David Hammer
Physics and Curriculum & Instruction.
University of Maryland at College Park
College Park, MD 20742

davidham@physics.umd.edu

Hammer, D. (2000). Teacher inquiry.  In J. Minstrell, & E. van Zee (Eds.), Inquiring into Inquiry Learning and Teaching in Science. Washington DC: American Association for the Advancement of Science, pp. 184-215. (Also 1999, In the Paper Series of the Center for the Development of Teaching at EDC, in Newton, MA.)
 

Abstract

The progessive agendas of science education reform, in particular that of promoting student inquiry, place substantial intellectual demands on teachers. If these reforms are to succeed, the education community must do more to appreciate and address those demands. This paper presents three examples of high school physics teachers' conversations about "snippets" of each others' work with students. The purposes are (1) to hightlight the central role and intellectual demands of teacher inquiry, in particular teacher diagnosis of students' strengths and needs; (2) to suggest that teachers often experience and express their diagnoses in terms of instructional strategies, and (3) to suggest that the value of education research for instruction should be understood primarily with respect to what it may contribute to teacher inquiry.
 

Introduction

To think of "inquiry" in the classroom is almost always to think of student inquiry. One does not often associate inquiry with the teacher's role, other than with respect to the questions that come up within the discipline, science questions for a science teacher, to which the teacher does not have an immediate answer. My first objective in this paper is to promote a view of inquiry as central to the teacher's role, particularly inquiry into student understanding, participation, and learning.

Although it is becoming more common to think of teaching as inquiry [1], the emphasis in education reform remains on methods, materials, and standards. Meanwhile, the progressive agenda of promoting student inquiry, along with the need to coordinate that agenda with the traditional one of "covering the content," places substantial intellectual demands on teachers. If these demands are not considered and addressed, the progressive agenda is unlikely to succeed. That is to say, to pursue science education reform through the development of new curricula, new materials, or new standards is not sufficient. To promote student inquiry, we must do much more to understand and support teacher inquiry.

To begin, teachers spend a significant portion of their days taking in and interpreting information about their students. Much of this data gathering is deliberate and explicit, as teachers take attendance, collect homework assignments and laboratory reports, give quizzes and exams. Other information arrives on its own, in a nearly continuous stream, in the questions students ask and comments they make as well as in their facial expressions, body language, tone of voice.

What teachers perceive in their students and how they interpret those perceptions (whether the students are paying attention, confused, interested, frustrated, etc.) can dramatically influence how they choose to proceed (pose a challenging question, provide information, continue to new material, digress to pursue a student's idea). Most of this interpretation happens ó must happen ó without explicit, articulate deliberation. In this respect teachers are like other reflective practitioners[2], from chess players to doctors, whose reasoning is and must be largely tacit.

For chess players and doctors, however, there is a general awareness that this perception and judgment is taking place, that it is intellectually demanding, and that its betterment is central to professional education. It is both possible and expected for chess players and doctors to make at least some of their reasoning explicit, as a matter of professional practice and development, and they do so in the contexts of specific games and cases. For teachers, in contrast, it is rare to have the opportunity, let alone the expectation, to present information from their classes to others, to make explicit their interpretations, or to consider alternatives.

Conversations among teachers

This paper describes work from a project designed to engage teachers in precisely this sort of conversation, centered on their ongoing experiences in the classroom. From March, 1995 through June 1998, a group of physics teachers and I met roughly every other week of the school year, for two hours, to talk about students and teaching. During the 1996-1997 school year, this group was comprised of myself and the following teachers:[3]

The body of this paper is organized around three examples of snippets and our conversations about them, from three consecutive meetings in the fall, 1996, contributed respectively by Robert, Hilda, and Bruce. I have chosen these examples to reflect a range of physics topics and forms of snippet and, in general, because they are representative of the substance and tenor of our work. Each example will begin with the teacher's snippet, present excerpts of our conversation about it, and end with an analysis of what the snippet and conversation may reveal about teacher inquiry. I will use these analyses, in turn through the examples, to advance the folllowing three objectives in this paper:

1) Teacher perception and judgment. The first objective, as I noted above, is to promote greater appreciation for the role and demands of teachers' inquiry into their students' understanding, participation, and learning.

2) A language of action. The second is to offer an insight that has emerged from our work regarding the language teachers use to express what they find in that inquiry. In our conversations, we have seen that the teachers often experience and communicate their interpretations in a language of action, that is to say as ideas for what to do in the given circumstance, rather than in an explicit language of diagnosis. For a simple example, a teacher may express an interpretation ("The students have forgotten what they learned about inertia.") by suggesting an action ("I would review the concept of inertia.") I will give examples of teachers' different suggestions that reflect subtle differences in interpretation.

