imply rotation, but that the carbon oxygen bonds “can’t break” (A2.328) and the double bond “won’t move, it’s like a, fixed feature” (A2.330). As it was now clear that Annie did not understand what the resonance structures were meant to represent, it was not possible to question her about the reality of the canonical forms.

9.5 The third interview: benzene - electron delocalisation through the complex, and canonical forms do not really exist.

Benzene was mentioned by Annie during the third interview as an example of a polar (sic) solvent (A3.223). “it’s neutral, but it’s got, erm, it’s got hydrogen atoms which can be, can be bonded to, they’re easily displaced. ‘Cause you’ve got delocalised electrons in an benzene, benzene molecule, er, the electrons aren’t, they’re sort of distributing throughout the, throughout the sort of complex, rather than, sort of in, in water they just sort of go towards the oxygen. Possibly meet between the hydrogens. It could, because you’ve got such a, a, such a structure with benzene whereby you haven’t got single bonds all the way around, you’ve got to have three double bonds out of six, they sort of delocalise so that everything’s sort of, equal in the end” (A3.231), “It doesn’t make it polar but it means that some of the hydrogens at times haven’t got sort of the full, full attraction or the full charge. For example if, if you’ve got the benzene ring, erm, with the double bond and the single bond and then, I don’t know somehow, a simplistic way of looking at it, and the bond moves, then you’ve got a hydrogen which is sort of, or you’ve got a chlorine, no, a carbon sorry, which has got a minus charge, on it then so the hydrogen can be displaced so it can sort of go off, with something else. For example if you’re going to put a sodium chloride in benzene then the hydrogen could join up with the chlorine molecule” (A3.233). When bonds can ‘move around’ we call it “delocalisation. It’s a (what’s it called?) A conjugated bond system, or something. I think I can spell it - whether I can pronounce it though! {Laughs}” (A3.263), and so you can draw different pictures of the same molecule, with the bonds in different positions, or “you can draw like canonical forms of benzene” Keith S. Taber – [email protected] A84




(A3.265) and “obviously the, • • • sort of all the, all the carbons are going to be sort of have bonding power of four anyway. But sort of where they are actually bonded. It won’t affect the structure or the way, in which sort of the, the compound reacts. But it just shows where the bonds could lie, but whether, they don’t really exist, it’s sort of something that scientist has in their minds to show, to explain something. So sort of three out of the six could be in one position or they could be, in the sort of reverse, although, sort of, I don’t know if I should say in nature, they don’t actually perform that way” (A3.269). Carbon atoms “are sort of neutral all the time, due to the fact that they’ve got a plus four charge anyway, but they’re being bonded to, sort of three other, well two other molecules normally. Because usually they get bonded to another carbon, or two other carbons and one hydrogen. So they always got, they’re always bonded to four things, well they’re sort of like using up four of their electrons to bond with, either of the carbons”. The carbon atoms are not actually positively (A3.275) or negatively (A3.277) charged, not even part of the time as “they should remain the same really because they’re, sort of held in this way, the actual charges, I mean whatever side of the carbon, it sort of lies on the right or the left side of the carbon then, it doesn’t really matter because they’re still being held, in that way” (A3.279).

Here Annie appears to be thinking things through as she talks. She initially suggests that “it’s got hydrogen atoms which can be, can be bonded to, they’re easily displaced” which is not strictly true, although perhaps Annie is referring to the tendency of benzene to undergo substitution rather than addition reactions because of the stability of the delocalised system. She correctly describes the “delocalised electrons in an benzene, benzene molecule” which are “sort of distributing throughout the, throughout the sort of complex”.

