Please cite as: Fletcher, P.R., (2004) PhD Thesis - How Tertiary Level Physics Students Learn and Conceptualise Quantum Mechanics (School of Physics, University of Sydney)

CHAPTER 2QUANTUM MECHANICS AND SCIENCE EDUCATION

LITERATURE REVIEW

2.1 INTRODUCTIONIt has already been noted that there has not been much education

research devoted to the teaching of quantum mechanics. The subject is far too specialised to have much presence in mainstream education literature. What work has been done is reported mainly in Chemistry and Physics journals.

The body of the literature summary has been presented in 3 sections. The Chemistry and physics articles have been treated separately to reflect the differences in the types and styles of articles, within each discipline area the articles have been classified and grouped under one of the following four headings – History; Teaching specific ideas and concepts; Course materials; or Education research. These cover a broad selection of articles which were intended by their authors to be used by educators of the subject. These reviews are followed by a broad overview of associated educational literature to situate the results of the research and provide the theoretical framework of learning underpinning this study.

For a comprehensive categorised literature bibliography covering quantum mechanics please refer to Appendix 8 for a Quantum Chemistry Literature Survey and Appendix 9 for a Quantum Physics Literature Survey.

2.2 CHEMISTRY RELATEDChemistry education research has had a presence since the 1920’s

with the publishing of the Journal of Chemical Education1 in 1924 and provided a broad forum for all chemical educators. Chemistry education reached a milestone in the late 1970’s when university chemistry departments recognised and began to appoint faculty to positions

1 Journal of Chemical Education – refer to http://jchemed.chem.wisc.edu/index.html

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specifically responsible for chemistry education. For example Purdue University in 1982 established a Division of Chemical Education2 and offers higher degree programs in chemical education.

In relation to the teaching of quantum mechanics, the period 1970 through to the commencement of this research has seen a steady number of articles in chemical education literature devoted to quantum theory and introductory quantum mechanics. These include short essays addressing historical and philosophical issues, descriptions of atomic models and bonding, representations of bonding and energy levels, example problems suitable for presentation and computer simulations.

In Appendix 8 Quantum Chemistry Literature Survey, the papers have been categorised and grouped into the following structure.

HISTORYQuantum Chemistry – History

TEACHING OF IDEAS AND CONCEPTSQuantum Chemistry - Teaching Concepts

InterpretationsBonding & StructureAtomsOrbitalsMathematicsSpecific

Quantum Chemistry - Lecture Demonstrations & LaboratoryDemonstrationsLaboratory

Quantum Chemistry - Computational IdeasCurriculum Changes & DeliverySoftware ProgramsWave Function SoftwareAtomic Structure & Orbital ProgramsWeb

EDUCATION RESEARCHQuantum Chemistry - Education Research

2 Completing the Program with a Division of Chemical Education by G.M. Bodner and J. Dudley Herron – refer to http://chemed.chem.purdue.edu/chemed/bodnergroup/archive/publications/completing.html

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2.2.1 Chemistry – History & Teaching of Ideas and Concepts PapersThough these papers cover a wide variety of topics, their approach

is surprisingly similar. By and large they focus mainly on providing teaching support materials. One paper, chosen more or less at random, can be taken to be representative and contain the common elements addressed. It is entitled Presenting the Bohr Atom (Haendlers, 1982) and is typical of the format of the majority of this literature.

The paper first acknowledges that the current available text material lacks context and treats the topic in a simplistic way, ignoring the events and debates that lead to the formalisation of theories. The paper then describes the context of the topic, in this case an historical outline of the development of Bohr’s ideas. It cites and contextualises the observations, theories and experiments from Faraday’s experiments with electrolysis through to the Schrödinger theory of quantum mechanics. The main body of the article then refers back to this preliminary information. The main topic of this article is entitled ‘Derivation of the Energies of the Stationary States’ and details the derivation of Bohr’s model. The summary section entitled ‘The Bohr atom in the Chemistry Curriculum’ then links the ideas presented in the article back to the undergraduate chemistry curriculum.

The primary inference from this paper, as in other similar articles, is that a more historically accurate and/or detailed treatment of the material should increase the student’s understanding of the development of scientific theories. Also it is proposed that this treatment of the material would also remove some of the frustration students feel at the arbitrary nature of current textbook presentations.

