between theory and data in a seventh‐grade science class

JOURNAL OF RESEARCH IN SCIENCE TEACHING VOL. 33, NO. 3, PP. 229-263 (1996)

Between Theory and Data in a Seventh-Grade Science Class

Maria Varelas

College of Education, University of Illinois at Chicago, Chicago, Illinois 60607-7133

Abstract

A conceptual framework is developed incorporating the dialectic of science (developing theories and collecting and analyzing data) and the dialectic of education (bringing preexisting sociocultural elements to the students and letting the students develop their own understandings). The theory-data dialectic is specified as including both the inductive and deductive directions. Discourse is seen as central to both the activity of science and the educative process, and hence as the bridge between them. In the context of this framework, an empirical study was designed and executed in a seventh-grade science class. This article presents and analyzes data focusing on (a) how teacher and students moved between theory and data in a unit on sinking and floating, designed to engage the students mostly in the deductive direction of scientific activity; and (b) how the dialectic of education was played out in the classroom as teacher and students were engaged in (a). A qualitative, interpretive methodology was used. Some of the complexities that this science class encountered as teacher and students attempted to engage in the deductive mode of scientific activity are presented and discussed.

The reform of science education has been in the forefront of attention in recent years (American Association for the Advancement of Science, 1989; International Association for the Evaluation of Educational Achievement, 1988; Linn, 1992; National Assessment of Educational Progress, 1988; National Science Board Commission on Precollege Education in Mathematics, Science, and Technology, 1983), and enhancing elementary and middle school students’ experiences in science has become a national priority. It seems appropriate that efforts dedicated to the improvement of science education take into account recent developments in understanding the sociocultural nature of both science and education. This involves a serious reconceptualization of the foundations of science education. This article examines the problematics of science education in this spirit, theoretically and empirically, focusing on the theory-data dialectic of scientific activity, and the sociocultural elements-individual meanings dialectic of education.

The background for the theoretical framework developed in this report is the movement in recent years from a traditional, teacher-directed perspective to a progressive, student-centered one. This movement came as an opposition to the traditional book- and lecture-centered approach that was seen as dominating science education and producing rote learning rather than understanding-and which therefore has been seen as based on a transmission model of education. The student-centered perspective has often taken the form of a hands-on, discovery learning approach which minimizes the role of the teacher and emphasizes the students’ development of new understandings through their own hands-on inquiries.

0 1996 by the National Association for Research in Science Teaching Published by John Wiley & Sons, Inc. CCC 0022-4308/96/030229-35

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The movement from the traditional book- and lecture-centered approach to the progressive hands-on, discovery learning approach has brought with it problems that are only now begin- ning to receive due attention, especially as concerns science education (Driver, 1995; Edwards & Mercer, 1987). First, the hands-on discovery learning emphasis has not appreciated the importance and necessity of discourse around the activities if the activities are to facilitate meaningful understanding (Bredderman, 1982; Duschl, 1990; Edwards & Mercer, 1987; Kuhn, 1991; Lemke, 1990; O’Loughlin, 1992). Second, the hands-on discovery learning emphasis in science education overemphasizes the inductive direction of scientific activity at the expense of the deductive one. In this approach to science education, students mostly collect data and identify patterns in them without developing theories that fit these empirical data. This decreasing emphasis on developing and formulating theories and increasing emphasis on collecting empirical data is apparent in programs developed over the last 2 decades, such as Science-A Process Approach (S-APA), Science Curriculum Improvement Study (SCIS), Activities that Integrate Math and Science (AIMS), Teaching Integrated Math and Science (TIMS), Founda- tional Approaches in Science Teaching (FAST), Developmental Approaches to Science and Health (DASH), and a descendent of SCIS, SCIIS. The emphasis on induction is associated with a decreasing emphasis on content and an increasing emphasis on process. However, these programs’ conception of process in scientific activity is a narrow one, because it does not incorporate the processes of theory development. As Hodson (1991) noted, “Induction is inade- quate as a description of scientific method and . . . methods often employed by science teachers [that mostly emphasize induction] project a distorted image of science” (p. 21).l

The National Research Council (1994) in their most recent working draft of the National Science Education Standards seem to (a) show equal emphasis on content and process and (b) emphasize theory development as an important aspect of scientific activity. However, most of the examples of teaching that are mentioned in this draft focus primarily in collecting and analyzing empirical evidence without providing examples of how teachers engage students in theory development.

The Conceptual Framework

The conceptual framework put forth in this article is quite distinct from either the traditional or the progressive approaches to science education, seeking to build on their strengths and to avoid their weaknesses. This framework arises from current understandings of teaching and learning and of scientific activity which are brought together in the context of science education. Science education is conceived as inducting students into mature2 scientific activity and helping the students make this activity meaningful to themselves. The conceptual framework adopts a constructivist approach: Learning is taken to involve an active construction of meaning by the student, one that nobody else can do for the student. Despite this emphasis, the approach is sociocultural: The individual’s meaning making is seen as situated within a preexisting cultural activity (in this case, the activity of science) and the role of the teacher is conceived as assisting the student to construct meaning within this cultural activity. The science student is considered to be a person who seeks to gain entrance to the cultural activity called science, and the teacher is considered to be a person who brings the student and the cultural activity together. My approach does not take as an aim of science education to develop only experts, or students who will specialize in science. The aim of science education that I espouse is to give to all students a feeling for and an understanding of the mature activity of science and help them have meaningful experiences with it.

The notion of science education as induction into the activity of science implies that a valid conception of science education must be based on coherent notions of the nature of scientific

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activity and the nature of the process of induction into that activity. I will deal in turn with each of these.

Regarding Scientij5c Activity

In my conceptual framework, science is a practice, an activity which has several charac- teristics. First, it is an activity that cannot be described by a set of clear-cut rules which, if followed to the letter, will enable somebody to do science. Second, science is a cultural activity characterized by specific tools and artifacts that scientists have developed and have been using over the years, such as diagrams, tables, graphs, terminology, etc. Third, science is a social activity in which scientists collaborate and work closely together with the ultimate aim of advancing their field, their practice.

My approach is based on the idea that science is an activity which centers on the interplay of theory and data. Science has two major levels: developing theories or models, and collecting and analyzing data. In their dialectical relationship, these two levels define the activity of science. I use the term theory to mean a network of concepts and ideas linked logically together, and not just the formulation of isolated hypotheses or predictions. I make a distinction between theories and empirically based generalizations or empirical laws in that theories have an explanatory power that comes from making sense of phenomena around us using concepts and ideas and linking them together, whereas empirical generalizations describe the world around us in organized and systematized ways but do not offer explanations. Thus, to an important extent, theory has its own integrity separate from the data (see below).

The dialectical relation between theory and data centers on the differentiation and also the fit between theory and data. Differentiating between theory and data implies distinguishing between two ways of knowing something-knowing from the theory, from developing conceptual, logical links between concepts and ideas; and knowing from empirical evidence. However, data and theory are not isolated from each other: They strongly interact, influencing each other significantly (Dewey, 1929; Duschl, 1990; Holton, 1988; Lythcott, 1991; Schwab, 1978). If theory and data do not fit, either or both might require further work. Nevertheless, each has its own integrity; to judge the fit of theory and data, scientists develop the trustworthiness of each of the two levels employing means that are particular to each level. For example, they gain confidence in the data level when they find that the data are reproducible. Similarly, scientists gain confidence in the theory level when they find logical coherence over a network of ideas and concepts.

In pursuing the theory-data dialectic, scientists sometimes use the inductive direction of scientific activity. They collect data, analyze them, and develop theories to explain these data. However, it is critical that scientists often use the deductive direction of scientific activity and, echoing Hodson (1991), overemphasizing the inductive direction of scientific activity at the expense of the deductive direction is a distortion. Working in the deductive direction, scientists develop a theory, derive from it testable statements, and collect and analyze empirical data to determine the fit between the testable statements derived from the theory and the empirical results. In the experimental mode of the deductive direction, the testable statement is a “question for experiment,” and the data are collected as part of an experiment carefully designed to obtain an empirical answer to this question.

Regarding Education

My approach is based on the idea that education centers on the interplay between sociocultural elements existing in a practice, in this case the practice of science, and made available

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to the students by the teacher, and the students’ own understandings which they have already achieved (Vygotsky, 1978, 1934/ 1987). This interplay has two directions: (a) a top-down component-preexisting cultural achievements brought to the students from the outside, and (b) a bottom-up component-students developing their own understandings (Becker & Varelas, 1995). Neither of the two by itself can lead to full and successful induction into the practice of science. Let us focus first on the need to integrate the top-down component with the bottom-up component. The top-down component is brought to the educative process by the more experienced teacher and practitioner. However, it is brought into action with the ultimate goal of helping students learn science meaningfully. If it is not successfully integrated with the understandings and meanings that students already have, that is, if it remains isolated, it will be poor in meaning and will not be owned by the students. As indicated earlier, my approach opposes the transmission model of education: teacher’s more advanced knowledge simply replacing the student’s more primitive knowledge. In contrast to the transmission model, my approach is based on the notion that students need to construct their own knowledge. In other words, the claim is that the sociocultural top-down elements of a practice cannot just be brought by the teacher and received by the students; students need to interweave them with their own prior bottom-up understandings if learning is to occur.

Focusing now on the need to integrate the bottom-up component with the top-down component, my conceptual framework is based on the position that students do not create by themselves the practice of science. Seen as a sociocultural practice, as argued earlier, science is appreciated as a rich and complex enterprise that students cannot just discover by themselves. Furthermore, students need to restructure their thinking as part of becoming practitioners of science. Students cannot do that without the help of the structure that governs the practice of science; they need this structure to transform their prior understandings. This structure is brought to the students by the skillful and experienced teacher who is a practitioner of both education and science. By participating in the existing forms of a specific practice (e.g., the practice of science) while guided by a sufficient member of the practice, students develop mental organizations and meaningful understandings which enable them to become autonomous participants in that practice.

The integration of these two components, top-down and bottom-up, is the responsibility of both the teacher and the students. However, initially, when the students are relatively unfamiliar with the basic elements and dynamics of a particular practice (in this case, the practice of science), the teachers’ responsibility in this process is greater than that of the students. In such an early stage, the teachers try their best to reveal students’ own conceptions, and engage the students in using, at the level they can, the necessary tools, artifacts, and methods that practitioners of science use. The teachers need to be on guard that these top-down elements do not remain isolated, and that the students use them to transform their prior understandings. Eventu- ally, as students become more familiar with the practice, the integration of the top-down and bottom-up components is increasingly the students’ responsibility, too.

