valeras - 1998 - between theory and data in a seventh-grade science class

8/3/2019 Valeras - 1998 - Between Theory and Data in a Seventh-Grade Science Class

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

Between Theory and Data in a Seventh-Grade Science ClassMaria Varelas

College of Education, University of Illinois at Chicago, Ch icag o, Illinois 60607-7133

AbstractA conceptual framework is developed incorporating the dialectic of science (developing theories andcollecting and analyzing data) and th e dialectic of education (bringing preexisting socioculturalelements tothe students and letting the students develop their own understandings). The theory-data dialectic isspecified as including both the inductive and deductive directions. Discourse is seen as central to both theactivity of science and the educative process, and hence as the bridge between them. In the context of thisframework, an empirical study was designed and executed in a seventh-grade science class. This articlepresents an d analyzes data focusing on (a) how teacher an d students moved between theory and data in aunit on sinking and floating, designed to engage the students mostly in the deductive direction of scientificactivity; and (b) how the dialectic of education was played out in the classroom as teacher and studentswere engaged in (a). A qualitative, interpretive methodology was used. Some of the complexities that thisscience class encountered as teacher and students attempted to engage in the deductive mode of scientificactivity 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 Sc ience, 1989; International Association fo r the

Evaluation of Educ ational Achievem ent, 1988; Linn, 1992; National Assessment of EducationalProgress, 1988; National Science Board Commission on Precollege Education in Mathematics,Scien ce, an d Technology, 1983), and enhancing elementary and middle sc hool students experi-ences in science has becom e a national priority. It seem s appropriate that effortsdedicated to theimprovement of science education take into account recent developments in understanding thesociocultural nature of both scienc e and educatio n. This involves a serious reconceptualizationof the foundations of science education. This article examines the problematics of scienceeducation in this spir it, theoretically and empirically, focusing on the theory-data dialectic ofscientific activity, and the sociocultural elements-individual meanings dialectic of education.Th e background for the theoretical framework developed in this report is the movem ent inrecent yea rs from a traditional, teacher-directed perspective to a progressive, student-centeredone. This movement came as an opposition to the traditional book- and lecture-centered ap-proach that was seen as dominating science education and producing rote learning rather thanunderstanding-and which therefore has been seen as based on a transmission model of educa-tion. The student-centered perspective has often taken the form of a hands-on, discoverylearning approac h which minimizes the role of the teache r and em phasiz es the students devel-opment of new understandings through their own hands-on inquiries.0 1996 by the National Association for Research in Science TeachingPublished by John Wiley & Sons, Inc. CC C 0022-4308/96/030229-35


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230 VARELASThe movement from the traditional book- and lecture-centered approach to the progressivehands-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 theimportance 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; OLoughlin, 1992). Second, the hands-on discovery learning emphasis inscience education overemphasizes the inductive direction of scientific activity at the expense ofthe deductive one. In this approach to science education, students mostly collect data andidentify patterns in them without developing theories that fit these empirical data. This decreas-ing emphasis on developing and formulating theories and increasing emphasis on collectingempirical data is apparent in programs developed over the last 2 decades, such as Science-AProcess Approach (S-APA), Science Curriculum Improvement Study (SCIS), Activities thatIntegrate Math and Science (AIMS), Teaching Integrated Math and Science (TIMS), Founda-tional Approaches in Science Teaching (FAST), Developmental Approaches to Science andHealth (DASH), and a descendent of SCIS, SCIIS. The emphasis on induction is associatedwith a decreasing emphasis on content and an increasing emphasis on process. However, theseprograms conception of process in scientific activity is a narrow one, because it does notincorporate 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).lThe National Research Council (1994) in their most recent working draft of the NationalScience 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 ofthe examples of teaching that are mentioned in this draft focus primarily in collecting andanalyzing empirical evidence without providing examples of how teachers engage students intheory development.

The Conceptual FrameworkThe conceptual framework put forth in this article is quite distinct from either the traditionalor the progressive approaches to science education, seeking to build on their strengths and toavoid their weaknesses. This framework arises from current understandings of teaching andlearning 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 helpingthe students make this activity meaningful to themselves. The conceptual framework adopts aconstructivist approach: Learning is taken to involve an active construction of meaning by thestudent, one that nobody else can do for the student. Despite this emphasis, the approach issociocultural: The individuals meaning making is seen as situated within a preexisting culturalactivity (in this case, the activity of science) and the role of the teacher is conceived as assistingthe student to construct meaning within this cultural activity. The science student is consideredto be a person who seeks to gain entrance to the cultural activity called science, and the teacheris considered to be a person who brings the student and the cultural activity together. Myapproach does not take as an aim of science education to develop only experts, or students whowill specialize in science. The aim of science education that I espouse is to give to all students afeeling for and an understanding of the mature activity of science and help them have meaning-ful experiences with it.The notion of science education as induction into the activity of science implies that a validconception of science education must be based on coherent notions of the nature of scientific


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BETWEEN THEORY AN D DATA 23 1activity and the nature of the process of induction into that activity. I will deal in turn with eachof 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, iffollowed to the letter, will enable somebody to do science. Second, science is a cultural activitycharacterized by specific tools and artifacts that scientists have developed and have been usingover the years, such as diagrams, tables, graphs, terminology, etc. Third, science is a socialactivity in which scientists collaborate and work closely together with the ultimate aim ofadvancing their field, their practice.My approach is based on the idea that science is an activity which centers on the interplayof theory and data. Science has two major levels: developing theories or models, and collectingand analyzing data. In their dialectical relationship, these two levels define the activity ofscience. 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 betweentheories and empirically based generalizations or empirical laws in that theories have an explan-atory power that comes from making sense of phenomena around us using concepts and ideasand linking them together, whereas empirical generalizations describe the world around us inorganized 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 thefi t between theory and data. Differentiating between theory and data implies distinguishing be-tween two ways of knowing something-knowing from the theory, from developing concep-tual, 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 othersignificantly (Dewey, 1929; Duschl, 1990; Holton, 1988; Lythcott, 1991; Schwab, 1978). Iftheory and data do not fit, either or both might require further work. Nevertheless, each has itsown integrity; to judge the fit of theory and data, scientists develop the trustworthiness of eachof the two levels employing means that are particular to each level. For example, they gainconfidence in the data level when they find that the data are reproducible. Similarly, scientistsgain confidence in the theory level when they find logical coherence over a network of ideas andconcepts.In pursuing the theory-data dialectic, scientists sometimes use the inductive direction ofscientific 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 theexpense of the deductive direction is a distortion. Working in the deductive direction, scientistsdevelop a theory, derive from it testable statements, and collect and analyze empirical data todetermine the fi t between the testable statements derived from the theory and the empiricalresults. In the experimental mode of the deductive direction, the testable statement is a ques-tion for experiment, and the data are collected as part of an experiment carefully designed toobtain an empirical answer to this question.Regarding Education