The themes contained within this grouping of papers does have variation when compared to the example above, some are less critical of the current material or methods and focus more on presenting an idea, the utilisation of a tool or simply offer advice on material delivery in a particular educational setting.

2.2.2 Chemistry – Education Research PapersThe proportion of specifically quantum mechanics education

research based papers is small when compared to the number of

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aforementioned papers. These papers predominately address the areas of bonding and atomic structure. Following is a representative selection of papers.

Patricia Keig and Peter Rubba in their paper Translation of Representations of the Structure of Matter and its Relationship to Reasoning, Gender, Spatial Reasoning and Specific Prior Knowledge (Keig, 1993) explore the abilities of students to appropriately translate between three representations of the structure of matter. The research uses interviews as the primary research instrument and three variates of paper-and-pencil instruments to measure reasoning, spatial reasoning and prior knowledge. The discussion section of the paper reiterates the research questions and comments on the findings in terms of translation errors, misunderstandings, misapplications, spatial reasoning and gender differences. The conclusion paragraph then relates the findings to models of knowledge and understanding, then briefly discusses strategies which may assist instruction to minimise the identified weaknesses.

Georgeios Tsaparlis’s paper entitled Atomic Orbitals, Molecular Orbitals and Related Concepts (Tsaparlis, 1997) analyses examination scripts of successful students. The students knowledge and understanding of the following topics was studied – the definition of an atomic orbital, the real mathematical verses the complex mathematical forms of the atomic orbitals, the representations (shapes) of the atomic orbitals, the approximate nature of atomic orbitals for many electron atoms, Slater determinants, the definition of a molecular orbital, and the nature of the chemical bond. The analyses revealed that students did not have a clear understanding of orbitals, they had difficulty in understanding the conceptual similarity between the real and complex mathematical forms associated with atomic orbitals, they confuse the orbital representations, and did not realise the approximate nature of orbitals for many electron atoms. The paper then discusses the implications of these finding for instruction and the curriculum, followed by instructional strategies and suggestions for secondary and general chemistry curricula.

The chemical education research papers related to quantum mechanics have adopted well tested educational tools which are

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commonly utilised in mainstream science education research. The research formats are narrow and tend to focus on exploring the understanding of a specific concept(s), addressing the difficulties and/or misconceptions students’ hold, followed by a discussion concerning the implications to instruction and curricula.

2.2.3 Chemistry – PapersIn summary, the majority of chemical education publications

relating to quantum mechanics, provide useful teaching materials such as historical reviews and presentation analogies. They generally conclude that these materials would enhance a student’s understanding of the quantum concepts, but do not make reference to supporting education research. There is therefore little emphasis on pedagogy.

This lack of pedagogical research into the deeper question of learning is most probably due to the fact that quantum mechanics is not currently considered a particularly important area for the chemical education research community. This would no doubt be related to the sheer number of topics that have to be covered, and quantum mechanics is perceived to be only a very small part of the undergraduate chemistry curricula.

2.3 PHYSICS RELATED Physics education research has been growing over the past 25

years. For a comprehensive literature reading list refer to the University of Marylands, Research in Physics Education (RIPE) WEB site (URL http://www.umd.edu/ripe). At the American Association of Physics Teachers meeting (AAPT) held in 1996, the members decided to form a sub-branch for Physics Education Research. It should be noted that a substantial portion of physics education research has been devoted to studying student conceptual understanding of topics in physics. Also of note is the recent increase in articles pertaining to theories of learning. However most research has focused on the area of mechanics and to a lesser extent electricity, magnetism, heat and optics. The amount that has been devoted to quantum physics is quite small.

The physics education literature associated with quantum physics published in the period 1970 to present can be categorised into four main

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types of articles. These could be broadly described as History, philosophy and interpretation of quantum mechanics; Teaching of specifics concepts - Ideas and methods for teaching quantum concepts, including isolated computer simulations; Teaching materials - Packaged teaching and assessment modules; and Education research. The associated reference list is as complete as possible and is presented in Appendix 9 Quantum Physics Literature Survey, the papers have been categorised and grouped into the following structure (see over page).

