learning and teaching science as inquiry: a case study of elementary school teachers'...

SCIENCE TEACHER EDUCATION

Mark Windschitl, Section Editor

Learning and Teaching Scienceas Inquiry: A Case Study ofElementary School Teachers’Investigations of Light

EMILY H. VAN ZEEScience Teaching Center, University of Maryland, College Park, MD 20742, USA

DAVID HAMMERDepartment of Physics and Science Teaching Center, University of Maryland,College Park, MD 20742, USA

MARY BELL, PATRICIA ROYPrince George’s County Public Schools, Upper Marlboro, MD 20772, USA

JENNIFER PETERMontgomery County Public Schools, Rockville, MD 20850, USA

Received 13 June 2003; revised 6 August 2004; accepted 27 August 2004

DOI 10.1002/sce.20084Published online 7 October 2005 in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: This case study documents an example of inquiry learning and teaching dur-ing a summer institute for elementary and middle school teachers. A small group constructedan explanatory model for an intriguing optical phenomenon that they were observing. Re-search questions included: What physics thinking did the learners express? What aspectsof scientific inquiry were evident in what the learners said and did? What questions did thelearners ask one another as they worked? How did these learners collaborate in constructing

Correspondence to: Emily H. van Zee; e-mail: [email protected] grant sponsor: National Science Foundation.Contract grant number: 99-86846.The opinions expressed are of the authors and do not necessarily represent those of the funding agency.

C© 2005 Wiley Periodicals, Inc.

1008 VAN ZEE ET AL.

understanding? How did the instructor foster their learning? Data sources included video-and audio- tapes of instruction, copies of the participants’ writings and drawings, field notes,interviews, and staff reflections. An interpretative narrative of what three group memberssaid and did presents a detailed account of their learning process. Analyses of their utter-ances provide evidence of physics thinking, scientific inquiry, questioning, collaborativesense making, and insight into ways to foster inquiry learning. C© 2005 Wiley Periodicals,Inc. Sci Ed 89:1007–1042, 2005

INTRODUCTION

My experience in science has been quite negative . . . Physical science in college was anightmare. This course is helping me rethink science . . . Science is not this big monster tofear but . . . ideas that can be challenged . . . I don’t feel I have to know a right or wronganswer but that I can explain what, why, how I’m thinking . . .

(Patricia Roy, journal, summer 2001)

Elementary school teachers often have negative attitudes toward science. In the journalexcerpt above, for example, Patricia Roy, a third-grade teacher, noted that such attitudes oftenreflect difficulties experienced as science learners. This paper presents an example of physicsinstruction that helped change her attitudes. She and her colleagues participated in a summerinstitute in which they explored the physics of light. They had had extensive everydayexperience with light but initially little formal, coherent knowledge about how people see.Together, however, they constructed explanations of optical phenomena that made senseboth to themselves and to physicists. The story of these teachers’ experiences in the summerinstitute exemplifies recent trends in science education reform: careful documentation ofstudent learning, in this case, about light; design and implementation of inquiry-basedscience courses for teachers; and discourse studies that focus upon questioning processesand collaborative sense making during science instruction.

Student Learning About the Nature of Light

Researchers have investigated student understanding of the nature of light by analyzingresponses in a variety of contexts such as questionnaires (Anderson & Karrqvist, 1983),computer simulations (Reiner, 1998), clinical interviews (Goldberg & McDermott, 1987;Guesne, 1985), class discussions (Brickhouse, 1994; Fetherstonhaugh & Treagust, 1992),and museum exhibits (Rice & Feher, 1987). Many of these studies have focused upon“misconceptions” or “alternative frameworks,” that is, on ways in which students’ ideasdiffer from those of physicists. Issues include whether light is a static entity that fills spaceor something that travels, how light interacts with objects and with other light sources,where an image is located, and how people see luminous and nonluminous objects. Manyof these investigators also explored students’ ideas about shadows.

Some investigators have designed instruction based upon their findings. Linn and Hsi(2000), for example, documented ways that computers could be used as “lab partners” toscaffold students learning from one another. They traced the evolution of a light curriculumdesigned to engage students in assembling evidence in support of arguments. Building uponthis curriculum, Bell and Linn (2000) developed ways for students to use the World WideWeb to debate issues such as “How Far Does Light Go?”

Bendall, Goldberg, and Galili (1993) identified two key ideas held by prospective ele-mentary school teachers who participated in their research: (a) “from each point on a source

LEARNING AND TEACHING SCIENCE AS INQUIRY 1009

light goes out preferentially in one direction” rather than in all directions and (b) “lightspreads out with distance from the source” (p. 1184). They hoped to foster conceptualchange with a discrepant event that would prompt the prospective teachers to reconsiderthe first idea. They viewed the second idea as a resource that could be used to show theprospective teachers that “many aspects of their initial thinking are valuable” when appliedin appropriate contexts (p. 1184). We share this perspective of building upon useful intu-itions in designing instruction that assists students in refining their ideas (Smith, diSessa,& Rochelle, 1993; Hammer, 2000).

Interpreting videotapes of instruction can yield detailed accounts of the learning process.Shapiro (1994), for example, developed complex case studies of six fifth-grade students’experiences in learning about light. She showed them videotapes of their class in action andasked them to talk about what was happening. One of the lessons was similar to the activityinterpreted below. The students viewed the apparent bending of a pencil placed partly in aglass of water. They also placed a coin in a saucer, crouched down until the coin was nolonger visible, and then observed the coin appear to rise into view when water was pouredinto the saucer. Shapiro used these and other contexts to ask the students to reflect upontheir thoughts and feelings about learning science.

Inquiry-Based Science Courses for Teachers

The National Science Education Standards (National Research Council, 1996) recom-mends that science courses for teachers in the United States be inquiry based so that teachersexperience themselves the approach to instruction recommended for students (p. 59). As-pects of inquiry identified in the standards include the following:

Inquiry is a multi-faceted activity that involves making observations, posing questions,examining books and other sources of information to see what is already known; planninginvestigations; reviewing what is already known in light of experimental evidence; usingtools to gather, analyze, and interpret data; proposing answers, explanations, and predictions;and communicating the results. Inquiry requires identification of assumptions, use of criticaland logical thinking, and consideration of alternative explanations.

(NRC, 1996, p. 23)

Some examples of inquiry-based instruction are provided in a second document, Inquiryand the National Science Education Standards (NRC, 2000).

Many efforts to design inquiry-based courses have involved a shift from large lectures, inwhich students sit quietly while listening to an instructor present information, to laboratory-centered courses, in which students work in small groups while conversing with one another,and occasionally with the instructor, as they explore natural phenomena. Examples includePowerful Ideas in Physical Science (American Association of Physics Teachers, 2001),Modeling Instruction in Physics (Hestenes, 1997), Workshop Physics (Laws, 1991), andPhysics by Inquiry (McDermott, 1990, 1996).

All of these curricula are designed both to guide students toward target conceptual un-derstanding and to foster practices of scientific reasoning. The materials vary in tone andemphasis with respect to coordinating these agendas, but all involve students in “interactiveengagement” (Hake, 1998). Much of the success of these courses depends on that engage-ment, on how instructors facilitate, recognize, and respond to student reasoning. Developersof interactive engagement curricula typically offer workshops for instructors to help themlearn new strategies of attending and responding to student thinking, and they offer general

1010 VAN ZEE ET AL.

advice for working with students, largely to help instructors learn to shift from explainingideas to posing questions.

That is a difficult shift, to move past “telling,” but it is not sufficient (Chazan & Ball, 1999).Effective instruction is more subtle than that involving judgments on several levels specificto particular moments (Barnett & Hodson, 2001). These judgments take place constantly,such as when instructors circulate among small groups, listen in on conversations, perhapsask questions, all the while gaining information about what students are thinking and howthey are approaching a task. Instructors interpret that information and use it to diagnose thestrengths and weaknesses of their students’ work. These ongoing, formative assessmentsare usually tacit, but they drive how instructors respond (Atkin, Black, & Coffey, 2001). Inthese reformed practices, instructors’ expertise is not typically evident in the cogency ofexplanations they deliver but rather in the insightfulness of their interpretations of studentreasoning and in the wisdom of their choices about what to say or do to help.

Instructors who attempt these reformed curricula often experience tension betweenpromoting canonical understanding and fostering scientific inquiry (Hammer, 1995). Formost, conceptual errors are more salient and disturbing; “inquiry” is more difficult to de-fine, let alone assess. As a result, implementations of reformed curricula tend to empha-size canonical understanding, teaching science by inquiry more than science as inquiry(Hodson, 1988).

This is a case study of students’ reasoning and an instructor’s interpretations and res-ponses, the students in this case being elementary teachers in a National Science Foundation-supported project. They were taking a course in physics during a summer institute that,like the reformed curricula above, emphasized student thinking. The environment and thelearning activities were similar, but the emphasis in this course was deliberately shiftedtoward inquiry. The participants did not work through handouts that had been preparedbefore class; that is, there was not a formal curriculum. Instead, the lead instructor drewfrom a framework he had developed for a course entitled How to Learn Physics (Hammer& Elby, 2003). That course, as the account below will reflect, has an explicit emphasis oncultivating productive beliefs about knowledge and learning in science. Because there wasno fixed set of materials, the instructor could make choices specific to the students’ ideas;the “curriculum” emerged from the group’s discoveries and the instructor’s knowledge ofrelevant issues and effective ways to explore these.