Ideally, students will strive to make things meaningful for themselves. However, because of various forces in home and school, many students have given up making meaning out of what is happening around them, especially in the classroom. As a result, there is an even greater responsibility on the part of the teacher to initiate and nurse this educative process. This presents its own difficulties, as it increases the likelihood of students passively receiving the top-down elements that the teacher provides. In such cases, the teacher must be constantly aware of this danger, probing for the students’ understanding and encouraging their meaning making. In fact, because of the students’ discouraging prior experience, the teacher has a responsibility to bring the students to feel that (a) they can make their school experiences meaningful, and (b) they have the right to have school experiences be meaningful.

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Using Vygotsky’s theory of intellectual development, I believe that in their dialectical relationship the top-down component of the educative process provides students a way to gain control over and further develop their own bottom-up understandings, whereas the bottom-up component helps the students imbue with meaning the top-down elements brought to them by the teacher. In a similar way, Dewey (190211956) saw the child and the curriculum (meaning a field of study, and in this case the practice of science) as “two limits which define a single process,” and he continued, “Just as two points define a straight line, so the present standpoint of the child and the facts and truths of studies define instruction” (p. 11). Furthermore, Dewey emphasized the interplay between the logical standpoint of experience that comes from the subject matter (similar to the top-down component in my description of Vygotsky’s approach) and the psychological standpoint of experience that comes from the child and his or her own experiences (similar to the bottom-up component in my description of Vygotsky ’s approach).

Discourse as a Bridge between Science and Education

For the teacher to induct students into the practice of science meaningfully and successfully, the teacher and students need to engage in constructing a common framework. This is best achieved through dialogue and argumentation (i.e., providing arguments that support the ideas and claims that are brought forward during the dialogue). Dialogue and argumentation, which are taken together to define discourse, are central to both the activity of science and the educative process-the latter being the way the teacher and the students interact in the process of induction (Damon, 1990; Vygotsky, 1934/ 1987). To a large extent, discourse constitutes the overlap, and hence the bridge, between the conceptions of science and education that underlie my conceptual framework.

The emphasis on discourse is in accordance with Vygotsky ’s theory of intellectual development, in which the relationship between thinking and speech (or thought and language) is seen as crucial for the student’s development. For Vygotsky (1934/1987), thinking and speech are intimately related and influence the development of each other: “It would be incorrect to represent thinking and speech as processes that are externally related to one another, as two independent forces moving and acting in parallel with one another or intersecting at specific points and interacting mechanically” (p. 243). Furthermore, Vygotsky conceptualized speech, or language, not as a mere expression of fully developed thought, but as a means toward the development of thought, “thought is restructured as it is transformed into speech. It is not expressed but completed in word” (p. 251).

Discourse allows students to express their own thinking, negotiate ideas and understandings with fellow students and their teacher, and develop them further. During discourse, students’ own ways of thinking and knowing are revealed, allowing the teacher to identify students’ understandings, validate them as ways of reasoning about the subject matter, and also help the students develop these understandings further. By negotiating their ideas through discourse, students begin to appreciate that science is a sociocultural enterprise with its own established ways of knowing where meaning is developed through a dialogical exchange of ideas (O’Loughlin, 1992). It is also through discourse that students can begin to appreciate that science is not an “objective” field of study standing apart from human perspectives. Students may begin to appreciate that scientific activity is marked by the particular nature of the human intellects engaged in it, and may come to experience that differing interpretations, which may or may not converge, are important and play a crucial role in science (Eger, 1992).

The emphasis on discourse in my approach is in keeping with the criticism noted earlier that the hands-on discovery learning emphasis of the progressive approach misses the importance of discourse around the activities. As Edwards and Mercer (1987) noted, “Experiences and activ-

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ities of the classroom are made meaningful by the sense made of those things by classroom talk. . . . A greater emphasis on the importance of language and communication in creating a shared conceptual sense of the meaning and significance of experience and activity may help to make classroom education a more open and explicit business, and therefore a less mysterious and difficult process for pupils” (p. 169).

In summary, my conceptual framework is based on two major dialectics. Regarding science, the focus is on the interplay of theory and data levels of scientific activity (dialectic of science). Regarding education, the focus is on the interplay between top-down sociocultural elements that the teacher brings to the students and the students’ bottom-up understandings (dialectic of education).

In the context of this conceptual framework, an empirical study was designed and executed in a seventh-grade science class. The focus of the analysis of the data presented here was to explore how this group of seventh graders and their teacher worked within the theory and data levels of scientific activity in the context of a unit that was designed to engage them mostly in the deductive direction of scientific activity. More specifically, and as I discussed previously in the conceptual framework regarding the dialectic of science, I was interested in studying how the teacher and her students approached theory and data, whether and how they differentiated between the two, whether each level-theory and data-had its own integrity, and whether and how the teacher and the students thought about the fit between theory and data. As teacher and students moved between theory and data, I was interested in studying how the dialectic of education was played out in the classroom: whether and how the teacher’s and students’ talk facilitated their understandings of theory and data, whether and how the teacher’s guidance and probing enabled students to differentiate between theory and data and develop the integrity of each level, and whether and how the students’ written work reflected the shared discussions among students and between teacher and students.

The Empirical Study

Method

Participants and Setting.

The empirical study was conducted in one seventh-grade science class of a middle school in a western suburb of Chicago. The teacher had over 20 years of experience in elementary school (mostly in primary grades), and her current responsibilities included teaching science in three seventh-grade classes. The class participating in the study consisted of 26 students, about two thirds female and one third male.

The teacher and the author met for roughly 30 sessions of 2 hours each throughout the academic year 1990- 1991 to discuss and further develop the conceptual framework of science education outlined earlier, and to plan and develop specific units which were used in the teacher’s class. In this way, the teacher and her seventh-grade students contributed significantly to the development of the conceptual framework and played an active and important role in the way this framework was shaped in practice.

The teacher and her seventh-grade science students worked on five units of scientific activity designed to include both levels of scientific activity: developing theories, and collecting and analyzing data. The five units were spread over the academic year 1990-1991 and covered roughly 25% of the science lessons for this year. The rest of the time, the teacher and her students followed their regular science textbook. The length of the units ranged from 6.5 to 12


periods, with the first unit being the shortest. The author was present in all science lessons related to this project and interacted with the students when they were working in small groups.

Science Units.

In each of these five units, the students studied a phenomenon familiar to them, and as mentioned before, they both developed a theory regarding this phenomenon and also did an experiment to collect and analyze empirical data related to this phenomenon. For the experimental part, cumculum materials from the TIMS program developed at the University of Illinois at Chicago by Goldberg and Wagreich (1989, 1990a, 1990b) were modified to fit the aims of this project. In each of these five units, there was a deliberate emphasis on discourse and the social nature of the practice of science. One way this was done was to include presentations by the students to their colleagues in the class, encouraging the development of norms of critique and argument.

For this article, I focus the discussion on the fourth unit of scientific activity on which the teacher and her students worked. This unit is called Sink and Float and was designed to engage students in the deductive direction: With the teacher, students develop a theory about sinking and floating, derive a question for experiment from this theory, find an empirical answer to this question, and determine the fit between theory and data. As mentioned in the presentation of our conceptual framework, the deductive direction of scientific activity is but one aspect of the practice of science. By centering this paper on students’ engagement and meaning making within this direction, I do not want to imply that scientific practice does not recognize or reward the inductive search for patterns in collected data. I do want, though, to explore how a group of seventh graders and their teacher approached a scientific phenomenon from a deductive perspective.

The author worked with the teacher to develop a theory, a scientific story that could help students associate materials denser than water with sinking in water and materials less dense than water with floating in water. At the theory levkl, this unit was intended to help the students make a coherent logical story linking the density of a material relative to that of water, with the relative strength of the upward and downward forces acting on a material submerged in water and with the resulting behavior of this material in water. In other words, the intention was to help students construct an explanation including, for example, that for bodies with density greater than water, gravity overcomes the buoyant force, and therefore, these bodies sink in water. For an account of the logical chain of ideas and concepts making up such a coherent theory, see the Appendix. These students had previously worked on a unit of scientific activity called Mass versus Volume, in which they explored the linear relationship between the mass and the volume of a given material and discussed the concept of density of a given material in terms of the mass of this material in a unit volume.

In this unit, the teacher and the students worked in a single large group to develop a theory or, as it was called in class, a scientific, logical story about the phenomenon of sinking and floating (Stage 1). Then, the students worked in small groups-most often in pairs or in groups of 4-to develop a written summary of their story and construct a meaningful question for investigation by an experiment (Stage 2). While students were working in their groups, the teacher and the author went around helping the students when necessary, or further probing their understandings.

The teacher and the students then got back together in a single large group to discuss the work that the students had done in small groups, to further develop a question for the experiment and design the experiment. To initiate this discussion, the students were asked to present to the

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rest of the class the work they had done in small groups (Stage 3). As it turned out, there was only one presentation, because of the length of the discussion that was generated by this presentation and the limited amount of time the teacher devoted to this stage. The discussion generated by the presentation focused on the question for experiment.

Continuing in the single large-group discussion, the teacher and the students proceeded to design the experiment (Stage 4). Next, the students worked in small groups to rewrite their question for experiment and collect and analyze their data (Stage 5). During the collection and analysis of the data, the teacher and the students occasionally came together in a single large group to discuss issues that arose in the small groups. In the next phase (Stage 6), the students worked in their small groups to produce in their logbooks a written summary of the unit that they had been working on, guided by three general sets of questions (Logbook Question 1: What was this experiment about? What did you want to find out?; Logbook Question 2: What did you find out?; Logbook Question 3: Do you think you’ve got good data? Do you trust these data? Why or why not?). Finally, the students made oral presentations to their classmates based on the summary in their logbooks (Stage 7). Generally, one representative of each group, either chosen by the teacher or a volunteer, presented to the rest of the class the group’s findings and conclusions. The teacher and students attended the presentations and participated through discussions and questions. The whole unit lasted for 11 periods with the collection and analysis of the experimental data taking roughly half of the time.3

Data and Methodology.

The main data sources for this study included (a) transcripts of the class dialogue between the teacher and the students and among the students themselves, and (b) these students’ written work over the series of lessons in the Sink and Float unit. These data were supplemented by the field notes taken by the author on the discussions with the teacher (in the 30 sessions mentioned earlier and in other discussions before and after the science lessons) and on the interactions the author had with the students when they were working in small groups.