HISTORY, PHILOSOPHY AND INTERPRETATION OF QUANTUM MECHANICS

Quantum Physics - HistoryQuantum Physics - Philosophy & Interpretation

TEACHING OF SPECIFIC CONCEPTSQuantum Physics - Teaching ConceptsQuantum Mechanics - Lecture Demonstrations & LaboratoryQuantum Physics - ComputationalQuantum Physics - Tests

TEACHING MATERIALS Quantum Physics – Computer & Book based Course Material Quantum Physics – Courses and commentsQuantum Physics - Textbook Review

EDUCATION RESEARCHQuantum Physics - Education ResearchRelated education research on waves

2.3.2 Physics – History, Philosophy and Interpretation of Quantum Mechanics

The physics and physics education journals contain many historical accounts that cover both the lives of the physicists, the theories they developed, philosophical debates and discussions concerning the interpretation of quantum mechanics. Although these are not directly aimed at addressing educational issues they are an important resource component accessible to both teachers and students.

2.3.3 Physics – Teaching of Specific Concepts The majority of physics education publications dealing with

quantum mechanics over the last 25 years predominately provided useful teaching materials outlining the authors’ thoughts concerning the manner in which an idea, topic or concept can be successfully presented. These

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articles, as do those in chemistry, generally conclude that the material would enhance a student’s understanding of the quantum concepts but make very few references to supporting education research. It is also noted that half the physics articles listed do not have conclusions or summaries that describe the outcomes one might expect from utilising the ideas presented. A representative example of a paper entitled “Quantum Mechanics made Transparent” (Henry, 1990) is outlined below:

The article is described as a ‘sampler’. It shows “...how quantum mechanics may be presented to students in a way that makes apparent how natural quantum mechanics is as a description of the world... The basic ideas of quantum mechanics are developed from intuitive first principles to the point where one can connect with the more traditional treatments of quantum mechanics.”.

The article then uses a Socratic dialogue between a teacher and his students which centres around a very detailed question and answer session. The conversation begins with a discussion of the postulates and leads into the uncertainty principle. The discussion then moves on to cover the development of the mathematical machinery associated with Hilbert Space and the idea of representing observables by operators. The terms ‘eigenstates’ and ‘probability amplitudes’ are discussed and each of the operators commonly used are presented. The author does not provide a summary or conclusion to the article.

A small number of articles describing selected lecture demonstration and experimental apparatus appropriate to quantum mechanics have been published. These articles provide a description of the apparatus, associated theory and comment on its usefulness in an educational delivery context. A comprehensive list of demonstrations and experiments and the primary information source for these is available from Physics Instructional Resource Association3 PIRA.

The advent of low cost semiconductors and programmable calculators in the mid 1970s spawned a series of papers describing how these could be used to generate graphical representations of quantum

3 The Physics Instructional Resource Association PIRA WEB site at URL http://physics.csufresno.edu/pirapub/default

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phenomena. Some examples include “The analogue computer as an aid to teaching elementary quantum mechanics” (Summers, 1976), an article which describes how analogue techniques can be use to tackle simple quantum mechanical problems; “Fundamental quantum mechanics - graphical presentation” (Wise & Kelley, 1977), provides a selection of computer generated displays including a computer simulated diffraction experiment, a derivation of the uncertainty relation, and several spatial distributions of momentum amplitudes and “Simulations of quantum-mechanical measurements with programmable pocket calculators” (Summers, 1978), which provides the reader with the mathematics and the code for the implementation of numerical integration and gives the example of a quantum isolator. These early papers and programs paved the way for quite sophisticated simulation software packages that were developed and distributed after the advent of the modern personal computer.

2.3.4 Physics – Teaching Materials Packaged teaching and assessment modules

At the commencement of this research project there were three large and two smaller computer assisted learning (CAL) packages currently available for teaching tertiary level quantum physics. These were:

Software Teaching of Modular Physics (SToMP) - a project funded under the teaching and learning technologies program (TLTP). Coordinated by Dr RA Bacon, Physics Department, University of Surrey, Guildford

Simulations in Quantum Mechanics - Consortium for Upper Level Physics Software (CUPS) produced by J.R. Hiller, I.D. Johnston and D.F. Styer.

Quantum Mechanics on the Personal Computer - developed by S Brandt and H.D. Dahmen (Berlin Springer).

and Visual Quantum Mechanics - Explorations of the Quantum world for

Non-Science Students, Physics Department, Kansas State University

Understanding the Unobservable - a reconstruction of First Year Quantum Physics for Engineers and Scientists by Andrew Cheetham and John Rayner, University of Canberra

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Although these packages had been reviewed by journals4 the quantum physics components appear to have been developed without reference to education research material. Since the commencement of this research project the Visual Quantum Mechanics team headed by Dean Zollman has significantly developed and has been guided by internal and external PER education research.