Studies of Discourse During Science Instruction

The National Science Education Standards (NRC, 1996) calls for a shift from science as“experiment and investigation” to science “as argument and explanation” (p. 113). Viewingscience as argument has many implications for teaching and learning scientific thinking(Kuhn, 1993). Driver, Newton, and Osborne (2000) set forth a research agenda for es-tablishing norms of scientific argumentation in classrooms. Researchers have designedinterventions to help students develop scientific communities (Herrenkohl et al., 1999) andto foster students’ collaborative scientific reasoning (Hogan, 1999).

During small group work and whole group discussions, students display their thinking bywhat they do and say. Critical in this approach to instruction is understanding how to engagestudents in discourse that fosters their progress (Bereiter, 1994; Gallas, 1995; Lemke, 1990;Polman & Pea, 2001; Simpson, 1997). Questioning is an important component of suchconversations about science (Iwasyk, 1997; Roth, 1996; van Zee et al., 2001). van Zee andMinstrell (1997a, 1997b), for example, documented the reflective discourse that Minstrellencouraged in his high school physics classes. Reflective discourse occurred when studentsexpressed what they were thinking rather than recited what a textbook said, the teacher


engaged students in an extended series of exchanges to develop their ideas, and studentstried to understand one another’s thinking.

An advantage of small group work is that students can collaborate in developing argu-ments and explanations and in reconsidering their ideas. Roschelle (1992), for example,documented convergent conceptual change as a pair of students worked through recurringcycles of displaying, confirming, and refining shared meanings. Meyer and Woodruff (1997)studied ways in which seventh graders worked together to develop “consensually drivenexplanations” of light and shadow effects. They identified three mechanisms for developingsuch explanations: mutual knowledge, convergence, and coherency.

Interpreting student thinking during vigorous discussions is a complex process, bothin-the-moment of teaching and later in viewing video of what was happening (diSessaet al., 1991; Hammer, 1995; van Zee, 2000). We articulate below a detailed account of avideotaped example of physics learning in which the learners, with assistance from theinstructor, engaged one another in developing an explanatory model for what they wereobserving.

Research Questions

This case study examines closely an instance of inquiry learning and teaching in whicha small group of learners collaborated in constructing an explanatory model of a physicalphenomenon. In spite of a vast literature on student thinking about the nature of light, thereare few examples of student inquiry in this context. The case study provides an examplefor physics faculty and others interested in this approach to learning and teaching. Carefulanalysis of what went well and why in a particular instance may help others think aboutwhat to look for in engaging their students in inquiry. Learning how to recognize positiveaspects of collaborative student inquiry can help instructors to support it.

In developing this case study, we were interested in several closely related aspects ofinquiry learning and teaching. Specifically, we asked:

• What physics thinking did the learners express?• What aspects of scientific inquiry were evident in what the learners said and did?• What questions did the learners ask one another as they worked?• How did these learners collaborate in constructing understanding?• How did the instructor foster their learning?

Note that these are not independent questions. We think of inquiry as part of physics think-ing and questioning as part of inquiry and all of these as occurring in collaborative settingsdesigned and enacted by effective instructors. We have chosen to focus on these aspects ofscience learning because they are central to deepening our own and others’ understandingof what it means to learn and teach science as inquiry. Our objectives were that the par-ticipants come to new understandings not only of light and vision but also of what inquiryentails.

METHODOLOGY

Qualitative Approach

This case study is in the tradition of ethnography of communication (Hymes, 1962,1972; Philipsen, 1992). Ethnographers of communication examine cultural practices byinterpreting who says what to whom, when, where, how, and why. They look for patterns in

1012 VAN ZEE ET AL.

ways of speaking among members of a “speech community,” individuals who share commonlinguistic practices in some way. Such patterns can provide insights into the cultural valuesof the community. Of particular interest are instances in which a pattern is articulatedexplicitly, as sometimes occurs when someone comments upon a violation of the patternby a less experienced member of the community or by an outsider. For example, a patterndiscernable in the instructor’s speech was consistent use of the word “reflect” to refer tolight bouncing off an object and the absence of such use in situations involving light passingthrough a surface between two media such as air and water. This pattern is indicativeof a speech community in which many words have precise meanings and precision oflanguage is valued. We selected one of the episodes to present here because the instructorcommented upon this pattern explicitly in the midst of a conversation with a small group ofthe participants. Later, one of the participants corrected her own use of the word “reflect”as she was explaining her thinking. Thus this study illustrates the evolution within a speechcommunity formed by learners, from everyday language toward more scientific ways ofspeaking.

This is a focused exploration (Philipsen, 1982) of learners’ collaborative developmentof an explanatory model in physics. The framework guiding analysis included physicsthinking, scientific inquiry, questioning, and collaborative sense making. The naturalisticsetting was a summer institute in which elementary and middle school teachers exploredoptical phenomena. Participants in this case study included a small group of three elementaryschool teachers, the lead instructor, and the researcher. Data sources included video- andaudio- tapes of instruction, copies of the participants’ writings and drawings, field notes,interviews, and staff reflections. This case study presents an annotated example of inquiry-based instruction for interested instructors and adds to the corpus of data available forformulating and evaluating more theoretical perspectives.

Setting. The summer institute met 9:00 a.m. –3:30 p.m., Monday–Thursday, for 3 weeks.The institute was part of a 3-year project supported by a grant from the National ScienceFoundation. This project involved the participants in developing case studies of their stu-dents’ inquiries into physical science. During the mornings of the summer institute, theparticipants worked on writing and refining their case studies, from data collected in theirclassrooms during the prior academic year. During the afternoons, they learned physics.They primarily worked in small groups on questions such as “how much of yourself can yousee in a small mirror? How much can you see if you move the mirror twice as far away?”They also gathered periodically for whole group discussions. The emphasis was on talkingtogether to make sense of what they were thinking and seeing, to develop a model for lightthat they could use to predict, and explain a variety of optical phenomena.

Participants. The small group that is the focus of this case study was selected by their deci-sion to sit at the table nearest a video camera. Mary Bell, an elementary reading teacher, andJennifer Peter, an elementary math teacher, were in their second year in the project. PatriciaRoy, a third-grade teacher, had just joined the project. Jennifer and Pat were sitting acrossfrom one another. Mary was between them, at one end of the table. Another small group wasworking close by, at the other end of the table. The lead instructor, David Hammer, is an as-sociate professor of physics and science education. His instructional approach emphasizeslearners’ ideas and ways to develop these through discussion and exploration (Hammer,1995, 2000; Hammer & Elby, 2003). The researcher, Emily van Zee, is an associate pro-fessor of science education. She studies collaborative discourse during conversations aboutscience (van Zee, 2000; van Zee et al., 2001; van Zee & Minstrell, 1997a, 1997b). Mary


and Pat were enrolled in a Master’s program in Teacher Leadership for which Emily wasan instructor.

Selection of Activity for Analysis. This case study focuses upon an activity duringthe first day of the third week of the Institute. The three teachers, with little formal back-ground in physics, constructed the essence of a textbook account of an intriguing opticalphenomenon that is one of the classics of instruction in the physics of light. The analysisof their collaboration provides a detailed account of physics learning in this context.

The session had five major segments: whole group discussion that re-created the contextfor thinking about light, small group exploration of an intriguing phenomenon, whole groupdiscussion of findings, additional small group work, and individual writing of reflections.This paper presents a detailed analysis of about 10 min during the second segment. Weselected this excerpt because it is a good example of group members coming to agreementabout an idea and then drawing an inference on that basis. The excerpt includes smallgroup interactions both with and without the instructor. It begins with the group members’articulation of two points of view and traces some of their efforts to reconcile these. It alsoincludes their attempts to draw visual representations of what they were observing as wellas several explorations that they initiated within the context established by the instructor.This is an example of “doing well” at scientific inquiry. The case study is an attempt tounderstand and articulate what “doing well” entails.

Division of Transcript into Episodes. Emily began constructing the analysis by sum-marizing the whole group discussion and by dividing the small group exploration intoepisodes that seemed to represent conceptual entities. Table 1 lists the episodes interpretedhere. She divided the transcript into episodes based upon her perceptions of shifts in focusin what the small group members were saying and doing. She began Episode 1, for example,with an utterance in which one of the group members, Mary, proposed a new idea to explainthe phenomenon they were exploring. This was the beginning of a series of utterances andactions in which the group members considered this idea. Emily chose to end the episodewith an utterance in which Mary articulated a question. She chose to end the episode therebecause this was the moment that another group member, Jennifer, reached for a notebook

TABLE 1Steps in the Collaborative Construction of Consensus About a ParticularIdea

Episode 1 Noticing an important aspectEpisode 2 Sketching a visual representationEpisode 3 Enhancing a visual representationEpisode 4 Tracing the path of lightEpisode 5 Becoming more precise in the use of languageEpisode 6 Identifying two different ideasEpisode 7 Doing “what if” thinkingEpisode 8 Trying things out/Sketching a modelEpisode 9 MeasuringEpisode 10 Constructing a modelEpisode 11 Continuing to examine the situationEpisode 12 Pondering connections among phenomenaEpisode 13 Positing a “foothold” and making an inference based on that idea

1014 VAN ZEE ET AL.

and started sketching a diagram, That act was the beginning of a new direction of thinkingthat is presented in the second episode. Also there was an interruption from a neighboringgroup at this point that created a natural break in the dialogue.

Narrative Interpretation. Emily developed a narrative interpretation by adding com-ments to the transcript to help the reader follow the story of what the participants saidand did. In crafting a title for an episode, she tried to convey the progress that the groupmembers were making. For example, during the first episode, one of the group members,Pat, stated “So angle has something to do with it.” This was an explicit articulation ofan important aspect of the phenomenon they were exploring. Emily drew attention to thisprogress by titling the episode “Noticing an important aspect.” She titled the second episode“Sketching a visual representation” because this describes the progress one of the groupmembers, Jennifer, initiated by drawing a diagram to represent how she was interpretingwhat she was seeing.

