the concept map as a tool for the collaborative construction of knowledge: a microanalysis of high...

JOURNAL OF RESEARCH IN SCIENCE TEACHING VOL. 30, NO. 5, PP. 503-534 (1993)

The Concept Map as a Tool for the Collaborative Construction of Knowledge: A Microanalysis of High School Physics Students

Wolff-Michael Roth

Faculty of Education, Simon Fraser University, Burnaby, B . C . , Canada V5A IS6

Anita Roychoudhury

Miami University, Hamilton, Ohio 4501 1

Abstract

Although concept mapping has been shown to help students in meaningful learning, particularly when done as a collaborative activity, little has been done to understand the microprocesses during the activity itself. However, in order to be able to improve the activity as a teaching and learning heuristic, we have to know more about the microprocesses that constitute concept mapping as process and as product. This study was designed to investigate concept mapping as a means of assessing the quality of student understanding from two perspectives: the analysis of the process of constructing meaning and the analysis of the products of this cognitive activity. An interpretive research methodology was adopted for the construction of meaning from the data. Twenty-nine students from two sections of a senior level high school physics course participated in the study. The data sources included videotapes, their transcripts, and all concept maps produced. Students worked in collaborative groups during all of the concept mapping sessions. Individual concept mapping was assessed twice, once delayed by a week, another time delayed by 6 weeks. To assess what happened to the cognitive achievement as the context of concept mapping changed from collaborative to individual activity, we used a tracer. A tracer is some bit of knowledge, procedure, or action that allows the researcher to follow a task through various settings. The concept maps as products differed in their hierarchical organization, the number of links, and the benefit to the individual students. Three major processes emerged, which students used to arrive at suitable propositions. Students mediated propositions verbally and nonverbally, they took adversarial positions and appealed to authority, and they formed temporary alliances based on presumed expertise. Both product and process hold promise but also show some limitations. On the positive side, concept mapping led to sustained discourse on the topic and improved the declarative knowledge of several students both in terms of the hierarchical organization and “local” configuration of the concepts. In contrast, concept mapping also let unintended and scientifically incorrect notions become ingrained and go unchallenged. On the basis of the outcomes of our study we formulated specific recommendations for the use of concept maps in the classroom. These include continued instruction in establishing proper hierarchies and cross-links to increase the quality of the concept maps’ structure and the number of high quality links. Then, instruction should facilitate students’ attempts to reflect on the nature of the relationships expressed in their maps. And finally, specific roles could be assigned to individual students to improve the overall quality of the process of constructing the map and, thus, of the final product.

0 1993 by the National Association for Research in Science Teaching Published by John Wiley & Sons, Inc. CCC 0022-4308/93/050503-32

504 ROTH AND ROYCHOUDHURY

Science educators have long sought techniques to integrate the learning of subject matter with learning how to learn. One such technique that has found more and more acceptance during the past decade is the concept map (Novak, 1990; Novak & Gowin, 1984). This acceptance was brought out by the fact that the Journal of Research in Science Teaching devoted one whole issue to the topic of concept maps (JRST, Vol. 27, No. lo), which was followed up by a symposium held during the 1991 NARST meeting. Although there is some evidence demonstrating positive effects of concept mapping on cognitive learning, affect, and metacognitive strategies, many questions remain unanswered.

In the past, concept maps have been shown to help students in meaningful learning of science concepts, albeit these studies were not always conclusive (Heinze-Fry & Novak, 1990; Lehman, Carter, & Kahle, 1985; Novak, Gowin, & Johansen, 1983; Okebukola, 1990; Okebukola & Jegede, 1988; Pankratius, 1990; Stewart, Van Kirk, & Rowell, 1979). This meaningful learning is thought to arise from at least two features of concept mapping. First, concept maps assist learners to become aware of, and control the cognitive processes of the task. Second, they assist learners to develop more integrated conceptual frameworks (Heinze-Fry & Novak, 1990; Novak et al., 1983; Okebukola, 1990; Stensvold & Wilson, 1990). Jegede, Alaiyemola, and Okebukola ( 1990) showed that besides higher achievement, concept mapping was also associated with a reduction of anxiety. Although a reduction in anxiety levels was observed for both males and females, there was a treatment-gender interaction that favored males. In addition to these findings, Okebukola and Jegede (1988) demonstrated that students who collaborate in the construction of concept maps “attain meaningful learning better than students working individually” (p. 498).

Concept maps are ideal for helping students examine and reflect on their knowledge. They also help students to examine and reflect on the changes in the organization of this knowledge during learning and thus emphasize the constructive nature of learning (Beyerbach & Smith, 1990). As such, concept mapping is an activity that is compatible with a constructivist theory of learning, which views knowledge as constructed by an individual alone or in collaboration with others. From a constructivist perspective, learning something new “means finding a way of fitting available conceptual elements into a pattern that is circumscribed by specific constraints” (von Glasersfeld, 1987, p. 9). There are two major schools of thought on constructivism, one that derives from the work of Piaget (von Glasersfeld, 1987), the other that derives from the work of Vygotsky (Newman, Griffin, & Cole, 1989). Both schools of thought, the Piagetian, which focuses on the intraindividual process in knowledge construction, and the Vygotskian, which focuses on interindividual construction processes, stress the importance of social interaction to learning.

From a Piagetian point of view, learning in a collaborative situation is facilitated by the continual conflict between antagonistic forms of thinking (Rogoff, 1990). The resolution of these conflicts is achieved as the collaborating individuals try to reestablish cognitive equilibration in their understanding through reciprocal consideration of alternative views. From a Vygotskian point of view, knowledge is collaboratively constructed between individuals, from where it can be appropriated by each individual. This process of appropriation is equivalent to the intraindividual construction of knowledge (Newman et al., 1989). Thus, while Piagetians focus on the individual as locus of the construction of knowledge, Vygotskians consider both the social situation-including culture, its artifacts, tools, and language-and the individual. In both traditions, the notion of intersubjectivity, that is, the understanding that the collaborating individuals have of each other, is of considerable importance. From a Piagetian perspective, intersubjectivity allows “the meeting of two minds . . . each operating on the other’s ideas,

CONCEPT MAPPING: A MICROANALYSIS 505

using the back-and-forth of discussion to advance his or her own development” (Rogoff, 1990, p. 149). From a Vygotskian perspective, intersubjectivity allows for joint thinking, problem solving, and decision making processes from which the learner appropriates new knowledge. According to Wertsch (1984), “intersubjectivity exists between two interlocutors in a task setting when they share the same situation definition and know that they share the same situation definition” (p. 12). At one level, intersubjectivity may consist of no more than agreement on the location of physical objects in a setting. On the other hand, intersubjectivity is almost complete if two interlocutors represent objects and events in nearly identical ways. In order to negotiate meaning, share, or form consensus, students have to achieve intersubjectivity. Thus, intersubjectivity becomes an important concept in the study of collaborative learning situations.

Over the past three decades, much work has been done to find out whether or not students learn better in collaborative situations. Johnson and Johnson (1990) reported the results of a meta-analysis of 323 studies, which indicated that the average student from a cooperative situation achieved about three-fourths of a standard deviation (SD) above the mean. Social interactive teaching methods show a lot of promise when the construction of meaning is emphasized and positively valued (Brown & Palincsar, 1989; Greeno, 1986). Students who engage in collaborative problem solving are required to make their own understanding explicit. In this effort, they evaluate, integrate, and elaborate on their understanding in new ways that further improve their comprehension (Brown, 1988). Hatano and Inagaki (1987, 1991) pointed out that when students have to explain themselves or defend their own positions, they begin to examine their understanding in detail. In this, they are often helped by their collaborators who add to or elaborate further what has been said. As they examine their comprehension in detail, students become aware of the inadequacies in their understanding, which may lead them to reconstruct their conceptual framework.

Increasingly, collaborative learning has become an instructional tool used by educators at various levels, from primary school to university. But in spite of much research effort, many questions remain unanswered (Tobin, 1990). The process of students’ interactions has yet to be documented and described and more needs to be learned about the mechanisms through which the effects of collaborative learning are achieved (Hertz-Lazarowitz, Baird, Webb, & Lazarowitz, 1984; Kinder, 1990). The purpose of the present study was to find answers to some of the many questions in the area of collaborative activity in science learning, pressing questions that were left unanswered by past research (Tobin, 1990). In this connection we propose that persistent vagueness in the collaborative construction of knowledge may be related to the fact that research studies seldom explore the details of negotiations involved in collaboration. Also, the activities in which students engage need to hold the potential for students to express/ elaborate their ideas, seek clarification of, or reject/accept other ideas. Concept maps, due to their usefulness as a metacognitive tool may provide an ideal context for overt negotiation of meaning and construction of knowledge because they require individuals to externalize their propositional frameworks (Novak & Gowin, 1984), particularly when students collaboratively construct these maps.