2.3.5 Physics – Education ResearchThe following papers have been selected and are representative of

the major quantum mechanics education research programs. Please refer to Appendix 9 for a complete literature review.

In 1991 a research team at the Free University of Berlin, Germany, headed by Helmut Fischler and Michael Lichtfeldt, presented a paper “Learning Quantum Mechanics” at the International Workshop for Research in Physics Learning : Theoretical Issues and Empirical Studies, held at the University of Bremen (March 4-8, 1991). This was the first published research article to investigate into students’ conceptions and their learning processes in relation to quantum mechanics.

The article reports on findings from a study that compares a teaching unit that avoids the use of mechanical models commonly presented in texts with a control group. The premise was that clinging to a historically orientated development of the subject means the teaching will also cling to the conceptions of classical physics. The researchers propose that these mechanical models will set up additional obstacles to understanding quantum physics.

The teaching unit was trialled at several high schools in eleven physics courses (150 students). The study consisted of an evaluation questionnaire; video recordings of 32 lessons across six courses, in order to discover correlations between student conceptions and their answers given in lessons; pre-interviews for two courses, to find out what conceptions the student had at the beginning of the teaching unit; a post questionnaire five to six weeks after course; and post-interviews of three

4 For articles referring to these and other CAL & video refer to the software clearinghouse UniServe Science WEB site at URL http://www.usyd.edu.au/su/SCH

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courses. In addition the same pre- and post- questionnaire was administered to a control group of students in a further 14 courses (120 students).

The range of topics covered by the questionnaires and interviews was —light, atom-electron, particle-body and students’ ideas on the philosophy of science. The questions took the form of open-ended free answer (eg. What is light really?) and word pair associations. The verbal answers were transcribed from videotapes.

The study yielded results covering an overview of the students’ conceptions before and after the teaching unit and a comparison between the test and control groups; and case studies for individual students providing conceptual maps that summarised the students’ network of ideas.

The article’s summary section provides an illustration of the results based upon the examples provided in the results section. Referring to the test group, ”A teaching concept, for example like the one here, which in the first stage of planning already considers in detail possible conceptions of students, and consciously provides room for these conceptions to develop in the physics course, will achieve an increased cognitive conflict situation which will then lead the students to grapple with the subject matter in an intensified manner. In this way the students became conscious of their own conceptions and began to question them”. Whereas the results from the control group tended to incorporate the “new” phenomena into the “old” mechanistic ideas. “Here, the different ideas in quantum physics were merely acquired verbally in the science language level and forgotten again afterwards.”

Fischler and Lichtfeldt published a second paper entitled “Modern Physics and Students’ Conceptions” (Fischler and Lichtfeldt, 1992) the article extends upon the previous analyses and quantifies the “Change of students’ conceptions of an atom’s stability” and provides “Comparisons of conceptual change between the test and control groups”.

The article, “Common misconceptions regarding quantum mechanics” (Styer, 1996), Daniel Styer presents fifteen preconceptions that students can have concerning quantum mechanics. The article’s

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content has been drawn from his own experiences and covers misconceptions relating to the idea of quantal state, measurement and identical particles. Styer points out that misconceptions are operational as well as conceptual and recommends a variety of ways to utilise the presented material. These include guided discussions, essay questions and diagnostic examinations.

Reflecting the increasing interest in educational aspects of quantum mechanics during the period of this research two conferences have held dedicated sessions. The first was at the 1999 NARST Annual Meeting - Looking Forward, Looking Backward : Reflections on the Future and Past of Science Education Boston with a session entitled “Research on the Teaching & Learning of Quantum Science” where eight poster papers were presented. The second was the 2002 Gordon Conference -Physics Research and Education: Quantum Mechanics, Mount Holyoke College, South Hadley MA, where twenty six papers were presented covering the following areas of physics education research and developing curricula, quantum mechanics curricula and teaching quantum mechanics, research experiments in quantum curriculum, student understanding of physics concepts, theoretical research and teaching quantum mechanics, topics in quantum mechanics, photon experiments with undergraduates, quantum curricula, experimental research that could influence quantum curricula.