In the transcript below, an ellipse of three dots . . . indicates omitted words. [Text inbrackets adds explanatory information.] (Text in parentheses was difficult to hear and maynot be correctly transcribed.) Underlining directs attention to utterances that illustrate theinterpretation presented.

Construction of Tables of Evidence. Emily also constructed tables that presented herinterpretations of each utterance. An example from Episode 1 is shown in Table 2. For eachutterance, she considered ways in which the thought expressed the participants’ emergingphysics understandings, instantiated an aspect of scientific inquiry, formed a question, and/orcontributed to collaborative sense making. Next she summarized the participants’ physicsthinking across all of the episodes. In Tables 3–5, she identified utterances that provideevidence of scientific inquiry, questioning, and collaborative sense making across all of theepisodes. In addition, she summarized the interactions of the instructor with the small groupmembers.

Emily identified questions by using a framework based on grammatical forms (Saha,1984). The framework included utterances that ended with a rising intonation (e.g., you do. . . ?), began with an interrogative word (e.g., what . . . ?), began with a verb (e.g., do you. . . ?), ended with a tag ( . . . , isn’t it?), or had a disjunctive form (e.g. you do or do not . . .).She also included statements that articulated questions such as “And I don’t know how to saythat” and “I wonder if . . . ” For each question, she articulated the function it seemed to serve.She examined whether categories developed in an earlier study (van Zee & Minstrell, 1997a,1997b) were useful in this new context. In the earlier study, she had examined questionsMinstrell asked to help his high school physics students develop shared understandings. Thisteacher thought of himself as “negotiating meaning” with his students. Many of his questionsmirrored recommended practices for successful negotiations: (a) making meanings clear(such as “now what do you mean by “average” here?”), (b) exploring various points of viewin a neutral and respectful manner (such as “if you were to take the arithmetic average ofthese numbers, what would you do?”), and (c) monitoring the discussion and their ownthinking (such as “does that make sense?”). Note that “making meanings clear” is one ofmany ways to explore various points of view and is a form of monitoring the discussion.Thus some questions are representative of more than one category.

In considering ways in which each utterance was connected to other utterances as evidenceof the participants’ collaborative sense making, Emily built upon an earlier analysis ofa student-generated discussion (van Zee, 2000). She had classified utterances into fivecategories: referring explicitly to previous speakers (such as “as (student name) says”),


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1016 VAN ZEE ET AL.

TABLE 3Evidence of Participants’ Engagement in Scientific Inquiry

Aspects mentioned in National Science Education Standards descriptionof inquiry (NRC, 1996, p. 23)

Making observations Proposing explanations[Utterances 1.7–1.8, 2.4, 6.8, 7.2–7.7,

7.15–7.22, 9.5, 9.11, 13.1–13.10][Utterances 2.9–2.14, 10.1–10.14;

13.11–13.18]Posing questions Proposing predictions[Utterances 1.1–1.3, 1.13, 2.2–2.3, 2.6,

7.2, 7.5, 9.4–9.5, 10.15, 11.10, 11.13,12.1–12.2, 12.9]

[Utterances 1.11–1.12, 7.4–7.5,7.11–7.14, 9.7–9.10]

Examining books and other sources ofinformation to see what is already known

Communicating the results(no utterances)

(no utterances)Planning investigations Identifying assumptions[Episodes 7, 8, 9, 11] (no utterances)Reviewing what is already known in light of

experimental evidence[Utterances 10.1–10.6]

Using critical and logical thinking:Considering an extreme case (1.7)Reasoning by analogy (1.6, 11.4, 11.16),

Using tools to gather, analyze, and interpretdata

Considering whether two quantities areequal (1.13, 2.6)

[Episode 9]Proposing answers Proposing alternative explanations[Utterances 11.1–11.4] [Episodes 1, 11]

Aspects not explicitly mentioned in NSES descriptionUsing visual representations Trying to measure change[Episodes 2, 3, 8, and 10] [Episodes 8 and 9]

relating directly to previous utterances (such as “You made an observation at the sametime?”), reflecting upon one’s own thinking (such as “I think I have at least a few thingsfigured out”), monitoring the discussion (such as “Okay, that makes sense because . . . ”),and acting (such as asking permission: “Can I draw a picture of what you said?”

Member Checks. Periodically Emily checked her interpretations with the three groupmembers and lead instructor and made modifications as needed. Interpreting collaborativetalk can be difficult, however, even for the speakers themselves when reviewing their owncomments later. Particularly troublesome are referents for the many “it”s that typicallyoccur in discourse among interlocutors who know one another well and who are engaged inshared activities. Where speakers could not clarify the meaning of their utterances severalinterpretations are provided.

INTERPRETATIVE NARRATIVE

We have selected an example of a collaborative process that we consider to be importantduring inquiry approaches to learning and teaching: coming to consensus about a particularidea. We present and discuss below this on-going conversation as a coherent entity sothat the reader can get a sense of what happened. This narrative approach contrasts withpresenting and discussing disconnected excerpts of dialogue in support of a set of claimsthat the researcher has developed from the data. The commentary below also provides an


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nce

5.13

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TABLE 5Examples of Evidence of Collaborative Sense Making

CollaborativeSense Making Utterances

Referring explicitly toprevious speaker

2.1 Pat: Mary, what were you saying?

Relating directly toprevious utterances

Providing a correspondence in support of a colleague’sanalogy

1.4 Jenn: See, I was thinking (the water was) like amagnifying glass.

1.6 Pat: Yeah, because you’re able to still see through it butit’s at a bend

Offering an element of an explanation in response to acolleague’s question

10.15 Mary: The question is why does this look up.11.1 Jenn: There’s something with the top surface, the

surface of the water.Confirming and elaborating a colleague’s suggested

explanation11.2 Mary: Yeah, cause that’s what’s causing the bend.

Reflecting upon one’s ownthinking

Referring to one’s own prior statements7.19 Mary: That’s what I was saying. Yeah, it almost looks

like it disappears.Confirming one understands what another is trying to do8.13 Pat: I think I know what you are trying to see.Explaining what one was trying to do9.5 Jenn: I was trying to see if we could tell that it really does

look up higher.Monitoring the discussion Completing the prior speaker’s utterance

1.1 Mary: Could the water be acting like a1.2 Jenn: a magnifying glass?Requesting confirmation that one has been understood1.14 Mary: You know what I mean?Requesting information about what a colleague is seeing8.7 Pat: What’s happening?

Acting Telling another what to do13.3 Jenn: But move your head, move your head and then it

changes.

example of the kind of thinking one might encourage in a professional development settingby showing a video clip of learners in action and inviting participants to consider: How dowhat the speakers say and do contribute to the group’s evolving understanding? The videoanalyzed here is available from the first author. The session opened with a whole groupdiscussion in which the lead instructor re-created the context for thinking about light. Thenthe small groups explored an intriguing optical phenomenon.

Re-Creating the Context for Thinking About Light

The main purpose of instruction during the summer institute was to promote the partici-pants’ coming to understand and approach science as “the refinement of everyday thinking”(Einstein, 1936). In particular, the instructors hoped the participants would see and approach


learning as starting from their everyday sense of causes and effects---tangible ideas and ex-periences of physical phenomena---as emphasized in accounts of intuitive physics (diSessa,1993) and elementary science teaching (Newton, Driver, & Osborne, 1999). Starting with“everyday thinking” the “refinement” is toward consistency, first among ideas that mayconflict and ultimately with respect to a principled framework. In this respect, the coursereflected emphases in the literature on argumentation (Kuhn, 1993; Driver et al., 2000).

David based the summer workshop on a course he had developed for nonscientists, with anexplicit focus on students’ “epistemologies”: How students think about what knowledge,reasoning, and learning entail (Hammer & Elby, 2003). This focus is represented by avocabulary for talking about aspects of knowledge and reasoning. During the first week ofthe summer institute, for example, he had invited the participants to shop for ideas that theyalready had about light: What did they know and how might they use this knowledge tomake predictions and explain findings?

By the end of the second week of the summer institute, the participants had developed a setof foothold ideas that seemed to work pretty well in explaining their findings in explorationsof mirrors, pinhole cameras, and lenses. A foothold idea is something one chooses to acceptas true, at least for a moment, and use as a basis for further thinking, like a temporaryfoothold that helps a rock climber move higher. This contrasts with a hidden assumptionthat one makes without realizing it. The notion of a foothold brings with it the importanceof precision---everyone should share an understanding of what the idea is. It also carries asense of some level of commitment, whether the foothold is a tentative supposition or anidea that must be true. For example, a foothold idea that the participants had developed inearlier sessions was initially that light travels in straight lines; they modified it later to allowfor phenomena of reflection and refraction.

In addition to shopping for ideas from previous experiences that might be relevant andadopting temporary footholds that seem useful, David encourages learners to begin rec-onciling ideas that seem in conflict with one another or with observations. As tentativefootholds prove to be consistent with other ideas and observations, and useful as elementsof an explanatory model, they move to higher levels of commitment. In this way, a processof inquiry can lead to high commitment footholds, and this is a way of understanding thedevelopment of scientific principles.

During the opening discussion, David and the participants reviewed the working set offoothold ideas that they had developed during the previous sessions. By the end of thatreview, they had discussed the following:

• Light travels in straight lines unless something happens to make it do otherwise.• If you see an object, it is because light either originated there or reflects off of it and

hits you in the eye; light travels from that object to the eye.• An image happens [appears on a screen] if there is a one-to-one correspondence

between the object and the screen.• Light sprays out from a point on an object in all directions.