My approach is based on the idea that education centers on the interplay between socio-cultural 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 alreadyachieved (V ygotsky, 1978, 1934/ 1987). This interplay has two directions: (a) a top-downcomponent-preexisting cultural achievements brough t 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 ofscience. Let us focus first on the need to integrate the top-down com ponent with the bottom-upcomponent. The top-down component is brought to the educative process by the more experi-enced teacher and practitioner. However, it is brought into action with the ultimate goal ofhelping students learn science meaningfully. If it is not successfully integrated with the under-standings and mea nings that students already have, that is, if it remains isolated, it will be poorin meaning and will not be owned by the students. As indicated earlier, my approach opposesthe transmission m odel of education: teachers more advanced know ledge simply replacing thestudents more primitive knowledge. In contrast to the transmission model, my approach isbased on the notion that students need to construct their own knowledge. In other words, theclaim is that the sociocultural top-down elements of a practice cannot just be brought by theteacher and received by the students; students need to interweave them with their own priorbottom-up understandings if learning is to occur.Focusing now on the need to integrate the bottom-up component with the top-down compo -nent, my conceptual framework is based on the position that students do not create by them-selves the practice of science. S een as a sociocultural practice, as argued earlier, science isappreciated as a rich and complex enterprise that students cannot just discover by them selves.Furthermore, students need to restructure their thinking as part of becoming practitioners ofscience. Students cannot do that without the help of the structure that governs the practice ofscience; they need this structure to transform their prior understandings. This structure isbrought to the students by the skillful and experienced teacher who is a practitioner of botheducation and science. By participating in the existing forms of a specific practice (e.g., thepractice of science) while guided by a sufficient member of the practice, students developmental organizations and mean ingful understandings which enable them to become au tonom ousparticipants in that practice.The integ ration of these two components, top-down and bottom -up, is the responsibility ofboth the teacher and the students. H owever, initially, when the students are relatively unfamiliarwith the basic elements and dynamics of a particular practice (in this case, the practice ofscience), the teachers responsibility in this process is greater than that of the studen ts. In suchan early stage, the teachers try their best to reveal students own conceptions, and engage thestudents in using, at the level they can, the necessary too ls, artifacts, and m ethods that practi-tioners of science use. The teachers need to be on guard that these top-down elements do notremain 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 andbottom-up components is increasingly the students responsibility, too.Ideally, students will strive to make things m eaningful for themselves. H owever, because ofvarious forces in home and school, m any students have given up making meaning out of what ishappening around them, especially in the classroom. As a result, there is an even greaterresponsibility on the part of the teacher to initiate and nurse this educative process. This presentsits own difficulties, as it increases the likelihood of studen ts passively receiving the top-downelements that the teacher provides. In such cases, the teacher must be constantly aware of thisdanger, probing for the students understanding and encouraging their meaning making . In fact,because of the students discouraging prior experience, the teache r has a responsibility to bringthe students to feel that (a) they can make their school experiences meaningful, and (b) theyhave the right to have school experiences be meaningful.


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BETWEEN THEORY AN D DATA 233Using Vygotskys theory of intellectual development, I believe that in their dialecticalrelationship the top-down com ponent of the educative process provides students a way to gaincontrol over and further develop their own bottom-up understandings, whereas the bottom-upcomponent helps the students imbue with meaning the top-down elements brought to them bythe teacher. In a similar way, D ewey (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 singleprocess, and he continued, Just as two points define a straight line, so the present standpointof the child and the facts and truths of studies define instruction (p. 11). Furtherm ore, Deweyemphasized the interplay between the logical standpoint of experience that comes from thesubject matter (similar to the top-down compo nent in my description of Vygotskys approach)and the psychological standpoint of experience that comes from the child and his or her ownexperiences (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 bestachieved through dialogue and argum entation (i. e., providing arguments that support the ideasand claims that are brought forward during the dialogue). Dialogue and argumentation, whichare taken together to define discourse, are central to both the activity of science and theeducative process-the latter being the way the teacher and the students interact in the processof induction (Dam on, 1990; Vygotsky, 1934/ 1987). To a large extent, discourse constitutes theoverlap, and hen ce the bridge, between the con ceptions of science and education that underliemy conceptual framework.The em phasis on discourse is in acco rdance with Vygotsky s theory of intellectual develop-men t, in which the relationship between thinking and speech (or thought and language) is seenas crucial for the students development. For Vygotsky (1934/1987), thinking and speech areintimately related and influence the development of each other: It would be incorrect torepresent thinking and speech as processes that are externally related to one another, as twoindependent forces moving and acting in parallel with one another or intersecting at specificpoints 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 thedevelopment of thought, thought is restructured as it is transformed into speech. It is notexpressed but completed in word (p. 251).Discourse allow s students to express their ow n thinking, n egotiate ideas and understandingswith fellow students and their teacher, and develop them further. During discourse, studentsown ways of thinking and knowing are revealed, allowing the teacher to identify studentsunderstandings, validate them as ways of reasoning about the subject matter, and also help thestudents develop these understandings further. By negotiating their ideas through discourse,students begin to appreciate that science is a sociocultural enterprise with its own establishedways of knowing where meaning is developed through a dialogical exchange of ideas(OLoughlin, 1992). It is also through discourse that students can begin to appreciate thatscience is not an objective field of study standing apart from human perspectives. Studentsmay begin to appreciate that scientific activity is marked by the particular nature of the humanintellects engaged in it, and may come to experience that differing interpretations, which may ormay not converge, are important and play a crucial role in science (Eger, 1992).The emphasis on discourse in my approach is in keeping w ith the criticism noted earlier thatthe hands-on d iscovery learning emphasis of the p rogressive approach misses the im portance ofdiscourse around the activities. As Edw ards and Mercer (1987) noted, E xperiences and activ-


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ities of the classroom are made meaningful by the sense made of those things by classroomtalk. . . . A greater emphasis on the importance of language and comm unication in creating ashared conceptual sense of the meaning and significance of experience and activity may help tomake classroom education a more open and explicit business, and therefore a less mysteriousand difficult process for pupils (p. 169).In summary, my conceptual framework is based on two major dialectics. Regarding sci-ence, the focus is on the interplay of theory and data levels of scientific activity (dialectic ofscience). Regarding education, the focus is on the interplay between top-down socioculturalelements that the teacher brings to the students and the students bottom-up understandings(dialectic of education).In the context of th is conceptual framework, an empirical study was des igned and executedin a seventh-grade science class. The focus of the analysis of the data presented here was toexplore how this group of seventh graders and their teacher worked within the theory and datalevels of scientific activity in the context of a unit that was designed to engage them mostly inthe deductive direction of scientific activity. More specifically, and as I discussed previously

in the concep tual framewo rk regarding the dialectic of s cience, I was interested in studying howthe teacher and her students approached theory and data, whether and how they differentiatedbetw een the two , whether each level-theory and data-had its own integrity, and whether andhow the teacher and the students thought about the fit between theory and data. A s teacher andstudents moved between theory and data, I was interested in studying how the dialectic ofeducation was played out in the classroom: whether and how the teachers and students talkfacilitated their understandings of theory and data, whether and how the teachers guidance andprobing enabled students to differentiate between theory and data and develop the integrity ofeach level, and whether and how the students written work reflected the shared discussionsamong students and between teacher and students.