However her next comments suggest that there are single and double carbon-carbon bonds, but they are are not fixed, although it is not very clear what this means: “you’ve got to have three double bonds out of six, they sort of delocalise so that everything’s sort of, equal in the end”. The delocalised pi electron system does not directly effect the hydrogens, which are sigma bonded to the carbon ring, but for Annie “the hydrogens at times haven’t got sort of the full, full attraction or the full charge” because when “the bond moves, then you’ve got a ... carbon ... which has got a minus charge, on it then so the hydrogen can be displaced so it can sort of go off, with something else”. Although Annie herself labels this as “a simplistic way of looking at it” - Keith S. Taber – [email protected] A85




remembering perhaps being told that the bonds don’t actually move, it is just a way of representing the structure (“it just shows where the bonds could lie, but whether, they don’t really exist, it’s sort of something that scientist has in their minds to show, to explain something ... I don’t know if I should say in nature, they don’t actually perform that way”) - she suggests consequences (formally charged carbon atoms) which would arise from such bond movements. Of course the canonical forms (usually the two Kekulé structures) and resonance mechanism usually represented for the molecule does not lead to charged carbon atoms, but here it seems likely Annie is confusing these with mechanisms for reactions involving benzene, where intermediates or transition states can have such charges, and then confusing such reactions with benzene as a solvent: “for example if you’re going to put a sodium chloride in benzene then the hydrogen could join up with the chlorine molecule.”

Annie is certainly clear that the canonical forms are equivalent as “obviously” “all the carbons are going to be sort of have bonding power of four anyway...It won’t affect the structure or the way, in which sort of the, the compound reacts”, “it just shows where the bonds could lie ... So sort of three out of the six could be in one position or they could be, in the sort of reverse”, “whatever side of the carbon, it sort of lies on the right or the left side of the carbon then, it doesn’t really matter” as “they’re always bonded to four things, well they’re sort of like using up four of their electrons to bond”.

Annie is a little less clear in her comments about whether carbon atoms are charged in benzene, when she says they “are sort of neutral all the time, due to the fact that they’ve got a plus four charge anyway”. Once again Annie’s alternative ‘deviation’ definition of charge is apparently being used: an isolated carbon atoms has four electrons in excess of a noble gas electronic structure, i.e. “a plus four charge”.

10. Dative bonding.

10.1 First interview: no concept of dative bonding.

If a covalent bond is a pair of electrons shared between two atoms Keith S. Taber – [email protected] A86




then a dative (or co-ordinate) bond is a special case when both electrons originate from the same atom, rather than one electron originating on each atom as in most examples. Figure 15 showed a dimer of aluminium chloride. An interpretation of the information directly available from the diagram suggests that all the bonds are covalent, and all seem equivalent (although not all six chlorine atoms are equivalent as two occupy bridging positions and four terminal positions.) In order to realise that dative bonding is taken place the subject would need to apply additional background knowledge about the valency requirements of the elements involved: i.e. aluminium can only service three covalent bonds, and chlorine only ‘needs’ to form one covlant bond to achieve a noble gas electronic configuration (which is usually associated with stability.) In the figure all eight atoms appear to have stable electronic configurations, but each aluminium atom has formed four bonds, and the two bridging chlorines have each formed two bonds. Figure 16 shows the same dimer, but with bonding shown by lines rather than electron dots on overlapping atomic shells. As is conventional dative bonds are signified by arrowheads on the bond lines: thus indicating how aluminium is able to achieve a noble gas electronic configuration, rather than the ‘electron-deficient’ molecule that the normal valency limitations would imply.

When Annie is asked the origin of the electrons in the four bonds for one aluminium in figure 15 she reports that “one comes from the aluminium and one comes from the chlorine” (A1.626, and equivalent comments: A1.628, 630, 632 and 634). So aluminium had “four” (A1.636) outer shell electrons prior to bonding. Annie does not find this problematic as “you can get different, erm, not isotopes, but different aluminiums which have different, electrons in, their outer shell” (A1.638). However Annie knows that all chlorine atoms start of with “seven” (A1.640) electrons in their outer shells (A1.656), which does cause difficulties when she is asked to try and identify the electrons which originated in a bridging chlorine: “four at the bottom” (A1.662) “two up the sides, and maybe one from there” (A1.664). The “maybe” hints at the arbitrary nature of this assignment, and this is made even more explicit when Annie undertakes the same exercise regarding the other bridging chlorine: “those four there” (A1.674) “er, two at the bottom and one at the side. Or else it could be two at the side and one at the bottom” (A1.676). Either way both electrons in one aluminium-chlorine bond came from chlorine (A1.670).

Annie demonstrates that although she did not know how many valence Keith S. Taber – [email protected] A87




electrons an aluminium atom would be expected to have she can deduce this logically: there are forty eight valence electrons shown (A1.692), and six chlorines should provide forty two (A1.688), so six did not originate in chlorine (A1.694) and therefore three must have started in each aluminium (A1.696).