3) A role for education research: My third objective is to propose a view of the role of education research in instructional practice. Specifically, I will suggest that its primary role is to contribute to teacher inquiry, to teachers' perceptions of their students and judgments for how to proceed, rather than to prescribe effective methods. The conversation between teachers and researchers should therefore be understood to take place mainly at the level of their respective interpretations of students' understanding and participation. This conversation, however, may be difficult to recognize and to facilitate, owing largely to differences in the language by which researchers and teachers experience and communicate their interpretations.
 
 

Interpreting a class discussion about free fall: Teacher inquiry into student understanding and participation.

The first snippet we discussed in our meeting on November 18, 1996 was a transcript Robert had prepared, of a discussion in his "college prep"[4] level class about the forces on a skydiver. Robert wrote in the snippet that his goal for this activity was "to reinforce the idea of the Net Force as the driving engine for acceleration." The following is roughly half of the transcript.[5]

Bruce started our conversation with the suggestion that S6's comments revealed a common misconception. Robert's response showed that he too considered S6's contribution significant, but for different reasons.[6]

Hilda reminded us that the students were talking about a skydiver, who had no initial downward velocity. In this case, she noted, the students' reasoning may have been appropriate, because "there had to be a force, otherwise [the skydiver] wouldn't come down." Robert maintained, nevertheless, that the students were not distinguishing force as causing velocity from force as causing acceleration.

After a brief digression on the sensitivity of students' understanding to particular wording, I asked Robert to say more about the snippet. He reflected on his impressions of the discussion, reiterating his pleasure and surprise at how it went, and recounted more of what happened in the class after the segment he had transcribed.

Teacher perceptions of students' understanding and participation

The snippet continued further, as did our conversation; we spent roughly half an hour talking about it, the amount of time we typically allocate. Our conversation was also typical in the range of perceptions it reflected, by the snippet's author and by the rest of the group. Among their interpretations of the students' understanding and participation, Robert and the other teachers noted the following:

ï a misconception, on the part of S6, "that the speed is proportional to the force." Bruce mentioned this in our conversation, but Robert had evidently seen something similar in S6's contribution, since, a moment later in the snippet, he told the students, "The difficulty, as I see it, is that you're confusing the MOTION with the FORCES."

ï an original contribution by a student, S6, who was more inclined to memorization. Robert recognized the same misconception Bruce did, but he perceived S6's idea in several other ways as well. First, he saw S6 as participating in a way that was new for her, a perception not available to the rest of us from the snippet itself, since it depended on Robert's experience from the start of the year.

ï a valid insight in S6's idea that "there needs to be something else," and a productive "turning point" in the class discussion. Second, in addition to seeing S6's reasoning as reflecting a misconception, that is a conception inconsistent with the Newtonian understanding he wanted students to develop, Robert saw it as containing a insight that could help her and the class progress toward that understanding.

ï the misconception as possibly reinforced, inadvertently, by the explanation, "it's the forces which make things move." This was not, directly, a perception of the students' understanding, although indirectly it attends to how they might reasonably interpret a statement by the teacher.

ï students' difficulty with the idea of an initial velocity. Bruce and Robert had been talking about the students' confusing the concepts of motion and force, both with respect to this particular situation and as a more general misconception. Here, Robert connected their reasoning to a related pattern he had seen in students' reasoning, that of their difficulty thinking of an object having an initial velocity.

ï students' interest, engagement. Robert was enthusiastic about the outcome of the discussion, both for the students' engagement ("The class ended; the kids didn't want to go!") and for the substantive progress they initiated ("The kids did most of it.").

To be clear, the point here is not these particular perceptions, and I am not claiming they are "correct." To be sure, I expect other teachers would offer different interpretations, as happens routinely in our conversations. My point is that these perceptions represent multiple dimensions of teacher awareness, concerning the students' conceptions of forces and motion, their modes of reasoning and participation, the level of their interest and engagement. It is awareness of individual students and of the class as a whole, in general, over the school year, and in particular moments.

In fact, this list of teacher perceptions is incomplete, as it reflects only those Robert and the rest of the group made explicit. Much, it is clear, always goes unsaid in our conversations about snippets. For instance, Robert saw something in the students' reasoning that led him to press them with respect to vocabulary: "What's the common English word for 'force of gravity'?" It is a reasonable guess that he saw the students' distinguishing as two ideas (the weight of an object and the force of gravity on that object by the earth) what a physicist considers one idea. By insisting on their use of the "common English word," he was insisting they apply their everyday understanding of weight, in particular that the weight of an object is independent of its motion, to their reasoning about 'force of gravity.' From Robert's comments on other occasions, it is likely as well that he perceived and hoped to address a general pattern of students' treating physics as disconnected from their everyday experience.