The Empirical StudyMethod

Participants and Setting.The empirical study was conducted in one seventh-grade science class of a middle school ina 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 threeseventh-grade classes. Th e 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 theacademic year 1990- 1991 to discuss and further develop the conceptual framework of scienceeducation outlined earlier, and to plan and develop specific units which were used in theteachers class. In this way, the teacher and her seventh-grade students contributed significantlyto the developm ent of the concep tual framework and played an active and imp ortant role in theway this framework was shaped in practice.The teacher and her seventh-grade science students worked on five units of scientificactivity designed to include both levels of scientific activity: developing theories, and co llectingand analyzing data. The five units were spread over the academic year 1990-1991 and coveredroughly 25% of the science lessons for this year. The rest of the time, the teacher and herstudents followed their regular science textbook. The length of the units ranged from 6.5 to 12


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BETWEEN THEORY AND DATA 235periods, with the first unit being the shortest. The author was present in all science lessonsrelated 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 asmentioned before, they both developed a theory regarding this phenomenon and also did anexperiment to collect and analyze emp irical data related to this phenom enon. For the experimen-tal part, cumculum materials from the TIMS program developed at the University of Illinois atChicago by G oldberg and W agreich (1989, 1990a, 1990b) were modified to fit the aims of thisproject. In each of these five units, there was a deliberate emphasis on discourse and the socialnature of the practice of science. One way this was done was to include presentations by thestudents to their colleagues in the class, encou raging the development of norms of critique andargument.For this article, I focus the discussion on the fourth unit of scientific activity on which theteacher and her studen ts worked. T his unit is called Sink and Float and was designed to engagestudents in the deductive direction: With the teacher, students develop a theory about sinkingand floating, derive a ques tion for experiment from this theory, find an em pirical answer to thisquestion, and determine the fit between theory and data. As mentioned in the presentation of ourconceptual framework, the deductive direction of scientific activity is but one aspect of thepractice of science. By centering this paper on students engagement and meaning makingwithin this direction, I do not want to imply that scientific practice does not recogn ize or rewardthe inductive search for patterns in collected data. I do w ant, though , to explore how a group ofseventh graders and their teacher approached a scientific phenomenon from a de ductive perspec-tive.The author worked with the teacher to develop a theory, a scientific story that could he lp

students associate materials denser than water with sinking in water and materials less densethan water with floating in water. At the theory levkl, this unit was intended to help the stud entsmake a coherent logical story linking the density of a m aterial relative to that of water, with therelative strength of the upward and downward forces acting on a material submerged in waterand with the resulting behavior of this m aterial in water. In other words, the intention was tohelp students construct an explanation including, for example, that for bodies with densitygreater than water, gravity overcomes the buoyant force, and therefore, these bodies sink inwater. For an account of the logical chain of ideas and concepts making up such a coherenttheory, see the Appendix. T hese studen ts had previously worked on a unit of scientific activitycalled Mass versus Volume, in which they explored the linear relationship between the mass andthe volume of a given material and discussed the concep t of density of a given material in termsof the mass of this material in a unit volume.In this unit, the teacher and the studen ts worked in a single large group to develop a theoryor, as it was called in class, a scientific, logical story about the phenomenon of sinking andfloating (Stage 1) . Then, the students worked in small groups-most often in pairs or in groupsof 4-to develop a written summary of their story and construct a meaningful question forinvestigation by an experiment (Stage 2). While students were working in their groups, theteacher and the au thor went arou nd helping the studen ts when necessary, or further probing theirunderstandings.The teacher and the students then got back together in a single large group to discuss thework that the students had don e in small groups, to further develop a question for the experimentand 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 wasonly one presentation, because of the length of the discussion that was generated by thispresentation and the limited amount of time the teacher devoted to this stage. The discussiongenerated by the presentation focused on the question for experiment.Continuing in the single large-group discussion, the teacher and the students proceeded todesign the experiment (Stage 4).Next, the students worked in small groups to rewrite theirquestion for experiment and collect and analyze their data (Stage 5). During the collection andanalysis of the data, the teacher and the students occasionally came together in a single largegroup to discuss issues that arose in the small groups. In the next phase (Stage 6), the studentsworked in their small groups to produce in their logbooks a written summary of the unit that theyhad been working on, guided by three general sets of questions (Logbook Question 1:What wasthis experiment about? What did you want to find out?; Logbook Question 2: What did you findout?; Logbook Question 3: Do you think youve got good data? Do you trust these data? Why orwhy not?). Finally, the students made oral presentations to their classmates based on thesummary in their logbooks (Stage 7). Generally, one representative of each group, either chosenby the teacher or a volunteer, presented to the rest of the class the groups findings andconclusions. The teacher and students attended the presentations and participated through dis-cussions and questions. The whole unit lasted for 11 periods with the collection and analysis ofthe 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 betweenthe teacher and the students and among the students themselves, and (b) these students writtenwork over the series of lessons in the Sink and Float unit. These data were supplemented by thefield 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 theauthor had with the students when they were working in small groups.The study employed a qualitative, interpretive design. The transcripts of the classroomdialogue4 were annotated and the students written work was coded. These annotations andcodings were produced in relation to each other rather than in isolation. The focus of theanalysis of these data was the search for themes and patterns that would shed light on thequestions 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 thefollowing section.The types of the data and the interpretive approach used in the data analysis diverged, ofcourse, a great deal from the classical experimental design that has been used extensively inresearch in science education. However, 1believe that this way of studying a science classroomgave me an opportunity to explore how the teacher and her students moved between theory anddata 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, asspecifically related to the phenomenon of sinking or floating? Let us start addressing thisquestion by taking a closer look at a relatively small excerpt of classroom dialogue which tookplace as a student shared with the whole class her groups summary of the theory and theirquestion for experiment (Stage 3). For me, this excerpt is a window into one students (Lenas)


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BETWEEN THEORY AND DATA 23 7conceptua l iza t ion of theory and da ta in the context of the specif ic unit . In addit io n, i t raises in astudents voice, in a very acu te form, the cent ra l ques t ion of constructing the dist inct ion betw eenempir ica l and theore tica l knowing, which i s necessary for working in the d educt ive d i rec t ion .Teacher: Excuse me. All right, were going to get started right now. Okay, Birute, will you please start?

