Physics Problem Solving in Cooperative Learning Groups

Traditionally, college physics teachers have emphasized problem solving as a way to learn physics (Fuller, 1982). Teachers and students alike are not always satisfied with their problem-solving efforts. One reason for this may lie in the different approach that an expert (teacher) and novice (student) take to a problem (Larkin, McDermott, Simon and Simon, 1980). Novices tend to concentrate on the superficial features of a physics problem, whereas experts use principles of physics to analyze and solve a problem. For example, a novice would examine a problem like At the Gasthaus, see a sign suspended by a post and a cable, and interpret it as a "sign problem." On the other hand, an expert would most likely see the same problem and interpret it as a "static equilibrium problem." Novices also tend to immediately seek the proper equations that will solve the problem.  That is, they attempt a quantitative analysis of the problem before constructing an adequate qualitative analysis.

Above the entrance door of an old German

"GASTHAUS" hangs a sign. A 200 N metal beer mug hangs at the end of a 3 meter long strut that is attached to the wall by a hinge. The weight of the strut is 100 N. A support cable is attached to the strut at a point 2 meters from the wall and makes a 30° angle with the strut. Find all the forces acting on the strut.  Useful information: )F = 0 and )t = 0        

GASTHAUS    

This qualitative analysis, or physics description, is crucial to a problem solution.

The physics description includes aspects of problem solving such as deciding what general approach to take, describing the problem in terms of general physical principles, defining coordinate systems, drawing idealized diagrams, and, in the case of problems involving static or dynamic forces, constructing free-body diagrams. The failure of novices to solve problems may be their failure to develop adequate physics descriptions. (Heller and Reif, 1984) Recently, cooperative learning groups have been employed in college physics courses as a means to develop the problem-solving skills of beginning students (Heller and Hollabaugh, 1992).

Cooperative Learning

Research on cooperative, competitive and individualistic learning strategies dates back to at least 1897. Johnson and Johnson (1989) did a meta-analysis of nearly 400 studies spanning 90 years. These studies encompass all age groups of students from kindergarten to college, and all academic fields including science. About 40% of the studies were done with college-level students. In 85% of the studies students were randomly assigned to either a cooperative group treatment or an individual or competitive treatment. Johnson and Johnson note that the statistical probability that the results of these accumulated studies are merely due to chance is less than one in 100,000. Based on this cumulative research, they conclude that a cooperative effort will produce higher productivity and achievement than a competitive or individualistic effort will produce.
It is implied from the cooperative learning research that students in groups are involved in the process of co-construction. That is, students construct the knowledge and procedures necessary to complete a group task or achieve a shared goal. (The criteria for co-construction will be discussed in depth in Chapter 2). Mostly of the evidence for co- construction from the cooperative learning research literature is indirect. That is, much of the prior research in cooperative learning has focused on either comparing individual achievement of students in cooperative groups to students in competitive or individualistic learning environments, or on specific components of cooperative learning such as group size or gender and ability mix in groups. For example, Johnson and Johnson contend that “A conservative interpretation of the overall data would be that participating in cooperative groups does not hurt, and often facilitates the achievement of high-ability individuals, and clearly benefits the achievement of medium- and low-ability individuals” (Johnson and Johnson, 1989; p. 47).

The inference that there is co-construction in groups comes from looking at outcomes and products of the group. For example, a study by Heller, Keith, and Anderson (1992) supports co-construction of a physics problem solution by college students. Students solving physics problems in cooperative groups produced better physics descriptions than the best student in the group working as an individual on a matched problem. It was clear that the superior group product was not the work of the best individual in the group. Indeed, even the lower ability student appears to have contributed to a problem solution (Heller and Hollabaugh, 1992). That is, one thing that is already known about cooperative groups is that the outcome or product of the group is superior to the product of an individual. Groups are engaged in co-construction of a product. What is important to note is that almost all studies have focused on outcomes as opposed to the group process. “Few studies in science [education] have investigated the collaborative processes within groups and examined the negotiation of meaning that occurs” (Tobin, Tippins, and Gallard; 1994; p.45, emphasis added). And, “although studies of cooperative learning in the context of science education abound,... the focus of these studies has not been so specifically on the learning process” (Tobin, 1990; p. 418, emphasis added).

These findings suggest there is something about the group process that, for example, facilitates the co-construction of an effective physics description. Somehow, the group process guides the translation of the problem statement into a physics description that properly depicts the conceptual basis of the problem. Thus, what we already know about physics problem solving in cooperative groups is that groups co- construct a superior solution that is not merely the work of the best individual in the group. What is not known is how this occurs. That is, what is not well-understood is the sequence of behaviors and actions that lead to a superior product.

Toulmin Argument Structure

In a major summary of cooperative learning practice and research, Ann L. Brown and Annemarie Palincsar suggest a reason for the superior product of a group: There is “distributed thinking” and a “joint management of argument construction” in cooperative groups (Brown and Palinscar, 1989; p. 400). There are three terms that recur in this dissertation and there is a precise sense in which I am using them. Argument implies the students are engaged in developing an idea. It is very important to understand that argument doesn’t mean arguing. An argument is a logical, thought-out conceptual statement, and as such, it has a structure. Construction implies the students “build” or “construct” their argument out of prior knowledge and ideas that surface in the course of the discussion. Co-construction means the group members are doing this together.

Brown and Palinscar suggest using a systematic argument structure to describe the co-construction process.

“Because these tasks [i.e., co-construction] result in a great deal of spontaneous argument, systematic examination of relations between the discourse form and the type of posttest improvement should be possible. Such fine-grained analysis of what happens in group discussions and what type of learning occurs are badly needed.” (Brown and Palinscar,1989; p. 408)

Brown and Palincsar point to the argument structure proposed by Stephen Toulmin as a useful analysis tool in contexts such as cooperative groups (Toulmin, 1958, 1990; Toulmin, Rieke, and Janik, 1984; Nickerson, Perkins, and Smith, 1985). Toulmin’s structure is in keeping with the goal of a fine-grained analysis of the cooperative group process: “An argument is like an organism. It has both a gross, anatomical structure and a finer, as-it-were physiological one... The time has come to change the focus of our inquiry, and to concentrate on this finer level” (Toulmin, 1958, 1990, p. 94). Although arguments in different scientific fields may differ in fundamental ways, there is a commonality in the construction of an argument. In Toulmin's structure there are grounds, claims, warrants, backings, modalities and rebuttals. In developing his ideas he uses examples from both jurisprudence (“substantial arguments”) and mathematics (“analytic arguments”).

A claim is a fundamental assertion that is the goal or endpoint of the argument.

Grounds or data, are the particulars of a situation that support the claim. When solving a physics problem , the grounds are the data given in the problem statement. In many argumentative contexts, one may never make explicit just how the grounds support the claim. In this dissertation I will use the term grounds as opposed to data. In physics, “data” often implies a quantitative feature. In the physics problems I will discuss here, the “data” sometimes consist of a non-numerical, qualitative pictures or statements.
A warrant is a general rule connecting particular grounds to their implications.

The laws of physics or rules of mathematics are general warrants. The distinction between the grounds, or data, and warrants is not always clear, especially in science. In the simplest definition, “....data are appealed to explicitly, warrants implicitly” (Toulmin, 1990, p. 100).    This lack of distinction between grounds and warrants will sometimes make it difficult to classify statements in this study. A warrant requires support called a backing. The appropriate backing for a warrant differs from field to field. In physics, backings are typically the generally accepted validity of well-established laws and principles such as Newton's Laws of Motion, or the citation of other authorities such as the professor or textbook to support a warrant.

Brown and Palinscar cite studies in which elementary-school students who are learning to read follow a Toulmin-like argument form (Brown and Palinscar, 1989, p. 404-405; citing Paley, 1981; and Pontecorvo, 1985). They note that “adults’ argument structure follows certain identifiable sequences,” but that children follow the structure at a “very simple level” (Brown and Palinscar, 1989; p.404). The cited examples reproduce transcript excerpts and identify statements as providing “factual support” or “appeal to general principle.” Statements are not explicitly identified as Claims, Grounds, Warrants, or Backings. There is apparently no direct attempt to analyze systematically the movement of the argument from statement to statement or from person to person. What these prior studies lacked was a systematic, detailed analysis. What is not known is how to undertake such an analysis.

Summary

Previous research has revealed many findings about individuals working alone, competitively and in cooperative groups. We know the physics description is a key component of the problem solution. We know physics problem-solving groups co- construct a superior problem solution that is not merely the work of the best individual in the group. What will be different about this study is that the Toulmin argument structure will be used to systematically analyze the argument co-construction process within physics problem-solving groups.
 
PURPOSE AND RESEARCH QUESTIONS

The purpose of this study is to undertake a systematic, fine-grained examination of the argument co-construction process in fourteen college physics problem-solving groups using Toulmin’s argument structure. The research focuses on the groups while they completed their qualitative analysis (“physics description”) of algebra-based introductory physics problems. The following research questions guided the exploration:

Do these fourteen problem-solving groups engage in argument co-construction as they complete a physics description?

Are there self consistent argument co-construction patterns within a group?

Are there similarities in the argument co-construction patterns between the fourteen groups?

Do their argument co-constructions begin or end with a Claim?

What roles do challenges to the original claim play in the argument co- construction process of these groups?

Do the groups have a preferential means to support claims made in argument construction (e.g., Grounds, Warrants, Backings)?

OVERVIEW OF THE RESEARCH DESIGN

The nature of the group problem-solving process ultimately determines the research design and methods of analysis. For this study, I videotaped students in a University of Minnesota introductory, algebra-based, physics course while they were solving physics problems in cooperative groups. Fourteen problem-solving groups, spanning two 10-week academic quarters, comprise this investigation. Six different problems are represented in the sample and the texts of these problems are re-printed in Appendix B. This dissertation is a case study of these 14 groups, which compose the “elements” of the study.

The research proceeded as follows:    First, the 14 groups were videotaped while solving problems and the tapes were transcribed. The transcriptions then were compared with the original videotape to insure accuracy as well as to annotate non-verbal behavior and to make references to the written problem solution.

Second, I devised a method that considered not only the types of statements students made, but also the overall manner in which the group's constructed their problem-solving arguments. An important feature of this method is that the statement categories are based on what was observed in the groups’ discussions. That is, the coding categories were not predetermined. Predetermined analysis categories are often better suited for quantitative research (Gustafsson, 1977; Delamont and Hamilton, 1984). Even so, some starting point was needed for analyzing the groups’ discussions. I chose the argument structure of Stephen Toulmin for three reasons. First, I heard of the Toulmin argument structure in the context of scientific reasoning. Second, I believed I could identify Claims, Grounds, Warrants, and Backings in the students’ conversations. Third, Brown and Palincsar make specific mention of Toulmin as a useful argument structure in looking at cooperative groups (Brown and Palincsar, 1989).