Moreover, it is sobering to consider, this is only an excerpt of Robert's snippet, which itself represents only a fraction of what transpired in a single period from a single school day. Here, then, is a first illustration of this paper's opening premise: Teachers take in and process an enormous amount of information about their students' understanding and participation. Most of this inquiry is and must be tacit, because there is more information than explicit thought could accommodate. It would be impossible for any teacher to articulate all of his or her perceptions and intentions.

Still, it seems to be both possible and productive for teachers to articulate some of their perceptions and intentions. Nevertheless, at least in the United States, it is rare for this to occur. Teachers seldom have the opportunity or occasion to show others their "data," to present their interpretations, and to have those interpretations challenged with alternatives. Because of this, teachers are mostly left to themselves, individually, to develop the intellectual resources they need to meet the intellectual demands of interpreting their students' understanding and participation, diagnosing their strengths and needs, and making judgments for how to proceed.

We do not pretend that our conversations capture more than a fraction of teacher thinking. But, by capturing that fraction, they allow the teachers to exchange and compare, not only methods and materials, but perceptions of students in particular moments of instruction. Our conversations, grounded in specific instances from the teachers classes, provide not only ideas for instructional strategies, but also new diagnostic possibilities, an exchange of intellectual resources to support the intellectual work of teaching.

In this respect, in their ongoing inquiry into students' understanding and participation, teachers have much in common with education researchers, specifically those who conduct research on learning. They study essentially the same phenomena, namely student learning, although in different ways, and it is reasonable to expect teachers and researchers could support each other in their efforts. The central purpose of this project was to explore how that may happen, particularly how perspectives from education research may contribute to teacher inquiry. I will discuss this further in the section below, "A role for education research."

Before that, I will present another example of a snippet conversation. This will serve to further substantiate the view I am promoting of teaching as inquiry and of teacher expertise as involving intellectual resources for engaging in that inquiry. The main purpose of the section, however, is to reflect on the language by which the teachers articulate their interpretations: The teachers often experience and express what they perceive in students as ideas for how to proceed in instruction.
 
 
 

Interpreting lab reports on simple circuits: Describing perceptions in a language of action.

Our meeting on December 12, 1996 opened with a snippet from Lis, a videotape produced by two of her "college prep" students as part of an optional project. They had performed two experiments in projectile motion. First, they fired a "bb-gun" across a field at a target, measuring the distance the bb fell in its trajectory below the horizontal, and showing that this distance, ten inches, was consistent with a calculation from kinematics equations they had learned in class. Their second experiment was to throw two pumpkins from a cliff, launching them horizontally at qualitatively different speeds. They measured the times the pumpkins took to fall and the distances they fell outward from the cliff, again to compare with the theoretical predictions.

There was much to discuss about this tape, including the students' investment in their work, the validity of their reasoning and measurements, the value of their "seeing" the bb fall ten inches in its trajectory, as well as the students' campy humor. The conversation digressed often from the details of the videotape to talk in general about the motivational and conceptual value of "real world" and "open-ended" projects, as well as about strategies for assigning and assessing them. I am mentioning Lis's snippet mainly because it came up in our conversation about Hilda's, which is the main focus of this section.

Hilda assembled her snippet from student reports and her observations of much more traditional laboratory work on Ohm's Law.[7] In one lab, the students systematically varied the voltage and resistance in a simple series circuit, by changing the number of batteries or the resistor. They measured the voltage and current using three different resistors for each of at least five values of voltage, and they plotted their results on graphs.

Most of the students' lab reports were in line with what Hilda intended, but not all of them. For her snippet, Hilda collected some of the divergent responses to questions in the "results" section, including "What happens to the current when the voltage is increased (R constant)?" and "What happens to current when the resistance is increased (V constant)?" The following is quoted from Hilda's snippet.

John opened our conversation about Hilda's snippet with an interpretation of the difficulty some of the students had on the Ohm's Law lab and his suggestion of a way to address it.

We also spent some time talking about the group of students who discovered they were using the wrong bulb. In our conversation, Hilda recounted a similarly impressive episode in which a group of students, working on the Ohm's Law lab, found their measurements did not correspond to the markings on a resistor, ultimately to decide it was mismarked. Hilda described what impressed her about these cases:

Our conversation turned to this topic in general, of students who do not notice absurdities, in measurements or in calculations. Referring back to Hilda's examples of those who did notice and resolve inconsistent results, I asked why other students do not do this and whether it is something they could be taught.