The presentation of figure 15 immediately before figure 16 might be expected to provide a clue to the meaning of the arrows indicating dative bonds, however Annie does not appear to draw clear implications of this sequence of diagrams. The arrows “could represent how the chlorine, sort of they’ve all got lines, going to the aluminium” (A1.704) “but then the two in the middle have got arrows going to each aluminium, so if it means that they’re sharing with the aluminium, but I don’t really know” (A1.706). Annie could be confused by the use of line representing bonds, a formalism used for covalent bonds but not usually for the “ionic” (A1.574) bonds that Annie expects between aluminium and chlorine “because it’s a metal and a non-metal combining” (A1.578). Electrons in overlapping atoms also normally represent covalent bonds, but Annie identified bonding - albeit ionic - in figure 15, whereas she was “not really sure” (A1.702) if there were any bonds in figure 16, and despite it’s similarity to figure 15 she was not sure what it was meant to represent (A1.698). The expert would readily abstract the essential features that made these two diagrams similar: the number, types and arrangement of atoms, whereas a relative novice such as Annie was unable to ignore the (in this context) irrelevant aspects of the figures: circles and dots compared to lines and arrows. There is no evidence from her comments to suggest that at this time Annie was aware of the existence of dative bonding - if she was she did not apply the concept to this figure.

10.2 Second Interview: Annie suggests bonds with two electrons from the same atom.

In figure 15 chlorine “would need one electron, so some of the bonds, between like the aluminium and the chlorine, say one out of the four, may, might actually be like a chlorine-chlorine bond, but as the like electrons move round in a circuit anyway you wouldn’t be able to trace them” (A2.368). It would be difficult to interpret the figure as having any ‘chlorine-chlorine’ bonds in the usual sense of a bond between two chlorine atoms, but Annie could mean a bond with both electrons originating from chlorine. She could be attempting to describe a dative Keith S. Taber – [email protected] A88




bond, but lacking the appropriate (i.e. common with I) vocabulary. It is possible to interpret her next statement in this way: “if those three were aluminium bonds [i.e. bonds involving aluminium originating electrons as well as chlorine originating electrons?], say them [three of the four chosen arbitrarily], and then, those, that chlorine hasn’t got any aluminium on it at all [i.e. no electrons originating from aluminium in its ‘outer shell’?], so they could actually be chlorine bonds [i.e. bonds with both electrons originating from the chlorine]” (A2.378). Annie seems to have suggested - as an example - that one of the bridging chlorines is providing two dative bonds, which would satisfy aluminium’s valency requirements, but not that of either bridging chlorine atoms, however it seems clear that this was an arbitrary assignment: one would not be able to tell which was the chlorine (dative?) bond as “the electrons they don’t stay in a fixed state there, they go round, like in orbitals, or in spherical, things, then you wouldn’t be able to trace which is a chlorine [electron? electron pair?] because, they’re, they’re like all held, held in and going round and making up the, the shells” (A2.378).

In this interview when figure 16 was presented Annie recognised that “it’s the, same” (A2.382) as figure 15 (A2.383). She supposed that the arrows represented bonds that “can’t really be hydrogen bonds, bit like chl.., chlorine bonds I suppose. Between the opposite chlorines going to the aluminium, drawn with the arrow. So they’re sort of weak bonds, that are forming towards it” (A2.386). Here the ‘chlorine’ bonds are seen as analogous to hydrogen bonds, and therefore weaker than normal bonds, where the arrows “represent the, bonding” (A2.392) but both electrons “are chlorine” (A2.392) electrons. In contrast to her comments during the first interview Annie now seems to have a definite concept of dative bonding, although she struggles to find a suitable label for the idea.

There was no time to discuss dative bonding in the third and fourth interviews.