Then I made “rich descriptions” of the argument co-construction of four groups solving the same problem (At the Gasthaus). The basic unit of analysis was defined to be the episode. An episode is made up of students' statements, but it contains a complete thought. B. Othanel Smith and Milton O. Meux used episodes to categorize student- teacher interactions in an analysis of classroom behavior (Smith and Meux, 1970; Smith, Meux, Commbs, Nuthall, and Precians, 1967). An episode is "defined as one or more exchanges which comprise a completed verbal transaction between two or more speakers.

A new episode is determined by a shift in what the speakers are talking about, which may be a new aspect, or part of a topic or a complete change of topic" (Sandefur and Bressler, 1971, p. 23). In a sense, the episodes become “mini-contexts” that fit together into a larger context, namely the group’s construction of the physics description.

Next, I drew flowcharts that describe visually the “flow” of the physics description construction process. Differing symbols for claims, grounds, warrants, backings, and other statement types, enabled an easy visualization of an individual group’s argument pattern. Finally, common and unique features between the fourteen groups were noted. Generalizations answering the research questions were then made on the basis of all fourteen groups.

ASSUMPTIONS AND RATIONALE FOR A QUALITATIVE, CASE-STUDY DESIGN

Because a qualitative, case-study research design differs from the more common quantitative design, I will briefly explain the assumptions of the design and rationale for choosing this design. The design of quantitative research is well-established in science education. That type of research is based on a pre-determined set of analysis criteria, generally utilizes statistical measures to draw conclusions, and is readily duplicated. The qualitative, case-study research design has contrasting characteristics and actually emerges from the research being conducted (Creswell, 1994).  In this case, examination of the group process itself determines the nature of the analysis criteria (Delamont and Hamilton, 1984).
Two features of this dissertation research suggested that a qualitative approach was more appropriate than a quantitative approach. First, cooperative learning research is, by its very nature, research into applied social psychology. In this area of research, rich, qualitative descriptions of groups of people are as important, if not sometimes more important, than quantitative descriptions. People function in a social context, in this case the cooperative group. The group dynamics, hard to quantify, are crucial to understanding the group’s product and process. In an attempt to understand what students in a problem-solving group actually do, I will make “rich descriptions” of the problem solving groups. From these qualitative descriptions I will look patterns within and between the groups.

Second, although the groups’ solutions consists of verbal statements, I will argue that just counting types of statements students make is not a "fine-grained analysis." While individual statements are important, and form the basis of the analysis, the larger picture must also be considered. That is, the context of the statements must also be described and understood. Each group functions in the context of its cooperative group process, and each physics description, which is the product of the group, is jointly constructed in the same context. I will look for patterns in the co-construction of the argument that are a part of this problem-solving process. The emphasis is on the process of co-constructing the problem solution as opposed to the product, namely the “correct” answer.

These two features of this dissertation research suggested that I take this qualitative case study approach to the research. The case study is a qualitative research method in which the researcher explores a single entity, process, or phenomenon, and uses a variety of data collection tools including qualitative descriptions and records (e.g., video or audio tapes) (Creswell, 1994; Strauss, 1987 ). For this research, the qualitative descriptions and records include videotapes of groups solving the problems (and the subsequent transcriptions), copies of their written solutions, and pertinent notes made by the videographers. Some quantitative data are available, such as the scores on the students’ in-class examinations. These characteristics of this particular case study, along with the definition of the population being studied, delimit the boundaries of the study.
These boundaries will also serve to define and limit the outcomes of the research (Stake, 1988).

This design choice will influence the form and structure of this dissertation. The traditional “outline” will be modified. For example, instead of a separate “Review of the Literature” chapter, references to pertinent literature in cooperative learning, physics problem solving, and research methods will be made as they are needed to describe the “procedure” that evolved.

METHODOLOGICAL ISSUES AND LIMITATIONS OF THE STUDY

Any research, be it in physics or in education, has limitations. Some of the limitations of this study result from the choice of design, some from the analysis tools, and some from the data set (the 14 groups). Some of these limitations were apparent to me at the onset of this study. Other limitations emerged as the work progressed and these will be discussed when appropriate.

Toulmin Argument Structure

A fundamental component of this research is the argument structure proposed by Stephen E. Toulmin. A case must be made for the use of this argument structure over other possible structures. It would, for example, be possible to return to the 2500 year- old method of Aristotle and examine the arguments of these 14 groups in terms of syllogisms (Mills, 1968). This form of deductive reasoning consists of a major premise, a minor premise, and a conclusion. For example, When an object is in a state of static equilibrium (the major premise), the forces add to zero and the torques add to zero (the minor premise), therefore for this sign ZF=0 and Zt=0 (the conclusion). It is possible to develop a thorough model of scientific reasoning and argumentation using the Aristotelian structure (Giere, 1984). Some aspects of the Aristotelian structure could be useful in this research, but overall, the syllogistic approach is too cumbersome for use in analyzing everyday speech (Thompson, 1971).

The argument structure of Chaim Perelman is an “audience centered” theory of argumentation. Also based on Aristotle, Perelman’s structure emphasizes increasing the “mind’s adherence” to an idea. To accomplish this, one must carefully consider the audience to which one presents the argument (Rieke and Sillars, 1975). This structure focuses on the hearer of the argument and not on the speaker. Since this dissertation research is concerned primarily with a group process, and not what individuals hear and how it effects them, this structure is not particularly useful.
Interestingly, many authors writing about argumentation often start with a nod to Aristotle and but end with a lengthy discussion of Toulmin (Thompson, 1971). Toulmin is essentially a philosopher and historian of science (Toulmin and Goodfield, 1961).

Although well-grounded in classic logic, he goes a step beyond it. A large percentage of the existing scholarly papers and talks which use Toulmin are from various speech communication association meetings and journals. Within two years of the publication of The Uses of Argument, Brockriede and Ehninger (1960) introduced Toulmin to the field of speech and rhetoric. “Toulmin’s analysis and terminology are important to the rhetorician for two different but related reasons. First, they provide an appropriate structural model by means of which rhetorical arguments may be laid out for analysis and criticism; and, second, they suggest a system for classifying artistic proofs which employs argument as a central and unifying construct.” Within ten years of publication, Toulmin had been discussed or used as an analysis tool in at least eight speech textbooks, five doctoral dissertations (including one at the University of Minnesota), and several scholarly articles (Trent, 1968; Mills, 1968). Not everyone in the academic fields of speech and debate enthusiastically welcomed the Toulmin argument structure. Willard (1976), for example, eschewed the use of Toulmin-like argument diagrams because they were “mired in considerable (and unavoidable) conceptual confusion.... [and] persuasive arguments are too complex and dynamic to be adequately depicted diagrammatically.” Despite criticism Toulmin has nonetheless become pervasive in speech, communication theory and debate. Why is this?

While Aristotle might be useful in devising a legal argument, for example, the syllogism would be less helpful in normal, everyday speech. In the modern world, human speech is very unlike the speeches of the orators at the acropolis. Toulmin offers a more contemporary and useful model. Most high school and college debate courses include an introduction to Toulmin’s argument structure (Smith and Hunsaker, 1972). In such contexts, the emphasis is on the spoken word and supporting one’s ideas with evidence. Hence the language of Claims, Grounds, Warrants, and Backings is very beneficial. Thus, part of Toulmin’s appeal, and hence usefulness, is that his structure is more amenable to analyzing spoken arguments (Rieke and Sillars, 1975). The videotapes of these 14 problem-solving groups are a record of spoken words. But there is an even more important reason for using Toulmin in analyzing cooperative group problem solving.

The purpose of this research is to search for patterns in argument construction. This suggests that the argument construction must be described, both in terms of words and a “visual” pattern or diagram. There are four aspects of the Toulmin structure that make it attractive for this purpose. First of all, Toulmin would say an argument is constructed (Bettinghaus, 1966; Toulmin, 1958, 1990) by the maker of the argument. The support of a Claim with Grounds, Warrants, and Backings is constructivist: The meaning, and hence validity of the Claim rests in the choice of appropriate support statements. That is, the claimant constructs reality out of his or her understanding of the Claim. Second, the Toulmin structure is useful in describing an argument (Smith and Hunsaker, 1972). This is because it is based on actual speech patterns of people (Rieke and Sillars, 1975). The Claims, Grounds, Warrants, and Backings are types of statements. While the Claim is like a major premise, the Grounds, Warrants, and Backings classifications allow for greater descriptive nuances than just classifying secondary statements as minor premises. In a response to Willard (1976), Burleson (1979; p. 146) notes that an important condition for the Toulmin model to work “is the careful consideration of the context from which units of analysis are drawn, for it is the context which gives meaning to statements as features of an argument.” In this research, the arguments are based on a very specific context: physics problem-solving groups.

Third, Toulmin himself notes “...scientists in all cultures develop systematic procedures for representing the natural world and its makeup, functions and origins” (Toulmin, Rieke, and Janik, 1984, p. 315, emphasis in original). This suggests scientific arguments are systematic and have a structure. Finally, Toulmin’s structure readily allows for diagraming an argument (Rieke and Sillars, 1975; Trent, 1968). All books and articles that use Toulmin’s structure include diagrams to illustrate the argument’s flow and progress. Because I am looking for patterns of argument co-construction in this research on physics problem solving, it will be helpful to use Toulmin’s argument structure because this systematic structure is readily described in constructivist language and lends itself to being diagrammed. Ultimately, the choice of this argument structure is very utilitarian: Toulmin works. This is like physics. Physicists use wave mechanics and the Schrödinger Equation because, despite “uncertainties,” they work in many situations.

Hence, much of the validity of this study depends on the Toulmin structure of argumentation. Despite its appeal, the structure has inherent limitations. People do not strictly follow the Toulmin structure in normal, everyday speech, which is what is spoken in a problem-solving group. Likewise, the groups are concerned with not only the solution of the problem, but also the maintenance of the group, that is with the procedures of the group. The distinction between procedures and content isn’t always clear. The question arises, are the procedures a part of the co-construction of the argument? When reading the transcripts of the groups, it is easy to notice statements that relate to content (i.e., the physics) and are very analytic (“sum of the forces equals....”), those that relate to group functioning (“we’ve got to watch the time”), and those that relate to the Problem- Solving Strategy (“What’s our target variable?”). It would be possible to classify statements relating to group functioning or the Problem-Solving Strategy as procedural, but the strategy contains elements of physics content.