Teacher perceptions

Again, our conversation about the snippet reflected a variety of interpretations of the students' understanding and participation. To review, these included perceptions of students'

ï difficulty with the concept of electric potential (voltage). John opened the conversation with this thought and proceeded to describe a piece of software he has found helpful. Given a simple electrical circuit, this program depicts a mechanical analogy to help students visualize electric potential as analogous to height.

ï treating the mathematics as disconnected from the concepts... Some students, John noted, were struggling with the conceptual relationship, whereas others were just "looking at it as a mathematical equation," without regard to its meaning.

ï ...as well as from the procedure and measurements in lab. Hilda also felt that the students were "using the equation as though it were pure numbers," rather than as though it involved quantities with physical significance. In particular, Hilda was referring to the fact that the students' explanations did not correspond to the procedure they had followed in the lab.

ï trying to make sense of discrepant data. Hilda wrote about one case in her snippet, of students who discovered that they had inadvertently used a different type of bulb, and she told us about another in our conversation, of students who determined that a resistor was mismarked. Hilda was impressed that "they looked for what could make this happen so that they could talk about it," in contrast to others who simply attributed discrepancies to "experimental error" without looking for any specific cause.

ï ignoring their common sense in thinking about physics. Toward the end of this conversation we digressed from Hilda's snippet to talk about a general perception of students, that many do not treat physics as connected to "reality." Hilda told of her students' saying they expect her to "trick" them and of her developing the habit of reassuring them that there are "no tricks." Ed spoke of Lis's snippet as a means of teaching students to treat physics as real.

It may seem surprising that a group teachers could find so much to discuss in these snippets, which to the untrained eye are fairly sparse excerpts and observations. The first point in this paper, however, is that these are not untrained eyes. Working every day with students, teachers become adept at interpreting what they see and hear. Like physicians for whom a handful of symptoms in a patient may indicate a variety of possible conditions and courses of treatment, these teachers have developed a wealth of knowledge and experience, intellectual resources for thinking about students.

It is unusual, however, to understand teaching in this way, including among teachers. Even in these conversations, the teachers often seem more inclined to talk about instructional materials and techniques than about interpretations of student statements and behavior. If inquiry into student knowledge and reasoning is at the core of teaching and teachers' expertise, as I am suggesting, then why would teachers seem reluctant to have conversations about it? This section concerns the second point of this paper, that teachers often talk about their interpretations by talking about instructional materials and techniques.

A language of action.

To digress for a moment on some of this history of this project, I had tried at the outset to impose the following ground rule: In conversations about snippets, we should restrict ourselves to comments that concern students' statements and behavior rather than what the teacher did or should have done. I had two reasons for imposing this rule. The first was to promote a focus on perceptions of students, rather than on the means for addressing them. The second was to encourage an atmosphere of respect for the teacher presenting the snippet. Too often, I had experienced, conversations about teaching degenerate into uncomfortable and unproductive criticism of the teacher's actions.

My rule proved difficult to enforce, however, and, in the end, counter-productive. A key example from the first year was John's "turn on the room lights" strategy (which Bruce recalled during our conversation about Robert's snippet above). Discussing another teacher's snippet, John had offered the following:

This moment led us to the realization that a comment about teaching strategy may also serve to convey an interpretation, and we were then able to recognize that this was happening fairly often. In other words, the teachers were often communicating "what to see" in the students' understanding and participation by suggesting ideas of "what to do" to help them. Their suggestions for methods and materials thus often had a dual purpose, explicitly to suggest instructional action, and implicitly to suggest a diagnosis of the situation.

For this reason, to rule out comments about teaching would be to rule out a principal mode by which the teachers discuss their interpretations. From the teachers' perspective, adherence to my rule made our conversations inauthentic, disconnected from their knowledge and experience, and we decided to abandon it. Perhaps it had served a purpose at the beginning, promoting a level of sensitivity and mutual respect in our conversations, but we came to see it as an impediment.

Turning back to our conversation about Hilda's snippet, there were several examples of comments that explicitly concerned ideas for instruction serving as well the role of expressing an interpretation.