The study employed a qualitative, interpretive design. The transcripts of the classroom dialogue4 were annotated and the students’ written work was coded. These annotations and codings were produced in relation to each other rather than in isolation. The focus of the analysis of these data was the search for themes and patterns that would shed light on the questions that appear as the goals for this empirical study (see “The Conceptual Framework”). Details on the ways I used to look at the data will be discussed as I present these data in the following section.

The types of the data and the interpretive approach used in the data analysis diverged, of course, a great deal from the classical experimental design that has been used extensively in research in science education. However, 1 believe that this way of studying a science classroom gave me an opportunity to explore how the teacher and her students moved between theory and data in the context of investigating a well-known, everyday phenomenon: sinking and floating.

Results, Analysis, and Discussion

How did students operate within the two levels of scientific activity, theory and data, as specifically related to the phenomenon of sinking or floating? Let us start addressing this question by taking a closer look at a relatively small excerpt of classroom dialogue which took place as a student shared with the whole class her group’s summary of the theory and their question for experiment (Stage 3). For me, this excerpt is a window into one student’s (Lena’s)


conceptualization of theory and data in the context of the specific unit. In addition, it raises in a student’s voice, in a very acute form, the central question of constructing the distinction between empirical and theoretical knowing, which is necessary for working in the deductive direction.

Teacher: Excuse me. All right, we’re going to get started right now. Okay, Birute, will you please start? Now, you’re going to be, you’re going to be listening and see what elements you might think that Birute could include to make her story more complete and her question more complete. So, we’re going to help, okay?

Teacher: Read your story first. Birute: Do you want me to read my question first?

Birute: The pull of the gravity will make a ball go up or down. The gravity pushes the water down as the buoyant force pushes it up, keeping it at an equal spot. For steel, the gravity overpowers the buoyant force and it makes the ball sink. A substance that has a bigger density will sink, and if it doesn’t and has less density than water it will float.

Teacher: All right, and your question was? Birute: Does the amount of density determine if the substance floats or sinks?

Boy: Yes. Sarah: Yes.

Teacher: All right, so she took what she knew and she’s trying to see if in an experiment she could answer this question. Does [. . .I5 Read your question again, please.

Birute: Does the amount of density determine if the substance floats or sinks? Teacher: Okay. Uh, does anyone want to, uh, ask Birute a question, or [. . .] all right, Lena?

Lena: Do you [. . .] Maybe you know the [. . .] You wanted to find out the answer but what [. . .] You’re asking, the question, does the amount of density [. . .] But what we’ve shown already says what the answer is. I don’t know.

Boy: We’re just too smart. Lena: I just don’t understand the question. I understand the question, but [. . . I

Teacher: All right, you’re saying, um, Lena, go ahead and ask your question again. Lena: Like, well [. . .1

Teacher: You want her to read it one more time? Lena: Yeah.

Teacher: Okay.

Teacher: Okay, do we [. . .] Does it matter, um, when you say the amount of density, does it matter in Birute: Does the amount of density determine if the substance floats or sinks?

relation to the water? Do we need to put something in there? Lena: Aren’t we trying to find out the amount of density?

Lena: Aren’t we trying to find out the amount of density? Teacher: Pardon?

Teacher: Well, you are going to be finding density of about six different materials. And then you’re going to see if that affects whether they sink or float, but in relation to water, is the density greater than water or less than water? All right?

Cathy: I know what she’s saying. She’s trying to say what we’ve shown in our summary already says the answer.

Teacher: All right, is that what you’re asking, Lena? Now, all right, we know this by experience, past experience and by thinking about it, and we know it for a few things. But we’re wondering whether this is always consistently true, and can we prove this by testing out different materials? Will this density higher than water always sink or did this just happen with steel? So we want to find the density of other materials and see if it will cause them to sink if they have a greater density and cause them to float. So we want to apply it to others. That’s what we’re saying, Cathy. Does that make sense?

Cathy: A little. Teacher: Okay, leave your journals or logbooks back there, please.

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Lena struggled to verbalize an interesting concern about Birute’s question for experiment. Lena pointed out to Birute that she was asking a question for which she already had an answer based on the summary of her theory that she just presented (“Do you [. . .] Maybe you know the [. . .] You wanted to find out the answer but what [. . .] You’re asking the question, does the amount of density [. . .] But what we’ve shown already says what the answer is. I don’t know”). Lena was confused because she could not understand how somebody would write up a question for experiment for which she already had given an answer (“what we’ve shown already says what the answer is”). Lena seems to be saying that surely we do experiments to find out things we do not know and not things we already know. Lena’s point made a lot of sense to her and, of course, to Cathy, who had not worked in the same group with Lena, and who went back and restated Lena’s problem (“I know what she’s saying. She’s trying to say what we’ve shown in our summary already says the answer”). But Lena’s point probably also made sense to the boy who ironically noted that already knowing the answer to their question for experiment came just from being “too smart.”

Lena’s struggle to understand Birute’s question as a legitimate question for experiment may point to Lena’s struggle to differentiate between knowing from theory and knowing from empirical evidence. Birute’s question only makes sense if the answer was not already known. For us, the answer being unknown rests on the distinction between having an answer from theory and not having an empirical answer. But to what extent did the students, in interaction with the teacher, develop a theory? To what extent did the students develop a logical explanation constructed from conceptual links between ideas and concepts which they could then test by collecting and analyzing empirical evidence? The teacher’s answer to Lena and Cathy’s concern does not support the scenario that students and teacher were developing a logical explanation of sinking and floating (a theory). The teacher talked about knowing “by experience, past experience, . . . and . . . for a few things,” and therefore “want[ing] to apply it to others.” This is more consistent with an empirically based generalization or empirical law than with a theory having its own integrity that explains why sinking and floating happens and why the relative density of an object determines how the object behaves in a medium.

Having used this excerpt to focus us on a central problem of the deductive direction for teacher and students, let us look closely at the earlier extended classroom dialogue as students and teacher sought to understand sinking and floating, and let us examine to what extent they constructed a theory (Stage 1).

Working to Develop a Theory: Whole-Class Discussion.

Teacher: Okay, we have an imaginary little bit of water that we’re going to say is about 17 cc’s in this container of water. [The teacher draws Figure 1 on the board.] So, we’re just going to pretend that this water is in a little ball and it stays right in that spot. It doesn’t go up or it doesn’t go down. It just stays in that little spot. . . . And water has a density of 1 g per 1 cc. Do you remember that? . . . Okay. So when we have [. . .] When we have the little ball of water it just stays in this spot. Now we took [. . .] say we had a ball of steel, and I put a little ball of steel in the water, what would happen to it? [The teacher adds another circle in Figure I , as shown in Figure 2.1 Would it stay just like this little piece of water in that position?

Boy: No. Teacher: All right, what would happen to it, Larry?

Teacher: It would sink. All right. It would sink and it would go down to the bottom and you wouldn’t see Larry: It would sink.

it staying here very long if I let go of it. What would make that sink? Larry, do you know?


Figure 1. Teacher’s first drawing on the board on Day 1

Larry: Gravity. Teacher: Gravity. Okay, so we have a force of gravity pulling down. [The teacher draws an arrow on the

steel ball, as shown in Figure 2.1 Okay, so gravity [. . .] um, what is, uh [. . .] How do we measure gravity?

Girl: In pounds. Weight. Boy: In pounds. Boy: You can’t.

Girl: You can’t measure gravity. Boy: Yes, you can.

Teacher: You can’t? In pounds?

Teacher: Okay. Pardon, Larry? Okay, all right, now [. . .] Okay, if I- Student: -Quiet! Teacher: Excuse me. If I take this ball and I released it, what’s going to happen to it, Laurie? All right, it

Student: It’ll fall down. Student: To the ground. Student: In the midair. Teacher: All right. It will go down, won’t it?

Teacher: Okay. Now, if I put it in this empty container, what will happen to it?

Teacher: It’ll drop to the bottom, won’t it? It’ll drop to the bottom. Okay. So it’s gravity that is pulling it

will [. . .] [The teacher uses a plastic ball.]

Girl: And it’ll bounce.

Boy: It’ll drop to the bottom.

down. Girl: Yes, but in the water?

Teacher: Okay, what is [. . .] Why is that? [The teacher lets the plastic ball fall in a container filled with water.]

Girl: Because the gravity is pulling the water down. Boy: It’ll float. Girl: ’Cause it’s got air in the middle. Girl: It’s hollow.

Teacher: George, why do you think it didn’t fall to the bottom of the jar? George: Not heavy enough? Teacher: What? George: It’s not heavy enough. Teacher: It’s not heavy enough. Okay.

Figure 2. Teacher’s first drawing on Day 1, including her addition.

240

Student: Student:

Girl: Teacher:

Boy: Teacher:

Boy: Teacher:

Barbara: Teacher:

Boy: Teacher:

Joe: Teacher:

Joe: Teacher:

Joe: Teacher:

Joe: Girl:

Teacher: Joe:

Teacher Andy.

Teacher

Girl Teacher

BOY

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Shh! Shut up. The water weighs more. Shh. Okay. All right. Water is a fluid just like air, except that it’s more dense and SQ it can support the ball. So, the ball doesn’t go down because the force of water pushing up is keeping it from going down. But in the case of the steel, the force of the water is very, uh, small compared to the force of gravity. Do you remember, um, what the density of steel was from our experiment? Who can remember that? All right, what do you think? Eight. Eight what? How do we express density? Eight grams per cc. Okay. So, so, the density of steel is eight grams per one cc. Okay, so if you had a piece that’s one cc, what would the mass of it be? Okay, Barbara? What would it be? Eight grams. Okay, all right. So, with steel you have [. . .] Whoa, whoa. Let’s see who’s listening. Okay, now what I want you to do in your notebook, I want you to draw a little diagram of what two forces are working on a steel ball when you put it in water. What two forces? There is only one. All right, what 1 want you to do is draw a little diagram to tell what two forces are working on the steel. Okay, now, let’s look back at our little piece of water here. We have [. . .] We have the force of gravity going down and we have the force of the water holding this little piece up. [The teacher draws arrows on the piece of water, as shown in Figure 3.1 Now you are going to draw one that tells which two forces are working on the steel. Gravity. And use some arrows. You can use some arrows to show yours, too. [The teacher draws arrows on the ball representing a piece of steel, as shown in Figure 4.1 What do you mean? So, we gotta draw a little ball in a container with arrows on it?

That’s easy. And tell what the two forces are. Gravity and gravity. They are two different things. Okay, um, Laurie, were you able to figure out what the two forces are? Gravity 1. . .] Is density a force? [. . .] No! [. . .] Gravity is the only force on earth. Andy? It’s easy. Gravity is pulling it down and density is pulling it up. Well, actually, Andy, you could say that it’s the force of the water. The, 1. . .] well, the density of the water. You could say the density of the water. 1 put water pressure. Okay, so you have that little force pushing up. But this [. . .] on the steel 1. . .] I have the arrows like that.