It will be difficult in the descriptions of the groups to cleanly separate the analytic, physical principle arguments from the procedural arguments. The reason is because the problem-solving arguments specifically relate to the problem-solving strategy. Students were taught, for example, that a free-body diagram was an important part of the Physics Description. Thus, “We've got to draw the free-body diagram” is an anticipated procedural Claim that is a very necessary part of the solution. This inter- relatedness of the process and content may not allow for the clean distinction Toulmin would make between “analytic” and “substantive” or procedural arguments:

We shall therefore class an argument as analytic if, and only if, it satisfies that criterion-- if, that is, checking the backing of the warrant involves ipso facto checking the truth or falsity of the conclusion-- and we shall do this whether a knowledge of the full backing would in fact verify the conclusion or falsify it (Toulmin, 1990, pp. 133).

In the context of the Gasthaus example, drawing a free-body diagram is both a substantive and an analytic argument. If the negative statement was true, namely that drawing a free-body diagram is unnecessary, then the conclusion from that action, namely that the sign is in static equilibrium, would be false. This clearly contradicts the given information. Hence, it seems reasonable to utilize the Toulmin structure when describing the problem-solving group’s procedural conversations. These “arguments” are much more akin to legal arguments in that they focus on the procedure, process, and promotion of orderly progress through the problem.

I should note that a given segment of a group’s conversation may not contain all

components of the Toulmin structure. In Toulmin’s structure, the argument ends with the claim. But, verbal arguments often begin with the claim. It will be seen that the groups also use statements that are clearly not Grounds, Warrants, Backings, or Claims. Thus, I will define additional statement categories. This again is characteristic of the qualitative design: Analysis categories grow out of the data.

Validity, Reliability, Generalizability

If this research is to be meaningful and add to the sum of what we know about cooperative group physics problem solving, then it must have meaning beyond this discussion of these 14 groups. This issue generally is discussed in terms of validity, reliability and generalizability. Quantitative research is replete with statistical measures, such as analysis of variance (ANOVA), that allow for an objective determination of validity, reliability and generalizability. The validity, reliability and generalizability of a qualitative study are much more subjective, and hence open to different interpretations. Statistics are not always useful. The careful reader of this dissertation will uncover the single ANOVA buried within these pages. Even so, qualitative researchers have found ways to establish validity, reliability and generalizability (Wolcott, 1990; Maxwell, 1992).
A study, method, or technique is said to be valid if it actually measures what it claims to measure. One technique researchers have used to promote the internal validity of a study is triangulation. This research technique uses two or more data collection methods to study some phenomena or process. The term originates in navigation where two bearings are used to locate one’s position (Stake, 1988; Cohen and Manion, 1994). There is only a limited degree of triangulation possible in this study because there is only one data set (the videotapes of the 14 groups) and one data analysis method (the coded transcripts and flowcharts). I will, however, attempt whenever possible to view important findings from multiple vantage points. There are four of these vantage points, or as I will call them, “reference points.” These reference points are the videotapes, written problem solutions, quantitative data, and subjective opinions based on viewing the videotapes. Figure 1-2 (page 23) illustrates this idea.
One specific analysis technique that will become apparent is that one set of four group solutions continually revealed new insights into the groups’ argument construction processes. Before a new analysis idea was introduced or an new analysis tool applied to all 14 groups, it was first applied to groups 4A, 4B, 4C, and 4D. That is, the system was fined tuned on the four groups. This was done to promote “internal validity,” or consistency of the analysis method.

A case-study approach allows for limited replication. This is the issue of reliability. For this research to be reliable, it is important to carefully document the data collection and analysis procedures. Assumptions must be clearly stated. If these guidelines are followed, another researcher, with similar knowledge of the content and context of the research should be able to replicate the research. Even so, “...it is impractical to make precise replication a criterion of generalizability in qualitative work. Qualitative research is so arduous that it is unlikely that high-quality researchers could be located to engage in the relatively unexciting task of conducting a study designed specifically to replicate a previous one” (Schofield, 1990; p. 203). What is probably more important than precise replication is the stimulation of further qualitative and quantitative research.

Finally, the generalizability, or external validity, of the this study depends on applying it to a similar context and content. That is, are the results generalizable to other introductory, algebra-based, college physics courses, with similar implementation of cooperative learning and problem solving? Because each physics course has unique features, such as the professor, teaching assistants, textbook, and student population, it is not possible to exactly replicate the study. Rather than think in terms of generalizing the findings to the same context and content, it might be better to think in terms of translating the results to a comparable situation (Schofield, 1990; Goetz and LeCompte, 1984).

This Research is Exploratory

The very nature of a qualitative case-study approach makes this research exploratory and speculative, as opposed to definitive. This research will tell us “where to look” in attempting to understand cooperative group problem solving. That is, the patterns found in the group processes will help set the future research agenda, both qualitative and quantitative, in cooperative group problem solving.

The Researcher as a Participant

Finally, there is an epistemological question I must acknowledge. In a qualitative case-study design the researcher “interacts” with that which is being researched. Because of this, and because the design emerges from that which is being studied, the research is value-laden and biased. That bias, however, does not attempt to force specific results or conclusions. It rather recognizes that, for example, my choice of an analysis category reflects my world-view. In a sense, I am a participant in the research, despite my efforts to distance myself from any causal effect on the outcomes. The Heisenberg Uncertainty Principle is a useful analogy. The act of making the measurement disturbs the system.
The art of qualitative research is to keep the disturbance to a minimum (although perhaps not as small as Planck’s constant).

SIGNIFICANCE OF THE STUDY

With all of these limitations, it may seem that the choice of a qualitative case- study design severely limits the outcomes of this study. Although it may not be possible to specify what all physics students do in cooperative group problem solving, it will be possible to describe what these students in these 14 groups did. That in itself will be an accomplishment due to the relative paucity of insights into what students actually do in cooperative problem-solving groups. The ultimate value of this research is to extend the theoretical basis for understanding cooperative group problem solving. A better understanding of the theory of cooperative-group problem solving will enable the design of both qualitative and quantitative research to further investigate the theoretical base.

Then, teaching strategies and instructional materials to foster effective cooperative problem solving can be designed and tested.
Likewise, since research depends on valid analysis schemes, the design of a qualitative, case-study approach will contribute to research methods in science education. As far as we know, this is the first time a qualitative case study has examined cooperative group physics problem solving. At a very local and personal level, this study expands the types of research being done by the Physics Education group at the University of Minnesota.
Ultimately, I believe this study will be much like the manned missions to the moon in the 1970’s. About 400 kilograms of rock were collected from “only” six locations. Their analysis, plus seismic and other data, led to countless questions, and several new theories about the origin and evolution of our nearest celestial neighbor. Raising new questions and giving birth to new theories to test is the best goal of all research.

CHAPTER 2 PROCEDURES

Overview

In this chapter I will discuss the procedures used in this research. Because the researcher in a qualitative case study engages in different tasks than in quantitative research, I will explain how this study differs from the more common quantitative study. A description of the research setting, a college physics course, will include a discussion of prior research in physics problem solving and in cooperative learning. Because this study is based on the Toulmin argument structure, this chapter focuses on the identification of the Toulmin statements.
Readers familiar with the more common quantitative research design will note there is not a separate “Review of the Literature” chapter in this dissertation. Instead of a “positivist” approach to the literature, I will take a more “inductive”one. That is, the available literature on research and theory relevant to my research goals will serve to “frame” the discussion. I will introduce applicable ideas and findings as they are needed. This, by the way, is consistent with a constructivist approach to qualitative research.

THE ROLE OF THE RESEARCHER

One of the characteristics of a qualitative case-study approach is that the researcher is an integral part of the process. That means the research is dependent upon the researcher’s own presuppositions, assumptions and biases. The task I faced was to make sure that I was, first, aware of my own presuppositions, assumptions and biases, and second, aware of how these might prejudice or skew the outcomes of the study. Throughout this dissertation, I will attempt to explain where I believe I “interacted” with the data, the method, and the results.

I discovered some interesting aspects about doing this type of research from my perspective as a physics teacher. Physics by its very nature is exceptionally quantitative. Initially I tried to answer my research questions using quantitative measures. These efforts yielded few useful insights. So first I learned to throw away my quantitative analytical skills and concentrate on qualitative analytical skills. Second, I learned that a physicist is uniquely qualified to undertake this kind of qualitative research.

Understanding what the students were doing in solving these problems required that I understand the physics. That understanding came not only from graduate work in physics, but also from having taught (at Normandale Community College) the same algebra-based course as the University of Minnesota course used in this study.

RESEARCH CONTEXT AND SETTING

The physics courses used for this study were the two-quarter sequence Physics 1041 and 1042, taught winter and spring quarters 1991, at the University of Minnesota, by Professor Konrad Mauersberger (now at the Max Planck Institute, Heidelberg). This algebra-based, introductory course was taken primarily by pre-health science and pre- architecture students, plus others needing an introductory physics course. The textbook was Physics: A General Introduction, 2nd Edition, by Alan Van Heuvelen (1986). Each week, students met for three 50-minute lecture periods, one double-period lab (1 hour, 50 minutes) , and one 50-minute “recitation” period. A given group of students were in the same lab and recitation cooperative group. The graduate teaching assistant was the same for their lab and recitation. The only factor in determining the recitation/lab section in which a given student was registered was his or her individual employment or class schedule. That is, there was not a random assignment of students to a particular section. The teaching assistants, however, assigned students to their cooperative groups within the recitation/lab section. It was intended that there would be a heterogeneous mix within a group in terms of the students’ performance in the class (high, medium, low). However, the teaching assistants only occasionally followed this plan. Also, it was intended that there would be all groups of three, and no groups where the number of men was greater than the number of women. We found in previous research that heterogeneous cooperative groups of three, with attention paid to the gender mix, worked best for physics problem solving (Heller and Hollabaugh, 1992).

In reality, of the 14 groups in this study, there were 11 groups of three. Only four of these three-member groups met the gender criteria, and of these four, only one (Group 3A), met the ability composition criteria. That is, the assignment to groups was not what I would do in my own classes. However, I didn’t interfere with the teaching assistants, although at their weekly meetings I made some suggestions about the group compositions. Even so, I believe that these departures from the “desirable” may have contributed to some interesting outcomes.
Students in a group worked a “practice” problem one week, and then worked a problem for a grade the following week. Students were then reassigned to new groups for another two-week period. During each of the two quarters, there were four graded problems, offering eight data collection opportunities.

The main reason for reformulating the groups after each graded problem was to promote heterogeneous grouping. This also tends to avoid a situation where group members become dependent upon one person for the solution. Sometimes personality conflicts arise in a group and reformulation can alleviate the difficulty. A negative aspect of the periodic reformulation is the short “residence time” of a student in a group. Two weeks may be too short a time for students to become cohesive and work cooperatively.