The participants had developed these foothold ideas through their discussions of variousoptical phenomena during the previous 2 weeks. David had begun to refer to the set as amodel. During the opening discussion of this session, the group reviewed the meaning ofthese foothold ideas and the explanation they provided for pinhole cameras and convexlenses, complete with ray diagrams for these devices.

After some discussion among the full group, David introduced the day’s new activity.Earlier, a participant had raised the question of why a pencil in a glass of water appears

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bent. David had recognized this as one of a “menu of options”1 that he could choose topursue at that or another time. Today was the day they would explore that question and arelated intriguing optical phenomenon.

Exploring an Intriguing Optical Phenomenon

About 20 min into the session, David chose to shift from what had become a vigorouslarge group discussion to small group explorations. This involved setting up an intriguingactivity. Each small group had cups, a straw, and some water. David suggested two thingsto do: observe what happens when a straw is placed in a cup of water and also observewhat happens when a dot is drawn on the inside of a cup and the cup is filled with water.He explained that he wanted the participants to try to use the foothold ideas about lightthat they had been developing to explain what they were seeing. Although most, if not all,of the participants were familiar with seeing a straw seeming to bend when placed in water,they acted surprised when they saw the dot on the side of the cup seem to rise as water waspoured into the cup. After the small group members had observed the apparent rising of thedot, David explicitly articulated the issue that he wanted them to consider:

David: [The dot] sort of floats up a little bit.

So can you account for that using our model?

The episodes below present the details of this small group’s conversation. Working ontheir own, the group members noticed an important aspect of the situation. Jennifer sketcheda visual representation to explain her understanding of the phenomenon to her colleagues.Later, with David’s assistance, they enhanced the visual representation, traced a path ofthe light, clarified the language they were using, and identified two different ideas that hademerged during their conversation. After David left the group to converse with others, theseparticipants engaged one another in doing “what if” thinking, trying things out/sketching,measuring, constructing a model, continuing to examine the situation, pondering connec-tions among phenomena, positing a new foothold and making an inference based on that idea.

Episode 1: Noticing an Important Aspect. The three group members had been work-ing together for about 10 min when they compared what they were seeing now with thestraw in a cup of water with what they had seen in earlier sessions:

1.1 Mary: Could the water be acting like a1.2 Jenn: A magnifying glass?1.3 Mary: No, like a mirror.1.4 Jenn: See, I was thinking like a magnifying glass.1.5 Mary: Okay, well

Mary and Jennifer both were shopping for ideas in the sense that they were trying to makeconnections to their earlier experiences in order to understand this new phenomenon. Thisbegan an on-going discussion about whether a mirror or a lens was the appropriate analogyfor this situation.

1 The participants in the project had developed a way of thinking about instructional decisions thatincluded this notion of a “menu” of possibilities in any particular moment.


Then Pat and Mary both made moves to reconcile these two different views. Pat noted acorresponding element in the analogy that Jennifer was suggesting

1.6 Pat: Yeah, because you’re able to still see through it but it’s at a bend.

Mary focused their attention upon what happened in an extreme case:

1.7 Mary: It doesn’t bend though when you put it straight down.1.8 Do you see it bending? The straw?

Mary’s use of the word “though” suggests she intended this statement to counter the claimthat the water was acting like a lens. She may have been thinking about a light ray travelingperpendicularly from an object to a mirror, that is represented as bouncing straight backfrom the mirror.

This prompted Pat to identify an important aspect of this phenomenon:

1.9 Pat: Right, so angle has something to do with it. <Yeah>

She seemed to be referring to the angle at which the straw was placed in the water and tomean that this has something to do with how much the straw appeared to bend.

Jennifer elaborated on Pat’s thought:

1.10 Jenn: It changes the angle

Understanding what she meant here is problematic. She may have been referring to “theway the straw is placed in the water” and meant that this changes how big the angle isthrough which the straw appears to bend. Or she may have been referring to “the water”and meant that the water changes the angle which the straw appears to make with respect tothe horizontal surface of the water. The first meaning relates to a condition, how the strawis placed; the second meaning relates to a mechanism, what causes the apparent changein angle. These ambiguities might have been explored had a staff member been listeningclosely to this small group conversation.Pat followed up her thought about angles with a prediction:

1.11 Pat: Well, you know what, I bet it would bend,1.12 depending on how you look at it.

This introduced a different variable to be considered, the observer’s position, in addition tothe angle at which the straw was placed in the water.

Then Mary articulated a question:

1.13 Mary: But, is it the same angle that it’s going in at?1.14 You know what I mean?

Mary seemed to return to her thought about mirrors and a foothold idea that an incidentray bounces off at the same angle at which it hits the mirror. She seemed to be wonderingwhether that was the case here.

In this episode, the group members made progress by trying to apply what they hadlearned earlier to this new situation. Their dialogue provides good examples of ways to tryto reconcile alternative views: suggesting corresponding elements of a relevant analogy,

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examining an extreme case, identifying an important aspect of the situation, consideringthe role of the observer, and posing a question based upon one of the views.

Episode 2: Sketching a Visual Representation. As Mary finished stating her ques-tion (1.13), Jennifer reached for her notebook and pen and started sketching what she wasseeing. After a joshing interruption from neighboring colleagues, Pat directed their attentionback to Mary’s question:

2.1 Pat: Mary, what were you saying?2.2 Mary: I’m saying that if you’re putting it in straight,2.3 do you see it bend? [placing straw in water straight down]2.4 Pat: No [looking down on straw from above]2.5 Mary: Okay. So you have to put it in at an angle <right>2.6 So I’m saying, the angle that’s in the water, is it the same?2.7 [overlapping speech that can not be interpreted]2.8 Jenn: The angle changes when the water comes up.

Jennifer was describing what she had been seeing as water was poured into the cup. It isnot clear whether she was thinking about the same angle as Mary.

Rather than trying to understand a puzzling diagram someone else had drawn in a book,Jennifer constructed her own diagrams. She used them to explain to her colleagues herunderstanding of the phenomenon of the dot appearing to rise as water was poured into thecup. First she drew a sketch of the dot and cup without water:

2.9 Jenn: Right now with no water [sketching Figure 1A]2.10 there’s a dot in there <um hmm>2.11 And the light goes straight to your eye, right? <yup>2.12 Right? <um hmm>

She was drawing from her perspective of looking down on the cup from a position aboveand to the side. As shown in Figure 1 (left), she drew a square U-shape to represent the sidesof the cup as seen from the side and a line roughly in the shape of an ellipse to represent thecircular shape of the top of the cup as seen from above and to the side. She placed a dot inthe lower half of the ellipse to represent the dot on the inside of the cup as seen through thetop of the cup. She drew a line straight from the dot to the eye of an observer to representlight traveling from the dot to the eye. Then she continued:

2.13 Jenn: With water, here’s the cup rim <um hum> [sketching Figure 1B]2.14 That’s the water surface. <um hum> It makes it bend <right>

The “it”s are problematic here. She may have been thinking the surface of the water causesthe light to bend. That would support the second interpretation of her ambiguous commentin 1.10.

In the sketch with water (Figure 1, right), Jennifer drew lines that went straight from thedot to the surface of the water, bent at the surface, and then went straight to the eye of anobserver. She recognized, however, that the way she had sketched the dot and water surfacewas problematic

2.15 Jenn: . . . So this looks, well this drawing’s no good.


Figure 1. Jennifer’s drawing of path of light to observer’s eye from dot in cup with no water (on left) and withwater (on right).

Her attempt to represent the three-dimensional cup of water made it hard to perceive whereon the cup the dot was and where the bend was occurring. However, she had produced acredible description of what was happening.

Mary, however, did not understand how this sketch related to the issue of whether thewater was acting like a lens:

2.16 Mary: . . . I still don’t understand though how that compares to the lens.

Mary’s comment prompted the group members to find a magnifying glass and use it tolook at the dot in the cup with and without water. These learners designed this spontaneousexploration within a context established by the instructor. Presentation of that dialogue isomitted here, however, because of space constraints.

Episode 3: Enhancing a Visual Representation. About 10 min later, the lead in-structor joined these group members as they and a neighboring group were laughing andcommiserating about how complicated the situation was, particularly when the other grouphad been looking at the phenomenon with a glass jar rather than paper cup. David chose tohelp clarify by reviewing what was known:

3.1 David: So we know that if you don’t have any water in there,3.2 light leaves the dot <um hmm>3.3 having reflected off of it3.4 Mary: and goes straight to your eye3.5 David: And goes straight to your eye <right>3.6 Now you pour water in there <right>

[turning to Jennifer who was pointing to the sketches on her paper]3.7 Oh, so what is that showing?

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Jennifer described her understanding of what was happening:

3.8 Jenn: The dot hits the end of the water, this right here,3.9 [pointing to the surface of the water in the cup]3.10 <Okay> and bends [pointing to her sketch again, Figure 1B]

Her use of dynamic language such as “the dot hits” seems to refer to an entity moving. Shemay have been referring to the dot, the image of the dot, or rays of light but whatever wasmoving, she perceived the bending to be occurring at the surface of the water.

David chose not to clarify what Jennifer meant at this point. Instead he focused uponher sketches and suggested some changes to shift toward the two-dimensional cut-awaydrawings typical of physics diagrams:

3.11 David: Can you draw a side view so I can see?3.12 Jenn: That IS a side view (laugher). See the side of his head?3.13 David: You’re doing perspective. Can you draw a view here?3.14 [pointing to another part of the paper] Can you draw, I mean3.15 you’re doing the perspective <Okay> of the circle of the top of the cup.3.16 Make the top of the cup a straight line . . .