Our study was a specific attempt to understand (a) how students construct knowledge during collaborative concept mapping and (b) the processes that allow students engaged in collaborative activity to decide on the next step in conflict situations. Specifically, some of the questions we were interested in answering were, “How do students negotiate meaning?’ “What is involved in sharing meaning?” and, “What is involved in forming consensus?’ (Tobin, 1990). In our methodological approach we followed the advice of Cobb, Wood, and Yackel(l991) who called for an epistemology of science and mathematics that is descriptive and empirical rather


than a priori and normative. Our ultimate goal was to construct knowledge through observations in the classroom, on the basis of which we could improve concept mapping as a teaching and learning heuristic in the science classroom.

Method

To arrive at an appropriate level of description, we used an interpretive methodology based on constructivist inquiry (Guba & Lincoln, 1989; Lincoln & Guba, 1985) and constant comparative analysis (Strauss, 1987) with a particular interest for the ways in which the participants negotiated the context of the task at hand (Burrell & Morgan, 1985; Garfinkel, 1967). Direct observations, video recordings, and concept maps produced during collaborative sessions and formal examinations constituted the data sources for this study.

Sample

Twenty-nine students from two sections of a senior year physics course at a private school for boys participated in the study. All students had taken a junior year introductory physics course during which they learned to use concept maps. The students had used concept maps periodically to summarize the main ideas during their laboratory exercises. However, the concept maps had not been used for evaluative purposes.

Procedures

A total of seven concept mapping sessions were videotaped, each lasting from 45 to 60 minutes. Five of these sessions were scheduled out of regular class time. During these sessions, the students also did not have access to any other resource than their memory. Two sessions were videotaped during regular classes. In this way, we were able to ascertain the ecological validity of the study. Ecological validity is concerned with answers to the following question: “Is thought and action observed in one context [the out-of-class session] representative of that displayed by people in their natural context [the regular class]?’ (Roth, 1992). After accounting for the difference in the conversational resources between the two settings-interacting with the teacher or with peers and consulting with the textbook were available only in the regular classroom-we found identical patterns of interaction and similar achievements in terms of the quality of the concept maps produced. Our findings from the out-of-class sessions are thus representative of what we found in the actual classroom, which established the ecological validity of the study.

Two groups (Peter, Eldon, Michael and Max, Allan, Dan)’ came for two sessions spaced by a 2-week interval, one group (Rand, Mick, Marcus) came once, at the same day as the other two groups’ second session. One week later, all students had to make individual concept maps as part of a test on the unit which focused on concepts from the topic of light-as-a-wave phenomenon. A second individual map of light-as-a-wave concepts was constructed by all participants as part of the final examination, 5 weeks after the first test. Because of time restrictions during testing situations, the original number of concepts was reduced from 30 during the collaborative sessions to 14 during the individual testing sessions. Two groups (Rand, Mick, Kevin and Allan, Dan, Michael) were videotaped in class as they mapped concepts from the chapter on the quantum nature of light (Martindale, Heath, & Eastman, 1986). The videotaped students repre-


sented a cross section of the course. Using their physics marks, four students were within 1 SD below the mean, four students within 1 SD above the mean. Two students had marks between 1 and 2 SD above the mean. The concept maps constructed during the regular classes by the other six groups in the two sections of physics were also included in the analysis for comparison purposes. Rand, Mick, and nine other students had made available the concept maps that they produced on their own to study the quantum nature of light.

As the study progressed, the students completed two learning portfolios as regular class assignments, one that centered on light-as-a-wave, the other on the quantum nature of light. These portfolios included experiments, reading assignments, questions, word problems, and simulations. Two whole class interactions were conducted only to explicate the assumptions underlying the mathematical derivations in the students’ main textbook (Martindale et al., 1986). The concepts that we asked students to map all appeared in the relevant chapters of their textbook. These concepts appeared in bold-faced type to emphasize their importance regarding the scientifically correct understanding of the central idea in each topic. One should assume that students who demonstrated a good integration of all concepts into a unified whole had a good understanding of the topic as presented by the textbook. Near the completion of the collaboratively produced portfolios, the students were asked to prepare a concept map. The teacher emphasized in his instructions that the concept maps were designed to help them tie together the knowledge that they constructed in the various activities included in their portfolios. Their task was to express what they had learned about the topics of light-as-a-wave and light as a quantum phenomenon, respectively.

For the mapping activities, each group received a stack of 1.25” X 3“ cards, each imprinted with one of the concepts. Because we were interested in concept mapping as a way of sum- marizing and reflecting on prior activities, we limited the concepts to those that were highlighted in the students’ textbook. However, we allowed students to add further concepts if they deemed them necessary for the construction of the particular map. The selection of a set of specified concepts also limited the students’ discourse to the concepts of interest in the context of their present activities. Furthermore, the selection of concepts by the teacher-researcher team also provided some uniformity, which permitted us to more readily compare the products of different groups.

Before actually drawing their final concept map on paper, students used these cards to discuss the arrangement of concepts and the possible linkages. Once the group members seemed satisfied with an arrangement, they used a sheet of 14” X 17” paper for the drawing of their concept map. However, although they had often begun to construct part of the map, students still moved the concept cards to rearrange the structure. These changes were most often of local, rather than global, nature and continued until a local structure had been decided on and drawn in its final form.

Data Sources and Data Analysis

The students concept mapped in groups of three, a regular group arrangement for collaborative work in this physics course. Several students working together on a task that could be done individually (though in a different way) are faced with the problem of communicating with each other. In the interest of collaboration and to achieve the necessary intersubjectivity, students tell each other their thoughts about the nature of the next move, how much progress has been made, how much remains to be done, the rationale for making one move or statement over another, and so forth. In this way, the participants provide each other with a sense of the task’s status, and they provide the researcher with that sense as well. “An artifact of such a collaboration,


therefore, is naturally generated protocol” (Suchman, 1987, p. 1 IS). Such protocols of collaborative work are evidence for the individual reasoning of participants (Brown, Rubinstein, & Burton, 1976). For researchers, these protocols open windows on the processes of how the participants attribute meaning to the context. They also reveal how participants make evident and persuade each other that the events and activities in which they are involved are consistent and coherent (Burrell & Morgan, 1985).

In addition to the protocol transcripts we collected as data the following artifacts: (a) the concept maps produced during the sessions; (b) the concept maps produced individually during both test situations; (c) the concept maps produced by all other groups during the two regular class periods; and (d) the concept maps that Rand, Mick, and nine other students constructed individually to study the unit on the quantum character of light. To analyze our data, we adopted a technique used by anthropologists who study interactive behaviors. We repeatedly viewed the videotapes and read the transcripts to form tentative descriptions. These initial descriptions were refined, modified, or discarded on the basis of further comparisons within the set of data we had collected. We discussed disagreements until we reached consensus and discarded those descriptions on which we could not agree. Our goal was to develop categories from the data, which were to be used to characterize the interactions between participants and the concept maps they produced. This approach, which was developed by anthropologists to study a variety of interactive behaviors, was used successfully in an investigation of the interactions during tutoring (McArthur, Stasz, & Zmuidzinas, 1990).

Unit of Analysis

This study was mainly concerned with achievements, which were interactional, in terms of individual learning or in terms of a product of groups of students. In our effort to assess the interactions and learning of the participants, we found, similar to others, that the individual was not the most useful unit of analysis for many situations (Newman et al., 1989; Roth & Roychoudhury, 1993; see Wertsch, 1985 for a comprehensive review). Thus, we adopted the perspectives of others who seek to assess interactions and learning that are inherently connected to the context. That is, interactions and learning are connected to the environment, tools, and other resources in such a way that they cannot be understood without reference to them (New- man et al., 1989; Pea, 1987; Smith & Confrey, 1991). This is why in many cases an achievement could not be attributed to an individual, but had to be understood as arising out of the interaction of all three, the individual, the social, and the physical environment. In the past, various units of analysis have been suggested for the analysis of social units. Among these were activity or event (Cole, 1985); socially assembled situations or cultural practices (Laboratory of Comparative Human Cognition, 1983); task-within practices or work task (Scribner, 1984); “whole task” (Newman, Griffin, & Cole, 1984; Newman et al., 1989); and work sequences, networks, or techniques of argument (Latour & Woolgar, 1979).