The students were introduced to the four group roles of Manager, Recorder, Skeptic and Engergizer. Table 2-1 (page 32) is a handout we use in our classes to teach the group roles. The teaching assistants were introduced to these roles in their initial training and were asked to instruct their students in the use of the roles. There are numerous comments by the students in the transcripts that reference these roles. Also, some of the actions they take are actually the outcome of these roles. Hence, the “sounds like” ideas later helped me when I had to code statements in the transcripts. These roles are “metacognitive.” That is, they are thinking tasks individual, competent problem solvers do when faced with a physics problem. For example, physicists are very good at asking themselves skeptical questions when faced with a new situation. Novice problem solvers typically do not have the metacognitive skills necessary to engage in this type of activity. These roles are based on observations of what competent problem solvers actually do (Dreyfus and Dreyfus, 1984; Heller, Keith and Anderson, 1992).

Students were taught a problem solving strategy which was modeled in class by the professor (Heller and Hollabaugh, 1992). They were expected to use this five-step strategy in the recitation period when solving a complex problem as a group. Throughout their discussions, they make references to the steps of this strategy. Thus, it will be helpful for the reader to be somewhat familiar with the strategy and its theoretical background. Table 2-2 ( page 33) summarizes the main features of the strategy.
 
ACTIONS    WHAT IT SOUNDS LIKE

MANAGER

DIRECT THE SEQUENCE OF STEPS. KEEP YOUR GROUP "ON-TRACK."
MAKE SURE EVERYONE IN YOUR GROUP PARTICIPATES.
WATCH THE TIME SPENT ON EACH STEP.    
"LET'S COME BACK TO THIS LATER IF WE HAVE TIME."
"WE NEED TO MOVE ON TO THE NEXT STEP."
"CHRIS, WHAT DO YOU THINK ABOUT THIS IDEA?"

RECORDER/CHECKER

ACT AS A SCRIBE FOR YOUR GROUP.
CHECK FOR UNDERSTANDING OF ALL MEMBERS.
MAKE SURE ALL MEMBERS OF YOUR GROUP AGREE ON PLANS AND ACTIONS.
MAKE SURE NAMES ARE ON GROUP PRODUCTS.    
"DO WE ALL UNDERSTAND THIS DIAGRAM?"
"EXPLAIN WHY YOU THINK THAT." "ARE WE IN AGREEMENT ON THIS?"
SKEPTIC
HELP YOUR GROUP AVOID COMING TO AGREEMENT TOO QUICKLY.
MAKE SURE ALL POSSIBILITIES ARE EXPLORED.
SUGGEST ALTERNATIVE IDEAS.    
"WHAT OTHER POSSIBILITIES ARE THERE?"
"LET'S TRY TO LOOK AT THIS ANOTHER WAY."
"I'M NOT SURE WE'RE ON THE RIGHT TRACK."
"WHY?"
ENERGIZER/SUMMARIZER
ENERGIZE YOUR GROUP WHEN MOTIVATION IS LOW

BY SUGGESTING A NEW IDEA;

THROUGH HUMOR; OR

BY BEING ENTHUSIASTIC.

SUMMARIZE (RESTATE) YOUR GROUP'S DISCUSSION AND CONCLUSIONS.    
"WE CAN DO THIS!" "THAT'S A GREAT IDEA!"
"SO HERE'S WHAT WE'VE DECIDED..."

FOCUS the PROBLEM

Picture and Given Information

Construct a mental image of the problem situation.

Draw a picture which show the important objects, their motion, and their interactions.

Label all known information. Question

What is being asked?

How does this translate into some calculable quantity? Approach

Outline the concepts and principles you think will be useful in solving the problem(e.g., definition of velocity and acceleration, Newton's Second Law, conservation of energy).

Specify convenient systems to use in the problem solutions.

Specify specific time intervals over which the application of each principle will be the most useful.

Identify any constraints present in this situation.

Specify any approximations or simplifications which you think will make the problem solution easier, but will not affect the result significantly.

DESCRIBE the PHYSICS

Diagram and Define Variables


Translate your picture into a diagram(s) which gives only the essential information for a mathematical solution.

Define a symbol for every important physics variable on your diagram.

Usually you need to draw a coordinate system showing the + and - directions.

If you are using kinematics concepts,, draw a motion diagram specifying the objects' velocity and acceleration at definite positions and times.

If interactions are important, draw idealized, free-body, and force diagrams.

When using conservation principles, draw "before", "transfer", and "after" diagrams to show how the system changes.

To the side of your diagram(s), give the value for each physics variable you have labeled on the diagram(s) or specify that it is unknown.

Target Variable

What unknown is it that you must calculate from the list of variables?

Will the calculated quantity answer the question? Quantitative Relationships

Assemble your toolbox of mathematical expressions which use the principles and constraints from your approach to relate the physics variables from your diagrams.

PLAN the SOLUTION

Construct specific algebraic equations

Determine how the equations in your toolbox can be combined to find you target variable.

Begin with an equation that contains the target variable.

Identify any unknowns in that equation.

Find equations from your toolbox which contain these unknowns.

Continue this process until your equations contain no new unknowns.

Label each equation for easy reference.

Do not solve equations numerically at this time. Check for Sufficiency

You have a solution if your plan has as many independent equations as there are unknowns.

If not, determine other equations or check the plan to see if it is likely that a variable will cancel from your equations.

Outline of Math Solution

Indicate the order in which to solve the equations for a desired variable and which equation to substitute the expression for that variable.

Typically, you begin at the end of your plan and work backwards to the first step, which is an equation containing your target variable.

EXECUTE the PLAN

Follow the Plan


Do the algebra in the order given by your outline.

When you are done you should have a single equation with your target variable

isolated on one side and only known quantities on the other side.

Substitute the values (numbers with units) into this final equation.

Make sure units are consistent so that they will cancel properly.

Calculate the numerical result for the target variable (s).

EVALUATE SOLUTION

Is answer properly stated? Is answer reasonable?

Is answer complete?

Do vector quantities have both magnitude and direction?

Can someone else follow your solution?

Is the result reasonable and within your experience?

Do the units make sense? Have you answered the question?

THEORETICAL FOUNDATIONS

Many features of the Physics 1041/1042 course design and the cooperative groups result directly from fundamental research in problem solving and cooperative learning.

This section presents a summary of research and practice in physics problem solving and cooperative learning.

Problem Solving Strategy

Perhaps Morton Hunt (1982) gave the most concise definition of problem solving: "A person is confronted with a problem when he wants something and does not know immediately what series of actions he can perform to get it" (p. 236). This definition suggests several things about problem solving.  Problem solving is a process, consists of a series of steps, and the problem solver is involved in constructing the solution.  Much of the research on problem solving has proceeded with this kind of an operational definition. The research on physics problem solving has evolved over the last twenty years. Initial work on the acquisition of general problem-solving knowledge and
problem-solving skills progressed to problem solving in general, mathematics problem solving, and finally problem solving in areas like physics.

Early Research in Problem Solving

In their classic work Human Problem Solving, Herbert A. Simon and Allen Newell (1970) summarized the "information processing model" approach to human problem solving. First, one perceives the raw data and processes these perceptions far enough to recognize the problem context. Next, the solver makes a mental representation of the problem. This is an interpretation of what the goal is, where the solver is in relation to it, and what kinds of acts one must perform to get to the goal. The total set of mental operations used in the effort to move from the given data to the goal is what Simon and Newell call a “production system” or a program. In the course of carrying out the program, the solver notices whether any step, or series of steps, decreases the distance to the goal; if so, you continue with it, but if not, you move on to the next step or steps in the program (Hunt, 1982).
Due to the narrow limits of our short-term memory, we work our way through a problem in serial fashion, taking one thing at a time rather than simultaneously searching in disconnected parts of the problem. This avoids a trial and error approach. Sometimes the solver searches experience for an analogy, because all learning is based on prior knowledge and experience. (This emphasis on prior knowledge and experience is also a characteristic of constructivism in science education.) Simon and Newell’s work forms the foundation of subsequent research in problem solving.
Some of the earliest work recognized that there are stages of development in a person's knowledge or skill. For example, Dreyfus and Dreyfus (1984) delineated five stages of skill acquisition in any type of "problem solving":

Novice: learns to recognize various objective factors and features relevant to the skill and acquires rules for determining actions based upon those facts and features.

Advanced Beginner: Performance improves to a marginally acceptable level only after the novice has considerable experience in coping with real situations. Uses context-free facts.

Competence: With more experience, the number of recognizable context-free and situational elements present in a real-world circumstance eventually becomes overwhelming. People learn a hierarchical procedure of decision making.

Proficiency: Intuition is neither wild guessing nor supernatural inspiration, but the sort of ability we all use all the time. The proficient performer, while intuitively organizing, will still find himself thinking analytically about what to do.
Expertise: An expert generally knows what to do based on mature and practiced understanding. When things are proceeding normally, experts don't make decisions; they do what normally works.

This model represents a progression in the sense that a typical learner's best performance in a particular type of situation will initially stem from novice rule- following, then from the advanced beginner's use of aspects, and so on through the five stages. There is a progression from analytic behavior of a detached subject, following abstract rules, to involved, skilled, problem-solving behavior based on an accumulation of concrete experiences, and the unconscious recognition of new situations as similar to past ones. Because experts act rationally, competent performance is rational and the transition to proficiency is a process. This emphasis on process is equally important to cooperative learning.

Research in Physics Problem Solving

Research in physics problem solving has served to inform general problem solving research and has become a fruitful area for understanding the acquisition of problem solving skills. There may be two reasons for this. First, the research is empirically based on the performance of problem solvers. Thus the research changes the emphasis of the problem solving from the problem to the solver. Second, physics problems, which usually are highly quantified, function well as a key component of this research (Fuller, 1982). There are several examples of research on physics problem solving that show how research in this specific area has broadened the scope of problem- solving knowledge.

In science education, much of the early research in the cognitive psychology tradition was done in physics problem solving by Jill Larkin and her associates at Carnegie-Mellon University. She compared the problem solving performance of expert problem solvers (professors in physics) with that of novices (beginning students in physics courses) (Larkin, McDermott, Simon and Simon, 1980). This seminal article is cited in almost all other research papers on physics problem solving. Students were given training in qualitative analysis and “chunking.” Chunking is a process that allows experts to combine minor steps into a single procedure and thereby arrive quickly at a solution. Larkin sets a research agenda to enable students to solve problems in physics more effectively: “1. observe in detail what experts do in solving problems; 2. abstract from these observations the processes which seem most helpful; 3. teach these processes explicitly to students” (Larkin, 1979; p. 285). By observing what experts do, procedural "chunks" are decomposed into smaller more manageable, and teachable, steps.