3.17 So there’s the surface of the water.3.18 [Jennifer drew a flatter 3D cup with a straight horizontal line to represent the

surface of the water as shown in the completed diagram in Figure 2]

Mary contributed to the construction of this drawing by pointing to where the dot shouldbe:

3.19 Mary: The dot’s on the side of the cup3.20 David: side of the cup3.21 Mary: like right there

[pointing to a place on the line representing the side of cup in Jennifer’s new drawing]3.22 Jenn: Right there.

The new drawing (Figure 2) made clear that the dot is on the side of the cup rather thanwithin the water as it would seem to be in Figure 1B. Through this dialogue, David wasenhancing this learner’s initial efforts to visually represent the phenomenon.

Figure 2. Jennifer’s enhanced drawing of path of light to observer’s eye from dot in cup with water.


Episode 4: Tracing the Path of Light. Having helped Jennifer to construct a moreinterpretable drawing for the cup, dot, and water, David shifted attention to the path of thelight:

4.1 David: That’s good. Now draw, what does the light do?

Pat had been watching closely and responded to David’s query:

4.2 Pat: It’s taking it to the surface of the water

Jennifer continued this description:

4.3 Jenn: and then bends

A possible translation of the two “it”s in Pat’s statement could be “the light’s taking the dotto the surface of the water.” David chose not to explore this, however, nor what she mighthave meant by the use of the word “taking.” Instead he followed up on Jennifer’s responsewith a query:

4.4 David: It bends which way?

Appropriately drawing the direction of bending as the light ray emerged from the waterwould be crucial in developing a useful explanation. A bend up would represent a dotappearing lower in the water, a bend down would represent a dot appearing higher, whichhad been observed. Mary made the connection to the activity with the straw:

4.5 Mary: Well, it (makes) like a straw, it’s got to go this way, right?4.6 [moving her finger along the path she thought the light should go

in Jennifer’s drawing]4.7 Jenn: [drawing line slanted to the right as Mary indicated,

bending down toward the horizontal]4.8 David: Like that?

Then Jennifer recognized that the edge of the cup was too high in her sketch:

4.9 Jenn: Then we’re not looking through the cup

and Mary helped her represent the position of the observer:

4.10 Mary: No, our eyes are over here [pointing to right side of Jennifer’s drawing]

David suggested a resolution to Jennifer’s problem that she had drawn a cup with too highan edge and followed up on Mary’s reference to the straw:

4.11 David: So you can just have a shallower cup, cut off the cup or something4.12 If it’s like the straw, that’s the direction the straw bends?4.13 Mary: I think so.4.14 Jenn: Well, I don’t know, because then4.15 [overlapping talk]

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Jennifer appeared to recognize that she should extend the line to the left, below the linerepresenting the water surface, and that its intersection with the line representing the sideof the cup would represent the apparent location of the dot “higher”:

4.16 Jenn: Then it appears4.17 David: Is that the direction the straw goes?4.18 Jenn: that the dot is (on that straight line)4.19 [drawing line to left below surface of the water that continues

line drawn to right above the surface of the water]4.20 David: It appears the dot is here? [pointing to drawing]4.21 Jenn: up higher4.22 David: because that’s where the light seems to be coming from?4.23 It’s like the light is coming from that direction?

This joint construction of a visual representation occurred through intense collaborationby the participants, in the context of both direct and indirect nudging from the instructor.Although Jennifer had drawn an essentially correct diagram to represent the phenomenon,David did not celebrate nor even acknowledge this status. Instead he asked a series of queriesapparently designed to help clarify, for himself as well as for Jennifer and the other groupmembers, what the diagram she had drawn represented.

Episode 5: Becoming More Precise in the Use of Language. Jennifer seemed tobe unsure what David meant and echoed his question:

5.1 Jenn: The light . . . . where do you think the light’s coming from?

No one said anything until Pat responded tentatively:

5.2 Pat: From the water reflection?5.3 Jenn: From the water . . .

Learners often use the everyday word “reflection” in discussing various optical phenomena(Rice & Feher, 1987, p. 638). David had a choice here to accept Pat’s general use of theterm or to press for more precision. He chose the latter:

5.4 David: By reflection, what do you mean?5.5 Do you mean reflection like a mirror?5.6 Pat: No, <Okay> not like a mirror.5.7 David: So let’s use reflection to mean <Okay>5.8 what we mean with a mirror.<Okay>5.9 So, so you can make-up another word if you like,5.10 but let’s not, let’s use, let’s try to use the words. . . .

Pat, Jennifer, and David continued talking explicitly about language:

5.11 Pat: What’s another good word for it?5.12 Jenn: The surface of the water?5.13 David: What is the “it” that you are describing?5.14 Pat: The dot or the square or whatever we’re looking at.


5.15 David: Oh, the object <The object, yeah>.5.16 Okay. But, then you wanted another word for “reflection.”

Pat explained the need for a new word:

5.17 Pat: Right, because, it’s the water, the surface of the water . . . <yeah>5.18 is causing us to see the image at a higher point. <Okay>

She was attributing to the surface of the water the cause of seeing the image at a higherpoint. This was an early articulation of a relevant issue: What was the role of the surface ofthe water in what they were seeing?

Episode 6: Identifying Two Different Ideas. Understanding what was happening dur-ing this episode is complex because several conversations were occurring simultaneously.Pat continued her analysis:

6.1 Pat: And it’s as if you’re seeing it not where it is on the cup,6.2 but where it is on the top of the, on the surface of the water.

Then David checked his understanding of what she had said:

6.3 David: Oh, so it’s as if there is like an image on the surface of the water?6.4 Pat: Right

He was responding in the moment to her articulation of an issue for many learners, under-standing where an image is located. He may have heard a hint of this issue in Pat’s earlierresponse to his question “what does the light do?” (4.1). By “It’s taking it to the surface ofthe water” (4.2), she might have meant that the light was forming an image of the dot at thesurface of the water. At that moment, however, he had chosen not to explore the meaning ofthis statement, by deciding instead to follow up on Jennifer’s comment about bending (4.3).Now he acknowledged Pat’s agreement with his interpretation of her remarks and modeledthe kind of analysis he wanted the group members to be doing:

6.5 David: I see. Okay. <yes> You have, there are two ideas, then, in this group.6.6 [to Pat] Can you make that6.7 [to Jenn] So you have your idea of this line

David simply noted that two different views had been expressed. As the instructor, he washelping these learners to recognize what ideas they had rather than assessing whether theirideas were correct. In the midst of his articulation of one of these ideas, Mary commentedon something she was seeing happening. Her comment overlapped with the beginning ofJennifer’s response to David:

6.8 Mary: But, this almost makes <The image> the dot disappears for a minute.6.9 Jenn: on top of the water.

6.10 David: That’s a different idea from the6.11 Jenn: Right. This one [pointing to her diagram] is the “water bends the light”6.12 Mary: idea - and what’s the other idea?6.13 Jenn: When it bends the light, it does something to make the dot move up.6.14 And I don’t know how to say that.

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6.15 Mary: But, in reality the dot isn’t moving up.6.16 Pat: No, it’s not. That’s why it appears that way.

On the video, one can see David quietly moving away without further comment after observ-ing these group members productively continuing their conversation. By not interruptingtheir thinking in order to formally depart, he was “practicing quietness” (van Zee, 2000), animportant component of skilled instructors’ decision-making about when, how, and whetherto intervene in small group conversations.

This episode illustrates the importance of neutral responses when correct as well as incor-rect ideas are expressed. By not privileging the physicist’s view that had been constructed inthe diagram, David helped maintain an environment in which other ideas could be expressedand examined.

Episode 7: Doing ‘‘What If’’ Thinking. Now working on their own, the group mem-bers continued considering various possibilities by asking a “what if?” question. Theydesigned and conducted investigations of a series of issues that emerged in the midst oftheir deliberations.

Mary wondered what an observer would see if standing in a different way:

7.1 Mary: So, it has to be from where you’re standing.7.2 What if you’re standing up here and you’re looking at the dot?7.3 Pat: You mean you’re looking straight down on it? <un hmm>7.4 I don’t think anything changes.

Perhaps Pat was thinking of the straw not appearing to bend when placed straight downin a cup of water. Jennifer had a different interpretation, perhaps based upon previousexperiences:

7.5 Jenn: Making the object appear closer to the edge of the water?

Pat decided to try things out. She got an empty cup with a dot on the side and began pouringwater into it while looking down from above:

7.6 Pat: Okay, I’m looking straight down.7.7 Oh, it changes it.7.8 Mary: But, it’s not really. Your eye’s getting tricked.7.9 Pat: Because of the water.7.10 Mary: Right, but how?7.11 Pat: But, I was thinking that if I looked straight down on it,7.12 my eyes wouldn’t even be tricked if I looked straight down on it7.13 So, which means, when I look at it at an angle or not,7.14 it’s still going to do that.

Pat also demonstrated to the others something that could be seen with careful observationbut was not part of the intended phenomenon to be explained:

[Pat pours water back into a cup]

7.15 Pat: Because, see at this point, I can’t see the dot.7.16 Whoops, I put too much in.


7.17 There’s a certain point, as the water level rises,7.18 you can barely see the dot.7.19 Mary: That’s what I was saying. Yeah, it almost looks like it disappears.7.20 Pat: Yeah, disappears7.21 Mary: So, what’s happening to it?7.22 Pat: Okay, there I can’t see the dot at all. Now I see it again.