Now, youre going to be, youre going to be listening and see what elements you m ight think thatBirute could include to make her story more complete and her question more complete. So, weregoing 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 thebuoyant force pushes it up, keeping it at an equal spot. For steel, the gravity overpowers the

buoyant fo rce and it makes the ball sink. A substance that has a bigger density will sink, and if itdoesnt 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 shes trying to see if in an experiment she could answerthis 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 [ . . .]Youre asking, the question, does the amount of density [. . .] But what weve shown alreadysays what the answer is. I dont know.Boy: Were just too sm art.Lena: I just dont understand the question. I understand the qu estion, but [. . . I

Teacher: All right, youre saying, um, Lena, go ahead and ask your question again.Lena: Like, well [. . .1Teacher: 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 inBirute: Does the amount of density determine if the substance floats or sinks?relation to the water? Do we need to put som ething in there?Lena: Arent we trying to find out the amount of density?Lena: Arent we trying to find out the amoun t of density?Teacher: Pardon?Teacher: Well, you are going to be finding density of about six different materials. And then youre going

to see if that affects whether they sink or float, but in relation to water, is the density greater thanwater or less than water? All right?Cathy: I know what shes saying. Shes trying to say what weve shown in our summary already says theanswer.Teacher: All right, is that what youre asking, Lena? Now, all right, we know this by experience, pastexperience and by thinking about it, and we know it for a few things. But were wonderingwhether 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 tofind the density of other materials and see if it will cause them to sink if they have a greaterdensity and cause them to float. So we want to apply it to others. Thats what were 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 Birutes question for experiment.Lena pointed out to Birute that she was asking a question for which she already had an answerbased 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 [. . .] Youre asking the question, does theamount of density [. . .] But what weve shown already says what the answer is. I dontknow). Lena was confused because she could not understand how somebody would write up aquestion for experiment for which she already had given an answer (what weve shown alreadysays what the answer is). Lena seems to be saying that surely we do experiments to find outthings we do not know and not things we already know. Lenas point made a lot of sense to herand, of course, to Cathy, who had not worked in the same group with Lena, and who went backand restated Lenas problem (I know what shes saying. Shes trying to say what weve shownin our summary already says the answer). But Lenas point probably also made sense to the boywho ironically noted that already knowing the answer to their question for experiment came justfrom being too smart.

Lenas struggle to understand Birutes question as a legitimate question for experiment maypoint to Lenas struggle to differentiate between knowing from theory and knowing fromempirical evidence. Birutes 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 fromtheory and not having an empirical answer. But to what extent did the students, in interactionwith the teacher, develop a theory? To what extent did the students develop a logical explanationconstructed from conceptual links between ideas and concepts which they could then test bycollecting and analyzing empirical evidence? The teachers answer to Lena and Cathys concerndoes not support the scenario that students and teacher were developing a logical explanation ofsinking and floating (a theory). The teacher talked about knowing by experience, past experi-ence, . . . and . . . for a few things, and therefore want[ing] to apply it to others. This ismore consistent with an empirically based generalization or empirical law than with a theoryhaving its own integrity that explains why sinking and floating happens and why the relativedensity 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 forteacher and students, let us look closely at the earlier extended classroom dialogue as studentsand teacher sought to understand sinking and floating, and let us examine to what extent theyconstructed a theory (Stage 1).

Working to Develop a Theory: Whole-Class Discussion.Teacher: Okay, we have an imaginary little bit of water that were going to say is about 17 ccs in this

container of water. [The teacher draws Figure 1on the board.] So, were just going to pretendthat this water is in a little ball and it stays right in that spot. It doesnt go up or it doesnt godown. It just stays in that little spot. . . . And water has a density of 1 g per 1 cc. Do youremember that? . . .Okay. So when we have [. . .] When we have the little ball of water it juststays in this spot. Now we took [. . .] say we had a ball of steel, and I put a little ball of steel inthe water, what would happen to it? [The teacher adds another circle in Figure I , as shown inFigure 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 wouldnt seeLarry: t would sink.it staying here very long if I let go of it. What would make that sink? Larry,do you know?


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BETWEEN THEORY AND DATA 239

Figure 1 . Teachers first drawing on the board o n Day 1

Larry: Gravity.Teacher: Gravity. Okay, so we have a force of gravity pulling down. [The teacher draws an arrow on thesteel ball, as shown in Figure 2.1 Okay, so gravity [. . .] um, what is, uh [. . .] How do wemeasure gravity?Girl: In pounds. Weight.Boy: In pounds.Boy: You cant.Girl: You cant measure gravity.Boy: Yes, you can.

Teacher: You cant? 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 , whats going to happen to it, Laurie? All right, itStudent: Itll fall down.Student: To the ground.Student: In the midair.Teacher: All right. It will go down, wont it?Teacher: Okay. Now, if I put it in this empty container, what will happen to it?Teacher: Itll drop to the bottom, wont it? Itll drop to the bottom. Okay. So its gravity that is pulling it

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

Girl: And itll bounce.Boy: Itll drop to the bottom.

down.Girl: Yes, but in the water?Teacher: O kay, what is [. . .] Why is that? [The teacher lets the plastic ball fall in a container filled withwater.]Girl: Because the gravity is pulling the water down.Boy: Itll float.Girl: Cause its got air in the middle.Girl: Its hollow.Teacher: George, why do you think it didnt fall to the bottom of the jar?

George: Not heavy enough?Teacher: What?George: Its not heavy enough.Teacher: Its not heavy enough. Okay.

Figure 2. Teachers first drawing on Day 1, including her addition.