11. Hydrogen bonding.

11.1 First interview: no bonds between HF molecules.





Figure 11 was meant to represent a chain of hydrogen-bonded molecules of hydrogen fluoride. Electron density envelopes were drawn to show the polar H-F bond with electron density at the fluorine end distorted towards the adjacent hydrogen from the next molecule. Although the figure appears relatively simple it has a high schematic content. The bottom HF molecule is shown undistorted with a polar envelope as in figure 8 (lithium iodide), but the other molecules show distortions similar to that of the (sulphate) anions in figure 10. The diagram shows the linear geometry of the F --- H - - F sequence, and the angular geometry of the H --- F - - H sequence. As Annie has not appreciated the way electron density envelopes were used in the earlier figures (7-10) it is not surprising that she was unable to explain the significance of the “sort of shape” (A1.426). Annie recognised that the diagram showed a “chain of, hydrogen fluoride molecules” (A1.424) with bonding within each molecule, “within the sort of shape of the H-F, but when it meets up to like the H-F on the corners of the other shapes, they don’t actually bond” (A1.426). Annie did not class this as chemical bonding (A1.446) perhaps because no overlap was shown?

11.2 The second interview: ubiquitous bonds weaker than proper bonds.

The term ‘hydrogen bonding’ was introduced by Annie a number of times during the second interview, and in a variety of contexts. The atomic nucleus (in figure 1) was held together by “hydrogen, no it can’t be hydrogen bonds” (A2.6). In a piece of iron (figure 6) there are “hydrogen bonds, ... between the atoms. To give it a structure” (A2.59) In hydrogen the two atoms are “held together by hydrogen bonds” (A2.81), but in figure 2 “that’s, looks like it’s forming a molecule” (A2.83) so it would not be a hydrogen bond, but “it’s a, covalent bond” (A2.89). These comments seems to suggest a tendency to use hydrogen bonding as a ‘catch-all’ response.

Despite the earlier liberal references to hydrogen bonds inside nuclei, metallic solids and molecules, Annie was able to apply the idea in an appropriate context, when considering figure 11. “Hydrogen bonds” (A2.266) were present where “the foot of the [golf] club [shape] hits the top of the other one” (A2.268), i.e. between one “H-F” unit and “the next one along, the H and F sort of holds them together” (A2.268): a reasonable description of the intermolecular nature of the Keith S. Taber – [email protected] A90




bonding. In addition Annie was able to report that the bond “between the, the H and the F of the like neighbouring molecule, is a lot weaker, than the bond, actually in the substance”, “the proper bond of H-F” (A2.268). (Note than Annie seems to use the term ‘substance’ to refer to molecular species, not molar entities.) The ‘proper’ bond was a “covalent bond” (A2.270) and Annie was able to distinguish between the two types of bond present “intra-[molecular], covalent. Inter-[molecular] for the hydrogen bond” (A2.272).

When discussing figure 16 (aluminium chloride dimer) Annie commented that the dative bonds “can’t really be hydrogen bonds, bit like chl.., chlorine bonds I suppose” (A2.386) suggesting that Annie was extending the idea of intermolecular links by analogy to hydrogen bonds. Annie was able to give the folowing definition of hydrogen bonds: “a bond that went from like, like a hydrogen to another atom, in a, like in water, ... you’ve got the two hydrogens added to a, an oxygen. And then the hydrogen, brings like a, a small bonding between like another oxygen, to hold the structure together but it’s not like, it is a bond, but it’s not as strong, as like, the ionic bond would be” (A2.388). Despite not choosing optimum vocabulary to explain her ideas it seems clear that Annie is distinguishing between the intramolecular O-H bond and the weaker intermolecular hydrogen bond.

11.3 The third interview: attractions between lone pairs and hydrogen hold molecules together.

During the third interview there was not time to discuss any diagram showing hydrogen bonding, but when looking at figure 5 (sodium chloride) Annie volunteered “obviously there’s no hydrogen bonding involved, ‘cause there’s not any hydrogen there” (A3.82) “if I was to say like it’s hydrogen bonding then that’s, involved in just like basically holding molecules near each other like in water the oxygen, lone pairs will attract, to the other hydrogen” (A3.84), but there was no hydrogen bonding (A3.86), and Annie knew that “‘Cause no hydrogens there, basically” (A3.88). Annie seemed to have a clear understanding of the intermolecular role of hydrogen bonding (“basically holding molecules near each other”), and was able to give an example (“like in water”), and a mechanism (“the oxygen, lone pairs will attract, to the other [molecule’s] hydrogen”). There is clear progress in Annie’s reported comments related to hydrogen bonding in this study. In the first Keith S. Taber – [email protected] A91




interview Annie seemed to have no knowledge of this type of bonding, then in the second interview she was able to apply the idea in an appropriate context although she also introduced it as a suggestion in other less appropriate contexts, and then in the third interview Annie was able to produce a fairly competent orthodox description of this type of interaction.