2.4 THEORETICAL FRAMEWORK OF LEARNING – A LEARNING MODELAlthough little research has been carried in the specific area of

quantum mechanics in relation to learning there is a great deal of empirical research and theorising about student learning in science. One of the aims of this study as outlined in Chapter 1 was to situate the results of the research into the broader associated educational literature. This section provides an educational research backdrop and highlights aspects of the literature which were considered important to this specific investigation.

This thesis is concerned with student learning in the area of quantum mechanics and the scope of the research questions would yield a great deal of information collected from a number of different sources.

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To interpret this information and communicate the results it is necessary to introduce a theoretical framework for learning. This study defines learning in quantum mechanics as a complex process that is based on existing educational, psychological and scientific theories that underpin the work of the science education community. It draws on current work on learning theory from the fields of neuroscience, cognitive science, science education and physics education research.

This section will briefly survey the literature that directly influences the theoretical framework of learning underpinning this study. It will examine learning as a constructivist process and the factors that influence learning outcomes. This theoretical framework presupposes that learners develop cognitive structures to store and retrieve knowledge.

2.4.1 LearningIn the fields of behavioural, cognitive and humanist psychology a

definition of learning has three criteria (Schuell 1986):

1. a change (or a potential for change) in an individual’s behaviour or ability to do something;

2. a stipulation that the change must result from some sort of practice or experience; and

3. a stipulation that the change is an enduring one.

While there is some degree of consensus on a definition of learning, ideas and theories on how learning occurs are subject to debate and constant revision. A complete explanation linking the neurological behaviour of the brain to more abstract and high level processes of learning is still unattained. This study adopts a cognitive approach relying heavily on the constructivist view of learning to establish a theoretical framework.

2.4.2 ConstructivismThe fundamental tenet of constructivist learning theory is that

students construct knowledge from external experiences and interactions with their environment. The earliest references to the construction of knowledge are attributable to the philosophers Vico and Kant in the 18th

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century. What is now called constructivism incorporates ideas from a range of perspectives and is a large multi-faceted subject. Various types of constructivism are described by Phillips (1995) in terms of dimensions. This work assumes a socio-cultural perspective where learners are part of a collaborative environment actively building physical models that are abstract human constructions.

The proposed theoretical framework draws on neo-Piagetian ideas of knowledge construction. It also uses social constructivist ideas that originate with Vygotsky. Two schools of constructivism, initiated by the work of Piaget and Vygotsky have had an enormous impact on science education research and practise. Howe (1996) identifies three elements of Piagetian theory as being ‘particularly influential’ to science education:

1. the idea that a child learns through interaction with the environment has resulted in a widespread discovery and hypothesis testing teaching style in classrooms and laboratories;

2. the idea that cognitive development occurs in predictable stages has led to curricula designed to reflect the development level of children; and

3. the idea that students must construct knowledge and meaning for themselves has meant students are encouraged to have a more active role in the teaching and learning process.

Vygotsky’s description of learning as a collaborative or shared experience that is dependent of interactions with others has been widely interpreted and implemented in science education. Scholars who have made a substantial contribution to this end include: Driver (1995), Rogoff (1984, 1986 and 1990), Lave (1991), Roth (1990), Newmann, Griffin and Cole (1989, 1995). Social constructivism provided a change of focus and facilitated the introduction of group and cooperative learning styles. The use of language by students was encouraged children used their own language while they learnt scientific language. The zone of proximal development and scaffolding has become a common teaching and learning strategy.

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A learner’s zone of proximal development is defined as the learner’s range of ability with and without assistance from a teacher or peer. Thus one end of the range is the student’s ability level without assistance and the other end of the range is the learner’s ability level with assistance. This is an important concept to understand because it can guide what should be learnt next about a topic. For example, when applying this in a learning setting you would assess a learner’s present knowledge of a topic and identify a subset of new knowledge that would be most appropriate to learn next and other subsets would be best left alone until later. The subset that would be best to learn next is contained in the proximal zone. The subsets that should be left until later are contained within the distal zone.

When it became widely realised that Vygotsky’s work contradicted the idea that cognitive development precedes learning, emphasis was placed on the context of learning. It led to acceptance of the idea that students’ cognitive development progresses by learning science within a context that provides support and is relevant to them. It also led to the recognition of what Lave (1991) describes as situated learning. Transferring knowledge learnt in one context to another can be difficult or even impossible. This has many implications for physics teaching as identified by Johnston et al (1998).