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240

Student:Student:

Girl:Teacher:

Boy:Teacher:

Boy:Teacher:Barbara:Teacher:

Boy:Teacher:

Joe:Teacher:Joe:Teacher:Joe:Teacher:Joe:Girl:

Teacher:Joe:

TeacherAndy.Teacher

GirlTeacherBOY

VARELASShh!Shut up.The water weighs more.Sh h. O kay. All right. Water is a fluid just like air, except that its more dense and SQ it can sup portthe ball. So, the ball doesnt go down because the force of water pushing up is keeping it fromgoing d ow n. But in the cas e of the steel, the force of the water is very, uh, sm all compa red to theforce of gravity. Do you remem ber, um , what the density of steel was from our experiment? Whocan 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 on e cc. Okay, so if you had a piece thats onecc, what would the mass of it be? Okay, Barbara? What would it be?Eight grams.Okay, all right. So, with steel you have [. . .] Wh oa, w hoa. L ets see whos listening. Ok ay, nowwhat I want you to do in your notebook, I want you to draw a little diagram of what two forcesare working on a steel ball when you put it in water. What two forces?There is only one.All right, what 1want you to d o is draw a little diagram to tell what two forces are w orking on thesteel. Okay, now, lets look back at our little piece of water here. We have [. . .] We have theforce of g ravity going down and we ha ve the force of the w ater holding this little piece up. [Theteacher draws arrows on the piece of water, as shown in Figure 3.1 Now you are going to drawone 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 arrowson the ball representing a piece of steel, as shown in Figure 4.1What do you mean? So, we gotta draw a little ball in a container with arrows on it?

Thats 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? [. . .] N o! [. . .] Gravity is the only force on earth.Andy?Its easy. Gravity is pulling it down and density is pulling it up.Well, actually, Andy, you co uld say that its the force of the water. The , 1. . .] well, the densityof 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 drawsFigure 5 on the board.] So, this is water.

Figure 3 . Teachers second drawing on the board on Day 1


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BETWEEN THEORY AND DATA 24 I

Figure 4 . Teachers third draw ing on the board on Day 1 .

Girl:Teacher:

Boy:Girl:Teacher:

Student:Teacher:Girl:Teacher:Boy:Teacher:

The bells going to ring in, like, 30 seconds.Okay. Now, wh at if 1. . .] What if we ha d another little substance that was very light weight, andwe had 17 ccs of this other substance, and its density was less than water, what do you thinkwould happen to that?It floats,It would stay in the middle.Stay in the middle?If its less it would float.What do yo u 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 notebookright 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 atheory about this phenomenon in which they considered ideas such as density, forces that act onan object subm erged in water, their relative strengths, and the objects behavior in water. Theclassroom dialogue reveals the struggle that studen ts and teacher go through to dev elop the ideathat there are two forces acting on an object submerged in water: the weight of the object orforce of gravity and the buoyant force that the water exerts on the object. In the case of the steelball that sinks in water, Larrys first explanation of this behavior is that gravity will make itsink, with no reference to the second force acting on the steel ball. The teacher tried to help thestudents to think about this second force by sw itching to a material that would float in water, areal plastic ball. G eorge talked about the plastic ball not [being] heavy enough, indicating asort of comparison between gravity and something else that he did not make explicit. A girltalked about water weigh[ing] more. The teacher synthesized the two students answers(Water is a fluid just like air, except that its more dense and so it can supp ort the ball. So, theball doesnt go down because the force of water pushing up is keeping it from going down),

Figure 5 . Teachers fourth drawing on the board on Day I .


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242 VARELAS

bringing up very explicitly the second force, the force of the water pushing up. Going back tothe case of steel, she also told the students that the force of the water is very, uh, smallcompared to the force of gravity, and moved on to empirical information, asking the studentsthe density of steel.After the teacher asked the students to draw [in their notebook] a little diagram to tell whattwo forces are working on a steel ball when you put it in water, she proceeded to draw it on theboard herself as she sensed that the students may not have had a clear idea of what she askedthem to do, especially after Joes 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 thoughtabout this, different students had different ways of making sense of what they were discussing inclass. Joe was really having a difficult time dealing with the upward force of the water. He mayhave had a feeling for it and he probably associated it with the density of the water, but he couldnot 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 talkabout gravity and density as the two forces acting on the ball of steel (Its easy, gravity ispulling it down and density is pulling it up).The first lesson ended as students and teacher tried to connect various important concepts insinking and floating. I felt that the students had a pretty good sense that materials denser thanwater sink in water, and materials less dense float, knowledge probably coming from their ownexperiences in the real world. However, in terms of developing a scientific story, a theory, alogical network of ideas which could explain why this was true, the students were probablypretty shaky in conceptualizing the two forces acting on an object submerged in water. Therewere also a couple of attempts by the teacher to relate the relative strength of these two forces tothe 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 forthe density of steel.

The following day, the teacher and students continued to develop a scientific story forsinking 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 itwould be [. . . ] We just made up 17 ccs and it stays in that place, because the water pushingup 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 . 1.33Of water. Density equals [. . .] Larry?One gram per cc.I knew that.So, for 30 ccs, theres 30 grams.

Figure 6. Teachers first drawing on the board on Day 2 .


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BETWEEN THEORY AND DATA 24 3

water1gmI D=- steelD = 8 g m

Figure 7. Formulas written by the teacher on the board

Teacher: O kay. One-Okay, you remem ber it now?-per cc. This is water. And because the density ofthis little piece of water is the same, then, its going to stay in its place. But, then we knowsomething about steel. We know the density of steel. And, do you remem ber, in general, werereally 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 d o 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 7.1So, the mass, themass 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, wouldnt it? It

would be the greater force . [T he teacher adds to Figure 6, as shown in Figure 8.1 Okay. Then Ithink we just started to talk about a material. Oh , we could just say Styrofoam, a nd we haventactually found the density of Styro foam , but I know that you all have had experiences with, uh,putting Styrofoam into water. It doesnt sink. It just floats on the top. So, what do you thinkabout the density of some substance like Styrofoam? What do you think it would be? Greaterthan 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: Its just less than w ater.Teacher: Anything less? What do you think, Larry?

Teacher: All right, so its less than w ater. And so , were going to get the force pushing down would beless [. . .]Boy: Than the force pushing up.Teacher: So, well put it up there and then w e wou ld get more force from the water. [The teacher adds toFigure 6, as shown in Figure 9.1 Okay now , lets think about, um , a substance that has exactlythe same density as water, which would be something that was made up to be one gram per cc ,

water steel

Figure 8. Teachers first draw ing on Day 2 , including her first addition.


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244 VARELAS

ter

Figure 9. Teachers first drawing on Day 2, including her first and second additions.

and it wasnt water but it was a substance. Um , what do you think is going to happen w ith thepushing-down and the pushing-up forces? What do you think? If I were going to put it righthere, w hats going to happen to it, Cathy? Is it going to go down or up?

Cathy: Whats 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 itll stay right there?Teacher: Okay, so youre saying that the density push ing dow n 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, were go ing to take what we know abo ut density and think about it in relation to

what things would sink and float. And I want you to just sum marize the force of g ravity, uh,pulling down and the force of the water pushing it up. Does anybody know another name forthat force of the water pushing up? Cathy?