In our analyses we found the task as the most appropriate unit. Here, the task was to represent concepts in a hierarchical configuration. Cognitive tasks, particularly those that are performed in a collaborative setting, cannot be identified independently from their social context. Any transformations of the social organization of the actors, whether these are changes in group composition or changes to individual work, will change the nature of the task. In order to deal with this changing nature of tasks, we made use of a tracer, a device that had been used to study the Piagetian intersection tasks in individual laboratory and collaborative classroom settings (Newman et al., 1989).

CONCEPT MAPPING: A MlCROANALYSlS 509

Tracer

The concept maps that the students produced in both in-class and out-of-class settings resulted from collaborative work. When we later tested students individually, a third setting, the context had changed sufficiently that the task may no longer have been the same-an important issue that is little addressed in traditional educational research. For example, in the collaborative setting, the three students of a group had each other as a resource, the teacher, and the concept labels to be manipulated. When they worked on concept maps during regular class time, additional resources were available. During the testing situations, however, none of these resources were available, such as textbooks and students from other groups. To find out what happened during individual testing to the cognitive achievement that students had attained collaboratively, we decided to use a tracer. According to Newman et al. (1989), a tracer is “some bit of knowledge, procedure, set of actions, talk, or written symbol” (p. 29) that allows the researcher to follow a task in various settings or contexts. In the present case, because we could not assume that the overall maps would maintain any sort of consistency across participants during the two tests, we decided to trace the configuration of one set of concepts. In our view, this also coincides with Newman et al.’s (1989) recommendation of selecting “some bit” rather than the total task. To select specific concepts we studied the transcripts for a recognizable cluster of concepts that was also under considerable debate during the sessions. We conjectured that the debate might bring about changes in and/or stabilize students’ conceptual relationships, which would help us in finding the tracer in later tests. These considerations, the analysis of the transcripts, and the inspection of all concept maps on light-as-a-wave phenomenon led us to select the configuration of the concepts light, phase, interference, reflection, air wedge, diffraction, and double &/grating as the tracer.

Results

As we analyzed the data two major dimensions emerged, which we used to organize our results. First, we will discuss the cognitive achievements of individuals and groups as they were expressed by the concept maps submitted. Then we will present the analysis of the interactional processes during the collaborative work on concept maps.

Cognitive Achievement

Concept maps constructed within the same context differed in terms of the nature of the linkages between concepts and the organization of the concepts (see Appendices A and B). These differences led us to use the hierarchy of the concepts and the cross-links between parts of a map as criteria for the comparison of maps constructed in the same setting. These emerging criteria for comparison are not unique to this study. To assess concept maps, Novak and Gowin (1984) suggested that the relationships between concepts be evaluated on the basis of hierarchy and cross-links. A scientifically correct cross-link receives more weight in the evaluation than a correct level in the hierarchy, which in turn receives more weight than a correct link between concepts or to examples. In the following discussion, we used the term “local hierarchy” to refer to small clusters of concepts; we used “global hierarchy” (or arrangement) to refer to the arrangement of the local clusters, or to the general hierarchical ordering of all concepts.

Individual Achievement. The comparison of the concept maps done during the tests with those done during the collaborative sessions showed variations for some students in both global


and local arrangements of concepts, while others showed only little variation. The results with respect to the variation of the traces are presented in Table 1. One week after the last concept mapping session focusing on the phenomenon of light-as-a-wave, seven students used the configuration almost identical to that of their respective groups. Peter and Eldon, both from the same group, showed entirely different organizations, globally as well as locally. On the other hand, Michael, the third student in the group and in terms of achievement in this physics course between the other two, showed a remarkable consistency over both individual testing situations (Figure lc, d). We will discuss his performance in more detail below. Six weeks after the last session, only five students showed small variations of the tracer from the original. Five students showed identical maps or only minor modifications; two students’ maps showed moderate modifications; while Peter’s and Eldon’s maps still showed drastic modification from the original without any improvement.

Two of the students, Rand and Mick, produced individual concept maps virtually identical to the original group map, both in terms of local as well as global arrangement. However, the analysis of their maps showed a difference in one link that had already appeared during their discussion and had been heavily debated. Rand had held that for interference to occur, the sources of the waves must be out of phase. Mick on the other hand had argued that the two sources must be in phase. This issue had been repeatedly addressed during their session, and the group had finally decided that the sources (waves) must be initially in phase, then out of phase for interference to occur. However, their individual constructions showed that neither of the two had accommodated the other’s view and the maps expressed their views from before the discussion. This indicates the resilience of some conceptions to instruction, although it was in the form of a peer discussion during which the students had to make explicit their understanding and where the flaws in their argumentation could be detected.

We were interested whether quantitative comparisons between the two tests would confirm or disconfirm our qualitative observations. The small qualitative variations between the first and the second test were also apparent in our quantitative comparisons. The mean number of links (which we set equal to valid links minus invalid links) for all students participating in the study rose from I 1.5 to 12.9. Although significantly different from a statistical point of view, r (9) = 2.49 ( p < .05), the magnitude of the effect was small. The high consistency between both performances-in terms of the number of valid links-was also confirmed by the quantitative analysis. Those students who did well or poorly on the first test did likewise on the second test ( r = .94, p < .0001).

Most propositions had been intensely discussed, negotiated, or collaboratively constructed. This led us to believe that the students’ views were far from identical. Through the sessions, the participants had negotiated global and local hierarchies of concepts. The foregoing results indicate that the conceptual relationships developed collaboratively were stable in more than

Table I Similarity of Tracer After Delayed Testing

Number of students

Tracer ~

1 week 6 weeks

Identical and slight modification 7 5 Moderate modification 0 2 Drastic modification 2 2


half of the participants, even over a 6-week period. We may have here one of the contributing elements to the effectiveness of concept mapping in helping students to develop a better understanding of both individual propositions and an overall organization of the conceptual framework of a topic. On the other hand, Peter and Eldon did not seem to benefit from the collaborative concept mapping, at least in terms of being able to appropriate from the collaborative experience. At this point, there is no evidence to answer the question whether the concept mapping activity, the collaboration, or both in combination failed to assist the two in achieving what the other participants did.

An interesting question is how Michael was able to turn the collaborative experience into a successful learning experience. Although Michael had suggested during the mapping session to use light as a central concept, from which all concepts were to emanate (“I think light and waves are the most important, they are the most general . . . Make them both the center”), his individual maps were clearly hierarchical and ordered around the tracer. He not only maintained the structure of the original tracer in the group map (Figure la, b), but was able to improve on it (Figure lc, d). Consequently, he used this tracer to anchor his whole map, thus constructing a successful global and local hierarchical ordering of the concepts. For comparison purposes we included Eldon’s tracer configuration produced during the 6-week delayed test (Figure le). It is apparent that his tracer configuration has little similarity with that of the two collaborative sessions, Figure 1 also shows that four of his linkages were invalid (missing or incorrect linking words), more so than any other participant.

Group Achievement. We wanted to know more about the difference between a successful and a less successful group. For present purposes, we defined success in terms of individual appropriation from the collaborative experience. From the successful group, Rand, Mick, and Marcus (RMM) all “transferred” their group results into the individual text situation 1 week after their session, Rand and Mick transferred even into the second test, delayed by 6 weeks; at that time, Marcus’ tracer showed moderate modifications. From the unsuccessful group (Peter, Eldon, and Michael [PEM]), Peter’s and Eldon’s map did not show the group tracer either after 1 or after 6 weeks; on the other hand, Michael did transfer and even improve over the group results.

The transcripts of the sessions (RMM’s first, PEM’s second; see Appendices A and B, respectively, for the concept maps) showed that during the first 10 minutes, RMM had more than twice as many propositions formulated than PEM. After that, RMM formulated about 50% more phrases than PEM. We categorized phrases according to four groups: (a) phrases that made reference to the global hierarchy of the concepts, GH, such as “Light is the most inclusive and should be on the top”; (b) phrases referring to a local hierarchy, LH, such as “Phase goes above interference”; (c) phrases that simply expressed proximity, P, such as “Crest goes with wave”; and (d) phrases that expressed a clear relationship, R, such as “A node is a point of destructive interference .”