The first example was again John's, who identified in Hilda's snippet a pattern he had seen before, of students' difficulty with the concept of voltage: "essentially nobody knows what it is." He went on to describe what he has found to be an effective means of addressing this difficulty, namely a computer program that displays mechanical analogies of electric circuits, with voltage analogous to height. By describing the computer program, John was not only suggesting it as an effective approach, he was also specifying what he saw as the problem, clarifying considerably what he meant by "nobody knows what it is." In particular, John saw the students as lacking what researchers might call a "mental model."[8]

He went on to note that some students "were getting the mathematical equation right, but . . . they have no idea what they're talking about," and Hilda agreed, saying "that's the thing. . . the inverse proportion is there and the mathematical equation, but it's not there in terms of the concepts." As the conversation continued, however, it became apparent that Hilda and John had different interpretations of what was the problem, or, at least, they were focusing on different aspects of it.

When Hilda elaborated on her interpretation, she explained that the students were "using the equation as though it were pure numbers and not [as though it was] a measurement of anything that had significance." She then continued to explain how she tried to address this in class, and this clarified what she meant by "a measurement . . . that had significance:"

Hilda agreed with John that the students did not understand the concepts, but she attributed this to a more general problem that they did not expect ideas in physics to make sense. She was saying, in effect, that the students were all capable of keeping track of what quantity they were measuring. That their explanations did not reflect what they had seen suggested they did not expect the relationship they were studying, Ohm's Law, to have tangible meaning. John's interpretation, in contrast, was specific to this content: The students did not understand the concept of voltage. On this interpretation, these students may not have been able to keep track of what they were doing in the lab, because they needed a mental model for reference. To understand that the voltage in the circuit is determined by the number of batteries, for example, requires an understanding of voltage.

It was not our purpose in discussing this snippet, nor is it my purpose here, to decide which of these interpretations is correct. Either, I expect, could apply for particular students in particular situations. As a matter of principle it is probably best left to the teacher, in this case Hilda, to make that judgment, because, in the end, she has the most information about her students. My purpose here is to suggest that Hilda and John interpreted the students' understanding and participation in different ways, and that we learned this primarily from what they said about instructional action, John describing what he would do and Hilda recounting what she did.

Later in the conversation, I asked why some students do not try to reconcile inconsistencies, as did the students Hilda described who had worked hard to understand anomalous data, and whether this was something they could be taught to do. Ed suggested that "one answer" might be to give students more experiences of the sort we had seen in Lis's snippet, in which a group of students had conducted their own experiments in projectile motion, shooting a bb-gun across a field and tossing pumpkins from a cliff.

Ed's suggestion was another example of a perception described in a terms of instructional action. He was, in effect, offering another interpretation of why students may not expect physics to make sense. Hilda had described a conversation with her students in which they told her they thought she could do "something to trick them," and how she had responded by saying she would not, an interpretation of the problem as arising out of a specific, articulable belief. Ed was considering the possibility that, for some students, the disconnection between physics and everyday experience lies more deeply, in a more general and less articulate sense of physics as taking place in a different domain of experience from their own, an interpretation similar to perspectives of knowledge and reasoning as "situated."[9] For such students, addressing the problem would not be as simple as telling them common sense applies; it would involve constructing with them a context for physics that directly engages their everyday experience.

In this way, Ed was using the idea of assigning "real-world" projects to help him express and refine his ideas for why students may not expect physics to make sense. In fact, much of our conversation about Lis's snippet earlier could be seen in this way: Lis had presented us with an example of an assignment designed to address aspects of students' understanding and participation not addressed by more conventional assignments, and our conversation about it drew our attention to those aspects. By referring to Lis's snippet, Ed brought those considerations to bear on the issue we were discussing at this moment, of students not treating physics as meaningful.

Teachers spend much of their time and thought in gathering and interpreting information, trying to gain insight into their students' understanding and participation. In this way, they have much in common with those engaged in formal research on learning. Still, there are important differences. Researchers intend their inquiry to produce explicit, articulate perspectives and claims, supported with arguments and evidence, hopefully to withstand peer-review. Teachers inquire toward action, in the contexts of their classes and hopefully to the benefit of their students, with little time or opportunity for explicit reflection and awareness, let alone for public articulation. In short, researchers publish, whereas teachers act, and this difference is reflected in different ways in which they experience and express their respective insights into learning and instruction.

In the following section I present a third and final example from our conversations, one that illustrates a role for education research. I suggest that the interaction between teaching and education research should be understood principally on this common ground, between the practice of teaching and the practice of research, of inquiry into student understanding and participation.
 

Interpreting a test on planetary motion: A role for education research.