The work of Chi, Feltovich, and Glaser (1981) used physics problems to investigate the organization of knowledge. "Results from sorting tasks and protocols reveal that experts and novices begin their problem representations with specifically different problem categories, and completion of the representations depends on the knowledge associated with the categories. For, the experts initially abstract physics principles to approach and solve a problem representation, whereas novices base their representations and approaches on the problem's literal features" (p. 121)
A problem representation is a cognitive structure corresponding to a problem, constructed by a solver on the basis of his or her subject-related knowledge and its organization. The quality of a problem representation influences the ease with which a problem can be solved. The hypothesis guiding their research is that the representation is constructed in the context of the knowledge available for a particular type of problem.
Experts categorize problems differently than novices because of a more highly developed knowledge structure.

Joan I. Heller and Frederick J. Reif (1984) further showed the importance of knowledge organization and problem representation with their work on the "physics description" of a problem. It is important to “describe” a problem with care before attempting to search for its solution, explicit knowledge about what types of information should be included in an effective description, and explicit systematic procedures specifying how to generate such a description. The physics description contains the "physics" of the solution.

The work of Alan Schoenfeld in mathematics problem solving must also be mentioned. The problem-solving strategy students followed in this dissertation research is heavily based on Schoenfeld's work. Running as a thread through Schoenfeld's work, one can find the following many-sided argument for the merits of heuristic instruction (Schoenfeld, 1985; Schoenfeld, 1989; Nickerson, Perkins, and Smith, 1985):

Heuristics help students to solve problems when the students know and apply the heuristics.

Students lack a good set of heuristics.

Students do not reliably pick up heuristics spontaneously from examples; heuristics have to be taught explicitly.

Students do not reliably apply heuristics they know about; some sort of guidance or prompting is necessary.

A "managerial strategy" for approaching problems, taken together with heuristics, can help students to apply heuristics and lead to substantially improved problem solving performance in mathematics.

The Managerial Strategy of Schoenfeld has the following five phases:

Analysis: Understand the problem and get a feel for it by examining the givens, the unknowns, and so on. Simplify the problem by reformulating it without loss of generality.

Design: Maintain an overview of the problem-solving process, develop a broad plan for how to proceed, and ensure that detailed calculations are not done prematurely.

Exploration: Exploration is the choice when the problem presents difficulties and no clear plan for directly producing a solution is at hand. Exploration allows three heuristic steps of increasing extremity: Consider essentially equivalent problem, consider slightly modified problem, consider broadly modified problem.

Implementation: Plan should lead to tentative solution.

Verification: Check the solution.

Physics Problem Solving in Practice

Regardless of the context, research has shown that problem-solving can be studied by researchers and effectively taught to students. This large body of prior research forms the basis of the problem-solving strategy used in Physics 1041/1042 (Heller, Keith and Anderson, 1992; Heller and Hollabaugh, 1992). For example, there are five steps, similar to Schoenfeld. The Physics Description is the key step, and hence is the focus of my inquiry into argument co-construction. Many problem solutions of beginning physics students are incorrect because of an improper free-body diagram, a key step in the Physics Description. The subsections of a step teach students to “un-chunk” larger ideas. That is, smaller, more manageable pieces of the problem are tackled a step at a time. The emphasis on the qualitative analysis of the problem attempts to get students away from categorizing problems on the basis of the surface features, but rather on the basis of the physical principles involved.

The problem-solving strategy employed in Physics 1041/1042 is formulated on the idea that any problem can be solved if one has the right approach to problem is broken down into a series of more manageable steps. The ultimate goal is to move the student from the novice stage to a competence state (cf. pp. 36-37). The steps in the strategy were summarized in the Table 2-2, pages 33-34.

Students adopt this strategy more readily if they are given peer support through the use of cooperative groups (Heller and Hollabaugh, 1992). In fact the original motivation for using cooperative learning in physics courses at the University of Minnesota was to facilitate problem solving. The language of the problem-solving strategy is very evident when a group discusses a problem.

Several aspects of this research on problem solving shaped the design of this study as well as the Physics 1041/1942 course. Students worked in groups of three and used this specific problem solving strategy. The strategy broke larger steps into smaller, more manageable steps. This research focuses on the physics description due to the fundamental importance of the description to the solution of the problem.

Cooperative Learning

It was the intent of the Physics 1041/1042 course designers that the “Minnesota Model” of cooperative group problem solving would be followed. This model is based on the work of Roger Johnson (Science Education) and David Johnson (Educational Psychology) at the University of Minnesota. The language of their model of cooperative learning permeates this research, so a discussion of the model is necessary. Throughout this dissertation I will refer to this as the Johnson Model. At the University of Minnesota Kenneth Heller (Physics) and Patricia Heller (Science Education) have further applied this model to physics problem solving. Their motivation for utilizing cooperative learning was to provide a supportive environment to help students abandon their novice problem-solving strategies and adopt more “competent” approaches.

Cooperative Learning Theory and Practice

Cooperative learning is an educational strategy for personal and cognitive change that can be contrasted to competitive or individualistic strategies of learning (Johnson and Johnson, 1987). Much of the research on cooperative learning in science education has focused on elementary or secondary school children. This suggested to me that research was definitely needed on cooperative learning in college science instruction. Moreover, because of the emphasis on problem solving and laboratory work, college physics classes provide excellent contexts for cooperative learning research.
At its most basic level, cooperative learning methods require students to work in groups. Although working in groups is a primary requirement, it is not sufficient.

Cooperative learning must be structured. The instructional strategy in the courses used in this research relied on the Johnson Model (Johnson, Johnson and Holubec, 1988), and its application by Karl Smith (1989) to college teaching. There are five elements in this model of cooperative learning. Examples of how these elements are implemented in a classroom will serve to explain their use.

Positive Interdependence links students together so that their success in a course is dependent on one another. Group members work together, striving for consensus on goals, problem solving strategies and answers. Frequently there are shared resources and common rewards. One method to facilitate positive interdependence gives a group only one set of materials needed to solve a problem or answer a question.

Face-to-face Interaction promotes students' support for one another to learn. It is necessary to have a classroom where students can physically face each other ("eye to eye and knee to knee"). Traditional lecture halls will not work because moveable furniture is necessary.

Individual Accountability requires the instructor to assess each person's performance by asking questions randomly of individuals. Name tags can be worn to help the instructor to learn the students' names.

Using Collaborative Skills encourages leadership, trust, communication, conflict- management, and decision-making. Students who lack cooperative experiences frequently lack these experiences. Students come to college with thirteen years of learning experience that probably did little to build these collaborative skills.

Group Processing involves an evaluation by the participants of their group: What they did well and what they could do better the next time to improve the functioning of the group. Feedback can be formal and informal. Forms can be developed to give feedback to the instructor on a given exercise. It is important to focus the student evaluation on the process of the group in contrast to the product. Feedback is a dialog.  Giving students praise and encouragement, such as "you can do it", helps tremendously in subject matter where students might feel inferior.

Group structuring distinguishes this type of cooperative learning from other models. Indeed, structuring can be the key to effective cooperative learning groups (Johnson and Johnson, 1987; Johnson and Johnson, 1989; Johnson, Johnson, and Holubec, 1988; Smith, 1989; Heller and Hollabaugh, 1992). A structured model of cooperative learning considers, for example, how many students will be in a group, how they are to be assigned to the group, what roles they will assume in the group, and structuring the task. Structured groups fare better than unstructured groups. Structured cooperative learning does utilize more class time. Content may be sacrificed in order to make time for group activities. The results, however, are supportive of the method.

This cooperative learning model is based on extensive research on competitive, individualistic, and cooperative learning strategies (Johnson and Johnson, 1989). In a sense, the research in cooperative learning is an example of action research as advocated by Kurt Lewin who said, “...there is nothing so practical as a good theory” (Johnson and Johnson, 1987; Johnson and Johnson, 1986). Theory informs practice and practice informs theory in cooperative learning research. This interplay is not unlike the relationship between theoretical and experimental research in physics. There is always a dialog between these two approaches to understanding the physical world.

Frequently, theoretical questions originate in observations of cooperative learning in practice. Thus, in discussing the research foundations of cooperative learning, there is not always a clear dividing line between “theory” and “practice.” This is, perhaps, due to the complex nature of human learning and even how we attempt to understand learning itself (Hunt, 1982). Although many components of the research are quantitative, there is also a decidedly qualitative aspect to research in cooperative learning.

Much of the current research in cooperative learning focuses on the practical.

While there is nothing inherently misdirected about that emphasis, research into theory is also needed. In keeping with the Lewinian notion of action research, some of the theoretical research program is actually formed by questions raised in the practice of cooperative learning. In forming research questions, it is important to have a framework in which to ask the question.
Johnson and Johnson (1986) identify three types of "action research" studies that can be conducted on the use of cooperative learning in science education. A replicating study would give further support to cooperative learning theory. A refining study would look at ways of making cooperative learning more effective (e.g., Heller and Hollabaugh, 1992). An extending study examines the critical factors that make cooperative learning work, such as examing the patterns of argument co-construction in a cooperative group. Thus, this dissertation research is an example of an extending study.
For an example of this theory and practice interplay, consider the work of Karl Smith, of the Department of Civil and Mineral Engineering at the University of Minnesota. Smith has made extensive use of cooperative learning in college engineering classes. His techniques, are based on the cooperative learning theoretical research, especially that of Roger and David Johnson. In a research summary, coupled with arguments for the use of active learning strategies, Smith (1988) makes a strong statement for the efficacy of cooperative learning in engineering education. Although he specifically addresses engineering education, many of his findings and proposals can be transferred to science education in general.

Engineering education and physics education share an important goal: Movement towards becoming an “expert”. They also share a common obstacle: Students’ misconceptions. Based on Smith's actual classroom experience, one might conclude cooperative learning may indeed be the best way to teach problem solving and overcome misconceptions at the same time (Smith, 1987). This is due to the way students develop expertise.

Smith (1987) points out that the rehearsal aspect of cooperative learning is an effective means of developing expertise. This relates to the theory of encoding ideas in long term memory. The process of discussing a concept, or solving a problem, with peers allows for instant feedback.  There is a higher probability the "proper" connections will be made among ideas. This is the opposite of generating misconceptions. There is, of course, the possibility all students in a learning group will share and reinforce the same misconception or naive, novice approach. The monitoring function of the instructor serve as a check on student-generated misconceptions. While this may occasionally make more work for the instructor, it permits the assessment and addressing of misconceptions, observation of conceptual maturation, and ensures quality.