Figure 2 illustrates how the four categories were distributed over time. In both cases, a majority of the initial phrases pertained to the classifications “proximity” and “global hierarchy,’’ indicating that the students were concerned with the overall ordering of the concepts into groups and the ordering of these groups relative to each other. We have to keep in mind, however, that over the first 10 minutes, RMM had I 1 GH, but PEM had only 6 GH phrases. While the proportion of the relationship expressing phrases shows a similar pattern, there are significant differences in the use of phrases referring to the local hierarchy. PEM had used only one LH phrase over the first 12 minutes, while RMM showed a consistent concern for local hierarchies. On the other hand, the less successful group exceeded the more successful group in

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Figure 2 . A successful group’s and an unsuccessful group’s use of propositions that express a global hierarchy (GH), a local hierarchy (LH), a proximity (P), or a relationships (R).

the relative frequency of phrases that merely expressed proximity. These differences could also be seen from their concept maps. Other than the tracer (Figure 1, Appendix B), no hierarchical relationship could be discerned from PEM’s map. Rather, the concepts of light and wave were surrounded by starlike emanating propositions. On the other hand, RMM’s map was highly structured with a discernible global hierarchy, and many local, hierarchical relationships (Ap- pendix A).

When the concept maps of RMM and PEM produced during the sessions were compared, striking differences became apparent both in terms of the number of linkages produced and in the hierarchical organization. During the first session, PEM produced 29 links, of which 25 (4) were valid (invalid). A link was judged valid if the associated proposition was acceptable within the language of standard (canonical) physics. During their second session, they again produced 29 links, all of which were valid. RMM, on the other hand, produced 36 (1) links during the session, which was on the same day as PEM’s second session. The third group increased their linkages from 25 (4) to 36 ( 1 ) valid (invalid) ones. RMM’s concept map was highly structured, with definite hierarchies within local clusters of concepts and between local clusters, that is, on a global scale. For example, RMM developed local hierarchies for interference and for disper-

5 14 ROTH AND ROYCHOUDHURY

sion phenomena. However, equivalent concepts such as double slit and air wedge versus prism (i.e., devices that bring about interference vs. dispersion phenomena) or diffraction and reflection versus refraction (processes caused by these devices) still appeared at the same level in the overall map. This organization gave the map a highly structured overall look (Appendix A). On the other hand, PEM’s maps showed little global organization; the only apparent local hierarchy was that around the tracer concepts and was not without flaws (Appendix B). Concepts seemed to be connected with little regard of structure, in a more or less haphazard way. The concept maps between the two extremes very often showed well developed local hierarchies with little comparison between the local clusters or concepts. We were thus seeing a definite relationship between the concern for hierarchy, as expressed by the number of phrases pertaining to this issue, and the organization of the resulting product. It was also apparent that the less successful group’s comments pertaining to global organization such as “Light is the most important” did not lead to any hierarchical ordering.

Interactional Processes

Previous research has amply demonstrated the benefits of collaborative activity. Yet little has been done to understand the mechanisms of group work (Kinder, 1990). To remediate this lacuna, we took a close look at the interactional processes during collaborative activity. In the following we will try to present answers to the questions, “How do we know that students mean the same thing, that is, how do we recognize intersubjectivity?” “If they share meaning, how do students achieve this intersubjectivity?’ and, “If they hold conflicting views, how do students settle these differences?”

During our analyses, three major processes emerged, which students used to arrive at a suitable proposition in the concept map. First, during the collaborative construction of propositions, students used verbal, pictorial, and nonverbal mediation to assure that each participant knew what the others meant. In this case, the students had to presume or to ascertain the existence of intersubjectivity. Then, during adversarial exchanges, students made use of resources such as a teacher, a textbook, a prior problem, or a student with presumed expertise in order to convince each other. Students also sought to win an argument by changing socially established rules. Finally, the formation of temporary alliances describes a process during which two or more students who favor the same proposition force its acceptance by a majority rule.

Collaborative Construction of Propositions

lntersubjectivity. When students knew, implicitly, that they were talking about the same thing, their speech became shorter and shorter. They began to simultaneously talk about the same thing, or they completed each other’s sentences. In the following exchange, all three students were involved in formulating a new sentence (see Appendix C for the completed map of Michael’s, Dan’s, and Allan’s session from which we will quote repeatedly).

Dan: Light Michael: Is made of Allan: The wave Dan: And quantum theory Michael: Is made of Allan: Yeah

In constructing this sentence, the students showed that they understood what they were talking

CONCEFT MAPPING: A MICROANALYSIS 515

about, and that they must have assumed that the others did too. If not, something like the following could have ensued:

Dan: Allan: Hm? Michael: Sorry?

What about there is a link between photon and electron?

Neither Allan nor Michael knew what Dan was talking about, it was as if Dan had been on a different conversational plane. Certainly, they did not share an understanding of the situation in this case. The completion of each other’s sentences is a sign that speakers have achieved a level of intersubjectivity (Granott, 199 1). At the same time, this intersubjectivity allowed students to construct new propositions, that is, new knowledge that exists in declarative form. We also found that when speakers knew that they were talking about the same thing, they used words like “this” and “that,” or pointed to a written word, diagram, object, instead of naming the objects of their conversation. Such conversational means that can be understood only in the context of the conversation are known as “indexical.” An increased use of indexical devices is a sign that speakers know they have achieved intersubjectivity (Garfinkel & Sacks, 1986). Only when it becomes clear to the speakers that a shared understanding does not exist, will speech become more explicit, and objects and/or events are named.

Dan: Photoelectric effect and work function, I don’t see the relationship. Michael: The photoelectric effect, they did the experiment and they found that when, like a photon

hits the plate and electron leaves when it has enough energy, it gets absorbed, the electron absorbs the energy and the excess energy goes to kinetic energy, right?

Dan: Oh, Yeah, OK. Michael: Well, the work function is the kinetic energy, is equal to the photon’s energy plus. Allan: Minus. Michael: Minus. Allan: Dan:

No, yeah, photon energy plus, ah, photon energy minus the work function. So, the photoelectric effect shows that.

Dan didn’t share an understanding with Michael and Allan. Thus, Michael explicated his own understanding, which he shared with Allan who was able to correct Michael (“plus” to “minus”). In this situation, Dan was brought back into the shared space of the problem, so that he could become again a contributor to the joint work. It was, in a sense, conversational repair work in which these students were involved. Without it, Dan could not have continued in the conversation, which would not have made sense to him.

Verbal Mediation. One of the possibilities for deciding on a specific proposition for the concept map is by co-constructing it in the group. In such cases, rather than seeking conflict that has to be settled through other means, the students work together to resolve the problematic situation. Such was the case when Michael, Allan, and Dan were considering a proposition involving the concepts of light and complementarity. Here, Michael made the first proposal:

Michael: Light considered to be complementary. Allan: Yeah, make. Michael: Considered as complementary? Like, considered as?2 Allan: Yeah. Michael: I am thinking of the joining word.

516

Allan: Yeah, yeah, yeah. Dan: That’s the one! Michael: OK.

ROTHANDROYCHOUDHURY

However, at this point, the three have not settled on this proposition. Both Dan and Michael tried the formulation again, but did not seem to be satisfied. Michael suggested a new proposition, “Light can be thought of complementary.” When his peers did not immediately agree with it, he generated another one, “Light understood as complementary.” Allan seemed to agree with this new proposition, but he hesitated. Michael, who was the driving force in the development of this proposition, suggested yet a new one:

Michael: Allan: Michael: Allan: Michael: Allan: Michael : Allan: Dan: Allan: Michael: Allan: Michael:

What I think, it goes, to understand a specific experiment. It’s either, yeah, OK. So, light understood as, understood to be complementarity? Yeah, light consists of the wave and quantum. OK. Yeah. Light understood to be, understood to be. I used, is it considered as, before? Yeah. Considered as! Yeah, considered as? Or understood to be? Understood to be, I think, understood to be! (Writes the proposition onto the line linking light and complementarity.)