One of the snippets we discussed on December 16, 1996 concerned students' responses to two questions from a test on planetary motion and gravity, which Bruce had given to his twelfth-grade, college-prep students. As part of his snippet, Bruce explained that the class had seen and discussed the PSSC film Frames of References. Much of their discussion focused on what reasons there were for believing the earth goes around the sun, and what reasons there had been for earlier beliefs that the sun goes around the earth. Bruce noted that they explicitly addressed whether the apparent motion of the sun across the sky was a reason for believing the earth moves: Airplanes and clouds also move across the sky, but that is obviously not reason to believe the earth is moving.

In our conversation, Bruce explained that he sees this behavior often.

In a similar vein, Lis noted that both parts of the statement in the first, true/false item are "true": the sun does rise and set, and the earth does spin on its axis. Seeing two true statements joined together in a sentence, the students may have been distracted from the logic of their relationship, especially under the duress of a test. Hilda and John talked about these as general liabilities of true/false and multiple-choice questions, that they are open to such misreadings, that they invite test-taking strategies, such as trying to second-guess the test author's intentions, and that it is difficult to know why students answer as they do, even when their answers are correct.

Still, returning to the snippet, Hilda affirmed Bruce's interpretation, in part because of her own similar experience.

Later in the conversation, Lis observed that the students in the snippet had all approached the test question, which asked why people had favored earth-centered models of planetary motion, as a question about physical objects rather than about people and how they form beliefs. Thus they answered in terms of the sun's apparent motion in the sky and the earth's rotation, rather than, for example, in terms of the influence of the Church and popular religious convictions.

As in the previous two examples, the snippet and our conversation about it raised a range of interpretations of the data, in this case student responses to two questions on a test. Here, I will focus specifically on how research on learning may have contributed to that range.

A role for education research

By and large, the education community tends to think of the connection between research and teaching in terms of instructional methods and materials: Research on learning should have implications for what teachers should do in class, whether to form cooperative groups, adopt microcomputer-based materials, or assess through student portfolios. Research, in short, should establish and prescribe effective methods.

We set out in this project to develop a different understanding of the relationship between teaching and research on learning, at the level of interpretation rather than method. Instead of asking how researchers' findings should inform teachers' techniques, we have been asking how researchers' interpretations may inform teachers' interpretations. To that end, we read articles from the research literature, considered the perspectives they presented, and asked what insights they could provide into the snippets we were discussing. Instead of methods or general principles, we were looking for insights into particular moments of learning and instruction.

I have been especially interested to understand the possible contributions of my own research on student learning. During the first year of the project, I asked the group to read two of my articles on students' beliefs about knowledge and learning, or student "epistemologies." We read one of my articles in May, 1995 (Hammer, 1995) and another in November, 1995 (Hammer, 1994). Bruce was referring to that work when he called the exam results an "example of the 'pieces' approach to learning physics": "Pieces" was the term I had used to describe the belief that physics knowledge is a collection of independent, disconnected pieces of information, as opposed to a connected, coherent system of ideas.

The important point here is that Bruce's use of the perspective in discussing his snippet reflects an influence at the level of interpretation: He saw his students as not attending to the connections among ideas. In fact, Bruce described this sort of contribution to his thinking on several occasions. In one other case, for example, he was discussing a snippet he had written to recount how three of his better students had solved a problem about light reflection to conclude that one's image in an ordinary mirror is upside-down, contrary to everyday experience.

If this is the role I as a researcher expect my work to play, then conversations such as these are essential, both in developing the ideas themselves and in understanding how they may or may not contribute to teacher perception and judgment. To be sure, our conversations led me to reconsider both the perspective and how I have presented it. I will not pursue that topic here except as follows, specifically in regard to the language of action I discussed in the previous section.

In proposing and designing this project, I had assumed a clear distinction between diagnosis and action. That assumption helped shape my thinking about the role of education research. Consistent with the philosophy behind "Cognitively Guided Instruction" (Carpenter, Fennema, and Franke, 1996), I consider teachers to be in a much better position than I to derive methodological implications for their practices. For that reason I had been careful to avoid prescribing methods, in writing about student epistemologies.

I was taken aback, therefore, by how Bruce described what he found useful about my articles: It was not, he explained, the presentation of the theoretical framework but the ideas they contained for what to do in class, which he drew primarily from the classroom episode and discussion of instructional strategy (in Hammer, 1995). On the other hand, it has been clear from his comments that he used the perspective as a diagnostic option for understanding his students. That Bruce considered the articles most useful with respect to the ideas they provided for instruction, I contend, is another example of the melding of interpretation and method in the language of action I described in the previous section. As we discovered in the failure of the ground rule I tried to impose on our conversations, for teachers, diagnoses of student strengths and needs are tightly interwoven with strategies for addressing them.