Student: Density.Teacher: Not density.Student: Pressure?Teacher: I bet if I say it, I bet youve heard it. The buoyant force?Student: Buoyancy.Teacher: Have you heard of that? The buoyancy? All right, but you dont need to worry about that, but

you need to think about [. . .] you need to think about making a summary of what we havetalked abou t, som e things sinking, som e things floating, and how their density to water relatesto that. Then you are going to do two things. Lau rie? You are going to do two things when yougo to your lab stations. Youre going to write a brief sum mary of this story, plus your e goingto write your question . And then at 1155 , I mean at 12:10, which is about 15 minutes, you aregoing to , uh, sh are with the group the real short summ ary you made of the story of density andhow it relates to sinking and floating and your qu estion that we w ould 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 andfloating related to density. And were going to take a lot of different materials and see if wecould, uh, make some sense out of why some sink and why some float. We have an idea whysome would sink and why they would float, but, what would be our question, then, fordensity? The summary would be how different things work in water, okay? All right, noweverybody knows your new lab stations, so lets really get to w ork and Ill be here to help youif you need help.

Girl: Ive heard that!


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BETWEEN THEORY AN D DATA 245As the teacher and students continued to talk about sinking and floating in terms of relativedensities and relative strengths of the two forces acting on an object submerged in water, howdid their scientific story hang together? The teacher told the students that the two forces actingon an imaginary piece of water were equal and asked the students the density of water, anempirical 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 stillgot an answer from a boy (Gravity) that did not involve both forces but only gravity, Sheelaborated on the boys answer to include a comparison between the two forces (Gravity wouldovercome the force of the water, because it would be greater, wouldnt it? It would be thegreater force). Although the teacher talked about two forces, she drew a figure on the boardwhich 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 therelative density of a material submerged in water with the relative strengths of the two forcesacting on this material. Why is gravity stronger than buoyancy in the case of the steel ball? Howdoes the greater density of steel relative to water determine this? The logical links of sucharguments were never brought up in class. Interestingly, none of the students raised thesequestions. Furthermore, none of the students raised the question of why the effect of buoyancyon the Styrofoam ball, as depicted in Figure 9, was larger than that on the water ball, which, bythe way, is a mistake. Up until that point, critical links between ideas and concepts were missingfrom the story. In this way, one may wonder how students could get a sense that things do makesense 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 rightbased on their experiences with schooling so far, or maybe they would try to make more sense ofthings 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 theirstations to work with their partners to develop a summary of their scientific story and a questionfor experiment (Stage 2). But what was the nature of the scientific story that the teacher andstudents developed, and how could it lead to a meaningful question for experiment? As we haveseen 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 teachers questions; and (b)logical links between these elements were not explicitly brought up. The students were sent totheir stations to just summarize the force of gravity, uh, pulling down and the force of the waterpushing it up . . . think about making a summary of what we have talked about, some thingssinking, some things floating, and how their density to water relates to that. Would that beenough for the students to get a sense of the nature of a scientific logical story that links ideasabout density and forces and behavior in water? We will take a closer look at what happened asstudents worked with their partners to shed more light on this question. We will be following theteacher as she moved from station to station.

Developing a Written Summary of the Theory and a Question for Experiment: Small-Group DiscussionsStation 1

Girl 1: Mrs. C. Shore? Could you come back here? Were confused.Teacher: Okay, all right. All right, what youre supposed to do is , youre supposed to think about what weknow; ou r story is what we know about the density. Yeah, you do. You know the d ensity of steeland yo u know how to find the density of, of [. . .]


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246 VARELASGirl 2: I dont 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

an d [. . .]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, were going to try to find some way to m easure this and to, you know, prove toother 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.

um e [. . .]Teacher: Uh-huh. Okay, so, were going to take a lot of different materials and get the mass and vol-Girl 2: Were actually going to do this?Teacher: Yes, we are actually going to do it. Get the mass and the volume and then were going to, uh, seeif 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 ou t 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.

Th ere is a strong indication that these two girls were confused about what they had to do attheir 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 thedensity 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) madeseveral references to empirical issues, such as measuring (so, were going to try to find someway to measu re this and to, you know, prove to other people why som ething would sink or float.So, we need to get, um , som e measurements. And how d o we determine density? What do wehave to measure?; Okay, so, were going to take a lot of different materials and get the massand volume). In terms of developing their theory, the teacher wanted the girls to think aboutwhat we know, if it has more density, greater density than water, what do you think willhappen? In this way, the teacher was cueing the girls to develop a hypothesis that denser thingssink and less den se 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 werenot encouraged to do this as part of developing a theory. Indeed, it seems that the girls wereomitting the work of d eveloping a scientific story and proceeding to design an experimen t to findout whether the amount of density influences how things float or sink (Does the amount ofdensity matter specifically? If things could float?). The girls picked up on the teachers emph a-sis on measurement and moved quickly to formulate a question for experiment rather thanspending more time on the theory level. The girls did not have specific predictions about therelationship between density and sinking and floating, as is illustrated by their comment ofFloat o r sink or whatever, and they jus t wanted to find out inductively some things about therelationship between density and behavior in water. Although the teacher attempted to somedegree to get the girls to think about what we know, implying that they already had specificexperiences linking density to behavior in water, and to realize that they would do the experi-ment to see if that really is what determines whether something will sink or float, this is stillmore at the level of empirical generalization than constructing a theory and deducing from it,


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BETWEEN THEORY AND DATA 241Station 2

Boy: Can you help?Teacher: All right, youre going to talk [. . .] Youre going to think about what we talked about. Whatforces, uh, work on something when you put it in water, and which things sink or float, and whatdo you know about density.Boy: Okay.Teacher: So, just a real short summary that you guys can think of.

Teacher: All right, gravity, and theres something pushing up. Theres something pushing up.Teacher: Well, the force of the water. Its a fluid.Teacher: A ll right, and what do you know about density? Do you know how to find density?

Joe: What do you m ean about what forces or gravity?Joe: Its water, because water, the water aint a force.Joe: Then water. Okay. So there. Theres 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, dont yo u? Okay.So what w e want to know is if theres some way that we can tell whats going to sink or float bythe way, uh, we figure out density. We know from the density.Girl: Heres our question.Teacher: Does the amount of density matter if the, uh [. . .] All right, what if you said, does the amount ofdensity, um, determine . . .Girl: Have an effect.Teacher: All right. Have an effect. Okay.

Joe: What is the other ball were using? A steel ball and a what?Teacher: Were going to use six different kinds of materials. So-Joe: -How do we know what materials were going to use?Teacher: Were going to use six different kinds.