Uh-huh.

Teacher: Gravity is a strong force and the water pushing up is a very small force. [The teacher draws Figure 5 on the board.] So, this is water.

Figure 3. Teacher’s second drawing on the board on Day 1

BETWEEN THEORY AND DATA 24 I

Figure 4 . Teacher’s third drawing on the board on Day 1 .

Girl: Teacher:

Boy: Girl:

Teacher: Student: Teacher:

Girl: Teacher:

Boy: Teacher:

The bell’s going to ring in, like, 30 seconds. Okay. Now, what if 1. . .] What if we had another little substance that was very light weight, and we had 17 cc’s of this other substance, and its density was less than water, what do you think would happen to that? It floats, It would stay in the middle. Stay in the middle? If it’s less it would float. What do you think, Cathy? It really depends on the weight of it. Do you think it would float? Do you want us to keep our notebooks? Yeah [. . .] No, I would like you to [. . .] Excuse me. I would like you to leave your notebook right here. Leave your notebook right here as you leave. Thank you. Right here.

The teacher and students started exploring sinking and floating by attempting to develop a theory about this phenomenon in which they considered ideas such as density, forces that act on an object submerged in water, their relative strengths, and the object’s behavior in water. The classroom dialogue reveals the struggle that students and teacher go through to develop the idea that there are two forces acting on an object submerged in water: the weight of the object or force of gravity and the buoyant force that the water exerts on the object. In the case of the steel ball that sinks in water, Larry’s first explanation of this behavior is that “gravity” will make it sink, with no reference to the second force acting on the steel ball. The teacher tried to help the students to think about this second force by switching to a material that would float in water, a real plastic ball. George talked about the plastic ball “not [being] heavy enough,” indicating a sort of comparison between gravity and something else that he did not make explicit. A girl talked about “water weigh[ing] more.” The teacher synthesized the two students’ answers (“Water is a fluid just like air, except that it’s more dense and so it can support the ball. So, the ball doesn’t go down because the force of water pushing up is keeping it from going down”),

Figure 5 . Teacher’s fourth drawing on the board on Day I .

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bringing up very explicitly the second force, the force of the water pushing up. Going back to the case of steel, she also told the students that “the force of the water is very, uh, small compared to the force of gravity,” and moved on to empirical information, asking the students the density of steel.

After the teacher asked the students to “draw [in their notebook] a little diagram to tell what two forces are working on a steel ball when you put it in water,” she proceeded to draw it on the board herself as she sensed that the students may not have had a clear idea of what she asked them to do, especially after Joe’s comment that “there is only one” force acting on the steel ball. The students then had to name these two forces acting on the steel ball. As students thought about this, different students had different ways of making sense of what they were discussing in class. Joe was really having a difficult time dealing with the upward force of the water. He may have had a feeling for it and he probably associated it with the density of the water, but he could not associate this with a force, and he was confused (“Gravity [. . .] is density a force? [. . .] No! [. . .] Gravity is the only force on earth”). However, Andy was perfectly happy to talk about gravity and density as the two forces acting on the ball of steel (“It’s easy, gravity is pulling it down and density is pulling it up”).

The first lesson ended as students and teacher tried to connect various important concepts in sinking and floating. I felt that the students had a pretty good sense that materials denser than water sink in water, and materials less dense float, knowledge probably coming from their own experiences in the real world. However, in terms of developing a scientific story, a theory, a logical network of ideas which could explain why this was true, the students were probably pretty shaky in conceptualizing the two forces acting on an object submerged in water. There were also a couple of attempts by the teacher to relate the relative strength of these two forces to the relative density of the material, by talking with the students about the density, for example, of steel; but these attempts mostly focused on the empirical number the students had found for the density of steel.

The following day, the teacher and students continued to develop a scientific story for sinking and floating. Let us listen in.

Teacher:

Howard: Teacher:

Howard: Boy:

Lany:

Okay, and we talked about having a piece of water, an imaginary ball of water, and we said it would be [. . .] We just made up 17 cc’s and it stays in that place, because the water pushing up is equal to the force of gravity pulling it down. [The teacher draws Figure 6 on the board.] So, that piece of water will just stay in its place. And we talked about the density of water. Who remembers what the density of water is? Howard? 1 . 0 0 . 1.33 Of water. Density equals [. . .] Larry? One gram per cc. I knew that. So, for 30 cc’s, there’s 30 grams.

Figure 6. Teacher’s first drawing on the board on Day 2.


water 1gm I D=-

steel

D = 8 g m

Figure 7. Formulas written by the teacher on the board

Teacher: Okay. One-Okay, you remember it now?-per cc. This is water. And because the density of this little piece of water is the same, then, it’s going to stay in its place. But, then we know something about steel. We know the density of steel. And, do you remember, in general, we’re really rounding this off, but, what the density of steel was?

Boy: I S ? Teacher: 1.5. Do you agree with that, Frannie? Frannie: No. Teacher: What do you think? Frdnnie: Eight. Teacher: Eight what? Frannie: Eight grams per cc. Teacher: Okay, do you agree with that? Most of you found that it was-

Boy: --I agree with Phil. Teacher: Eight grams per cc. [The teacher writes on thc board, as shown in Figure 7.1 So, the mass, the

mass of, uh, one cc of steel is greater than the mass of water, so the case of the stcel [. . , ] This would be, water. Okay, so the steel, we said that it would go down because [. . , ]

Teacher: Gravity would overcome the force of the water, because it would be greater, wouldn’t it? It would be the greater force. [The teacher adds to Figure 6, as shown in Figure 8.1 Okay. Then I think we just started to talk about a material. Oh, we could just say Styrofoam, and we haven’t actually found the density of Styrofoam, but I know that you all have had experiences with, uh, putting Styrofoam into water. It doesn’t sink. It just floats on the top. So, what do you think about the density of some substance like Styrofoam? What do you think it would be? Greater than water or less than water, or what do you think? Lena?

Boy: Gravity.

Lena: I think it would be less than water. Not a lot, but anything less.

Larry: It’s just less than water. Teacher: Anything less? What do you think, Larry?

Teacher: All right, so it’s less than water. And so, we’re going to get the force pushing down would be less [. . .]

Boy: Than the force pushing up. Teacher: So, we’ll put it up there and then we would get more force from the water. [The teacher adds to

Figure 6, as shown in Figure 9.1 Okay now, let’s think about, um, a substance that has exactly the same density as water, which would be something that was made up to be one gram per cc,

water steel

Figure 8. Teacher’s first drawing on Day 2, including her first addition.

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ter

Figure 9. Teacher’s first drawing on Day 2, including her first and second additions.

and it wasn’t water but it was a substance. Um, what do you think is going to happen with the pushing-down and the pushing-up forces? What do you think? If I were going to put it right here, what’s going to happen to it, Cathy? Is it going to go down or up?

Cathy: What’s this substance?

Cathy: It would just stay right there.

Laurie: I agree.

Laurie: Yeah, ’cause if it has the same, then [. . .]

Teacher: This is just something that has exactly the same density as water.

Teacher: Stay right there?

Teacher: Who said they agreed? Laurie, you think it’ll stay right there?

Teacher: Okay, so you’re saying that the density pushing down will be equal to the density, I mean the- not density-the force pushing down will be equal to the force pushing up?

Rosemary: Uh-huh. Teacher: Okay, now, we’re going to take what we know about density and think about it in relation to

what things would sink and float. And I want you to just summarize the force of gravity, uh, pulling down and the force of the water pushing it up. Does anybody know another name for that force of the water pushing up? Cathy?

Student: Density. Teacher: Not density. Student: Pressure? Teacher: I bet if I say it, I bet you’ve heard it. The buoyant force?

Student: Buoyancy. Teacher: Have you heard of that? The buoyancy? All right, but you don’t need to worry about that, but

you need to think about [. . .] you need to think about making a summary of what we have talked about, some things sinking, some things floating, and how their density to water relates to that. Then you are going to do two things. Laurie? You are going to do two things when you go to your lab stations. You’re going to write a brief summary of this story, plus you’re going to write your question. And then at 1155, I mean at 12:10, which is about 15 minutes, you are going to, uh, share with the group the real short summary you made of the story of density and how it relates to sinking and floating and your question that we would be looking for in taking, uh, several materials and then trying to, urn, figure out whether density could help us [. . .] density could help us in deciding what [. . .] a question for an experiment for sinking and floating related to density. And we’re going to take a lot of different materials and see if we could, uh, make some sense out of why some sink and why some float. We have an idea why some would sink and why they would float, but, what would be our question, then, for density? The summary would be how different things work in water, okay? All right, now everybody knows your new lab stations, so let’s really get to work and I’ll be here to help you if you need help.

Girl: I’ve heard that!


As the teacher and students continued to talk about sinking and floating in terms of relative densities and relative strengths of the two forces acting on an object submerged in water, how did their scientific story hang together? The teacher told the students that the two forces acting on an imaginary piece of water were equal and asked the students the density of water, an empirical number they had found in previous lessons. Then she asked them about another empirical number, the density of steel. As she asked them why a steel ball would sink, she still got an answer from a boy (“Gravity”) that did not involve both forces but only gravity, She elaborated on the boy’s answer to include a comparison between the two forces (“Gravity would overcome the force of the water, because it would be greater, wouldn’t it? It would be the greater force”). Although the teacher talked about two forces, she drew a figure on the board which showed that on the steel ball that sinks in water, there is only one force acting on it: gravity (see Figure 8).

Throughout the class discussion, the teacher and students did not attempt to relate the relative density of a material submerged in water with the relative strengths of the two forces acting on this material. Why is gravity stronger than buoyancy in the case of the steel ball? How does the greater density of steel relative to water determine this? The logical links of such arguments were never brought up in class. Interestingly, none of the students raised these questions. Furthermore, none of the students raised the question of why the effect of buoyancy on the Styrofoam ball, as depicted in Figure 9, was larger than that on the water ball, which, by the way, is a mistake. Up until that point, critical links between ideas and concepts were missing from the story. In this way, one may wonder how students could get a sense that things do make sense in science. In some way, their right of having things make sense had been partly violated, and the students did not seek to restore it. Maybe these students had already given up this right based on their experiences with schooling so far, or maybe they would try to make more sense of things as they work with their peers in their small groups.