In this complete episode, the propositions “can be thought of,” “understood as,” and “considered as” did not sound right to the group members. They considered the different propositions together until they all felt comfortable with one of the choices. Although Michael took the lead here to generate new propositions, in most cases two or all three students were involved in doing so. Michael’s reasoning, “What I think, it goes, to understand a specific experiment,” used the verb “understand’ in a new, but supportive context. This was crucial in the present case for the group’s choice of this verb. Toward the end of the episode, each of them had “tried,” that is, verbalized, one of the propositions so that ultimately they could be sure that their selection was the best they could select at that moment. Often, the decision to use a specific proposition did not take up as much of the discourse as in the episode presented here. Rather, such as in the case of the nouns wave, crest, and trough, students quickly settled on the propositions “wave has crest” and “wave has trough” without much further discussions or comment.

Mediation by Means of Diagrams. All groups also used diagrams with which they were able to negotiate the meaning of a proposition in contention. For example, two different groups used a diagram representing three layers of optical media to talk about the experimental and theoretical evidence that both in reflection and transmission, interference patterns occurred as light was reflected in thin films. One of the three groups also discussed the interference patterns in an air wedge by means of a diagram. Another group discussed the phenomenon of Newton’s Rings and the superposition of waves with various phase delays by drawing diagrams. In all of these cases, the diagrams were used by the students to ascertain that they were talking about “the same thing,” or to overcome the difficulties they experienced to express phenomena in words. For example, when Peter, Eldon, and Michael had difficulties knowing what the others meant when they talked about constructive and destructive interference, Peter used diagrams of waves with various phase shifts as tools for negotiation:

CONCEFT MAPPING: A MICROANALYSIS 517

Eldon:

Peter:

Michae

See what we should actually, what we should do is put something like a, because we were talking about this earlier, put crest and trough like here. Which ones, when the crest and trough miss there is constructive, right? They can, they can. They have to be totally in line to be (begins to draw sine waves). Well it depends, they don’t have to be exactly cancelling each other out, and they can still be constructive (continues drawing). Like you can have a wave like this (points toward drawing), is like that, well not exactly like that (drawing overlapping waves).

:I: Like the interference still exists, what you probably have, any crest you have is gonna be constructive.

In his final comment, Michael summarized Peter’s drawings and utterings by indicating that even in the case of phase shifts-unless they are one-half of a wavelength-there will still be crests that are instances of constructive interference.

Nonverbal mediation. In the following transcript, although both Peter and Eldon seemed to know what they wanted to achieve, they did not know whether they were talking about the same thing.

Peter: Eldon: Peter: Eldon: Peter: Eldon: Peter: Eldon:

Do you want to join these or what? Put, now you put, which is unique, right there. Like that? Yeah. There? Right across there. Which way? Put an arrow going that way (points from wavelength-frequency-speed cluster to wave). Put, which is unique to, like wave.

The first tries in achieving the necessary intersubjectivity fail, Peter did not know what Eldon meant by “right there,” although he had pointed toward the concepts he wanted Peter to link. Peter had to ask three times for further clarification (“Like that?’ “There?’ and “Which way?’) before Eldon finally changed to give an unambiguous directive where to put the link and which proposition to use. Interestingly enough, Eldon seemed to feel that he understood what Peter meant, and that it was exactly what he himself meant. Although Eldon thought that intersubjectivity was achieved, Peter negotiated for a new level, yet he did not specify his own choice more clearly. For example, he could have elected to say “Do you want me to link wave and frequency, or wave and wavelength?” Wertsch (1984) pointed out that the level of intersubjectivity is negotiated even between very young children and adults, and that the level is not determined by the adult’s utterings. On the other hand, if one of the peers or the teacher is unwilling to negotiate the level of understanding then the process of learning will be stalled. For,

if the instructor tries to maintain unilateral control of the dialogue and the student submits to him, then it becomes difficult for the student to make a public test of her own under- standings or explore the instructor’s meanings (Schon, 1987, p. 138).

We consider Schon’s statement equally valid for the conversation between peers. Any co-construction of meaning, whether through verbal, nonverbal, or pictorial mediation will be stalled if one member of the team tried to take unilateral control of the discourse.

Adversarial Exchanges

Students settled many differences by referring to some authority. This authority could be either a resource external to the group such as the teacher, a textbook, or a word problem they


remembered from the past; or the authority could come from a resource internal to the group, such as when students were known to have an area of specialty, produced themselves as very knowledgeable, remembered an observation or inference from a lab, o r produced an agreed upon diagram that could be used to negotiate the issue.

The Teacher as a Conversationul Resource. Students used or sought to use the teacher as a resource to settle differences in various ways. At times, they referred to a teacher’s statement by indicating, “we learned that in chemistry,” “in the last class he [the teacher] said,’’ or (to the teacher) “as you showed us on the overhead.” As the following exchange shows, this authority was accepted without question, although one could easily imagine the possibility that the reference was incorrect.

Dan: That’s what Doc [the teacher] said last night! Michael: Well, if he told you.

For one, the student could have been wrong in matching the topics from one context to the next, or Dan could have used the reference as a device to win the others over to his point. However, it appears that there was an unspoken agreement on academic honesty. Breaking this agreement would ultimately cost all of them. At other times, one of the group members asked the teacher a question directly. The consequences were different in the two cases. When students referred to a teacher’s statement, their authority was accepted if their peers believed in the accuracy of their memory. However, the situation was more complex when students asked the teacher directly. For pedagogical reasons, the teacher’s answer was either direct, so as to help students in modeling the scientifically correct use of a proposition, or the question was countered with a question if it seemed necessary to encourage the students to continue their dialogue.

Textbooks as Conversational Resource. During the sessions videotaped in the classroom/laboratory, students had available all the resources of a regular classroom, such as various textbooks and equipment for quick demonstrations. We were surprised to see that students did not use the textbook more often as a reference in critical situations. In each of the two groups, the students referred to a textbook three and five times, respectively. In these circumstances, the students referred to a diagram they remembered and targeted directly, or they reread a passage to clarify a concept. Reference to the textbook was also indirect, especially in those sessions when the students did not have access to it. Then, they referred to it such as Mick in the following excerpt where he wanted to convince both Rand and Marcus that interference in thin film can cause reflection:

Mick:

Marcus: Mick: Rand: Mick: To reduce reflection!

Since it is one-quarter of a lambda [the wavelength] thick, I just remembered that from the book. I don’t know, I didn’t read it.

(to Rand) Do you know the question 35? (affirmatively) There is destructive interference.

One problem with using textbooks extensively as a resource is the time constraint on the activity. Given that students have only limited time within a class period, the extensive use of time for searching the book for support when 30 to 35 propositions, local, and global hierarchies had to be negotiated seemed prohibitive. Unless students wanted to recall specific items they had read previously, they were reluctant to use a textbook as a conversational resource.


Student Knowledge us Conversational Resource. Mick also used his authority as a photographer-he was well known for his contributions to the school year book, the student newspaper, and as a member of the photo club who developed his own pictures-to support his claim that polarization is an example of destructive interference. The following lines began a dialogue on the topic of polarization that lasted for about 4 minutes:

Mick: These two have to go together, because polarization reduces reflection, like in. Marcus: I’ll try to remember that. Rand: In the last class. Mick: Because a polarized lens is made of one-quarter wavelength to reduce reflection.

Although Rand and Marcus were two of the higher achieving students in this physics course while Mick had a grade about 10% lower than the other two, Mick was eventually able to convince them of his position. Of course, a crucial element of this episode was that the three had no other resources to settle the conflict. This case was interesting particularly from the point of view of developing alternate or incorrect ideas from experiences in the science lab. Here, Mick was able to convince two very strong physics students of a wrong concept, a reason why many teachers favor direct teaching over group discussions. Ultimately, there are no guarantees for any single teaching technique to ascertain that students construct the intended knowledge. In the present case, an intervention by the teacher could have easily supported the counter evidence raised by Marcus and Rand. However, one can only speculate about the outcome of this argument had it been in the regular classroom with other resources available such as students, teacher, or textbooks.

We have also observed episodes where a student used his authority in the subject to win others for his position. In the following example Max, who was known to be a “math guy,” though with less success in physics, was determined to win the argument:

Max: Wavelength Allan: is measured by Max: Determines frequency Dan: which is measured Max: Speed is measured in hertz Allan: But it’s frequency that is measured in hertz! (Looks at Max as if for confirmation. Max looks

back, but denies confirmation.) OK, so both can be measured in hertz and Max: Meters per second.