[Pat pours water into a cup again, past the level of the dot]7.23 Jenn: Now to me

When Pat poured water into the cup, the dot seemed to disappear as the meniscus of thewater surface passed the dot; the dot seemed to reappear when the meniscus rose above it.Such extraneous phenomena can divert learners from an activity’s intended objectives ifthey devote too much time and attention to an intriguing minor aspect of the situation. Itis difficult to know in the midst of an investigation, however, just what is and what is notcentral to the phenomena one is trying to understand; that is part of the nature of scientificreasoning. Had the instructor been with them, he would have had a choice of whether toguide them away from attending to this disappearance (and perhaps help them make progresstoward understanding refraction). As it was, they negotiated this aspect of scientific inquiryon their own.

Episode 8: Trying Things Out/Sketching a Model. At this point, the small groupseparated into two activities: Mary talking aloud to herself (in italics below) while be-ginning to sketch her own diagram of what was happening; Jennifer and Pat trying thingsout by watching the dot while repeatedly filling the cup with water:

8.1 Mary: This is the dot, this is the dot. [Pointing to a dot on her paper]8.2 Pat: Okay, what?8.3 Jenn: Will you do that again?

During earlier discussions, the group had described light reflecting off of surfaces otherthan mirrors as “spraying” in all directions. Mary was trying to apply the model that theyhad developed in class to what she was seeing in this situation:

8.4 Mary: Wait, this dot down here’s still spraying off a whole boat-load of stuff.8.5 Right?

Jennifer put a clear plastic ruler vertically into the cup of water:

8.6 Jenn: Go

Pat poured water into the cup:

8.7 Pat: What’s happening?8.8 Jenn: Um, I don’t know8.9 Pat: Did it start at one point and then move- appear to have moved?8.10 Jenn: You try it.8.11 Mary: Wouldn’t. . .if this is the dot. . .8.12 Jenn: Like I’m trying to see how - you know8.13 Pat: I think I know what you are trying to see.8.14 Mary: If this is the dot, isn’t it - it’s spraying off a whole bunch of rays

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During an interview, Mary mentioned that she sometimes dropped out of her group in orderto do some thinking on her own in this way. Here she was explicitly trying to connect thisphenomenon to an earlier foothold idea: Light sprays out from points on an object in alldirections. Meanwhile, Pat and Jennifer were examining the phenomenon, trying to identifyprecisely what happens when water poured into a cup rises above the height of a dot placedon the inside of the cup.

Episode 9: Measuring. Pat and Jennifer continued to try things out but drew Mary backinto their explorations with the effort to make a measurement. Pat picked up the clear plasticruler and placed it in the cup:

9.1 Jenn: Are you ready?9.2 Mary: Oh, go ahead.9.3 Jenn: Oops, sorry Mary.9.4 Mary: I just had a question. What are you guys measuring?

Jennifer explained that they were putting a ruler in the cup of water to try to see if theycould measure how much the dot appeared to move up:

9.5 Jenn: I was trying to see if we could tell that it really does look up higher.9.6 Which means are we seeing

These learners were perceiving an issue within a context established by the instructor andfiguring out ways to explore a question they had formulated for themselves. An importantaspect of such a process is recognizing limitations in various approaches:

9.7 Pat: but, see this [the ruler] is going to move as well, isn’t it?9.8 because it’s an object in the water.9.9 So, as the dot moves, this is going to appear to move.9.10 I don’t think it’s going to measure anything different.9.11 At least I didn’t see anything different.

Pat realized the water would affect how one saw the markings on the ruler as well as howone saw the dot and therefore there should be no apparent movement of the dot with respectto the ruler’s markings.

Episode 10: Constructing a Model. Then Mary was able to interest Pat and Jenniferin thinking with her about using the foothold ideas to make a drawing. Through this con-versation, they constructed a new diagram to show rays traveling from the dot to the surfaceof the water, bending at the surface, and traveling to an observer’s eye (Figure 3).

10.1 Mary: If this...isn’t the dot spraying off a whole bunch of rays? <yes> Right?10.2 It’s not just one.10.3 So all these rays are coming up here,10.4 hitting the surface of the water, right? [sketching rays]10.5 And - by putting this little thing in [picks up straw, puts it in cup water],10.6 we know it bends it at a particular angle.


Figure 3. Mary’s drawing of path of light to observer’s eye from dot in cup with water.

These learners were seeking consistency across several situations. Mary seemed to expectthat what they had come to understand in one context (apparent bending of straw in water)should be relevant to the other (apparent raising of the dot when water was poured into thecup).

Pat clarified the “it”s in Mary’s statement and together they constructed an explanationas Mary continued drawing her sketch:

10.7 Pat: The water causes the light to bend10.8 Mary: The water’s bending the light ray at a predictable angle10.9 Pat: At a very slight one <right>10.9 Mary: So, say these are shooting off [sketching rays]10.10 it’s bending off of this - how do we say? If it’s coming this way10.11 Pat: It’s hitting this way. It’s bending up a little10.12 Mary: <right> this way, <right> right? <right>10.13 Okay So these are coming up like this [sketching rays]10.14 And then some of them are hitting our eye.10.15 The question is why does this look up?

Mary was still pondering the question of why the dot seemed to appear higher on the cup.Mary had participated actively in the construction of Jennifer’s diagram (Figure. 2); herutterances and actions in Episodes 3 and 4 suggest she understood well what Jennifer’sdiagram represented. However, in Episodes 8 and 10 she was engaging herself and then hercolleagues in deep thought in order to generate her own diagram. The thinking she had donein Episodes 3 and 4 had not been enough for her to be able to do this readily herself. Oncemade, her diagram did not seem to be an adequate explanation for her although it was close

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to a physicist’s representation of the phenomenon. It did not yet include a line indicating theapparent path of the light, extended from the point of bending at the water surface back tothe side of the cup. Such a line would have indicated the direction from which light wouldappear to originate at the dot. Tracing back along that line would have shown where on thecup the raised image of the dot would appear to be. Even with the slight angle of bending inher drawing, such a line would have intersected with the line representing the cup at a pointhigher than the dot in her diagram, similar to the line that Jennifer had drawn in Figure. 2.

Episode 11: Continuing to Examine the Situation. Jennifer responded to Mary’squestion by focusing attention upon what was happening at the surface of the water:

11.1 Jenn: There’s something with the top surface, the surface of the water.11.2 Mary: Yeah, cause that’s what’s causing the bend.

Pat agreed and returned to the analogy they had discussed earlier:

11.3 Pat: Right, I think that’s acting as a lens

and Jennifer supplied a correspondence for this analogy:

11.4 Jenn: Cause it’s curved. <right> The water - the top of the water. <yeah>

Both a lens and the top of the water are curved. Jennifer seemed to be thinking of a similarfeature that could be responsible for bending the light at the place where she had identifiedthe bending to be occurring, the curved meniscus formed by the surface of the water. Marydisagreed and proposed a test. She seemed to be basing this on their work with lenses duringthe previous week, that if they had a light, there should be an image of a dot that they couldsee on a piece of paper held like a screen above the cup:

11.5 Mary: If it’s acting as a lens, then if we put a piece of paper up here11.6 we should be able to see that dot up reflected someplace.

[holding a piece of paper horizontally above the cup of water]

11.7 Pat: It’ll reflect.11.8 Mary: I don’t think it’s acting like a lens.11.9 If this is acting like a lens, then if we show - if we had light down here,11.10 shouldn’t we be able to see that dot on a piece of paper like this?

Mary was invoking a thought experiment in an effort to resolve differing points of view. Shewas drawing on the shared results they had discussed in the review earlier in the session, adiscussion that had included drawing a ray diagram on the board of a light bulb, lens, andimage on a screen. She seemed to be attempting to describe a similar line-up of a light, cupof water with dot, and paper screen, all to argue that if the surface of the water were a lens,it should be able to project an image onto the paper as they had seen.

Jennifer and Pat offered some thoughts about the feasibility of Mary’s proposed test:

11.11 Jenn: Is the dot on the bottom of the paper - of the cup?11.12 Pat: But, there’s not enough light.


This prompted Mary to generalize what she was attempting to do:

11.13 Mary: No, but I’m just trying to say how can you prove that this is like a lens?11.14 Jenn: I don’t know.

This was a sophisticated approach to argumentation: Mary seemed to be seeking a way toshow that the position with which she did not agree was correct. Pat and Jennifer providedsome rationale for their claim:

11.15 Pat I just said it’s acting like a lens because11.16 Jenn: because it’s bending the light.11.17 Pat: Right. I know what you’re saying though.11.18 Because if you do that it’s not going to do anything to the-11.19 I think there’s just not enough light hitting this to cause it to reflect11.20 I mean to appear on this.

Note the progress that Pat made during the session interpreted here: she self-corrected heruse of the word “reflect” in a general way, choosing to substitute the word “appear” instead.

Episode 12: Pondering Connections Among Phenomena. Next the group memb-ers considered whether there was a relation between the two phenomena they had beeninvestigating:

12.1 Mary: But, if we did - I wonder if the amount that it’s [dot] raised has12.2 something to do with this angle that it’s [straw] bending. Maybe not.

Mary was looking for consistency across these phenomena. Apparently Jennifer also hadbeen thinking about this relation:

12.3 Jenn: Say that again. Oh, That’s why I was trying to use the ruler12.4 to see if there was like some kind of

Mary assessed the feasibility of that approach and provided a specific example of why thiswould not work, in terms of features of the cup:

12.5 Mary: I don’t think that would work because, like,12.6 even if you match that dot up to this line on the outside

[pointing to decorative line on the outside of the cup],12.7 as you’re pouring it in, that line moves up there.12.8 Pat: It doesn’t change.12.9 Jenn: Right, but how much does it move up?

The referent for Pat’s “it” is unclear but Jennifer appeared to agree with Mary and reiteratedthe issue she had been pondering, how much does the dot move up?