This part of the second lesson on sinking and floating ended with the students going to their stations to work with their partners to develop a summary of their scientific story and a question for experiment (Stage 2). But what was the nature of the scientific story that the teacher and students developed, and how could it lead to a meaningful question for experiment? As we have seen from the class dialogue, (a) elements of the theory were brought up mostly by the teacher, as students did not ask any questions but mostly only answered the teacher’s questions; and (b) logical links between these elements were not explicitly brought up. The students were sent to their stations to “just summarize the force of gravity, uh, pulling down and the force of the water pushing it up . . . think about making a summary of what we have talked about, some things sinking, some things floating, and how their density to water relates to that.” Would that be enough for the students to get a sense of the nature of a scientific logical story that links ideas about density and forces and behavior in water? We will take a closer look at what happened as students worked with their partners to shed more light on this question. We will be following the teacher as she moved from station to station.

Developing a Written Summary of the Theory and a Question for Experiment: Small- Group Discussions

Station 1

Girl 1: Mrs. C. Shore? Could you come back here? We’re confused. Teacher: Okay, all right. All right, what you’re supposed to do is, you’re supposed to think about what we

know; our story is what we know about the density. Yeah, you do. You know the density of steel and you know how to find the density of, of [. . .]

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Girl 2: I don’t understand what you mean by the story. Teacher: Well, the story is, uh, what were we talking about up at the chalkboard? Some things that sink

and [. . .] Girl 2: Some things that float.

Girl 2: Float or sink, or whatever. Teacher: All right, if it has more density than water, you think it will 1. . .]

Teacher: All right, and so, we’re going to try to find some way to measure this and to, you know, prove to other people why something would sink or float. So, we need to get, um, some measurements. And how do we determine density? What do we have to measure?

Girl 1: Mass and volume.

ume [. . .] Teacher: Uh-huh. Okay, so, we’re going to take a lot of different materials and get the mass and vol-

Girl 2: We’re actually going to do this? Teacher: Yes, we are actually going to do it. Get the mass and the volume and then we’re going to, uh, see

if that really is what determines whether something will sink or float. If it has more density, greater density than water, what do you think will happen? So, think about what we know.

Girl 1: What about the question? Teacher: The question is, what are we going to find out if we do an experiment?

Girl 2: Does the amount of density matter specifically? If things could float? Teacher: Sounds like a good question. Okay.

There is a strong indication that these two girls were confused about what they had to do at their station and what the teacher meant by the story. During this interaction, the teacher (a) pointed to a set of empirical facts (“You know the density of steel and you know how to find the density of [. . .I”), (b) presented a set of general statements about sinking and floating (“Well, the story is, uh, what were we talking about up at the chalkboard? Some things that sink and [. . .] ”; “All right, if it has more density than water, you think it will [. . .I”), and (c) made several references to empirical issues, such as measuring (“so, we’re going to try to find some way to measure this and to, you know, prove to other people why something would sink or float. So, we need to get, um, some measurements. And how do we determine density? What do we have to measure?’; “Okay, so, we’re going to take a lot of different materials and get the mass and volume”). In terms of developing their theory, the teacher wanted the girls to “think about what we know,” “if it has more density, greater density than water, what do you think will happen?’ In this way, the teacher was cueing the girls to develop a hypothesis that denser things sink and less dense ones float. But where is the essence of the scientific story-that is, developing conceptual links that would lead them to deduce this as a prediction? The girls were not encouraged to do this as part of developing a theory. Indeed, it seems that the girls were omitting the work of developing a scientific story and proceeding to design an experiment to find out whether the amount of density influences how things float or sink (“Does the amount of density matter specifically? If things could float?”). The girls picked up on the teacher’s emphasis on measurement and moved quickly to formulate a question for experiment rather than spending more time on the theory level. The girls did not have specific predictions about the relationship between density and sinking and floating, as is illustrated by their comment of “Float or sink or whatever,” and they just wanted to find out inductively some things about the relationship between density and behavior in water. Although the teacher attempted to some degree to get the girls to think about “what we know,” implying that they already had specific experiences linking density to behavior in water, and to realize that they would do the experiment to “see if that really is what determines whether something will sink or float,” this is still more at the level of empirical generalization than constructing a theory and deducing from it,


Station 2

Boy: Can you help? Teacher: All right, you’re going to talk [. . .] You’re going to think about what we talked about. What

forces, uh, work on something when you put it in water, and which things sink or float, and what do you know about density.

Boy: Okay. Teacher: So, just a real short summary that you guys can think of.

Teacher: All right, gravity, and there’s something pushing up. There’s something pushing up.

Teacher: Well, the force of the water. It’s a fluid.

Teacher: All right, and what do you know about density? Do you know how to find density?

Joe: What do you mean about what forces or gravity?

Joe: It’s water, because water, the water ain’t a force.

Joe: Then water. Okay. So there. There’s our two forces.

Girl: Density is mass over volume. Boy: I cannot.

Teacher: Uh-huh. So, you have to have two variables. You have to have two things here, don’t you? Okay. So what we want to know is if there’s some way that we can tell what’s going to sink or float by the way, uh, we figure out density. We know from the density.

Girl: Here’s our question. Teacher: Does the amount of density matter if the, uh [. . .] All right, what if you said, does the amount of

density, um, determine . . . Girl: Have an effect.

Teacher: All right. Have an effect. Okay. Joe: What is the other ball we’re using? A steel ball and a what?

Teacher: We’re going to use six different kinds of materials. So- Joe: -How do we know what materials we’re going to use?

Teacher: We’re going to use six different kinds. Joe: Yeah, but we don’t know what materials we’re going to use.

Teacher: No, it doesn’t matter which materials, it just matters that they’re different.

In contrast to the previous excerpt of discourse, in trying to help these students who also requested help, the teacher brought up this time the idea of “forces [that] work on something when you put it in water.” However, she moved quickly to density and “how to find density,” without attempting to help the students develop logical links between the relative density and the relative strengths of these forces. The conversation shifted to the question for experiment which one girl showed to the teacher, to be interrupted by Joe, who wanted to know more about the experimental part rather than spending more time on the story and the question. The discussion in this group does not let us know whether the students even have a specific expectation regarding how the density of a material relative to the density of the water affects its behavior in water.

Station 3 .

Girl: We need your help. We know what we’re supposed to do, we just can’t do it. Teacher: Okay, I told Bunty I’d help her first and then I’ll come to you. Bunty?

Teacher: All right, what you need to do is put down what you know from the story that we had up here. And we know that some things [. . .] we’ve seen some things sink and some things float and some things stayed put. Okay, and what determines that?

Bunty: We don’t really understand this.

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Bunty: Um, the gravity and then the density. But I really don’t understand density.

Bunty: Isn’t it how [. . .] something [. . . I

Bunty: Yeah 1. . .] are packed?

Teacher: All right, density is [. . .] what is density?

Blanka: How close the molecules are or something?

Teacher: All right, uh, how dense are the molecules are packed together and what the mass is over volume. So, you take the piece, and the relationship between those two is density. Density equals mass over volume. [ . . .] And we know that water is one gram over one cc, and something that has a density greater than water, we know [. . .]

Bunty: Will sink. Teacher: Okay, but we want to find out [. . .] We know that was steel because we saw that. But we want to

find out if the density is going to be [, . .I If we can measure the density, do you think we could take six different materials and find the density of each one?

Teacher: How could we do that?

Teacher: And so we want to, though [. . .] We have this idea, now. We want to see if we can do an experiment to further prove it. To substantiate it. We want to, we want to find, uh, densities of different materials and then see if it’s less than water; what do you think will happen?

Lena: Well, see, if it’s less 1. . .] if it’s not in the middle, then it’s less. If it’s not in the middle of the thing, it’s got to be right in the middle. It doesn’t matter where you put it.

Teacher: Okay, and we want to do more than just say more or less than. We want to say the density is a certain thing. Okay? All right, so we take what we know and we know that some things sink and some things float. And we know it has something to do with density. And if it’s the same density as water, what happens to it?

Bunty: Yeah, I guess.

Bunty: Is that the idea?

Lena: It doesn’t go up or down. Teacher: It doesn’t go up or down. The buoyant force of water is pushing it up and gravity is pushing it

down so that, uh, now the question will be, is there some way that we could find [. . .] Do you think we can find the density of those things? I asked you that before.

Bunty: I guess.

Bunty: Yeah. Teacher: Could we measure [. . .] do we know how to measure mass and volume?

Teacher: Okay, we know how to measure mass and volume. So, we could take all these objects and we could quantify this by finding out the density of each one and then test it out to see if those things heavier than water would do what? Those that had a greater density than water would [. . .]

Girl: Sink. Teacher: Sink. But that’s what we think. But that’s what we’re going to test out. Blanka: Are we supposed to write that?

Teacher: Yeah.

Teacher: Does density determine if an object will sink or float? Okay.

Teacher: All right, and what does steel do? You know what steel does in water. What does it do? Does it

Girl: Look at my question.

Girl: Mrs. C. Shore? Can you read our question?

float, sink, or what? Boy: The steel sinks.

Teacher: Okay, so you know that, don’t you? So, now what we want to find out is, is this going to be [. . .] We know that the density of steel is greater than or less than water?

Boy: Greater than. Boy: Greater than.

Teacher: Greater than. So, we know that. But we want to take six different materials and find out if this will always be true. Does density really determine whether something will sink or float? And if we know the density.


Howard: Gravity and density. Teacher: All right, and gravity is always going to be the same. It’s going to be consistent pulling. But it

depends on the mass, how much pull there is. Okay, I’m going to put 1. . . I Will you help me, Howard? Okay, I’m going to put up something more that might help you. Okay, okay, all right. Okay. Okay, you might want 1. . .] I think what you meant was something that has a greater density than water, right?

Girl: Yeah. Teacher: Will sink. Something that has the same density as water will not go up or down. And something

with less density than water will float. Okay, great. So, we know something about density. Now, what our question is going to be, is, can we show [. . .] Is this the way it’s always going to be? You know, we know for a few things and so we’re going to [. . .] not always going to be, but, can we, uh [. . .]

Bunty: So, our question is, is this always true?

Bunty: What we just stated is always true. Teacher: All right, is what always true?

Teacher: All right. So, you have to put all those elements into your question and you’ll have a good question. In the real life.

Bunty: But what should we write? Teacher: Well, you said that things that are more dense [. . .] have a density greater than water are going

to [. . . I Girl: Sink.

Girl: Float. Teacher: Sink. And you said that things are less dense than water are going to [. . .]

Teacher: Float. All right, and we want to know if we can, um, measure the density of objects and then test it out and see if this really is true in real life.

Girl: So, can we measure density and prove that this is true? Teacher: Yes, but in your question, you need to be a little more explicit than just what you said. You have

to incorporate, if things have a density greater than water [. . .] Girl: Okay.