-

Although Max came out the “winner” in this situation, the group ultimately lost because the proposition “Speed is measured in hertz” is incorrect. Fortunately in this situation, the group decided later against this formulation and separated speed and frequency altogether. However, 2 weeks later when the three did another map with the same concepts, the structure apparent in the above conversation was the one chosen for the group’s map. We observed this pattern repeatedly, where a student who seemed to have a good understanding of a small section of the physics content was able to convince his peers simply on the basis of the certainty with which he was making his point. Peter, for example, had written a paper on the index of refraction, and for this reason felt that his understanding was superior to that of his peers. His peers could not but follow his lead and settled on his understanding without further argument.

These negotiations were not much different from those of everyday practice in the scientific community. Reference to the authority of an individual, whether internal or external to the collaborative group, is often made by scientists in their work (Knorr-Cetina, 1981; Latour &

520 ROTHANDROYCHOUDHURY

Woolgar, 1979). For example, Watson and Crick followed one of their office mate’s advice, against the current knowledge as portrayed by the then current textbooks in the field. This advice ultimately led to the Nobel Prize winning construction of the DNA model (Watson, 1968). In this case, the office mate’s authority and credibility was established by his prior success in the field. Similarly, years of experience with data recording devices or number of publications may establish the authority of a human source of information (Latour, 1987).

Observations as Controversial Resources. Students also used evidence that they had gath- ered in the lab to support their argument. In these cases, the authority came from observations that the speakers tried to help others to recall. However, as in other cases, past observations were sometimes used to support a scientifically incorrect argument. Such was the case in the following exchange:

Dan:

Allan: Max: Allan: Dan:

But we had the laser going straight, going straight through and if there hadn’t been bending of light it would have [had the interference pattern]. Refracting went in and diffracting went in (shows with his hands how the rays bent). So the refracted and diffracted. It doesn’t matter where it is. No, no, it does, we get that refracted.

Here, both Dan and Allan made direct reference to three experiments that they had completed just a few days before, one refraction and two diffraction experiments. However, they focused on a feature that did not help them at all to resolve the difference between diffraction and refraction. In both cases they had to deal with a beam that was “bent.” During another session, Peter got the polarization filters out of the storage cabinets in the lab to seek confirmation for his statement that reflected light was partially polarized. Triumphantly, he reported the result of his “experiment.” Eldon, however, pointed out that this fact was already recorded in their concept map, “I think that this is obvious from our concept map, you didn’t really need to experiment.”

Changing Established Rules of Discourse. Another way of trying to convince others of one’s own position was by not observing turn-taking rules, and, very insistingly drowning out another speaker. Although it was not clear whether it was the insistence, the raised levels of volume, or another factor that made the difference, we could observe this pattern repeatedly across groups. In the following excerpt, Allan and Michael seemed to settle for the same proposition. Dan, however, cut Michael off, with a raised voice that suppressed Michael’s concurrent speech:

Allan: Michael: Dan: Michael:

Our data do

[Quanta] consist of many photons. (Confirming) consist of manv Dhotons. v ,

A bunch, consist of bundles of photons. (Conciliatory) OK, consist of bundles.

not provide any conclusive evidence how such “bullying” affects a student’s understanding. If it is simply a matter of giving in to avoid conflict, then the agreement between Dan and Michael would only be temporary with little effect on Michael’s appropriations from the current session. During the present task of concept mapping, many propositions had to be co-constructed or negotiated in some form. Some of these negotiations involve adversarial discussions. Not all students are comfortable with such situations and thus try to avoid them (Eichinger, Anderson, Palincsar, & David, 1991).


Formation of Temporary Alliances

To settle an issue, several members of a group formed a temporary alliance to convince the other student(s). In some instances, such alliances were talked about overtly. In the following example, Marcus and Rand both agreed that double slit and air wedge were to appear at the same level in the hierarchy of the concepts, whereas Mick disagreed (this concept map appears in Appendix A):

Mick: Marcus : Rand: Mick: Marcus: Mick: Rand: Marcus: Mick: Rand:

All, examples have to be at the same level’? Yeah, they should be. Double slit and air wedge have to be the same. No, I don’t think so. I think so. Why can’t they, why can’t you just break down an idea into the same example? Because they are of the same importance! Yeah, this and this, and this and this, are all the same. So fine. Overruled!

After it became apparent that Mick had a different opinion, Marcus and Rand both turned toward Mick. They talked at Mick to convince him that he should accept their solution regarding the hierarchy of the two concepts. Rand and Marcus reinforced and supported each other’s argument (“they are of the same importance” and “this and this, and this and this, are all the same”) so as to make it difficult for Mick to stay with his opinion. However, less than a minute later arose a situation in which Mick sided with Marcus against a proposition that Rand had favored. In this instance, Mick saw an opportunity for a return and he commented, “Overruled!” We observed such instances where group members addressed the formation of alliances overtly also with other groups. In the following excerpt, Michael sided with Allan (this concept map appears in Appendix C):

Michael: I think 1 like Allan’s idea. Allan: Put it [work function] underneath it [photo electric effect], it’s the same thing. Dan: Hell, is there some alliance over here? Allan: (laughs) Dan: We can be friends!

Dan made it clear that he understood this temporary alliance not as a challenge to other social arrangements, but for the purpose of achieving comprehension and completing the assignment. The alliances we observed were temporary, formed by students with similar positions. However, many propositions had to be negotiated over the course of making a map, and the likelihood that the same two students always took the same position was minimal. It was clear in each context that students’ language was that of social situations nonscience talk. Their intent was to find, to side with, or to win over someone else of a comparable position. Then, by majority rule, or merely by force of outnumbering, the decision was made to go with a particular proposition. Similar group behaviors were observed by other researchers (Eichinger et al., 1991; Hatano & Inagaki, 1991). Hatano and Inagaki see in students’ tendency to form groups to give emphasis to their knowledge position a motivation they termed “partisan motivation.” This motivation can have an important impact on the comprehension of students, that is, the attempt of the group is at winning an academic competition and comprehension. At this point, the group is divided psychologically, not spatially or socially, into subgroups, each of which collects supporters for the purpose of winning the argument.


Discussion and Conclusion

In the present study, we explored the process of the construction of knowledge during the collaborative concept mapping by groups of high school physics students. These concept maps were on the topics of wave and quantum character of light. The mapping sessions presented us with a twofold opportunity. First, it allowed us to evaluate the cognitive achievements of groups and individuals. Second, the videotapes of the sessions provided us with a window on the processes involved in collaborative activity.

The comparison of group concept maps in terms of structure and content provided us with an insight into the conceptual frameworks of students. Some concept maps illustrated hierarchical ordering that complied with canonical (standard) science. More inclusive concepts appeared at higher levels than less inclusive ones, both globally and locally, and there were more scientifically correct linkages among concepts. According to Novak and Gowin (1984), these are the characteristics that distinguish better from poorer concept maps. We also observed differences between the groups during their discussions regarding the concept maps. The discussion of the group that constructed better concept maps not only produced more propositional linkages, but also focused on the hierarchical order of the concepts. Conversely, the group that produced maps that lacked hierarchical ordering also included fewer propositional linkages. The discussions in this group reflected little concern for hierarchical ordering.

Our constructions about the hierarchical organization of physical objects, concepts, and principles have their parallels in those of cognitive scientists. Thus, in the context of physics, understanding implies among others the relationship that exists between objects, concepts, and principles that experts have organized hierarchically along dimensions of abstractness (Cham- pagne, Klopfer, & Gunstone, 1982; Chi, Feltovich, & Glaser, 1981). On the other hand, novices have not integrated the different levels of this knowledge, which accounts for their relative ineffectiveness in accessing knowledge from one level of abstraction to another. Equally important to this issue of local and global hierarchies is DiSessa’s (1988) contention that students’ naive conceptions are not theory-like connected, that is, integrated into a coherent framework. Rather, these naive conceptions are disjointed, piecemeal, and fragmented. Chi ( 199 1) pointed out that learning processes fostering conceptual change which requires the reorganization of local hierarchies (reorganization within ontological categories) are inappropri- ate for achieving conceptual change that requires complete reconceptualization, or radical change across ontological categories. Thus, our concern for local and global organization of concepts has important educational relevance.

Another striking pattern emerged from the comparison of individual maps with the respective group maps. Students working in the group that produced maps with definite global and local hierarchies showed clear hierarchies during their individual performance. Conversely, students working in a group that produced concept maps without global hierarchy and only one local hierarchy did so when they worked individually, though there was an exception. From the group that produced local hierarchies, one student continued to produce a globally structured hierarchy, the others maintained the more local character of their maps.