Joe: Yeah, but we dont know what materials were going to use.Teacher: No, it doesnt matter which materials, it just matters that theyre different.In cont ras t to the previous excerpt of d iscourse , in t ry ing to he lp these s tudents who a l so

reques ted he lp , the teacher brought up th i s t ime the idea of forces [ that] work on somethingw h e n you put i t in w ater . However, she moved quickly to dens i ty and how to find density,wi thout a t tempt ing to he lp the s tudents develop logical l inks between th e relat ive densi ty and there la t ive s t rengths of these forces . The conv ersat ion shifted to the ques t ion fo r experiment whichone gi r l showed to the teacher , to be in ter rupted b y Joe , w ho w anted to know more abou t theexper imenta l par t ra ther than spending more t ime on the s tory an d the ques tion . The discuss ionin this group does not le t us know whe the r t he s tuden t s even have a specific expectationrega rding how the dens i t y o f a material relative to th e densi ty of the water affects i ts behav ior inwater .

Station 3 .Girl: We need your help. We know what were supposed to do, we just cant do it.Teacher: Okay, I told Bunty Id help her first and then Ill 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 [. . .] weve seen some things sink and some things float andsome things stayed put. Okay, and what determines that?

Bunty: We dont really understand this.


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248 VARELASBunty: Um, the gravity and then the density. But I really dont understand density.Bunty: Isnt it how [. . .] something [. . . IBunty: 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 overvolume. So, you take the piece, and the relationship between those two is density. Density equalsmass over volume. [ . . .] And we know that water is one gram over one cc , and something thathas 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. B ut we want tofind out if the density is going to be [, . .I If we can measure the density, do you think we couldtake 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 ofdifferent materials and then see if its less than water; what do you think will happen?Lena: Well, see, if its less 1. . .] if its not in the middle , then its less. If its not in the middle of thething, its got to be right in the middle. It doesnt 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 acertain thing. Okay? All right, so we take what we know and we know that some things sink andsome things float. And we know it has something to do with density. And if its the same densityas water, what happens to it?

Bunty: Yeah, I guess.Bunty: Is that the idea?

Lena: It doesnt go up or down.Teacher: It doesnt go up or down. The buoyant force of water is pushing it up and gravity is pushing itdown 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 wecould quantify this by finding out the density of each o ne and then test it out to see if those thingsheavier than water would do what? Those that had a greater density than water would [. . .]Girl: Sink.Teacher: Sink. But thats what we think. But thats what were 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, dont 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: G reater than. So, we know that. But we want to take six different materials and find out if thiswill always be true. Does density really determine whether something will sink or float? And ifwe know the density.


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BETWEEN THEORY AND DATA 249Howard: Gravity and density.Teacher: Al l right, and gravity is always going to be the same. Its going to be consistent pulling. But it

depends on the mass, how much pull there is. Okay, Im going to put 1. . . I Will you help me,Howard? Okay, Im 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 greaterdensity than water, right?Girl: Yeah.

Teacher: Will sink. Some thing that has the same density as water will not go up or down. And somethingwith less density than w ater will float. Okay, great. So, we know som ething about density. Now,what our question is going to be, is, can we show [. . . ] Is this the way its always going to be?You know, we know for a few things and so were going to [. . . ] not always going to be, but,can we, uh [. . .]

Bunty: So, ou r 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 youll 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 [. . . IGirl: 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 testit 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 q uestion, 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 ex plicit with that. But then youll have a good question. If things have a

density [. . . ]j us t 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 thequestion 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 orsink in water. Remember that when the teacher and students were developing the story ofsinking and floating, students talked about density being the second force that pushes anobject up when submerged in water. Probably, this is what Bunty was referring to, but she wenton to state that sh e did not understand density, t o lead the discussion to a definition of density,and the relationship between relative density and behavior in water-that is, things with densitygreater than water sink, things with density less than water float, and things with the samedensity stay put. The notion of the two forces acting on an object submerged in water and theirrelative strengths as determined by the density of the submerged object relative to water (itsrelative density) was never explored and developed. The discussion mostly focused on measur-ing , how students could m easure density and what they would do in the experiment. Th e teacherand studen ts did not generate a scientific story but a set of statements, predictions, or hypothesesthat were to be tested. There w as no explicit mention of where these statements came from , butit is pretty c lear that these statements did not co me from a co here nt, logical scientific story thatexplained why, for example, denser things sink. It seems that these statements came from priorempirical evidence that students and teacher had with things sinking and floating. Th e teachers


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250 VARELASversion of a question for experiment-is this the way its alway s going to be? You know, weknow for a few things and so were going to . . . -supports this interp retation .

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: M ass per unit volume, right? Or whatever. All right. Its the relationship between the mass andthe 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 thatyou 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 [. . . ILena: 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 yo u 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 dowhat?Marty: Sink.

Teacher: Sink. So, thats what you think.Girl: Yeah, so can we prove that [. . .] Can we prove by measuring the density of other objects ifwaters density do es affect something or other?Teacher: All right, write it down.

This piece of discourse brings us back to the opening of R esults, Analysis, and Discussion.We see here (Stage 2) again Lena , the girl who later challenged Birutes question for experimentin relation to her summary of the story (Stage 3), struggling with her partners to develop aquestion for experim ent. Lenas first question was: Can we find the density of an object? T hiswas 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 theanswer to her question. Soon afterw ard, Lena used the same line of reasoning the teacher usedwith 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 forexperim ent. Thus, if they knew the answer to the question, how could it make sense to pose thisquestion as their question for experim ent? Of co urse, the issue here is how they knew the answerto this question, and wh ere this answer came from . Did they know this answer from their theory


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BETWEEN THEORY AND DATA 25 Iand 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 othermaterials, too? These are two distinctly different modes of scientific activity; the former is onthe deductive side and the latter on the inductive side. Given the nature of the discussionsillustrated above, both fo r the single large group and for the small groups, and given thequotations and commentary appearing above, the latter seems more probable. As a matter offact, the teacher said to this group of students, All right, so you know that some things thathave densities greater than water will sink. Okay, now, what we want to know is if we can findo u t about other things. This is clearly on the side of empirical generalization rather than on theside 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. Letus listen in on the following day in class as the teacher addressed Lenas question, which alsobecame Cathys concern (Stage 3).