2.4.3 Model of student learningA useful way to summarise the teaching and learning ideas that

inform this study is by using a presage-process-product model (Biggs, 1978 and Prosser et al 1994, 1999). The model shows stages of the learning process and a possible logical sequence of these stages. Each stage is influenced by a number of factors. For example the learner’s prior knowledge, prior experiences, their attitude towards the learning context, epistemological factors and characteristics of the learning context itself.

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Figure 2-1 : Presage – Process - Product Model of student learning. Adapted from Prosser, Trigwell, Hazel and Gallagher (1994)

A model such as this allows us to see knowledge construction as a process consisting of understandable stages. However it is a greatly simplified model and one must remember that stages can occur simultaneously and multiplicable factors in each stage are influential. Thus it is usually not possible to completely isolate individual stages of the learning process, as interactions between the stages are complex. For an individual learner the extent of influence of individual factors can vary and this can result in a variety of learning outcomes for a group of students involved in the same learning context.

This model forms the skeleton of the theoretical framework, attached to this skeleton is the cognitive structure students develop while studying quantum mechanics, the discipline structure of quantum mechanics and the factors that influence student learning.

2.4.4 Cognitive structuresCognitive structures are metaphorical constructions that describe

the storing of knowledge and the mechanics of learning. Study of the brain function and human behaviour suggests that knowledge is stored in some organised manner, and relatively simple psychological experiments

Characteristics of Student- prior knowledge- prior experiences- affect- motivation

Characteristics of Learning Context-physical setting-resources-pedagogical model-content-structure-teaching strategies

Student Perceptions of the Learning Context- social interactions- physical setting- epistemological

Student Approaches- surface or deep- framing- constructing meaning

Learning Outcomes- student responses to a range of problem solving situations

Presage Process Product

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such as memory tests tend to confirm that individuals possess cognitive structures that they can access and add to as the need arises. Neural research suggests that knowledge and learning are facilitated by neurons and synapses. As an individual learns there is a growth in the number of synapses (connections) between neurons (Fuster, 1999). This study requires the use of a cognitive structure that is different from the detail of neuron activation and response. In order to clearly articulate the cognitive structures the work of Phillips (1987) is used. He defines three domains where a knowledge structure is present:

1. the structure of part of the external world;

2. the structure of our theories dealing with the structure of this part of the world; and

3. the structure of the psychological entities with which we master such theories or deal with such parts of the world.

Taking an electron as a quantum mechanics example, the electron is the external world structure, an individual’s cognitive structure is the way our brain records our understanding of the electron and the wave function is the structure by which we express our understanding of the external structure. It is clear that these structures are related and to a degree independent, but they are not the same. The second domain is called the cognitive structure and the third domain is the discipline structure.

The discipline structure for quantum mechanics will be established through a grounded study which is described in detail in Chapter 4 and the discipline structure will be presented and discussed in Chapter 7. The cognitive structure assumed is taken from Shavelson (1974), “The structure in a student’s memory is referred to as a cognitive structure: a hypothetical construct referring to the organisation (relationships) of concepts in memory.” .

This hypothetical structure consists of small elements or resources. Activation of one element or resource may lead to the activation of another. This process is called association. If an association exists between elements or resources they are said to be linked. A series of

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linked elements or resources is called a schema (Hintzman 1978). Although its origins are in memory research, the notion of schema has been extended to learning. Remembering is one form of learning, but human structures of knowledge are not simplistic and declarative, and theories have evolved to explain the specialised and complex nature of humans’ procedural or generative schemata. Schema is constantly modified by interactions with the environment and so has to be seen as an “active” organisation. To describe the processes of learning in terms of schema concepts of assimilation, accretion, accommodation, restructuring and tuning are used. For a more detailed explanation of these concepts see the work of Glasserfeld (1989), Ausubel (1968), Rumelhart and Norman (1978, 1980 and 1981).

This study assumes a schema-based cognitive structure for an individual’s understanding of quantum mechanics. Learning using schema has the following stages:

A new element or resource is encountered.

The new element triggers a recognition response.

The learner associates a specific activity or purpose with the new element based on existing schema.

If the learners expectation is reinforced the new element is assimilated into an existing schema.

If the learners expectation is NOT reinforced this perturbation leads to an adjustment of the schema called accommodation.

If the original processing of the new element in terms of existing schema is retained this is called accretion. This trace of the new element can be used to later reconstruct the original input.