Cooperative Learning in College Physics

If one is to use cooperative groups in physics education, then it must be demonstrated that cooperative learning is superior to a competitive or individualistic strategy in a given context. Problem solving in physics offers one test of the efficacy of cooperative learning. A common complaint against using groups for problem solving is that the product of the group is merely the product of the best individual in the group. A means of testing this is to compare the product of individuals with that of a group.

Using a problem-solving strategy based on the expert-novice research, Heller, Keith, and Anderson (1992) found the group solutions on six introductory physics examinations to be superior to that of the best individual in a group on matched individual problems. They used the Wilcoxon rank-sum test for two matched samples to compare group and individual scores. On one exam, the group score was better at the p <
.05 level, and on five exams, the group score was better at the p <. 01 level. That is, the group solution on a matched problem was significantly superior to the individual solution of the best person in the group. In examining each group's solutions, it was found that the group produced a better physics description with fewer misconceptions. This research supports co-construction of the problem solution.

The research on cooperative learning worked its way into the Physics 1041/1042 course design. Students were introduced to the group roles. The group membership changed every two weeks. The Teaching assistants who formulated the groups were supposed to keep a gender balance and performance mix. In applying the cooperative learning research to my own research, I knew that a superior group solution means co-construction of an argument. Hence, I knew I should define criteria (Chapter 3) for recognizing evidence of co-construction of an argument. These results, plus my own experience with cooperative learning, suggested that I should be attentive to not only what was being said, but how it was said and who was saying it. Thus, in the transcripts of the groups’ conversations reproduced in this dissertation, there will be numerous annotations indicating tone of voice or body language, as well as the identity of the speaker.

DATA COLLECTION PROCEDURES

In this section I will discuss the procedures used to gather the “raw” data. The videotaping of the groups began with the second graded problem. I felt the students needed at least one chance to experience a graded problem situation before experiencing the taping process. Also, the first taping session was not included in the analysis of the data. It served to solve logistical and technical problems associated with the taping. The original research plan called for the taping of 24 different groups working six unique problems. However, due mainly to technical problems (poor sound quality, equipment failure or unavailability), only 14 groups solving the six problems were actually included in the final study.
I visited the entire class before the first taping session and explained the nature and purpose of my research. All students in a group had to agree to be taped and signed consent forms. The other videographers (other graduate students, a munificent advisor) and I, remained passive observers of the groups as they were videotaped, but at times we made verbal or written comments about something interesting that had transpired in a group. A log sheet recorded the students’ names, phone numbers, addresses, a serial number identifying the tape, and comments by the videographer.
Photocopies of the written solutions of the videotaped groups were made available to me, as well as the complete quarterly grade records for the class. Teaching assistants worked in pairs and took turns grading all the written problem solutions so there would be consistency within a given problem. The teaching assistants and the professor were not allowed to view the videotapes.

Immediately following each taping session, the videotapes were transcribed by a transcription assistant. Although the transcriber was a passive observer of the groups, he frequently mentioned to me certain “fascinating” things he had observed a group doing. I then watched each tape, making corrections to the transcript, noting any interesting non- verbal behavior, and annotating references to the written problem solution. Each taping session was assigned a number (2,3,4,5,6,7) and within each session each group was assigned a letter (e.g., 4A, 4B, 4C, 4D). Thus a reference in this dissertation to Group 3A means the “A” group of the third taped problem. It is important to note that each videotaped group was in a different room and under the tutelage of a different teaching assistant. Thus, the teaching assistant who appears on Tape 4B is not the same teaching assistant who appears on Tape 4D .

DATA ANALYSIS PROCEDURES

Since a primary part of this research focuses on the argument structure of Stephen Toulmin, I needed to find a way to look at the 14 groups using his structure of argument construction. The first step in applying the Toulmin structure to the groups’ problem solutions was to learn how to identify Grounds, Warrants, Backings, and Claims. It was soon learned that other categories would be needed as well. I chose a single problem, solved by four diverse groups, to begin the process.
The primary “reference point” for this part of the analysis is the set of 14 videotapes and the transcripts made from them. The other three reference points will help explain the analysis process I developed. For example, the written problem solutions will be very useful in determining what the students were writing while they talked. Diagrams from their written solutions will appear in the transcript excerpts.

Initial Transcript Coding

I selected the fourth graded group problem of Physics 1041, given during the eighth week of the Winter Quarter. I chose this problem (Shown in Figure 2-1, page 51) for two reasons. First, this is the one problem for which I had four videotapes and transcripts. These four groups exhibit a spectrum of ability and functioning, and this is what I had hoped to find. Secondly, I felt that by this time of the quarter, the students would have become accustomed to the problem solving strategy as well as working in cooperative groups. It seemed that it would be “easier” to understand what they were doing as I viewed the tapes.

Above the entrance door of an old German

"GASTHAUS" hangs a sign. A 200 N metal beer mug hangs at the end of a 3 meter long strut that is attached to the wall by a hinge. The weight of the strut is 100 N. A support cable is attached to the strut at a point 2 meters from the wall and makes a 30° angle with the strut. Find all the forces acting on the strut.  Useful information: )F = 0 and )t = 0        

GASTHAUS

Applying the Toulmin categories and argument structure to the At the Gasthaus problem, an overall diagram of the solution can be visualized. This kind of visualization helped me understand the types of statements students made as they solved the problem. Figure 2-2 (page 53) shows the overall structure of this problem using the Toulmin terminology.

The students are immediately presented with a picture and information. In a sense they do not have to “decode” the problem and can start immediately with the Physics Description. The data in the problem statement (e.g., 200 N, 3 m, etc.) constitute the "Grounds" for the problem. Throughout the solution, students will refer back to the problem statement for these grounds and will make either explicit or implicit references to the grounds.
The "Warrants" in this problem are the same for other problems in statics, namely that the sum of the forces and torques must be zero for equilibrium. A general warrant in this problem is that both SF = 0 and Si = 0 must be used. This general warrant has many specific and detailed sub-warrants, such as the selection of the point about which to take the torques.

In a problem involving static equilibrium, the application of Newton’s Second Law to the situation requires that SF = 0. Students (or physicists for that matter) seldom apply this law and explicitly state “This is valid because of the generally accepted validity of Newton’s Laws.” Toulmin, I believe, would see physics warrants as unequivocally supporting a claim:

Warrants are of different kinds, and may confer different degrees of force on the conclusions they justify. Some warrants authorise us to accept a claim unequivocally, given the appropriate data--- these warrants entitle us in suitable cases to qualify our conclusions with the adverb ‘necessarily’; others authorise us to make the step from data to conclusion either tentatively, or else subject to conditions, exceptions, or qualifications--- in these cases other modal qualifiers, such as ‘probably’ and ‘presumably’, are in place (Toulmin, 1990, pp. 100-101).

It is, however, necessary to support warrants with backings.

In what ways does the backing of warrants differ from the other elements in our arguments? To begin with the differences between B and W: statements of warrants, we saw, are hypothetical, bridge-like statements, but the backing for warrants can be expressed in the form of categorical statements of fact quite as well as can the data appealed to in direct support of our conclusion (Toulmin, 1990, p. 105).

It would, for example, be somewhat unlikely that a physicist would directly or explicitly state, “categorically,” that Newton’s Laws are valid. When students cite backings, they may refer to the professor in deference to the teaching assistant or textbook. "That's how he did it in class," is the simplest example of this type of statement.

In the context of introductory physics problems, there is seldom an opportunity for "rebuttal" of a claim. A rebuttal is a condition that negates the claim. In this problem, a rebuttal might be "The sign is not in equilibrium if the tensile strength of the cable is too small." However, the diagram given with the problem statement clearly shows the sign in an equilibrium position and thus the rebuttal is invalid. A rebuttal usually begins with "unless," implying that situation is true unless other conditions apply. (A rebuttal in kinematics might be, "Unless the object is moving at or near the speed of light.") A rebuttal is not the same as a challenge to a claim.

A challenge is generated by the student and not by the inherent characteristics of the problem. Although the Toulmin structure does not explicitly allow for a challenge, I expected to see challenges because of the roles the students were introduced to in their cooperative groups. The skeptic role is basically a challenging role.

GROUNDS
WB = 100N, WM = 200N,
L = 3 meters, 0 = 30° Picture ? Equilibrium        
†        
WARRANTS        CLAIM
Unknown forces can be found by applying S F = 0 and S i = 0.
S F = 0    ?    
S i = 0        
Vector components        
T        T
BACKINGS
General validity of Newton's Laws, nature of vector algebra, both as expressed in the text, by the professor, or teaching assistant.        REBUTTAL
External forces (none are indicated) could cause the sign to collapse. Thus, no rebuttal in this case.

Individual subsections of At The Gasthaus could be diagrammed in a similar theoretical fashion, illustrating an idealized solution to the problem. Likewise, discussions relating to the group process and procedures or the problem solving strategy can be diagrammed. It will not always be possible to cleanly distinguish or separate content (i.e., the physics, as described above), group maintenance, and Problem Solving Strategy statements in the course of one argument.

Identification of Statement Types Using Descriptions of the Session Four Groups

The four groups (4A, 4B, 4C, 4D) used to develop a coding scheme were diverse and presented a variety of group dynamics, personalities, and problem solving competence. I will draw from these four groups to illustrate two types of statements: Those statements which are specifically Toulmin-like and those which do not fit a Toulmin category, and hence provide the basis for defining new categories. I do not consider these statements as outcomes, because in themselves they do not say anything about patterns. I will repeatedly draw upon some examples from the four groups that solved At the Gasthaus. Each time I re-read their transcripts, or watched the videotapes, I saw something I had missed in the prior reading or viewing. The process I experienced over four years will be mimicked by seeing the different levels of analysis unfold within these four groups. Although the dialog becomes familiar, new meaning appears at every turn.
Group 4A consisted of two women (MK and MR) and one male student (RM).

Based on their individual cumulative exam scores at the time of this problem session, this was an above average group. The women were each in the top third of the class and the man was in the middle third of the class. This ability mix is seen in their aggregate class average: they were above the class mean at the time of the group problem (z = .8). All three students were full-time, residential students at the University. MK was the Recorder, MR was the Skeptic (She actually wrote "Spy" on the video log sheet, but verbally identified herself as the skeptic), and RM identified himself as the Energizer.

Here is an extended example from Group 4A, an example of a “raw” transcript.