Without trying to establish causal relationships, we can only conjecture about the factors related to the students’ conceptualizations. First, the group discussions were geared towards finding a global hierarchy. Because the quality of interaction in a group is dependent on communicative skills of individual members (Pope & Gilbert, 1986), the subsequent appropriation (intraindividual construction) by each member is likely to be affected by the group’s composition. Second, we can also contend that the discussion in a group was related to the prior knowledge of individual students. However, light-as-a-wave phenomena and the quantum char-


acter of light had not been the subject of the students’ prior physics experience. Thus, at least from the point of view of the school curriculum, all students were at the beginning of their study of these phenomena. Any differences in understanding are likely to have arisen shortly before or during the study. Also, motivation could make a difference in individual appropriation from group discussion. Students who are better motivated are more likely to reflect on any conflict that remained between their own framework and that expressed by the group map. Such reflection could well lead to the integration of different views after the discussion and to the extent of individual appropriation observed in this study. This motivation could be the factor involved in the construction of an improved individual map over the group map. Although the map constructed by Michael’s group had various flaws, his own maps constructed during the tests demonstrated significant improvement. Michael’s remarkable motivation for resolving his conceptual conflict (Roth & Roychoudhury, 1993) could very well have been the driving factor for his improvement.

We found in our analysis of the collaborative discussion that the students in this study achieved agreement on issues arising in their work (a) in a completely collaborative manner and (b) collaboratively, but with adversarial techniques such as argumentation, support from authority, or mere domination. When students worked in a completely collaborative manner, the propositions arose as collaboratively constructed (or co-constructed) entities. This process of co-construction included three different forms of mediation, verbal, nonverbal associated with physically pointing, and nonverbal by means of diagrams. During verbal mediation, the propositions evolved as students tested variants of the linking word or alternate linking word. They seem to stop when the link in the proposition sounded right. In this case, the proposition evolved as some or all members of a group contributed to the modification of the link. Linkages were also constructed as students negotiated lines between concepts. To ascertain the correctness of beginning and ending concept, students sometimes had to resort to directly touching the concept labels they had previously referred to simply with indexical terms such as “there” and “that.” A third form of mediation occurred by using diagrams that students used to illustrate exactly what they meant when they talked, for example, about interference of waves with phase shifts. The diagram as a whole or its parts could be pointed to and talked about such as for students to know what the other student meant, that is, for students to achieve intersubjectivity. These three forms of achieving intersubjectivity can be summarized as semiotic mediation, because students used signs in one form or another to mediate meaning. Semiotic mediation plays a fundamental role in Vygotsky’s approach to learning, which focuses on the social character of knowing and learning (Wertsch, 1984). Vygotsky’s theory is particularly suited for learning as in the present situation where students coconstruct a proposition (i.e., knowledge). For, in his approach, “New, more powerful [cognitive] structures may be constructed interpsychologically and the new structure can interact with the child’s intrapsychological structures to result in individual cognitive changes” (Newman et al.. 1989, p. 68). This process, however, is not automatic or without problems because the meaning that individual students attribute to the co-constructed cognitive objects is not likely to be exactly the same. At best, these co-constructed cognitive objects can be taken as shared. We demonstrated these differences by showing how students seemed to have learned different things in the same situation. Michael’s individual concept maps had used a local structure from the group map as the new center of a highly organized structure. On the other hand, both of his team mates’ maps lacked adequate hierarchical ordering, Who, how much, and what students appropriate from collaborative work, that is construct individually, is still uncertain and cannot be specified in advance (Newman et al . , 1989). It was equally impossible to attribute any accomplishments by the grout to individual members. The products of collaborative work have to be seen as always socially constructed.

5 24 ROTHANDROYCHOUDHURY

The use of mediators such as diagrams and maps, the figurative language to talk about these, and the gestural rendering of these visual means are important from another point of view. They are the key aspects of scientific discourse, and their appropriate use distinguishes experts and novices in a field (Heller & Reif, 1984; Kindfield, 1991). Thus, “No scientists will ever attempt to explain what he or she means by a ‘start in CAT’ without resorting, if possible, to a more or less elaborate version of this drawing, or at least a gestural rendering thereof” (Knorr- Cetina & Amann, 1990. p. 268). Over the past 5 years, many researchers have indicated that school learning should be conceptualized as a process of enculturation and cognitive apprenticeship (Brown, Collins, & Duguid, 1989; Hawkins & Pea, 1987; Lave, 1988; Prawat, 1991; Wiggins, 1989). Learning to use such mediating tools to enhance verbal expression should thus be a primary goal of bringing students into scientific culture. Ethnographic research of scientists at work has also looked at the “ownership” of ideas or discoveries. According to this research, there is ample evidence that scientific objects (knowledge) are co-constructed by groups of individuals who are unavoidably linked to their contexts. The source of an idea cannot be attributed to either individuals or environment, and has to be considered a social construct contingent on the local conditions of the construction (Garfinkel, Lynch, & Livingston, 1981; Knorr-Cetina, 1981; Latour & Woolgar, 1979; Zenzen & Restivo, 1982).

In contrast to the co-construction of new propositions was the construction of propositions involving adversarial moves; that is, to overcome the differences in their viewpoints, students rallied support from some sort of authority, whether it was internal or external to the group. The equilibration involved in the negotiation of conflicting viewpoints has been Piaget’s argument for collaborative learning. According to Vygotsky, in Piaget’s theory learning and “development [are] reduced to a continual conjlict between antagonistic forms of thinking; it is reduced to the establishment of a unique compromise between these two forms of thinking” (cited in Rogoff, 1990, p. 140. Italics in the original). In the present study, students achieved such compromises by explicating their own understanding, particularly when they believed to be more of an authority than their peers; by using the authority of direct observation that they made on the spot or recalled; by calling on an authority such as the teacher or a textbook; or by challenging established norms of social interaction in order to cut off others. However, we have seen that in such situations, incorrect ideas can be disseminated unchallenged because of the air of authority of the student. Thus, the student may be reinforced in his belief instead of abandoning the inadequate notion. On the other hand, students also used moves to “win” an argument where their own comprehensions were involved only implicitly. For example, using observations to support one’s contention could potentially lead to scientifically incorrect ideas because students often attend to features of the object or event different from those that a scientist would attend to (Roschelle, 1991). Or students could refer to the authority of the teacher or textbook. In this case, the move was challenged only if another student remembered something differently, or was certain of his own understanding.

In the scientific community, “Many adversarial exchanges do not end with an agreement but nonetheless produce a conclusion on which participants can proceed” (Arnann & Knorr-Cetina, 1988, p. 152). Adversarial exchanges are thus important inference and knowledge producing devices. Among students, however, the adversarial style also has the potential to exacerbate status differences within a group. Then, only students already most skillful in constructing scientific arguments will benefit from such interaction (Eichinger et al., 1991). We did not observe such dominance by some individuals. However, our participants all had chosen physics as an elective for a second year. Thus, we would expect smaller discrepancies in academic status between our students than those in the Eichinger et al. (1991) study that was done in a heterogeneous grade six class.

The case of forming alliances takes a middle position between complete co-construction


and adversarial collaboration. Two or more students have to agree that they share a common point of view; or a student finds enough supporters because of other tactical moves of an adversarial nature. At some critical point, the parties finally come to make a decision by majority rule. However, even when an agreement is reached, this does not mean that the problem has been solved, “as illustrated by the frequency of what one might call ‘negative solutions’-ways of undoing the problem without solving it” (Amann & Knorr-Cetina, 1988, p. 152).

Co-construction, adversarial interaction, and the formation of alliances replicate the interactions in scientific communities. While collaborative constructions are observed inside a research group, the discussion between research groups at professional conferences and in jour- nals may be characterized by the vigor of the attacks on weak arguments (Eichinger et al., 1991; Garfinkel et al., 1981; Knorr-Cetina, 1981; Latour & Woolgar, 1979; Zenzen & Restivo, 1982). Through these various forms of interactions, propositions, that is, declarative knowledge, are constructed, deconstructed, and/or reconstructed. Thus, the experience in scientific forms of discourse, whether through collaborative, adversarial, or mixed discourse activity appears to be paramount in a curriculum that has the objective of enculturating students into normal scientific practices. The concept map is an ideal tool to engage students in such discourse.