Teacher: So, you have to be pretty explicit with that. But then you’ll have a good question. If things have a density [. . .]just what we said. Go try it. I know you can do it.

Here is another group of students who struggled with the summary of the theory and the question for experiment. Bunty was trying to make sense of the things they had talked about in class. She brought up gravity and density as two reasons that determine whether things float or sink in water. Remember that when the teacher and students were developing the story of sinking and floating, students talked about density being the second “force” that pushes an object up when submerged in water. Probably, this is what Bunty was referring to, but she went on to state that she did not understand density, to lead the discussion to a definition of density, and the relationship between relative density and behavior in water-that is, things with density greater than water sink, things with density less than water float, and things with the same density stay put. The notion of the two forces acting on an object submerged in water and their relative strengths as determined by the density of the submerged object relative to water (its relative density) was never explored and developed. The discussion mostly focused on measuring, how students could measure density and what they would do in the experiment. The teacher and students did not generate a scientific story but a set of statements, predictions, or hypotheses that were to be tested. There was no explicit mention of where these statements came from, but it is pretty clear that these statements did not come from a coherent, logical scientific story that explained why, for example, denser things sink. It seems that these statements came from prior empirical evidence that students and teacher had with things sinking and floating. The teacher’s

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version of a question for experiment-“is this the way it’s always going to be? You know, we know for a few things and so we’re going to . . . ”-supports this interpretation.

Station 4.

Lena: For the question, can we find the density of an object?

Lena: Yeah.

Lena: By using water?

What is density?

Teacher: You know you can.

Teacher: All right. So, if you know [. . .]

Teacher: No, to find the density, no, the density you know you can find, because you have to find [. . .]

Lena: Density is, um, yeah, volume. Teacher: Mass per unit volume, right? Or whatever. All right. It’s the relationship between the mass and

the volume. So, you know that you can find density of any object that we give you, right? Because you know how to do that. All right, now your question is, what you know up here is that you know that steel has a greater density than water and you saw it sink. So, you know [. . .]

Lena: All right, how about, does density affect 1. . . I Does density affect, uh [. . .I

Lena: But we know the answer. It does. Teacher: All right, but what we want to know [. . .I

Lena: How does density?

Bunty: Does density affect how an object sinks or floats? Why an object sinks or floats?

Bunty: How does density affect [. . .] Teacher: All right, what do you know though? You know that, uh, steel has the greater density than water.

Do you know that? Girl: Yes.

Teacher: All right, so you know that some things that have densities greater than water will sink. Okay, now, what we want to know is if we can find out about other things. If we measure the density, can we predict if other things will sink or float?

Marty: Yeah. So, okay. Teacher: So, we want things that [. . .] We think that things that have a density greater than water will do

what? Marty: Sink.

Teacher: Sink. So, that’s what you think. Girl: Yeah, so can we prove that [. . .] Can we prove by measuring the density of other objects if

water’s density does affect something or other? Teacher: All right, write it down.

This piece of discourse brings us back to the opening of Results, Analysis, and Discussion. We see here (Stage 2) again Lena, the girl who later challenged Birute’s question for experiment in relation to her summary of the story (Stage 3), struggling with her partners to develop a question for experiment. Lena’s first question was: “Can we find the density of an object?’ This was challenged by the teacher, who said that this could not be a question for experiment, because she knew she could find the density of an object, or in other words, she knew the answer to her question. Soon afterward, Lena used the same line of reasoning the teacher used with her to one of her partners, Bunty, claiming that they knew the answer to the question, “Does density affect how an object sinks or floats?” that Bunty proposed as a question for experiment. Thus, if they knew the answer to the question, how could it make sense to pose this question as their question for experiment? Of course, the issue here is how they knew the answer to this question, and where this answer came from. Did they know this answer from their theory

BETWEEN THEORY AND DATA 25 I

and want to acquire empirical proof for this? Did they know it from limited empirical evidence, empirical results for some materials, and want to find out whether it holds true for other materials, too? These are two distinctly different modes of scientific activity; the former is on the deductive side and the latter on the inductive side. Given the nature of the discussions illustrated above, both for the single large group and for the small groups, and given the quotations and commentary appearing above, the latter seems more probable. As a matter of fact, the teacher said to this group of students, “All right, so you know that some things that have densities greater than water will sink. Okay, now, what we want to know is if we can find out about other things.” This is clearly on the side of empirical generalization rather than on the side of theory construction and deduction from theory.

At this point, it is worth going back to the first piece of discourse quoted in this report. Let us listen in on the following day in class as the teacher addressed Lena’s question, which also became Cathy’s concern (Stage 3).

Knowing from Theory and Knowing from Data: More from the Whole-Group Discussion.

Teacher: Okay, I’ll tell you about that in a minute. Yesterday, just as class was about to end, uh, Cathy and Lena expressed a very good concern, and do you remember what your question was? Or should I read it for you?

Lena: Read it for us. Teacher: All right, this is the way I interpreted what your question was. Um, you both kind of said, if we

know the answer from our story, that materials with a higher density will sink and materials with a lower density than water will float, why would we do the experiment? Is that kind of the question you had?

Lena: Yeah. Teacher: Okay, all right. The reason that we would do the experiment is that, um, we have something in

our mind and we know a little bit about it, and so we have a story. We take all the information that we have and we have a story. And that’s what scientists also do. Now, we took the density, we know the density of steel, and we took the density of Lucite also. Did we actually experiment with something that has a density lighter than water?

Girl: No. Teacher: No, we didn’t. So, we definitely think that we’re right, but we’re not absolutely certain, are we?

No. Remember, a long, long time ago, that the scholars thought that the earth was flat? And in their mind, that made perfect sense. Didn’t it? And from everything that they could see, it looked like the earth was flat. But, they had to go out there and experiment and go over the horizon, so to speak, and then find out that their original idea wasn’t extensive enough. There was a time when, there was a time when scientists thought that, um, if you dropped two balls, and one of them had a greater mass, that the ball with the greater mass would drop to the ground quicker, because that made sense to them. And it took a long time before they could ever discover that that wasn’t true, because they had to, uh, overcome some things like wind resistance and so forth, but [. . .] air pressures and so forth. But [. . .] So, people can have ideas in their mind, and be really sure that they’re correct. But that’s what a scientist has to do, he has to test it out, get some real quantitative, uh, data, and then he’s sure. Now, if we wanted to make sure that everything with a density less than water would float, and everything with a density greater than water would sink, we’d have to go out, uh, test everything that there was, every material. Is that possible?

Class: No. Teacher: No. And scientists also have to do samplings. They have to get as big a variety of materials as

they can and then apply that to, uh, a more generalized, um, experience. So, they start with whatever they can and then they expand, but, um, we do have to test things out, because that’s our story and that’s where we get our question from.

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In her attempt to help the students see why scientists do experiments if they already know the answers from the theory, the teacher gave a top-down monologue to the students without trying to engage them in relating this to their own understandings. Although the teacher tried to develop a distinction between the theory level and the data level, she kept mixing in her talk (a) elements that are more associated with knowing as a way of developing logical links between concepts and ideas (“The reason that we would do the experiment is that, urn, we have something in our mind“; “We definitely think that we’re right, but we’re not absolutely certain”; “Remember, a long, long time ago, that the scholars thought that the earth was flat? And in their mind, that made perfect sense. Didn’t it?’ “People can have ideas in their mind, and be really sure that they’re correct. But that’s what a scientist has to do, he has to test it out, get some real quantitative, uh, data, and then he’s sure”) with (b) elements that are more associated with knowing through empirical evidence (“We know the density of steel, and we took the density of Lucite, also”; “And from everything that they could see, it looked like the earth was flat”). This may have not helped the students develop the differentiation between the two ways of knowing. The teacher’s talk once again does not make clear whether the organization of ideas-the relationships discussed-comes from developing logical, conceptual links among relevant concepts, as is necessary for the deductive direction of scientific activity, or from previous empirical evidence, being a relatively direct generalization of these previous findings and thus remaining in the inductive direction.

The teacher’s and students’ talk as they developed their theory for sinking and floating and their question for experiment points to several findings: (a) the teacher and students discussed and struggled with some important ideas that could help them develop a theory to explain why and how the relative density of a material with respect to that of water determines whether the material would sink, float, or stay put when submerged in water; (b) as they attempted to develop a scientific story for the phenomenon of sinking and floating, the class oscillated between two different modes, developing a logical explanation of this phenomenon and discussing an empirically based generalization of this phenomenon; and (c) most of the time, there was not a clear indication whether teacher and students were operating in one or the other mode. But how does the students’ written work relate to these findings? Does this written work reflect the shared discussions among students and between teacher and students, and how does it do that? What does the students’ written work reveal in terms of the students’ understandings of theory and data and their interrelationships? I now turn to these questions.

As mentioned earlier, before doing the experiment, the students wrote a summary of the theory they developed with the teacher, and then had two opportunities to formulate in writing a question for experiment. We just listened in to some groups of students as they worked on a summary of their theory and their first attempt to develop a question for experiment (Stage 2). After class discussion, all students had a chance to revise, if they wanted to, their question for experiment (Stage 5 ) . Let us now explore the summaries of the theory that the students wrote.

Looking at Theory and Data: Students’ Written Work

What kind of summaries of the theory did the students write? Did they indicate in these summaries some kind of relationship or link between relative density of a material with respect to water and its behavior in water? That would be a first step toward having an expectation for the phenomenon of sinking and floating. But this expectation could still be derived from an empirically based generalization and not a logical, coherent, scientific story that explains why this relationship exists. One way to achieve this kind of theory, a logical network of concepts and ideas, is through linking the relative density of an object with respect to water to the relative strengths of the two forces acting on this object when submerged in water. To achieve this,


students need to think about the two forces and link the relative strength of these two forces with the density of the submerged object and the object’s behavior in water. However, to achieve a further level of logical coherence, an additional step is necessary. In this step, the link between the relative strength of the forces and the density is explained by linking the upward force on a submerged body, having a given volume, to the density of the water, and the downward force to the density of the body. Therefore, the students’ summaries of the theory were examined in terms of five features‘?

Criterion A: Directionality of the link between the density of a material and its behavior

Criterion B: Specificity of the link between the density of a material and its behavior in

Criterion C: Reference to two forces acting on a material submerged in water. Criterion D: Linking the relative strength of the two forces with the density of the

Criterion E: Explaining the link between the relative strength of the two forces and the

in water.

water.

submerged object and the object’s behavior in water.

density of the submerged object.