Thus, I maintain that it is a more appropriate role for education research to offer insights into student understanding and participation than to prescribe methods, but I do not maintain that it is inappropriate for education research to suggest methods. From our experience in this project, suggestions of method are an important means of communicating those insights.

We would also expect a parallel influence by teacher inquiry on education research. This project was designed to study how perspectives from research may contribute to teacher perceptions, but there have been signs throughout our conversations of what teacher perceptions may have to offer education research. One example is Lis's observation, in this conversation, that the students' had used "technical" rather than "social" language to answer the question on the test. This could be the kernel of a doctoral dissertation: What might affect students' choice of a mode of reasoning or discourse? Under what circumstances would they have approached the question in terms, for example, of how people are swayed by popular opinion? More to the point, her insights in this regard should be of interest to researchers investigating discourse in science teaching (e.g. Lemke, 1990; Roth and Lucas, 1997).

In sum, teacher inquiry overlaps substantially with research on learning. Both involve observing students and examining what they produce, so it is not surprising that they arrive at similar ideas. But there are important differences in the practices of teaching and research: Researchers publish whereas teachers act.[10] Having an insight into student understanding and participation, a researcher asks, in essence, "What can I say about this?" whereas a teacher asks "What can I do about this?"

The differences in their respective practices are reflected in differences of language, as we have found in this project, and these present a challenge to substantive exchange between teacher inquiry and research on learning. At the same time, the differences in their approaches represent complementary strengths: Researchers can and must focus on developing narrow, articulate views; teachers can and must be more broadly aware and responsive. We have explored the role perspectives from research may play in supporting teacher inquiry, but the benefit should certainly be mutual.[11]
 
 

Teacher inquiry and student inquiry

Nowhere is effective exchange of insights among teachers and researchers more important than with respect to student inquiry. There are many calls in state frameworks and national standards for a greater emphasis on student inquiry in science education. As general nicety, student inquiry seems a simple, desirable goal. In specific contexts of instruction, however, it is not a simple matter at all.

The core of the problem is that, whereas everyone recognizes the importance of student inquiry, no one understands clearly how to discern and assess it, or how to coordinate it with the more traditional but still important agenda of "covering the content" (Hammer, 1997). This, of course, is not for lack of trying, but attempts by philosophers of science to define what is the "scientific method" (e.g. Popper, 1992/1968) or by educators to specify "process" skills as appropriate educational objectives (starting with Gagné, 1965) are widely considered unsuccessful. If it is possible to capture the essence of scientific reasoning (and some agree with Feyerabend (1988) that it is not), it has not been done.

The "hard" sciences have achieved stable, precise, and principled systems of knowledge. Working within these systems there is much that is, at least in practice, "objectively true": There are clear, reliable, and reproducible methods, for example, for determining atomic masses or for manufacturing light bulbs. Education research has not achieved this quality of understanding; for good or ill, it is not possible to provide teachers clear, reliable, and reproducible methods for assessment and instruction. Interpreting student understanding and participation remains highly subjective, and the onus of that interpretation inevitably falls to the teacher, in specific moments of instruction like those recounted in the snippets above.

Moreover, this discrepancy between the quality of knowledge within science and the quality of knowledge about science and science education has particular significance for teachers trying to coordinate objectives of student inquiry and traditional content. It is, in general, relatively straightforward for a physics teacher to recognize when a student's answer to a question is correct or incorrect, judging it against the established body of knowledge. It is not difficult, for example, to see that the student in Robert's snippet was incorrect, from a Newtonian standpoint, when she said that "the force of gravity is getting bigger." It is not at all straightforward, however, to assess her understanding, to determine whether her comment reflects a misconception, which will prevent her from learning Newton's Laws if it is not eliminated, or a valid insight that will help her if she is encouraged to develop it. Nor is it straightforward to assess her reasoning as inquiry, for example to measure the value for her of having contributed an original idea or to weigh that value against the fact that it was incorrect.

Robert has often expressed his concern that students learn to engage in scientific reasoning, rather than simply "cover the content" with a superficial understanding of the ideas. To pursue his inquiry-oriented objectives, however, to have conversations such as that he presented in his snippet, Robert must compromise the traditional content of the course. Not only must he be able to reconcile this for himself, he must also be able to justify it to concerned administrators, parents, and students, all of whom will be well aware that his class has not "covered" as much of the textbook as other classes. What should he tell them? How can he make what they have gained as tangible as what they have lost?

Similar tensions arise in other snippets. To pursue many activities of the sort Lis assigned, which led to the students' videotaped experiments in her snippet, would similarly diminish the traditional content. How should she consider and describe the relative value of that activity, as compared to other more familiar activities, as she plans the distribution of time over her year?