Episode 13: Positing a ‘‘Foothold’’ and Making an Inference Based on ThatIdea. Pat persisted in trying to explain her thought that the angle of the bend does notdepend upon how much of the straw is in the water:

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13.1 Pat: At this point of the straw hitting the surface,13.2 the angle does not change regardless of whether the straw is raised13.3 Jenn: But move your head, move your head and then it changes.13.4 Pat: Move my head? No, what I’m saying is13.5 the point of the straw coming out of the surface of the water,13.6 no matter where I look at it, that point, the angle is the same13.7 whether it’s all the way in the water or raised out13.8 the angle right here doesn’t change.

Mary provided an interpretation of what Pat meant

13.9 Mary: It still looks bent, but what she’s saying is it doesn’t matter.13.10 Pat: It doesn’t bend any more or less.

Mary then explained further her understanding of Pat’s interpretation, which became anew foothold: the point that the straw appears to bend is at the surface.

13.11 Mary: So, what you’re trying to prove is that the point that it bends,13.12 or appears to bend is the surface.13.13 Pat: Right at the surface of the water.13.14 Mary: Okay I agree with that.13.15 Jenn: Yeah, I think it’s definitely at the surface.

All three of the group members explicitly concurred. Then Mary made an inference basedon this foothold idea:

13.16 Mary: I do too. And it could <so why!>-13.17 it could have something to do with the light ray moving through13.18 the water and then all the sudden it’s through the air and it bends.

She recognized that the bending could be caused by differences in the way the light raymoves through water and then through air. This is a different explanation from that suggestedin 11.4, that the bending occurs because of the curvature of the water surface. Instead offocusing upon the location where the bending occurs, the surface, and its properties, acurved meniscus, this explanation focuses on the behavior of light in the two media throughwhich it is traveling. The conversation continued with the three group members exploringthe connection between the angle that a straw was bent and the amount the dot appeared torise.

This glimpse of inquiry learning and teaching demonstrates its fluid nature both duringparticipants’ interactions with an instructor (Episodes 3–6) and on their own (Episode 1,2, 7–13). What they said and did next evolved out of what they had just finished doingand saying rather than from following a set of prescribed directions. The instructor listenedclosely to the participants and responded in ways that reflected his diagnosis of where theywere in their thinking, his knowledge of what they needed to learn both about physics andabout learning, and his insights into what might help them make progress. The participantsalso listened closely to one another. They responded in ways that generated possibilities(shopping for ideas) and sought consistency (reconciling) in developing an explanation thatmade sense to themselves as well as to physicists.


SUMMARY OF ANALYSES

This case study documented an example of inquiry learning and teaching in physics thatoccurred during a summer institute for elementary and middle school teachers. A smallgroup constructed an explanatory model for an intriguing optical phenomenon that theywere observing. Like Shapiro (1994, p. 88), we found that ideas students state in simpleeveryday language, such as that water bends light rays, may represent complex thinking. Thegroup members worked intently for most of an hour to make sense out of their observationsthat a straw appears to bend when placed at an angle in a cup of water and that a dot appearsto rise as water is poured into a cup on the side of which the dot has been drawn.

Example Table of Evidence

For each episode, a table presents evidence of physics thinking, scientific inquiry, ques-tioning, and collaborative sense making. For example, Table 2 presents an excerpt from thetable of evidence for Episode 1. The physics thinking involved a prediction about how astraw appears to bend in water and a question about angles, perhaps prompted by thinkingabout how light behaves with mirrors. Aspects of scientific inquiry that matched the de-scription in the National Science Education Standards (NRC, 1996, p. 23) included makinga prediction and thinking critically by identifying a possible variable (1.12) and by con-sidering the equality of two quantities (1.13). Both questions fit in categories identified ina previous study (van Zee & Minstrell, 1997b). One posed an issue for exploration andthe other asked group members to monitor their understanding. Three of these utteranceswere examples of collaborative sense-making. They related directly to previous utterancesand monitored the discussion. Similar tables for Episodes 2–13 provide evidence for thesummaries below.

Physics Thinking

Physics thinking occurred in all 13 episodes. Like other learners (Rice & Feher, 1987,p. 638), these elementary school teachers initially used everyday terms like “reflection”in general ways (5.2). However, progress in increasing precision in their use of languagewas evident even within the brief excerpt interpreted here. After the instructor commentedexplicitly on the need for precise use of the word “reflection” (5.7), for example, one of thegroup members corrected herself in the midst of explaining her thinking (11.19–11.20).Like other learners (Goldberg & McDermott, 1987), these formed views about the locationof images that did not match those of physicists (6.1–6.4). However, their instructor chosenot to correct these but rather to encourage them to identify different ideas and try to makesense of what these were (6.5–6.13), scaffolding practices of argumentation (Driver etal., 2000). Many learners seem to be able to think about light traveling from a luminoussource such as the sun or a light bulb but have trouble thinking about light reflecting offnonluminous objects; the direction of travel from object to eye or from eye to object canalso be an issue (Fetherstonhaugh & Treagust, 1992). Evident here, however, was learners’use of the idea that a point on a dot sprays off a bunch of rays in many directions, travelingthrough the water, and then the air to an observer’s eye (8.4, 8.14, 10.1–10.3). Rather thanpuzzling over a complex ray diagram drawn by someone else (Colin, Chauvet, & Viennot,2002), these learners constructed essentially correct diagrams by reasoning about what theythought was happening (Episodes 2, 3, 8, and 10).

These learners came to consensus on the “foothold idea” that the bending occurred at thesurface of the water (13.11–13.15). Their agreement followed much discussion in which

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this idea had been mentioned (2.14, 3.8–3.10, 5.17, 6.11, 10.6–10.9, 11.1, 11.2) and usedin drawing a series of diagrams (Figures 1–3) (Episodes 2, 3, 8, and 10). One of the groupmembers proposed that the bending had to do with a property of the surface of the water,its curvature (11.4). However, another made an inference that matches the physicist’s view:that the bending has to do with differences in the way a light ray moves through water andthen through air (13.17, 13.18).

Scientific Inquiry

As indicated in Table 3, these learners demonstrated many of the aspects of scientific in-quiry mentioned in the description from the National Science Education Standards quoted inthe introduction (NRC, 1996, p. 23). These included making observations, posing questions,planning investigations, reviewing what is already known in light of experimental evidence,using tools to gather, analyze, and interpret data, proposing answers, explanations, and pre-dictions, using critical and logical thinking and proposing alternative explanations. Duringthe episodes presented here, they did not examine books or other sources of information,communicate results, nor identify assumptions. However, they also demonstrated aspectsof inquiry learning not explicitly mentioned in the NSES: using visual representations andtrying to measure change.

Questioning

As shown in Table 4, questions asked during the episodes presented here could be groupedaccording to categories identified in a previous study (van Zee & Minstrell, 1997b). Onlytwo questions seemed to be intended to help make meanings clear, 26 explored variouspoints of view in a neutral and respectful manner, and 15 monitored the discussion andone’s own thinking. The instructor’s questions also could be grouped in these categories.

Collaborative Sense Making

As shown in Table 5, some of the sense-making functions observed in an earlier study(van Zee, 2000) were evident here. In contrast to the whole group discussion in the previousstudy, this was a small group conversation in which the speakers did not refer to one another’sideas by name. There were many complex ways, however, in which the group members’comments and questions were directly related to previous utterances. In addition, the groupmembers referred to their own thinking in several ways. There was only one utterancethat represented an act, such as issuing an order to another group member. In Episode 13,Jennifer told Pat “Move your head. Move your head” (13.3) as Pat was looking at the dotin the water.

The processes of “shopping for ideas,” “developing footholds,” and “reconciling” arefundamental to the collaborative sense making that occurred during the discourse presentedhere. By seeking connections to prior knowledge that might be helpful, these learners gen-erated analogies to optical phenomena they had studied in previous sessions. This “mutualknowledge” (Meyer & Woodruff, 1997) included detailed understandings such as that theangle that light bounces off a mirror is equal to its angle of incidence. In the process ofcoming to agreement on a specific aspect of the situation, “that the point that it appearsto bend is right at the surface of the water” (13.11–13.15), these learners enacted a socialand incremental refinement of shared meanings typical of convergent conceptual change(Rochelle, 1992). By seeking consistency across the phenomena they were trying to explain,such as wondering if the angle the straw appeared to bend was related to the amount the dot


appeared to rise (12.1, 12.2), the learners were expressing the need to develop explanationsthat were coherent (Meyer & Woodruff, 1997).

Fostering Science Learning

The instructor interacted with this small group during four of the episodes presented here(Episodes 3–6). He joined the group in the midst of a social moment in which members weregood naturedly expressing their confusion. Although he often joined a group by silentlylistening to what was being said, in this case he stepped right in to the conversation to helpclarify what was known (3.1–3.6). When one of the group members drew his attention tosketches she had drawn to try to explain to her colleagues what she was seeing, he respondedby working with her to enhance her ability to represent visually what was occurring (3.7–4.23). He typically asked questions in guiding the drawing process (3.11, 4.1, 4.4, 4.8,4.12, 4.17, 4.20) but was directive when it seemed necessary (3.16). Although the smallgroup members collaboratively produced a diagram that a physicist would recognize asappropriate, he did not acknowledge its status. He chose instead to try to make sure that theartist understood what she had drawn (4.20–4.23). During discussion of the drawing, hepressed for the precise use of language (5.4–5.16) and helped the group members identifythe different views being offered so that these could be examined (6.5–6.7, 6.10). Afterlistening to the group members talk productively among themselves, he quietly moved awayto check on another group’s progress.