12. Van der Waals forces.

12.1 First interview: integrity of molecular solids due to forces stabling-up.

At the time of the first interview Annie did not seem to know of van der Waals forces. The only bonds in the solid iodine represented in figure 17 were “between the two iodines in each molecule” (A1.718). Annie knew that such solids have structural integrity, that they would “stay together” (A1.728), but this was “probably just the forces of pressure and, the, like the charges from each thing would be stable” (A1.730). It is not clear exactly what these charges “from each molecule” (A1.732) were, but Annie’s use of ‘charge’ appears here to be related to “forces, the forces from each iodine should have combined to stable-up. But there’s probably other forces, which erm, hold it together, in a solid, so it wouldn’t break off or anything” (A1.736) There were “no” (A1.738) chemical bonds, but there was some other type of force (A1.740) .

12.2 The second interview: ubiquitous weak bonds, readily disrupted.

By contrast, at the time of the second interview, Annie was certainly aware of the existence of van der Waals forces, and knew they were relatively weak forces that were readily disrupted. Annie now reported that such forces occurred in iodine (figure 17), but she also suggested a wider range of examples. The atom (e.g. sodium, fig. 1) was held together by “van der Waals forces ... weak forces, which pull towards the nucleus. Which are readily disrupted” (A2.2). In metallic iron (figure 6) “it’s probably van der Waals forces, holding it together” (A2.93), although these forces are not the same as metallic bonding “‘cause you can get van der Waals forces in, covalent things as well” (A2.107). Keith S. Taber – [email protected] A92




Indeed lithium iodide (figure 8) is “ionically bonded, but the forces holding it together will be, (pause, 5s approx.) van der Waals I suppose” (A2.125).

In figure 17 (iodine) the molecules stick together because of “the van der Waals forces” (A2.405), which are the “forces holding like atoms together, to form weak bonds, they sort of form weak bonds between each other. And they’re, they’re readily disrupted. Like if you, heated them [sic], or boiled them or whatever, or say erm, if you froze them, liquefied them or something, they’re easily, they’re more easily disrupted, than would be the bond between the two elements [atoms?] within a molecule” (A2.407). The reference to “them” suggests a confusion between molecular and molar phenomena. Also although increasing molecular energy through heating the substance would ‘overcome’ (“disrupt”) the van der Waals forces, “freezing” is an effect, caused by the presence of van der Waals forces in the absence of sufficient such molecular energy. To find out if the inclusion of “freezing” was a mere ‘slip of the tongue’ Annie was asked a series of questions to reiterate. Melting the solid would “disrupt the, the van der Waals forces” (A2.409) but not the covalent bond (A2.411). Boiling would also disrupt the van der Waals forces (A2.415), as would freezing, “yeah, it would like condense them, if you froze them” (A2.417). It is not clear what Annie means by “them” - as gases can condense, but not intermolecular forces, or individual atoms. The interviewer suggests an interpretation, that the molecules would be brought closer together: “bring them closer, whereas, like if you, if you boiled them, and turned them into a vapour, they would get really pushed apart, so they’d be like all over the place, and so they’d be weaker” (A2.419). Annie seems to have learnt about van der Waals forces since the first interview, but although she knows they are relatively weak forces she has not fully thought through how they may be “readily disrupted”. Annie also applies this new concept inappropriately to bonding in structures she cannot otherwise explain.