Knowing from Theory and Knowing from Da ta: More from the W hole-Group Discussion.Teacher: Okay, Ill tell you about that in a minu te. Yesterday, just as class was about to end , uh, Cathy andLena expressed a very good concern, and do you remember what your question was? Or should Iread 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 weknow 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 thequestion you had?Lena: Yeah.Teacher: Okay, all right. Th e reason that we would d o the experiment is that, um , we have som ething in

our mind and we know a little bit about it, and so we have a story. We take all the information thatwe have and we have a story. And thats what scientists also do. Now, we took the density, weknow the density of steel, and we took the density of Lucite also. Did we actually experimentwith something that has a density lighter than water?Girl: No.Teacher: No, we didnt. So, we definitely think that were right, but were not absolutely certain, are we?No. Remember, a long, long time ago, that the scholars thought that the earth was flat? And intheir mind, that made perfect sense. D idnt it? And from everything that they could see, it lookedlike the earth was flat. But, they had to g o out there and experiment and go over the horizon, so tospeak , and then find out that their original idea wasnt 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 hada greater mass, that the ball with the greater mass would drop to the ground quicker, because thatmade sense to them. And it took a long time before they could ever discover that that wasnt true,because they had to, uh, overcome some things like wind resistance and so forth,but [. . .] airpressures and so forth. But [. . .] So , people can have ideas in their mind , and be really sure thattheyre correct. But thats what a scientist has to do, he has to test it out, get some realquantitative, uh, data, and then hes sure. Now, if we wanted to make sure that everything with adensity less than water would float, and everything with a density greater than water would sink,wed 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 asthey can and then apply that to, uh, a more generalized, um, experience. So, they start withwhatever they can and then they expand, but, um, we do have to test things out, because thatsour story and thats where we get our question from.


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25 2 VARELASIn her attempt to help the students see why scientists do experimen ts if they already knowthe answers from the theory, the teacher gave a top-down monologue to the students without

trying to en gage them in relating this to their own understandings. Although the teacher tried todevelop 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 develop ing logical links betweenconcepts and ideas (The reason that we would do the experiment is that, urn, we havesometh ing in our mind; We definitely think that were right, but were not absolutely certain;Rem ember, a long, long time ago , that the scholars thought that the earth was flat? And in theirmind, that made perfect sense. Didnt it? People can have ideas in their mind , and be reallysure that theyre correct. B ut thats what a scientist has to do , he has to test it out, get some realquantitative, uh, data, and then hes sure) with (b) elements that are more associated withknow ing through em pirical evidence (We know the density of steel, and w e took the density ofLucite, also; And from everything that they could see, it looked like the earth was flat). Thismay have not helped the students develop the differentiation between the two w ays of know ing.The teachers talk once again does not make clear whether the organization of ideas-therelationships discussed-comes from developing logical, conceptual links among relevant con-cepts, as is necessary for the deductive direction of scientific activity, or from p revious empiricalevidence, being a relatively direct generalization of these previous findings and thus rem ainingin the inductive direction.The teachers and students talk as they developed their theory for sinking and floating andtheir question for experimen t points to several findings: (a) the teacher and students discussedand struggled w ith some im portant ideas that could help them deve lop a theory to explain whyand how the relative density of a m aterial with respect to that of water determines whether thematerial would sink, float, or stay put when submerged in water; (b) as they attempted todevelop a scientific story for the phenomenon of sinking and floating, the class oscillatedbetween two different modes, developing a logical explanation of this phenomenon and discuss-ing an em pirically based generalization of this phenomenon; and (c) most of the time, there wasnot a clear ind ication whether teacher and students were operating in one or the other mode. Buthow does the stude nts written work relate to these findings? Does this written work reflect theshared discussions among stude nts and between teacher and students, and how does it do that?Wh at does the students written work reveal in terms of the students understandings of theoryand data and their interrelationships? I now turn to these questions.As mentioned earlier, before doing the experiment, the students wrote a summary of thetheory they dev eloped with the teacher, and then had two opportunities to formulate in w riting aquestion for experiment. We just listened in to some groups of students as they worked on asumm ary of their theory and their first attempt to deve lop a question for experiment (Stage 2).After class discussion , all stud ents had a chance to revise, if they wanted to, their question forexperiment (Stage 5 ) . Let us now explore the summaries of the theory that the students wrote.

Looking at Theory and Data: Students Written WorkWhat kind of summaries of the theory did the students write? Did they indicate in thesesumm aries some kind of relationsh ip or link between relative density of a material with respectto w ater and its behavior in w ater? That would be a first step toward having an expectation forthe phenomenon of sinking and floating. But this expectation could still be derived from anempirically based generalization and not a logical, coherent, scientific story that explains whythis relationship exists. One way to achieve this kind of theory, a logical network of c oncepts

and ideas, is through linking the relative density of an object with respect to water to the relativestrengths of the two forces acting on this object when submerged in water. To achieve this,


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BETWEEN THEORY AND DATA 253students need to think ab out the two forces and link the relative strength of these two forces withthe density of the submerged object and the objects behavior in water. However, to achieve afurther level of logical coh erence , an additional ste p is necessary. In this step, the link betweenthe relative strength of th e forces and the density is explained b y linking the upward force on asubm erged body, having a give n volume, t o the density of the water, and the downw ard force tothe density of the body. Th erefore, the students sum marie s of the theory were exam ined interms of five features?

Criterion A: Directionality of the link between the density of a material and its behaviorCriterion B: Specificity of the link between the density of a material and its behavior inCriterion 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 theCriterion E: Explaining the link between the relative strength of the two forces and the

in water.water.

submerged object and the objects behavior in water.density of the submerged object.

Students sum marie s that related sinking with higher density an dj oa ti ng with lower densitywere c onsidere d to have directionality. Students summaries th at specified that it w as the densityof the body relative to that of water that was critical were considered to have specificity.Students responses were co nsidered not t o have directionality o r specificity if the responses didnot include a link between the density of a material and its behavior in water, or if the link thatthey 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 inthe same place.Larrys summary of the theory had both directionality and specificity. However, Larry did notrefer to any forces. Thus, Larrys sum mary satisfied Criteria A and B, but did not satisfy Crite riaC , 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 waterforce and pushes the object down. If the object has a less density than the water force the waterforce is then stronger than the gravity force and the object floats. If the objects density is exactlythe same as the water than [sic] the object stays in the same place.

Ivys ela borate sum mary of the theo ry had both directionality a nd specificity. It also included areference to two fo rces nam ed gravity and wa ter force, and also linked their relative strengthwith the relative density of the objec t and its behavior in water (If the obje ct ha s a greaterdensity than the w ater, the force of gravity is stronger than the water force and pushes the objec tdown). However, Ivys summary did not explain this link. Thus, Ivys summary satisfiedCriteria A-D, but did not satisfy Criterion E.

Vida: The gravity pushes down as the water pushes it up.Vidas summary of the theory did no t include a link between the density of a material and itsbehavior in water, thus lacking both directionality and specificity. However, Vida referred to


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254 VARELAStwo forces: gravity pushing down and water pushing up. Her summary did not link the relativestrength of these two forces with the densit

valeras - 1998 - between theory and data in a seventh-grade science class

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