Students’ summaries that related sinking with higher density andjoating with lower density were considered to have directionality. Students’ summaries that specified that it was the density of the body relative to that of water that was critical were considered to have specificity. Students’ responses were considered not to have directionality or specificity if the responses did not include a link between the density of a material and its behavior in water, or if the link that they included did not have directionality or specificity.

To clarify these criteria, let us look at some students’ summaries of the theory.

Larry: Things less dense than water float. Things more dense sink. Things with the same density stay in the same place.

Larry’s summary of the theory had both directionality and specificity. However, Larry did not refer to any forces. Thus, Larry’s summary satisfied Criteria A and B, but did not satisfy Criteria C, D, and E.

Ivy: We have learned that the force of water and gravity work together to make an object float or sink. If the object has a greater density than the water the force of gravity is stronger than the water force and pushes the object down. If the object has a less density than the water force the water force is then stronger than the gravity force and the object floats. If the object’s density is exactly the same as the water than [sic] the object stays in the same place.

Ivy’s elaborate summary of the theory had both directionality and specificity. It also included a reference to two forces named gravity and water force, and also linked their relative strength with the relative density of the object and its behavior in water (“If the object has a greater density than the water, the force of gravity is stronger than the water force and pushes the object down”). However, Ivy’s summary did not explain this link. Thus, Ivy’s summary satisfied Criteria A-D, but did not satisfy Criterion E.

Vida: The gravity pushes down as the water pushes it up.

Vida’s summary of the theory did not include a link between the density of a material and its behavior in water, thus lacking both directionality and specificity. However, Vida referred to

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two forces: gravity pushing down and water pushing up. Her summary did not link the relative strength of these two forces with the density of the object and its behavior in water. Thus, Vida’s summary satisfied Criterion C and did not satisfy Criteria A, B, D, and E.

Howard: I have learned the density of water, which is 1 g/cc. I have also learned the density of steel, which is 8 g/cc. The gravity pulls down and the density makes it go up. The summary of our story is that gravity pulls down and density makes it go up.

Howard’s summary, like Vida’s, included reference to two forces, although he named one of them incorrectly (density instead of gravity), satisfying Criterion C but not satisfying any of the other four criteria.

Joe: Gravity holds balls down water pushes balls up. If it floats, its [sic] got a low density; if it sinks, its [sic] got a high density.

Joe’s summary of the theory had directionality, but it did not have specificity. It included reference to two forces, gravity and the force of the water, but it did not link the relative strength of these two forces with the density of the object and its behavior in water. Thus, Joe’s summary satisfied Criteria A and C, but did not satisfy Criteria B, D, and E.

The summaries of the theory that the students produced either did not include a link between the density of a material and its behavior in water or included a directional link. There was no summary that included a link with no directionality. Furthermore, there was no summary that satisfied Criterion E-explaining the link between the relative strength of the two forces acting on a submerged object and its density.

There were 24 students for whom I have a record of summaries of the theory. Table 1 shows the percentages of those students who met particular criteria for the integrity of their theory level. A student’s theory level is considered to have internal coherence and integrity when all five criteria are satisfied in the student’s summary of the theory.

Table 1 indicates that most of the students included a directional link between the density of a material and its behavior in water, although this link had specificity in only about half of the students’ responses. This may be due to an underlying common assumption the students were making that, for example, bigger density implies bigger than that of water, as the only liquid that they were talking about was water. In this way, it seems that most of the students had a pretty clear expectation regarding the phenomenon of sinking and floating and how it related to the density of a material. However, many fewer students had in their summary the other elements that are necessary for the theory to become a network of logical links between ideas

Table 1 Percentages of Students Meeting Particular Criteria for the Integrity of Their Theory Level

~ ~~

Linking relative strength Explaining link be- Reference to of forces with density tween relative strength

Directionality Specificity two forces and behavior in water of forces and density (Criterion A) (Criterion B) (Criterion C) (Criterion D) (Criterion E)

79 58 63 17 0

Note. n = 24.


and concepts. Furthermore, whereas more than half of the students included two forces in the summary of their theory, less than a fifth of the students linked the relative strength of the two forces with the density of the submerged object and the object’s behavior in water. There were only 4 students (the 17% who succeeded in Criterion D) who succeeded in all four criteria, A- D. These results support the idea that most students’ theory level of the Sink and Float unit lacked much of the internal coherence that is necessary if this level is to achieve full integrity.

It is worth making a distinction between Criteria A and B, and Criteria C, D, and E. Satisfying Criteria A and B might come more directly from generalizing empirical evidence and be less connected with a logical story that explains them. In other words, Criteria A and B remain at a more descriptive and less explanatory level than Criteria C, D, and E. Furthermore, Criterion D (linking relative strength of forces with density and behavior in water) provides a greater degree of integrity than does Criterion C (reference to two forces). The results are consistent with this: Students who satisfied Criterion D also satisfied Criteria A, B, and C. Criterion E (explaining the link between relative strength of forces and density), which provides the highest degree of integrity was not reflected in the students’ summaries. This is not surprising in the light of the classroom discourse. Both in a single large group and in small groups, the discussions of teacher and students did not include exploring how the relative density of a submerged object determines the relative strength of the two forces acting on it.

In contrast to students’ difficulty in adequately establishing the integrity of the theory level, students succeeded in establishing the integrity of the data level. The students discussed the trustworthiness of their data primarily in terms of reproducibility (comparing it with fellow students’ data) and accuracy. They did that in response to Logbook Question 3: Do you think you’ve got good data? Do you trust these data? Why or why not? Here are two examples of students’ responses discussing reproducibility and accuracy:

Phil: Yes we I have good data and trust it because we compared with other groups. Bunty: We trust our data and think it is good because when we compared it with other groups our data

was very close to theirs we also took our time and were as accurate as possible.

However, a few students also gave other reasons for trusting their experimental results, such as the help they got from others and the effort invested in collecting and analyzing their data. Table 2 shows the percentages of students who gave each type of reason for trusting their experimental results, of the 20 students for whom I have a record of answers to Logbook Question 3. Some students gave more than one type of reason. The maximum number of reasons a student gave was three.

Table 2 Percentages of Students Giving Various Reasons for Trusting Their Experimental Data

Type of reason % Students

Reproducibility 85 Accuracy 45 Help from others 10 Effort invested 5 Uncategorized 10

Note. n = 20.

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In light of students’ success in establishing integrity on the data level, but their difficulty in establishing integrity on the theory level, it is not surprising that reference to the fit between theory and data was minimal. In fact, in answering Logbook Question 3, only two students referred to such a fit by indicating that their experimental results were “logical .” Interestingly, these students were two of the four students who demonstrated integrity in the theory level by succeeding in all four measures, Measures A-D referred earlier. One of the other two students was absent the day the class worked on that, and the other one did not refer to the fit between theory and data. Of course, the two students who referred to their results as being logical did not elaborate on what they meant by that. However, it seems reasonable to me to interpret logical as meaning making sense based on our theory, based on the way we thought about sinking and floating before we did the experiment. In other words, it seems appropriate to interpret the statement that the experimental results were logical to mean that the experimental results agreed with the theory.

We have been exploring students’ summaries of the theory to examine the integrity of the students’ theory level and how this was related to the integrity of the data level. As mentioned in the conceptual framework presented earlier in this article, an important element in the dialectical relationship of theory and data, which links theory and data, is a question for experiment that, in the deductive direction of scientific activity, derives from the theory and requires an empirical answer. This question for experiment is like a hypothesis or testable statement that will be answered by doing an experiment. What kind of questions for experiment did these students develop? We glimpsed some of these when we listened in on the class discussions, but let us now explore more systematically the students’ written work on their two attempts to develop a question for experiment.

Looking at Questions for Experiment and Theory: Students’ Written Work.

The main goal of the experimental part of this unit was to collect and analyze data on the empirical relationship between the relative density of a material with respect to the density of water and its behavior in water; that is, whether this material sinks or floats in water. Did the students refer to this relationship in their questions for experiment, and how did they talk about this? Did they talk in terms of a particular expectation for the experimental results that they wanted to test out by actually collecting and analyzing experimental data? This is an essential part of operating in the deductive mode, that is, having detailed expectations before collecting experimental data, which is quite different from an inductive mode where we just search for patterns without any specific and detailed expectations for the data.

With these questions in mind, it seemed appropriate to analyze students’ attempts to develop a question for experiment in terms of directionality (Criterion A) and specificity (Crite- rion B) of the link between the density of a material and its behavior in water, as described previously. Let us look at some questions for experiment to get a feeling for them, and let us focus on three of the students at whose summary of the theory we looked.

Law: (First attempt to develop a question for experiment) If you find the density, can you predict if it will sink or float [sic] Do materials that sink in water have a greater or lesser density than water? Do materials that float in water have a density greater or lesser than water? (Second attempt to develop a question for experiment) Do objects that sink in water have a greater or lesser density than water? Do objects that float in water have a greater or lesser density than water?

Both of Larry’s questions for experiment had directionality and specificity and had practically the same content.


Ivy: (First attempt to develop a question for experiment) Does the amount of density determine whether the object floats or sinks? (Second attempt to develop a question for experiment) Does the amount of density determine whether the substance floats or sinks?

In contrast to Larry’s questions, Ivy’s did not have either directionality or specificity. Ivy did not feel a need to revise her question for experiment.

Howard: (First attempt to develop a question for experiment) Is gravity stronger than density? (Second attempt to develop a question for experiment) If we find the density of different objects can we tell if it will sink or float?

Howard did change his original question for experiment, but both of his attempts did not have either directionality or specificity, although he changed from not including the link between density of a material with its behavior in water to including such a link.

Like Howard, another student, Cathy, changed from not including the link between the density of a material with its behavior in water to including such a link in her second attempt. The link had specificity but lacked directionality.

Cathy: (First attempt to develop a question for experiment) Does the mass effect [sic] the force on a substance? (Second attempt to develop a question for experiment) In relation to the density of water, does density affect if an object sinks or floats?

Let us now look at the students’ questions for experiment in terms of directionality and specificity and in relation to their summary of the theory in terms of these two features. Table 3 shows the percentages of students whose summary of the theory and first and second attempts to develop a question for experiment had directionality and specificity, taking into account the 22 students for whom I have a complete set of data (i.e., written responses for a summary of the theory and the first and second attempts to develop a question for experiment).