REFLECTION

If you were to peek through our classroom door, what would you see? Participantstalking with one another in small groups; staff standing or sitting nearby, sometimes quietlylistening, sometimes engaging a small group of participants in conversation. Sometimes onewould see a staff member facilitating a whole group discussion. We share with other inquiry-based programs a commitment to a major shift in role for instructors: from explaining whatone knows oneself toward diagnosing what students are thinking and then responding inways (including staying silent) that prompt progress. Lecturers display knowledge andreasoning through the clarity and correctness of their expositions. During inquiry-basedinstruction, however, staff members display expertise by the insightfulness and accuracy oftheir diagnoses of student thinking, the appropriateness of their decisions to intervene ornot in the students’ on-going conversations, and the effectiveness of what they choose tosay or do.

This paper is an invitation to step through our classroom door and spend a little timewith several of the participants in the midst of learning. Such a visitor might ask, in whatways does this approach differ from other inquiry-based programs? One visually salientdifference is the absence of instructional handouts. These participants were not referringfrequently to written directions telling them how to do a set sequence of activities or whatto talk about to elaborate particular issues. They were trying to use what they knew andcould figure out to develop an explanatory model for an intriguing phenomenon.

Many inquiry-based programs begin with some “messing about” with simple equipmentto give participants experience with the phenomena. The first day of this summer institute,however, began with a small group discussion. Only after the participants had talked withone another about what they knew about light, shared their ideas in a whole group discussion,considered whether their ideas were based on what they had learned from experience oron what they had been told, pondered whether there were any conflicts in these ideas thatneeded reconciling, worked in small groups to develop predictions for a situation the lead

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instructor had described, and discussed these predictions and their bases with the wholegroup---only after more than an hour of such intensive conversation did the participantsbegin to explore with mirrors.

Underlying the differences between this approach to inquiry learning and others is a majorphilosophical issue: What is the purpose of instruction? In many inquiry-based programs,the focus of attention is on the subject matter, on learning about science and the nature ofscience. Here the focus of attention was on learning about learning. The lead instructor’sobjectives during the summer institute were not to teach the principles of geometrical optics,although he expected increasing competence in this area of physics to occur. Rather, hisobjectives in this, as in other physics courses he teaches, were epistemological (Hammer,1995; Hammer & Elby, 2003). He wanted these learners to form the beliefs that they neededto think for themselves, that understanding physics involves accessing and incorporatingtheir own knowledge and experiences, and that it is important to coordinate and reconcilealternative ways of thinking. His intent was to develop a stance of inquiry, rather than toimpart knowledge, and his belief was that this would prepare these teachers to teach sciencein ways that their students would learn, not just to recite facts and formulas, but to thinkand reason as scientists do.

A dilemma faced in many inquiry-based approaches is what to do when a student ex-presses a “wrong” idea. If the goal is to build canonical content knowledge, then the in-structor’s response might be to correct the speaker or at least initiate a move to addressthe issue. In Episode 3, however, this instructor chose not to pursue what Jennifer mighthave meant by “the dot hits the end of the water” (3.8) even though this language suggestssome confusion about where an image is. He chose instead to focus on helping her refineand interpret her sketch. When this issue emerged later in Pat’s comment “it’s as if you’reseeing it . . . where it is on the top of the---on the surface of the water” (6.1, 6.2), the in-structor again chose not to correct the speaker. Instead he initiated a reconciling processby noting that this group had expressed two ideas. He left the group as the participantsbegan clarifying with one another what those two ideas were. By doing so, he risked theparticipants continuing to think of the image as being on the surface of the water as it mighthappen that this issue would never be directly addressed during the limited time availablein this institute. What he ensured by his actions, however, was that these participants wereusing that limited time to gain facility in expressing their thinking through sketches and inarticulating and reconciling different points of view.

A reviewer noticed that we have chosen not to refer to “constructivism.” This terminvokes an image of individuals actively engaged in building something. Certainly thathas occurred here, these participants can be described as actively building their knowl-edge about how light behaves. The approach known as “constructivism” also is associatedwith eliciting students’ current knowledge as the base upon which to build. That alsooccurred here in the lengthy conversations that this instructor initiated before introduc-ing any equipment with which to explore phenomena. However, in a speech communitythat values precision of language, both of the terms “constructivism” and “inquiry” re-main remarkably imprecise.2 Both carry a huge array of assumptions and meanings thatreaders may associate with their use. We have chosen to provide a detailed descriptionof the kind of learning in action that we value without burdening it with more than oneimprecise term. We have chosen the term “inquiry” that invokes an image of individualsactively asking questions and seeking understanding, one that occurs in the rhetoric of manydisciplines.

2 The term “constructivism” has migrated from its original meaning, as a theory of knowledge, to referto a wide range of instructional approaches.


Looking through the titles of the episodes listed in Table 1, one sees several that link to theNRC definition of inquiry: “Identifying two different ideas” and “doing ‘what if’ thinking”are aspects of critical thinking. “Trying things out, “measuring, “ and “constructing a model”fit within the actions listed in the definition. Table 3 makes explicit the connection betweenparticular utterances and episodes and aspects of inquiry mentioned in the NSES definitionquoted above.

The learners were guided, but not in the usual sense of “guided inquiry” wherein the in-structor or materials guide students through a predetermined flow of discovery and reason-ing. These participants engaged in scientifically oriented questions they posed themselvesin the context of exploring phenomena presented by the instructor. They were guided inthe sense that the instructor drew upon extensive personal resources to suggest appropriatephenomena and issues for them to explore. He did not, however, specify in detail what con-stituted evidence and how they should collect it. For example, these participants initiatedan effort to measure the changes they were observing. They articulated the issue, decidedhow to explore it, attempted to collect relevant data, and assessed its validity themselves(Episodes 8 and 9). The instructor regularly engaged the whole group of participants indiscussions of what evidence they had gathered and how this might be interpreted in devel-oping explanations for the phenomena they were observing. He was guiding the thinkingby facilitating these wide-ranging conversations. In the small group, however, these partic-ipants developed an explanation on their own with occasional assists from staff members.

What sense did the participants make out of this informal yet intense experience of thesummer institute? One way to assess the progress of learners in such settings is to askparticipants to write a reflection at the end of the session, about what they learned, and whatquestions are still puzzling them. At the end of the session portrayed here, Mary wrote:

• The surface of the water bends light• When light is bent, and your eye is focused on something---say under water---your

eye will be tricked and perceive the objects as if viewed in a straight line• Light is reflected in predictable angles• There is a “geometry” about light and how it is bent, and what you see and how it’s

perceived and reflected, etc.• It’s all in the angle

(Mary Bell, journal, 2001)

Jennifer and Pat chose to record some of their understandings about a mirror problem onwhich they had also worked during this session. However, Jennifer also wrote a questionabout the cup of water activities:

Why does the water cause the light to bend?(Jennifer Peter, journal, 2001)

Near the close of the summer institute, the participants also wrote comments about theirlearning process. Pat described the shift in attitude toward learning science that she hadexperienced as follows:

My experience in science has been quite negative. I never felt “good at science” . . . Physicalscience in college was a nightmare . . . What’s been different in [this course] is that I didn’tfeel inferior about science even if I didn’t feel very knowledgeable. It makes a lot of senseto encourage us to connect with our life experiences. I never thought of science in thatway. This course is helping me rethink science. Science is not this big monster to fear but

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“footholds” or ideas that can be challenged. I’m learning to keep referring to the footholdsestablished and that it’s Okay to throw out a foothold, add to it, take away from it. A footholddoesn’t have to be cut in stone if you can disprove it otherwise. It’s a way of thinking. Idon’t feel I have to know a right or wrong answer but that I can explain what, why, how I’mthinking. Seeing illustrations and actually trying different scenarios has been helpful to meto make the footholds internal. Being able to discuss my thoughts and not feel intimidatedvalidates my thoughts and values.

(Patricia Roy, journal, 2001)

We interpret these reflections as evidence that teachers know a lot about the physical worldfrom their everyday lives and they can build productively upon these experiences if encour-aged to do so.

Limitations of the Study

This case study examined about 10 min of one small group’s work within one sessionof a summer institute that was part of a 3-year project. Much of interest has not beenportrayed here, of what was happening in the other small groups, of what occurred beforeand after these minutes in this session, in this summer, and in the project as a whole. Thecomplexity of what was happening within just this small group is difficult to portray onpaper. The transcripts do not convey well the tone, timing, or tenor of what was said andprovide little information about what the group members did. The analysis omits muchthat occurred before the episodes reported here that influenced these participants’ thinking.No information is provided about what occurred after these episodes that built upon theunderstandings they had constructed together. The analysis and interpretations reflect theexperiences and biases of the first author. Others may perceive these episodes differently,but that is part of the purpose of presenting them: Science education reform depends notonly on general calls for shifting emphases toward inquiry but also on having instancesto clarify what those emphases may entail. Just as we hope and expect learners in scienceto move back and forth between particular explorations and general principles, so do weexpect the education community to do the same. Here we offer analysis of a particularinstance and invite debate with respect to how it aligns with the goals and values of scienceeducation reform.

Directions for Future Research

This is the first of a series of case studies intended to portray in detail the learningexperiences of participants in a project during three summer institutes. The physics portionof the first summer institute focused on motion, the second on light, and the third onelectricity. These case studies will provide examples of inquiry-based instruction for physicsfaculty interested in addressing the needs of prospective and practicing elementary schoolteachers. Our belief is that physics faculty can and should teach courses for prospective andpracticing teachers that invite them to enter an enticing community of science learners andteachers. Two questions are critical in designing such communities: What fosters teachers’inquiries into physical science? How can science faculty and science education faculty learnhow to engage teachers in learning this way?

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