Hilda saw differences between her students, not only in the correctness of their reasoning, but also in the quality of their reasoning. A number of her students had followed the instructions of the lab and arrived at mathematically correct conclusions, but she was troubled by their thinking nonetheless. It contrasted with the work of other students who had identified sources of discrepancies in their measurements. Precisely how should she interpret the differences between these students - was it interest, intellectual ability, confidence, all of these? ó and, what is largely an equivalent question in the practice of teaching, how might she design instruction to promote the more impressive reasoning? And, again, how should she weigh the value of that agenda against the value of covering more material?

Bruce saw, in his students' responses to two test items, an indication that they were approaching physics as a collection of incoherent facts. How should he value that perception against his perceptions of the correctness of the individual responses? Should students who are less consistent in their responses to questions on an exam, but get a greater percentage "correct," receive a higher or lower score than students whose answers are more consistent but have a smaller percentage correct? This may be seen as a conflict between valuing "inquiry" (the internal coherence of a student's reasoning) and valuing traditional content (the correctness of a student's individual answers with respect to the intended body of knowledge).

It is clear that there is much work to be done. If we are to achieve student inquiry-based science instruction, we must do more to appreciate and address the intellectual demands that agenda places on teachers. I believe this will require developing conversations among and between teachers and researchers, much more than is currently occurring, and that these conversations should begin from specific, authentic episodes of learning and instruction.
 
 
 

Acknowledgements

This project was funded by a joint grant from the John D. and Catherine T. MacArthur Foundation and the Spencer Foundation under the Professional Development Research and Documentation Program, and by the Dewitt WallaceóReader's Digest Fund under a grant to the Center for the Development of Teaching at the Education Development Center in Newton, MA. However, this paper is solely my responsibility and does not necessarily reflect the views of any of these organizations.

I am most grateful to Lis, Hilda, Ed, Bruce, John, and Robert, for participating in this project, for all their help and ideas in designing and redesigning it along the way, for the windows they provided into their practices, as well as for their critical readings of several drafts of this paper. Thanks also to Denise Ciotti, Kass Hogan, June Mark, Jim Minstrell, Peggy Mueller, Barbara Scott Nelson, Mark Rigdon, Ann Rosebery, Annette Sassi, Deborah Schifter, and Emily van Zee, for helpful comments, suggestions, and questions.
 
 
 

References

Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18(1), 32-42.

Carpenter, T. P., Fennema, E., & Franke, M. L. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics education. Elementary School Journal, 97(1), 3-20.

Cochran-Smith, M., & Lytle, S. L. (1993). Inside/Outside: Teacher Research and Knowledge. New York: Teachers College Press,

Duschl, R. A., & Gitomer, D. H. (1997). Strategies and challenges to changing the focus of assessment and instruction in science classrooms. Educational Assessment, 4 (1), 37-73.

Feyerabend, P. K. (1988). Against Method. New York: Verso.

Gagné, R. M. (1965). The Psychological Bases of Science--A Process Approach. Washington, D.C.: AAAS.

Gentner, D., & Gentner, D. R. (1983). Flowing waters or teeming crowds: Mental models of electricity. In D. Gentner, & A. Stevens (Ed.), Mental Models (pp. 75-98). Hillsdale, NJ: Erlbaum.

Haley-Oliphant, A. E. (1994). Exploring the Place of Exemplary Science Teaching: This Year in School Science, 1993. Washington, D. C.: American Association for the Advancement of Science,

Hammer, D. (1994). Students' beliefs about conceptual knowledge in introductory physics. International Journal of Science Education, 16 (4), 385-403.

Hammer, D. (1995). Epistemological considerations in teaching introductory physics. Science Education, 79 (4), 393-413. Also 1995, EDC Center for the Development of Teaching Paper Series, Newton, MA.

Hammer, D. (1997). Discovery learning and discovery teaching. Cognition and Instruction, 15 (4), 485-529.

Lemke, J. L. (1990). Talking Science: Language, Learning & Values. Norwood NJ: Ablex.

Popper, K. R. (1992/1968). Conjectures & Refutations: The Growth of Scientific Knowledge. New York: Routledge.

Roth, W.-M., & Lucas, K. B. (1997). From "truth" to "invented reality": A discourse analysis of high school physics students' talk about scientific knowledge. Journal of Research in Science Teaching, 34(2), 145-179.

Schifter, D. (submitted). Learning geometry in the elementary grades: Some insights drawn from teacher writing.
 
 
 

Appendix: The forces on the skydiver