Slightly more than three fourths of students’ summaries of the theory had directionality, and half had specificity. However, even in the students’ second attempt to develop a question for experiment, only a third of the responses had directionality, and slightly more than a third had specificity. The majority of the students in their two attempts to develop a question for experiment produced a question which was less explicit and more vague than their own summaries of

Table 3 Percentuges of Students Who Had Directionality and Specificity in Their Summary of the Theory and in Their Two Attempts to Develop a Question for Experiment

Students’ work Directionalit y Specificity

Summary of the thcory I7 55 First attempt to develop a 23 21

question for experiment

question for experiment Second attempt to develop a 32 41

NOW. n = 22.

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the theory. They produced questions at a relatively general level (e.g., Does floating and sinking depend on the body’s density?) instead of more explicit questions (e.g., Do bodies with higher density than a liquid sink in the liquid, and bodies with lower density float?), even when their summaries of the theory contained both directionality and specificity. Students seemed to formulate the question for experiment in such a way that the empirical answer to this question would provide them with extra detail (bodies denser than the liquid sink; bodies less dense float) as something that they obtained only from doing the experiment. This is supported by an analysis of the students’ answers to the first two logbook questions that they worked on at the end of the unit: Logbook Question 1: What was this experiment about? What did you want to find out? Logbook Question 2: What did you find out? A total of 23 students responded to both of these two logbook sets of questions. Table 4 shows that roughly a fifth of these students gave responses having directionality to Logbook Question 1 (the question for experiment), but roughly four fifths of them gave responses having directionality to Logbook Question 2 (the empirical answer to the question for experiment). Similar results are shown for specificity. Less than a third of the students gave responses having specificity to Logbook Question 1, but a little bit more than two thirds gave responses having specificity to Logbook Question 2 .

Regarding Logbook Question 1, only two students (Laurie and Blanka T.) formulated a very explicit question for experiment (one having directionality and specificity), and also related it to the theory level.

Laurie: We conducted an experiment to prove our story that anything with density greater than water

Blanka T.: We conducted this experiment to prove our story that an object that has a density greater than would sink. [We wanted to find . . I

that of water will sink and anything with a density less than that of water will float.

Conclusions

The findings of the study presented in this article indicate some of the complexities that a science class encountered as teacher and students attempted to engage in the deductive mode of scientific activity, developing a theory and collecting and analyzing empirical data to test this theory, in the context of the phenomenon of sinking and floating. First, together with the teacher, the students attempted to develop a theory for the phenomenon of sinking and floating. Their own formulations of the theory often contained critical elements of the theory: (a) Most of the students’ summaries of the theory included a directional link between the density of a material submerged in water and its behavior in water (e.g., materials denser than water sink in

Table 4 Percentages of Students Who Had Directionality and Specifcity in Their Responses to the First Two Logbook Questions

Student’s work Directionality Specificity

Logbook Question 1 17 30 (question for experiment) Logbook Question 2 78 70 (empirical answer to question for experiment)

Note. n = 23


water). Such a directional link is a necessary and important step toward organizing some of their knowledge and expectations about sinking and floating and indicates a degree of meaning making about this phenomenon. Such meaning may be coming more directly from prior empirical evidence, for example, experience with some materials which are denser than water and which also sink in water; or it may be coming more directly from developing logical connections between concepts and ideas, such as mass, volume, density, gravity, buoyancy, etc. (b) More than half of the students’ summaries of their theory included reference to the two forces that act on a piece of a material when submerged in water. Such a reference may indicate students’ attempts to develop a theory as a network of ideas and concepts that can explain the phenomenon and thus going beyond empirically based generalizations or laws. However, from the students’ formulations of the theory level, it was also apparent that the students had not constructed for themselves a logical network of ideas having sufficient integrity and providing a truly coherent explanation of this phenomenon. There were critical links missing from their summaries (i.e., linking the relative density and the interplay of the two forces) that would prohibit them from developing full meaning in the sense of being able to explain the phenomenon fully.

Second, in their attempts to develop a question for experiment after they had a theory, the majority of the students developed questions that did not include the detailed knowledge they had from their theory. Students avoided formulating their question for experiment to test specific predictions from the theory. They formulated their questions for experiment in such a way that the empirical answer to this question would provide them with extra knowledge obtained from doing the experiment. What does this mean? Usually, the questions we ask arise in specific ways from the context as we construe it. The students may have felt that they did not need to be very detailed and specific when they were formulating their question, because they had just produced a detailed and specific summary of their theory. Furthermore, the students might have responded differently to a request from the teacher for hypotheses or testable statements, rather than questions for experiment. Alternatively, students’ avoidance of formulating directional and specific questions may come from their tendency to operate within an inductive mode more than a deductive mode.

The students’ tendency toward the inductive direction of scientific activity may be related to their difficulty in differentiating between the two ways of knowing: that from developing logical and coherent links between ideas and concepts (knowing from the theory) and that from empirical evidence (knowing from the data). From this perspective, students were reluctant to formulate a question for experiment for which they already had an answer because they had not conceptualized that they had an answer as knowing-from-theory as opposed to knowing-.om- data. Furthermore, the students’ difficulty in differentiating these two ways of knowing may be strongly related to their difficulty in developing an internally coherent, logical theory.

In a sociocultural framework such as the one put forth here, the role of the teacher in inducting students into the practice of science meaningfully, so that they come to own the understandings already achieved as part of this practice, becomes a crucial one. The findings of the study point toward the complexities of working within the deductive mode of scientific activity as both teacher and students encountered them. The teacher’s job is a difficult one, especially when the teacher has been operating for years in a more hands-on, inductive, perhaps also empiricist, approach to science.

The analysis of the classroom discourse pointed to several instances where the teacher’s talk did not differentiate between knowing from prior empirical evidence and knowing from developing conceptual, logical links between ideas and concepts, a differentiation that needs to be explicitly brought to the students if we are to help them develop a clearer sense of the nature of a

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theory and differentiate it from empirical data. In the last excerpt of discourse quoted in this article, we saw the teacher giving a top-down monologue to the students without trying to engage them in relating this to their own understandings of why scientists do experiments if they already know the answers from the theory. Although the teacher tried to develop a distinction between the theory and data levels, she mixed together in her talk (a) elements that are more associated with knowing as a way of developing logical links between concepts and ideas with (b) elements that are more associated with knowing through empirical evidence. In this way, her talk did not make clear whether the organization of her thoughts comes from developing logical, conceptual links among relevant concepts, as is necessary for the deductive direction of scientific activity, or from previous empirical evidence, being a relatively direct generalization of these previous findings and thus remaining in the inductive direction.

There is no doubt that finding the limits of our empirically based generalizations is an important aspect of scientific activity. However, as emphasized earlier in this article in The Conceptual Framework, science is not constituted only by empirically based generalizations, and ignoring the deductive direction at best presents only a partial image of science. If the teacher constantly operates within the inductive direction and does not help the students differentiate between the two directions, then the students are not sufficiently helped to understand the deductive direction. Considering the dialogue between teacher and students and the written work presented and analyzed here, it is possible to contend that in each isolated case we can be satisfied that the teacher and the students are working in an inductive manner testing the limits of empirically based generalizations. But if we use only this perspective, we will end up without appreciating the problematics of the pedagogy of working in the deductive direction.

Realizing that the teacher herself was newly inducted to the theory-data dialectic of scientific activity, the present study points to an interaction between the teacher’s flexibility or difficulty with the subject matter (defined broadly to include both content and process) and her flexibility or difficulty in helping students use her top-down guidance to develop their own bottom-up understandings. Although we need more research to investigate this interaction further, such a finding suggests that we may do well to rethink the separation between content and methods courses in many teacher preparation programs.

Appendix

The basic steps in the logical chain of ideas and concepts in the theory level of the unit on sinking and floating are as follows.

Let us imagine isolating a “piece” of water within a container filled with water. There are two forces acting on this piece of water: gravity acting downward and buoyancy acting upward. The piece of water does not move up or down; therefore, we know that the two forces balance each other. That is, for a piece of water, the buoyant force acting upward has the same magnitude as the gravitational force acting downward.

Now imagine that the piece of water is replaced by some other material, by a body of the same volume but not necessarily the same mass. The buoyant force is a function of the density of the water, the medium surrounding the body, and not of the body itself. Thus, the buoyant force acting on this body (which exactly displaces that piece of water) will be the same as the buoyant force acting on the piece of water. This buoyant force is the same for all bodies which exactly displace the original piece of water-that is, all bodies which have the same volume as the piece of water-and is not affected by the mass of the body. However, the force of gravity acting on a body of given volume may be different for different bodies depending on the density of the body.

In the special case when the body has a density equal to that of water, the force of gravity acting on the body will be the same as that acting on the piece of water. In this case, the force of

BETWEEN THEORY AND DATA 26 1

gravity and the buoyant force will balance for the body, just as they did for the original piece of water, and the body will stay where it is placed in the water. If the body is denser than water, the force of gravity acting on it will overcome the buoyant force and the body will sink. If the body is less dense than water, the force of gravity acting on it will be less than the buoyant force and the body will float.

I am indebted to my teacher, mentor, colleague, and friend Joe Becker for all his contributions to this article. Although final responsibility for the study remains mine, he played an important role in its conceptualization, content, and form. I am grateful to the teacher and her students with whom I spent a school year together. I am also grateful to the reviewers of an earlier draft for their helpful comments and suggestions. Thanks to Christina Matyskela Balga for her careful transcriptions of class dialogue. An earlier version of this article was presented at the meeting of the National Association for Research in Science Teaching, Atlanta, Georgia, April 1993. Some parts of the article were presented at the meeting of the Society for Research in Child Development, New Orleans, Louisiana, March 1993, and the meeting of the American Educational Research Association, Atlanta, Georgia, April 1993. The work reported here is part of a larger project combining research and service in science education, particularly in urban, inner- city schools.

Notes

A different critique of the discovery learning approach derives from von Glasersfeld’s (1979) radical constructivist epistemology. There, the critique is that invention rather than discovery is required, since in the activity of science we do not get to know an independently existing reality. The arguments put forward in this article are consistent with, but do not require a radical constructivist perspective. They are also consistent with a less radical constructivist approach which falls under the heading of convergent realism (Chapman, 1988).

* By mature I mean the more developed form practiced by adults and not some finished, completed, and static entity.

For completeness, I note that the unit was motivated by presenting to the students the paradox of the Cartesian diver, and at the end of the unit this paradox was revisited in the light of what had been learned. However, the related discussions are not part of this article and will be dealt elsewhere.

Pseudonyms are used to protect the identity of students and teacher. [. . .] signifies pause in the speech. These features do not constitute the only way of dividing up the continuum of increasing theoretical

coherence and integrity, but they are the ones which emerged from examining the data.

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Received August 18, 1993 Revised June 22, 1995 Accepted July 18, 1995

between theory and data in a seventh‐grade science class

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