If in cases where there is no recognition response, entirely new schema may be constructed, this is called restructuring.

By applying the schema the schema is slowly modified and refined. This tuning allows schema to conform better and better to the sorts of situations to which it is to apply.

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Schema are small structures and it would take many schemata to represent a students understanding of quantum mechanics. Adopting a higher order knowledge structure from Scherr (2002) and Redish (2004) it is proposed that schema are grouped to form a larger model. The models of student knowledge form a continuum between two extremes. On one extreme the model consists of many strongly associated elements or resources that can be activated in a variety of contexts and is stable and resistant to change. At the other extreme is a set of largely independent elements and resources with weak associations, which are activated in only limited contexts and are labile and easily changed.

The value of cognitive structure is the ability to retrieve, process and apply knowledge to solve a range of problems.

2.5 IN RELATION TO CURRENT INVESTIGATIONThe quantum mechanics education research literature review

shows that very little formalised research had been undertaken by either the Chemistry or Physics education research communities by the commencement of this project in 1997. During the intervening period 1997-2003 a number of concurrent related studies concerned with aspects of visualisation, understanding of the wave nature of matter, student views and conceptions have been reported. The area of focus of the current investigation, mainly the isolation of key concepts, identification of learning difficulties, exploration of the role of mathematics, and the exploration of visualisation and analogy in learning quantum mechanics in relation to 2nd year undergraduate through to postgraduate has essentially no associated research literature. This study will collect information on students’ understanding of quantum mechanics through observation, interviews, review and problem solving activities, the data will be analysed and interpreted internally and with respect to wider educational literature outlined in the Learning Model section

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CHAPTER 2 - REFERENCES

Ausubel, D.P., (1969) Chapter 3 – Meaningful reception learning and retention. Educational psychology a cognitive view (Holt, Rinehart and Winston), pp83-123

Biggs, J.B., (1978) Individual and group differences in study processes, British Journal of Educational Psychology, 48, 266-279

Driver, R., (1995) Constructivist approaches to science teaching. In L.P. Steffe and J.Gale (Eds.) Constructivism in Education (Hillsdale, NJ:Lawrence Erlbaum Associates), pp385-400

Fischler, H., Lichtfeldt, M., (1990) Learning Quantum Mechanics, ? Proceedings of the International Workshop for Research in Physics Learning : Theoretical Issues and Empirical Studies, University of Bremen (March 4-8, 1991), pp240-258

Fischler, H., Lichtfeldt, M., (1992) Modern physics and students’ conceptions, International Journal of Science Education, 14(2), 181-190

Fuster, J.M., (1999) Memory in the Cerebral cortex: An empirical approach to neural networks in the human and nonhuman primate (MIT Press)

Glassersfeld, E. von, (1989) Cognition, construction of knowledge and teaching. Synthese 80(1), 121-140

Haendler, B.L., (1982) Presenting the Bohr Atom, Journal of Chemical Education, 59(5), 372-375

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Hintzman, D.L., (1978) Comments on the papers by Hunt and by Rumelhart and Norman. In J.W. Cotton and R.A. Klatzhy (Eds.) Semantic factors in cognition (Hillsdale, NJ: Lawrence Erlbaum Associates), pp55-60

Howe, A.C., (1996) Development of science concepts within a Vygotskian framework. Science Education, 80(1), 35-51

Johnston, I.D., Crawford, K.P. and Fletcher, P.R., (1998) Student difficulties in learning quantum mechanics, International Journal of Science Education, 20, 427-446

Keig, P.F. and Rubba, P.A., (1993) Translation of representation of the structure of matter and its relationship to reasoning, gender, spatial reasoning, and specific prior knowledge, Journal of Research in Science Teaching, 30(8), 883-903

Lave, J. and Wenger, E., (1991) Situated learning, legitimate peripheral participation (Cambridge: Cambridge University Press)

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Newman, D., Griffin, P. and Cole, M., (1989) The construction zone: Working for cognitive change in school (Cambridge: Cambridge University Press)

Phillips, D.C., (1987) Chapter 12 – On describing a student’s cognitive structure, Philosophy, science and social inquiry (New York: Pergamon Press) pp137-157

Phillips, D.C., (1995) The good, the bad and the ugly: The many faces of constructivism. Educational Researcher, 24(7), 5-12