MK: OK, so then what? We'll need to draw the bar. [Draws bar.] And this is a weird force. We have a weight going.  We have tension this way, right? [draws T vector]
RM:/MR: Yeah
MK: So we label that T?
RM: You have a weight right here. [Points to where WB goes on diagram.]
MR: The bar weight. In the middle. RM: Yeah, goes in the middle.
MR: That [weight] always goes in the center [i.e., center of mass]. MK: OK, so this is weight bar. [labels diagram while talking.] MR: That should be at one end, 1.5 meters.
MK: What?
MR: The weight of the bar? They always do it from the center. We always do it from the center. We're going to have to know how far over it is. [Indicating labels for the distances.] So it's always at 1.5.
MK: Oh, OK [Draws and labels the 1.5 meters.] MR: Meters

In problems involving forces (either static or dynamic), students were taught the importance of drawing an idealized sketch of the problem situation, a free-body diagram, and force-vector diagrams. The grading of the solution considered the correctness of this step and this group thus gives much attention to drawing these three diagrams. This segment of their dialog opens with a procedural discussion about drawing the “free-body” and “force thingy” diagrams. These statements are all claims that relate to the process of the solution.
 
An excellent example of an explicit claim with implicit, or non-verbal grounds, is found in RM’s statement about the location of the center of weight of the bar: “You have a weight right here.” When he points to where WB goes on diagram, he is supplying support in the form of grounds. This is an example of grounds because the idea is inferred from the diagram. When member MR says, “always goes in the center” she is supplying a warrant that the center of weight for a uniformly dense object is at the center of geometry. Note then that both members RM and MR support the initial Claim by simply reiterating the statement in their own words.

Note student MK’s statement, “OK, so then what?” She often ends a segment of dialog with such statements which either can be seen as requesting another problem solving claim, or as summarizing what she has just done. In fact, a prime characteristic of MK’s contribution to the group is the summarizing statement. Likewise, when she says, “So we label that T,” she is not questioning but summarizing. MR’s statement “Meters,” while hardly profound, clarifies the previous “1.5”. Such clarification statements are an integral part of the elaboration process but do not precisely fit into any of the four Toulmin categories.

In this segment of dialog, there is a variety of statements. Some statements (Claims, Grounds, Warrants and Backings) clearly follow the Toulmin categories, and some statements do not. (For a summary of the Toulmin Claim, Grounds, Warrants, and Backings categories, refer to Table 2-4, page 58). Assuming that students do use grounds, warrants and backings to support claims, and assuming they also make requests, clarify and summarize statements, I defined additional categories to account for these other statements.

I defined these additional statement categories after a thorough analysis of what students actually said and did in the Problem 4 session. Categories such as Summarizing, Skeptic, and Consensus checking, as well as Challenges, result from the assigned roles based on the Johnson Model. In addition, I noticed that utterances like “OK”, “What”, and “umm” don’t fit any category, and I realized I was seeing statements of Clarification, Support, Acknowledgment, and Request. So, in addition to the four Toulmin statement categories, I defined nine additional statement types. These additional statement types augment the Toulmin statement types summarized in Table 2-4. The examples are drawn from the At The Gasthaus problem to illustrate the various statement types. My new definitions and some example statements are summarized in Table 2-5 (page 59). The section of transcript shown above in its “raw” form is shown coded in Table 2-6 (page 60). I have added annotations, explanations and diagrams to clarify the students’ discussion.
It is very important to note that these non-Toulmin categories were not determined before the analysis began, but grew out of the analysis. That is, the coding scheme originated within the students discussions (Gustafson, 1977). The result of the process was nearly 3000 lines of coded transcripts for the 14 groups. In the following two chapters there will be numerous examples of coded transcripts.
 
Statement Type    Definition    Example

Claim

A claim is a fundamental assertion central to the argument at hand.

Warrants, grounds, and backings establish the validity of a claim.    For an object in equilibrium, a claim might be, “It's not moving so it's in equilibrium.”

Warrants

Warrants make reference to general physical principles or laws. Warrants also apply to mathematical principles such as resolving vectors into components. Newton's Laws of motion are warrants fundamental to physics. Statements like “because it's in equilibrium, the forces must all add to zero” are examples of warrants that derive from these physical laws.

Grounds

Surface features of a problem or the physical data give meaning to a claim and are classified as grounds.    “The sign weighs 100 N,” or “the angle is 30 degrees,” are data from the problem itself. In problem-solving groups, a gesture at a diagram can also serve as a ground. (Toulmin also refers to grounds as data.)

Backings

Any appeal to an authority such as the textbook, teaching assistant, or professor is a backing.    “That's how she did it in class.”


Statement Type    Definition    Verbal Cue Examples

Consensus checking

(Ck) These statements ensure there is agreement among group members before proceeding to another point.    "Are we agreed on this?" “So is that OK?”

Summary

(Sm) Summary statements restate a claim. Ideally a summary statement ends each episode. These statements may be used in concert with consensus checking (Ck) statements.    "So we're saying here that..." Some groups frequently use summary statements in the form of a question, "So, this is the x-component of the force?"

Skeptic

(Sk) The skeptic inhibits too quick agreement on any point by asking "why" questions and by demanding warrants, grounds and
backings for any claims made.    "What?"
“Why?”
“Why is that?”
“Why do you say that?”
Encouraging
(En) This often occurs as an informal, often humorous, energizing of the group when it gets stuck. Groups lacking in fundamental physics knowledge make
frequent use of this type of statement.    "Hey, this makes sense!" "Wow!"
“Great.”

Challenge

(Ch) A request for proof of a statement or a disagreement with a statement.    The most simple challenge is "No." Other examples include, "I don't think that's right," or,
"No, it should be..."

Clarifying

(Cl)Clarifying statements further explain an idea by means of analogy or by restating in different but equivalent words. These statements do not necessarily carry the idea forward or develop it further.    A student who is talking aloud while writing may say, "1.5," meaning a distance. This clarifies the written material. Another student may add, "meters," which further clarifies.

Support

(Sp) Supports statements previously given.    "Yeah," "Yes," or "OK."

Acknowledgment

(Ak) These statements recognize a previous statement without making any judgment or qualification.    These include "Umm" and sometimes "OK" if the response can be interpreted as not being in support of the previous statement. Context, tone of voice, or body language help
suggest this difference.

Request

(RQ) The Request (RQ) code precedes any request or question. RQCl requests clarification, RQW requests a Warrant. RQ may be answered with another claim, warrant, ground, backing, or clarification. "What?" is the simplest example of a request. However, "What?" could indicate a challenge if tone of voice or a gesture suggests that interpretation.

Additional Quantitative and Qualitative Data

Quantitative data on the groups’ written solutions was available to me. This data relates solely to the written solutions and I view the written solution primarily as a source of insights into what the groups were talking about. Table 2-7 (page 62) lists this quantitative data for the 14 groups. The percent of the total points possible is listed, and the mean and standard deviation are given at the bottom of each column. There are two types of data listed. First, there is an objective evaluation by an independent evaluator (Dr. Bruce Palmquist) of how closely each written solution follows the steps of the problem-solving strategy. Table 2-8 (page 63) lists the criteria used to judge the written solution. It is important to note that only the data on “Generating a Physics Description” is included in the tabulated scores. Hence, the total possible points is six. These evaluation scores are the only quantitative, objective measure of the completeness of their physics description in terms of following the prescribed problem-solving strategy.

Second, the grade the teaching assistant gave their solution is reported in the second and third columns of Table 2-8. The two columns break down the grade on the physics description portion of the problem and on the remainder of the problem. The percent of possible points is shown. For example, Group 5A received 75% of the points possible on the Physics Description portion, but only 50% of the possible points on the remainder of the problem. I did not use these grades the students received on the problem in forming my opinions about how well they functioned as a group.

SUMMARY

At this point, the data collection and initial analysis was complete and I was ready to embark upon answering the research questions. The research process to this point consisted of these procedures:

Videotaping 14 groups solving six physics problems (“raw” data).

Transcribing the videotapes.

Editing the transcripts with annotations to written solutions and the videotapes.

Identifying the Toulmin statements of Claims, Grounds, Warrants, and Backings.

Identifying new statement categories based on the cooperative group roles and the problem-solving strategy.

Characterizing each group qualitatively and their written solutions quantitatively.

This “processed” material comprises the “data” in this research. Next I turned to a major part of the analysis. Since my research question involves looking for patterns, I realized I could not look for patterns within single statements. Rather, I had to look for patterns in a group of statements. That group of statements became known as “the episode”. In order to answer the research questions, another analysis tool was used, the flowchart. Both of these tools will be discussed in the next chapter.

CHAPTER 3 PATTERNS WITHIN A GROUP

Overview

The very nature of a qualitative case study makes this research an exercise in discovery. As I worked out the procedures, I had some outcomes in mind, but the true nature of the outcomes did not come into focus until I actually attempted to answer the research questions. As I addressed the research questions, I continuously devised new ways to look at the data. Hence the usual distinction between “method” and “results” is not always clear and sharp. The “patterns” emerged very slowly.
At every turn, there was a surprise embedded in the students’ conversations. The whole project was much like Forest Gump’s box of chocolates: I never knew what I was going to get. Thus, although the following discussion of “Outcomes” discusses the research questions one at a time, it will be clear that additional “procedures” evolved as I attempted to answer the questions. The reference point of my own subjective interpretation of the outcomes will play a large role in this chapter and the one that follows.
This chapter examines argument co-construction within individual groups. Before patterns or similarities common to all fourteen groups can be examined, each separate group must be examined. It also is necessary to demonstrate that these groups are engaging in the process of argument co-construction.

ARGUMENT CO-CONSTRUCTION

A major hypothesis behind this study is that these fourteen groups are engaging in argument co-construction. The superior product of the group’s solution over an individual’s problem solution is in itself evidence that argument co-construction is occurring. Yet, the solution could be primarily the work of one individual in the group. Thus I asked myself, “What are the criteria for group argument co-construction? How can it be recognized?” These are fundamental questions and there are two points to be made in answering them.

First, the choice of the Toulmin argument structure presupposes there is an argument. If there is an argument, then within a group’s transcript, there should be Claims that are supported by Grounds, Warrants, and Backings. That is, the discussion should contain recognizable, classifiable components of the Toulmin structure. Likewise, these components, particularly Grounds, Warrants, and Backings, should appear in repeating patterns. Brown and Palincsar recognized this as an important component of the Toulmin structure: “Adults’ argument structure follows certain identifiable sequences. For example, an argument is usually supported by data; these data are then supported by warrants for their pertinence and credibility, and finally further backing is provided in terms of recourse to general law (Brown and Palincsar, 1989; p. 404).” This is the argument portion of argument co-construction.