12.3 The third interview: Annie still does not discriminate examples and non-examples of van der Waals forces.

When discussing figure 5 (sodium chloride) Annie suggested that the ions were held together “partly due to the attraction of the opposite charges ... probably van der Waals forces” (A3.82), which “can occur to hold a molecule or atoms together as well as being sort of involved in Keith S. Taber – [email protected] A93




bonding, whereas you know, if I was to say like it’s hydrogen bonding then that’s, involved in just like basically holding molecules near each other” (A3.84). Annie believes that in sodium chloride van der Waals forces (A3.90) and electrostatic attractions between the opposite charges (A3.92) may be involved, these two phenomena being “separate, but they’re sort of related in a way, because they are both involved in sort of holding molec.., or atoms close together without sort of committing, total electrons” (A3.94). For Annie there is no chemical bonding shown in figure 5 (A3.96, 98, 105), although there is attraction between the ions (A3.105). Sodium chloride crystals (the substance - rather than figure 5) comprise of “sodium and chlorine atoms joined to form the sodium chloride molecule” (A3.120) “by, by van der Waals forces” (A3.122).

Figure 17 represented “an iodine molecule” (A3.126) which had bonding between the atoms (A3.128), “Van der Waals forces” (A3.130). Annie confirmed she meant between the atoms (A3.132), as well as between molecules (A3.134, 136). There were interactions between the atoms within the molecule (A3.138), but “no” (A3.139) bonding, “No. No, it’s not bonding. But there’s sort of van der Waals forces. ‘Cause it sort of exists as a solid at room temperature, so although it doesn’t need, the forces hold it together so that when heat’s applied, ‘cause it sublimes” (A3.140) when “it turns from the solid to a gas. It doesn’t go through the liquid phase” (A3.142). In the vapour “it still exists in a molecule” (A3.146) with “some sort of attraction, between them both, erm, to basically hold the atoms together” (A3.150). When one “heated this then the van der Waals forces between the molecules would break down, but the actual sort of forces and bonds between [within] the molecule aren’t disrupted” (A3.156). The forces within the molecule “stay the same, it’s just” (A3.157) those “between them, that change” (A3.157), “the force is still there. It’s just become weaker” (A3.159) “‘Cause you’ve disrupted. If you’re applying heat, in either, either direction really, erm, you’re obviously putting pressure on the molecules to behave in a certain way. So by say applying heat to something like an iodine, I don’t know, some mark, some solid iodine, then, erm, you’re going to disrupt the bonds, or the forces, between the molecules, er, which will break down, so that they’re going to change in state, although they’re not going to be, the sort of the bonding between, the forces within the molecule, are going to remain the same, although, the sort of the, the attraction for the other molecules are weakened so then its going, they’re all going to sort of like, be sort of, sort of erm, whizz off kind, sort of turn into a gas Keith S. Taber – [email protected] A94




because they’re not held together, so closely, because they’ve been disrupted” (A3.161). What Annie meant by putting pressure on was “if you apply heat to something then you are breaking down, you’re causing the bonds, in between, most bonds have sort of, er, sort of er, er, a level whereby they can go up to a certain heat and then they’ll be broken down” (A3.162).

In these comments we see that Annie gives quite an orthodox explanation of the sublimation of iodine as due to the effect of heating in allowing the molecules to overcome the relatively weak intermolecular forces (which are indeed due to van der Waals forces),

“the van der Waals forces between the molecules would break down”, “change”, “the force is still there. It’s just become weaker” “‘Cause you’ve disrupted ... the bonds, or the forces, between the molecules, er, which will break down, ... the attraction for the other molecules are weakened so then its going, they’re all going to sort of like, be sort of, sort of erm, whizz off kind, sort of turn into a gas because they’re not held together, so closely”;

whilst the stronger intramolecular interactions are maintained into the vapour phase,

“it still exists in a molecule” with “some sort of attraction, between them both, erm, to basically hold the atoms together”, “the actual sort of forces and bonds between [within] the molecule aren’t disrupted”, “the forces within the molecule, are going to remain the same”;

although these “forces and bonds” are covalent bonds, not van der Waals forces as Annie suggests. She is also correct in that at a high enough temperature all bonding will break down - van der Waals at a much lower temperature than covalent. Although seems to have an orthodox understanding of van der Waals forces as weak, readily overcome, intermolecular attractions, although this appears somewhat confused by a tendency to ascribe other types of interaction {ionic (A3.82), covalent (A3.130) and previously metallic (A2.93) and even atomic binding (A2.2)} to this class of bonding.



stability and lability in student conceptions: · web viewalthough the details of his stage theory...

Documents