Prosser, M., Trigwell, K,. Hazel, E., and Gallagher, P., (1994) Students’ experiences of teaching and learning at the topic level, Research and Development in Higher Education, 16, 305-310

Prosser, M. and Trigwell, K., (1999) Understanding learning and teaching: the experience in higher education (Open University Press, Buckingham)

Redish, E.F., (2004) To be published in The Proceedings of the Enrico Fermi Summer School in Physics Course CLVI (Italian Physical Society, 2004)

Rogoff, B., (1984) Introduction: Thinking and learning in social context. In B.Rogoff & J.Lave (Eds) Everyday cognition: Its development in social context (Cambridge, Massachusetts: Harvard University Press), pp1-8

Rogoff, B., (1986) Adult assistance of children’s learning. In T.E. Raphael (Ed.), The contexts of school-based literacy (New York: Random House), pp27-40

Rogoff, B., (1990) Apprenticeship in thinking: Cognitive development in social context (New York: Oxford University Press)

Roth, K.J., (1990) Chapter 4 – Developing meaningful conceptual understandings in science. In B.F. Jones and L.Idol (Eds.) Dimensions of Thinking and Cognitive Instruction (NCREL/Erlbaum)

Rumelhart, D.E and Norman, D.A., (1981) Analogical processes in learning. In J.R. Anderson (Ed.) Cognitive skills and their acquisition (Hillsdale, NJ: Lawrence Erlbaum Associates), pp335-359

Rumelhart, D.E. and Norman, D.A., (1978) Accretion, tuning and restructuring: Three modes of learning. In J.W. Cotton and R.A. Klatzhy (Eds.) Semantic factors in cognition (Hillsdale, NJ: Lawrence Erlbaum Associates), pp37-53

Rumelhart, D.E., (1980) Schemata: The building blocks of cognition. In R. Spiro, B. Bruce and W. Brewer (Eds.) Theoretical issues in reading comprehension (Hillsdale, NJ: Lawrence Erlbaum Associates)

Scherr, R., (2002) AAPT Announcer 31(4), 92

Shavelson, R.J., (1974) Some methods for examining content structure and cognitive structure in instruction, Educational Psychologist, 11, 111

31

Shuell, T.J., (1986) Cognitive conceptions of learning, Review of Educational Research, 56(4), 411-436

Styer, D.F., (1996) Common misconceptions regarding quantum mechanics, American Journal of Physics, 64(1), 31-34

Summers, M.K., (1976) The analogue computer as an aid to teaching elementary quantum mechanics, Physics Education, 11(4), 296-302

Tsaparlis, G., (1997) Atomic orbitals, molecular orbitals and related concepts: Conceptual difficulties among chemistry students, Research in Science Education, 27(2), 271-287

Wise, M.N., Kelley, T.G., (1977) Fundamental quantum mechanics – a graphic presentation, American Journal of Physics, 45(4), 384-394

Note: For a comprehensive categorised literature bibliography covering quantum mechanics please refer to Appendix 8 for a Quantum Chemistry Literature Survey and Appendix 9 for a Quantum Physics Literature Survey.

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CHAPTER 2................................................................................................................................. 11

QUANTUM MECHANICS AND SCIENCE EDUCATION LITERATURE REVIEW...................112.1 INTRODUCTION...........................................................................................................112.2 CHEMISTRY RELATED................................................................................................11

2.2.1 Chemistry – History & Teaching of Ideas and Concepts Papers...............................................132.2.2 Chemistry – Education Research Papers..................................................................................132.2.3 Chemistry – Papers..................................................................................................................15

2.3 PHYSICS RELATED......................................................................................................152.3.2 Physics – History, Philosophy and Interpretation of Quantum Mechanics................................162.3.3 Physics – Teaching of Specific Concepts.................................................................................162.3.4 Physics – Teaching Materials...................................................................................................182.3.5 Physics – Education Research..................................................................................................18

2.4 THEORETICAL FRAMEWORK OF LEARNING – A LEARNING MODEL....................212.4.1 Learning..................................................................................................................................212.4.2 Constructivism.........................................................................................................................222.4.3 Model of student learning........................................................................................................232.4.4 Cognitive structures.................................................................................................................24

2.5 IN RELATION TO CURRENT INVESTIGATION.......................................................27

Figure 2-1 : Presage – Process - Product Model of student learning. Adapted from Prosser, Trigwell, Hazel and Gallagher (1994)..................................................................................................24