In this study, students worked out propositions and interpretations acceptable to all members. If such activities are implemented over longer periods of time such as the school year, or even longer, they could lead to the establishment of a supportive classroom culture. Here, students “come to believe that they should cooperate as they work in groups to produce mutually acceptable answers and, ideally, mutually acceptable interpretations and solution methods” (Cobb et al., 199 1, p. 3 I). The establishment of such classroom cultures is desirable from the perspectives of many educators, because they allow students to experience science and math in authentic ways, and they allow students to recognize the essentially social nature of all knowledge construction (Brown et al., 1989; Cobb, 1989; Hawkins & Pea, 1987; Lampert, 1990; Lemke, 1990; Schoenfeld, 1985).

Irrespective of the nature of the discussion, concept mapping in groups allowed students to engage in sustained science discourse over the length of a whole school period. The students rarely disengaged from the topic and the amount of nonscience sidetalk was insignificant. Thus, concept mapping in groups offers opportunities to practice the language of science before students find themselves in testing situations. In that, collaborative concept mapping provides essential learning opportunities in science: “The one single change in science teaching that should do more than any other to improve students’ ability to use the language of science is to give them more practice actually using it” (Lemke, 1990, p. 168). The specificity of the concepts, which are either selected by the students themselves or suggested by the teacher, constrains the classroom conversations in their content to that of the current topic. By using the resources available in the classroom, teacher, peers, textbooks, and equipment, students can engage in constructing essential meanings in their own words, or by using slightly different words depending on the situation. Peers serve as a first instance to validate or invalidate a proposition. Talking to one another gives students a chance to try to talk science, free from the real or imaginary pressures of the teacher’s presence (Lemke, 1990).

Some student conceptions appeared to be very stable, even in the case of intensive discussion during which differences seemed to be resolved. Mick and Rand who believed that for interference to occur, two sources of waves had to be in and out of phase, respectively, both held on to their original beliefs. As the individual concept maps showed, the negotiations had done little to persuade one or the other to reconstruct his notion. They had done little to persuade both to come to the conclusion that interference occurs in either case, though these interferences are constructive and destructive, respectively. In a longitudinal study conducted over 12 years of


schooling, Novak and Musonda (1991) also found remarkable stabilities in student conceptions over time. One possible explanation for such stability was advanced by Cobb et al. (1991). These researchers proposed that the students in a classroom act in a variety of realities that are incommensurable rather than incompatible. To be able to take the point of view of another student necessitates a conceptual change equivalent to a paradigm shift for a scientific culture (Kuhn, 1970; Posner, Strike, Hewson, & Gertzog, 1982). Such conceptual change only occurs when students’ realities are seriously challenged and plausible alternatives are available. Teach- ers’ expectations for such shifts to occur may sometimes by unrealistic in the face of such incommensurability.

We concluded from our results that group work in itself does not always accrue to better individual performance, although in our case, the students seemed to be well motivated; individual achievement was measured during the unit test and final examination, which make it likely that students did their best. Techniques that help students to reflect on collaboratively produced concept maps need to be implemented to increase the likelihood that traditionally low achieving students benefit from the experience. To increase individual performance in using the language of science, educators have also called for more student participation in classroom discourse (Lemke, 1990). However, as we saw with two of our students, an increased student participation in classroom discourse in itself does not solve the problem of low achievement as long as student achievement is measured against teacher established norms. Negotiation of the meaning of tasks and instructional goals between teachers and students seems to be of paramount importance. Some df the problems that the students encountered may have had to do with the structuring of the environment. Research had shown that structured interaction produced significantly better results than unstructured (Yager, Johnson, & Johnson, 1985). In this study, we had not provided the students either with instruction on monitoring their cognitive strategies or with help to structure their interaction so that they had to take on specific roles.

A second explanation for the “poorer” performance of some students and groups may be found in the task itself. What if students simply attended to connecting, instead of establishing a hierarchy of connected concepts? We found that most students, alone or in groups, focused on establishing the hierarchical relationships between more general and inclusive concepts and those that are more specific. Thus, their concept maps expressed the hierarchies according to the teacher’s definition of the task. On the other hand, a less successful group such as PEN verbalized few hierarchical relationships and established poorly organized maps. This in spite of the fact that the teacher had reminded the students throughout the school year of the goals of concept mapping, namely the establishment of a hierarchy from the most inclusive to the most specific. Thus, these students had defined the task in a way substantially different from the teacher. Such differences in understanding between the goals as understood by the teacher who sets them and as understood by the students who are to accomplish them may not be the same. This difference was made very clear by Newman et al. (1989) who attributed diagnosing of children’s poor performance to the mismatch between the goals as perceived by students versus teachers or researchers. But they also pointed out that these discrepancies arise because of the instructional situation. In everyday life, people have to figure out the problem its constraints, as well as how to solve it. Thus, solutions evolve out of the interaction between setting and the people who are doing whole tasks (Lave, 1988). At school, however, learning goals are always set by people other than the learner. This creates a context in which students “experience themselves as objects, with no control over problems or choice about problem solving processes” (Lave, 1988, p. 70).

This study is of special significance to science education. Tobin (1990) had identified some of the most pressing questions to be answered by science education research. Among these questions were, “How do students negotiate meaning?” “What is involved in sharing meaning?’

CONCEIT MAPPING: A MICROANALYSIS 527

and, “What is involved in forming consensus?’ We have provided and discussed answers to these questions for the context of concept mapping. Prior to this study, little was known about the microprocesses during concept mapping, a metacognitive teaching and learning strategy that is increasingly being used in science classrooms. However, before we, as practicing classroom teachers, could begin to improve the use of collaborative concept mapping, we had to know more about the students’ interactions during the activity.

We established here the usefulness of concept mapping as a tool for engaging students in sustained science discourse. Such discourse is of considerable importance in the establishment of a classroom culture that reflects the authentic practices of scientists. We could also show that students externalize their conceptual framework regarding the concepts of interest. Thus, the concept map is a valuable evaluation tool for classroom teachers. They can use both the process and the final products of concept mapping to examine the quality of student understanding. Using concept maps as an evaluation tool for process and product also permitted us to identify potential dangers in collaborative concept mapping. Students may perpetuate alternative views or construct scientifically incorrect knowledge. In order to facilitate the collaborative construction of concept maps, the following instructional features are possible. First, there should be specific instruction to foster students’ abilities in the three modes of discourse we identified. Second, students may need instruction for establishing hierarchies and seeking cross-links between local hierarchies. Third, teachers should support students’ efforts for understanding the special significance of general concepts and principles and how they organize the knowledge in the scientific field; and the teacher should support students’ efforts in establishing the relationships between the various levels of abstraction in the hierarchy of concepts. Fourth, there should be specific instruction urging students to reflect at the end of the mapping session on the nature of the hierarchical relationships between the concepts. And finally, the interactions within the group could be more structured by assigning specific roles to each individual. For example, members in each group could be assigned specific responsibilities for checking the correctness of propositional linkages, the validity of the concept hierarchy, and the cross-links between different parts of the hierarchy.

Although we have been able to provide some answers, new questions have arisen to direct future studies. Among the pressing ones are, “How does the availability of time and information resources change the task of concept mapping in different settings?’ “How does the structuring of the interaction change the nature of discussion and the maps produced by a group?’ “How can student involvement in goal setting reduce the mismatch between teacher goals and student goals?’ and, “Are the interactional processes similar for collaborative student work in different contexts such as the lab?’ At the time of this writing, we are in the second year of our study establishing a large data base. Our goal is not only to answer the above questions but also to document the changes in the classroom use of concept maps as we change our practices in response to our newly constructed knowledge.

Notes

We used pseudonyms throughout the article. 2 We used the following conventions for transcription: (a) Bold-faced, emphases in speech, “Like,

considered as?”; (b) square brackets, “[I”, to add words that would facilitate the comprehension of the transcript: “It [light] consists of quanta”; (c) parentheses, “()”, to indicate nonverbal cues and actions (e.g., begins to draw sine waves); (d) underlining, to mark overlapping speech (Don: Which is measured; Max: Which speed is measured in hertz); (e) comma, “,”, and period, L ‘ . ” , to indicate breaks in the flow of speech; (f) question mark, “?’ if the context allowed the speech act to be interpreted as a question.

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Appendix B

Concept map produced by Peter, Eldon, and Michael to summarize the activities in their portfolio on light-as-a-wave phenomenon.

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Appendix C

Concept map produced by Michael, Allan, and Don to summarize the activities in their portfolio on light as a quantum phenomenon.

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Manuscript accepted January 15, 1992.

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