Second, there is co-construction of the argument. the discourse should be connected, that is, group members listen to each other and discuss the same claim. Claims should not always be made and supported by the same group members, that is, claim- making shifts among group members. When there is a disagreement, group members resolve the disagreement in a reasonable manner. That is, they resolve conflicts of ideas without arguing or criticizing the another person. In short, the conversation should progress in an orderly manner and all group members should participate.
To summarize, these are the criteria for argument co-construction in the Toulmin structure: (1) Claims are supported by Grounds, Warrants, and Backings, (2) Grounds, Warrants, and Backings appear in repeating patterns, (3) Group members listen to each other and discuss the same claim, (4) Claim-making role shifts among group members, and (5) disagreements are resolved in a reasonable manner.

When I first began looking at the transcripts, I saw that students made Claims, supported them with Grounds, Warrants, and Backings, and made the other types of supporting statements that are identified in Table 2-5 (page 59). As an initial analysis, I plotted the “flow” of the discussion from one student to another. The conversations were like a tennis game with the ball moving from one player’s court to another. I noticed that the groups seemed to discuss a single idea for a short period of time. Typically, there was a Claim and supporting statements. In most of the groups, there was progression from idea to idea. That is, the discussion was in “chunks.” The students were discussing the problem and interacting with each other in an episodic fashion. This led me to see their conversation in terms of episodes.

Episodes and Interaction Analysis

For the last forty years, many instruments have been devised to analyze classroom interactions. The emphasis has been almost entirely on the teacher-student interaction.

This emphasis arose out of a need to understand what happens in the classroom. It was thought that in order to prescribe instructional materials or strategies, the teacher-student relationship had to be observed and understood. While this dissertation research is concerned with student-student interactions in groups, it is important to understand the limitations of interaction analysis as found in the teacher-student research.
One of the best known instruments was the Flanders System of Interactional Analysis. It endeavored to provide a measure of the degree to which a teacher's verbal behavior in the classroom was student-centered. Other interaction scales included the Roark Dimensions of Psychological Distance, Hill Interaction Matrix, and the Teaching Strategies Observation Differential. These instruments have three things in common (1) they focus on a limited aspect of classroom behavior, (2) each one has a bias, and (3) they measure only what actually occurred in the classroom (i.e., statements) without making any qualitative judgments (Amidon and Hough, 1967; Stanford and Roark, 1974).

In general, all classroom observation instruments, schemes, or techniques focus on exact, prespecified behaviors on the part of the teacher or the student. Because the observation instruments are linked to specific behaviors, they often tally verbal statements made by the student or the teacher. One might, for example, define categories such as elaborating, explaining, or defending, and then classify student statements into those categories. Typically, a researcher would then count the number of times a student gave the teacher an explanation, and perhaps evaluate the validity of the explanation.

Comparisons could then be made between different students, teachers, or instructional strategies by using variables related to the types of statements.
It is important to note that this type of analysis is appealing because of its quantitative nature. It allows for a factor analysis (ANOVA) of classroom behavior on the part of the students and teachers. This method, however, is self-limiting. In a summary of research on classroom observations, Delamont and Hamilton (1984, pp. 8- 10), gives seven reasons why the teacher-student interaction coding schemes are inherently limiting. These warnings are appropriate to student-student schemes as well.

The aim of coding schemes using prespecified categories is to produce numerical and normative data. ...the data produced tell the reader about 'average' or 'typical' classrooms, teachers, and pupils.

Systematic observation schemes typically ignore the temporal and spatial context in which the data are collected. Divorced from their social and temporal (or historical) context in this way, the data collected may gloss over aspects relevant to their interpretation.

Prespecified coding system are usually concerned only with overt, observable behaviour. They do not take directly into account the differing intentions that may lie behind such behaviour. ...by concentrating on surface features, interaction analysis runs the risk of neglecting underlying but possibly more meaningful features. [emphasis added]

Prespecified coding systems are expressly concerned with what can be categorized or measured. They may, however, obscure, distort or ignore the qualitative features which they claim to investigate by using crude measurement techniques or having ill-defined boundaries between categories.

Prespecified coding systems focus on small bits of action or behaviour rather than global concepts.

[These] category systems may assume the truth of what they claim to be explaining.

By placing arbitrary (and little understood) boundaries on continuous phenomena category systems may create an initial bias from which it is extremely difficult to escape.

Brown and Palinscar (1989) continually point out the necessity of the "fine- grained" analysis to understand the process of cooperative learning. "Unfortunately, the written reports, on the outcomes of Jigsaw [a specific cooperative learning method] leave us somewhat in the dark about the learning process... A further look at Jigsaw and other cooperative learning methods...should concentrate on what students actually do in these groups" (Brown and Palinscar, 1989, p. 402, emphasis added).

If there is argument co-construction, then students in the group should participate in a dialog about one idea, and then the next idea, and so on. They would not make isolated statments. The dialogical nature of the group suggested looking at groups of statements. For this study the episode is the unit of analysis. An episode is made up of students' individual statements, but it contains a complete thought. And it turns out, episodes are not a new idea in education research. Smith and Meux used episodes to categorize student-teacher interactions in an analysis of classroom behavior (Smith and Meux, 1970; Smith, Meux, Commbs, Nuthall, and Precians, 1967). In their scheme, an episode is "defined as one or more exchanges which comprise a completed verbal transaction between two or more speakers. A new episode is determined by a shift in what the speakers are talking about, which may be a new aspect, or part of a topic or a complete change of topic" (Sandefur and Bressler, 1971, p. 23). This definition of an episode is essentially the same as the definition I am using for this research. However, I defined the episode in my research before actually reading this prior research.
 
Episode Delineation

When does a new thought take over? This is the basis of defining an episode.

Defining the episode is one of the most difficult, and subjective, aspects of this analysis. Groups may use recognizable episode delineators, such as "OK, what's next?" There also might be a change of speakers. In a rigid analysis, using the Toulmin categories, there would be a series of statements leading up to the claim. But an episode does not necessarily begin or end with a claim. For example, an episode may begin with a request. Since the order of events in an episode is a part of the research questions, I tried to not prejudice the outcomes by saying all episodes must begin (or end) with a claim.

Group 4A provides an example of a coded, delineated discussion. Further examples will be drawn from this group and other groups’ discussions. Many of the examples will reappear later. This repeated use will parallel my increasingly deeper understanding of what the students were doing. In Table 3-1 (page 75), and the tables that follows, the group’s discussion is presented in the first column (Dialog), the statement identification (Coding) is in the second column, and my comments are in the third column. These comments will help the reader understand my interpretation of what the group is doing. When appropriate, the third column will contain diagrams taken from the group’s written solution. If a diagram changes substantially I will show it as it exists at the beginning of the transcript segment and then at the end. The lines are numbered sequentially for easy reference. In some cases, I broke sentences by a single speaker into separate lines during my initial editing (e.g., 42, 43, 44, 45, 46). In some cases, as I was coding statements, I realized there was a significant shift in the thought and broke the sentence into smaller fragments (e.g., 41, 41B, 41C). This second numbering method makes it easier to follow one person’s statements. The first numbering method, makes it easier to count lines or, as will be seen in the next chapter, construct flowcharts. In some cases I have included a few lines preceding or following the episode of interest in order to make the discussion more sensible. Table 3-1 (page 75) illustrates how the statements in the “raw” transcript discussed on page 55 were coded and episodes delineated. The reader should note that some longer transcript excerpts span two pages. Often I will discuss an idea and then reproduce the corresponding transcript excerpt.

The students in Group 4A had just written down the “Question” and identified the principles they will use (equilibrium and torque). In this specific segment they are beginning to draw the free-body diagram. In the first episode (lines 39 to 43) they identify the diagrams (“free-body” and “force thingy”) they will draw in the Physics Description. Member MK, who is the Recorder, makes the Claim (line 43) that they will need to draw the bar before they can draw the free-body diagram. From identifying the necessary diagrams in this episode they next go to a discussion of which forces to include on their free-body diagram. This was a change of thought, and thus the new episode takes over in line 44. The statement “And this is a weird force,” is difficult to interpret.

It could be a reference to the normal force, which, in my experience, some students call a “weird” force. It could also be a part of an interrupted statement, “And this is a weird force diagram.” Because the students begin a discussion of specific forces in line 49, I believe this was a cryptic reference to the normal force.

In line 29, member RM takes over the conversation and indicates the location of the weight of the bar. This is a new episode for two reasons. First, there is a change of speaker. Second, now they begin a discussion of a specific force, whereas in the previous episode, they were talking about all the forces in general. From this discussion of the weight of the bar, which ends in line 61, they then went on to talk about the weight of the mug, the normal force, and the tension. In Table 3-3 (page 79) the translation of their free-body diagram is evident in the force-vector diagram they drew earlier. Thus, in this transcript segment there are three episodes:  In lines 39 to 43 they discuss which diagrams to include in the Physics Description. The conversation turns to which forces to include on the free-body diagram in lines 44 to 48. Finally in lines 49 to 61, they discuss in detail one particular force, the weight of the bar. It is interesting that as they move from the general to the specific and the discussion becomes more detailed, their episodes become slightly longer.  To summarize, there are two primary cues that a new episode has begun: (1) a change of thought or topic, and (2) a change of speaker.  When these two cues are both present, the new episode is easiest to define.

Examples of Coded Discussions

Examples from Groups 4A, 4B, 4C, and 4D will further illustrate the episode definition process, as well as the details of each group’s discussion. In each case, I will draw upon the four reference points. The videotapes and transcripts continue to be the primary reference point. The quantitative data such as standing in class will help form a better picture of the groups and the students in them. The written solutions provide the diagrams that illustrate the problem solutions. My own subjective opinions, as well as those of the transcription assistant and my adviser, provide the fourth vantage point for viewing these groups.

Example of Group 4A

I will now turn to some more examples from Group 4A. In an appeal to a "higher authority" (Backing) they note how the professor solved a similar problem in class. Note, in the example in Table 3-2 (page 78), how RM plays the skeptic role, and how MR responds to his inquiry.  RM is the "silent partner", and his academic standing in the class is lower than the two women. He does, however, contribute important concepts to the discussion or voices support for ideas of others. RM’s lesser degree of participation in this group is a part of this group’s dynamic. It was frequently observed that in groups of two women and one male, particularly where the male's academic standing is lower that both the women, the male student frequently was less active. Nonetheless, RM's contributions are an important part of the solution of this problem.

The other “reference points” provide additional insights. The class average on this group problem was 7.46 (Out of 10 total points, o = 1.80). Their teaching assistant graded their problem solution at a perfect 10 points (z = 1.46). Their written solution to the problem was very neat and clear and generally followed the five-step problem solving strategy. I looked at the group as a whole, subjectively evaluating their functioning.

While MK is the most involved of the three students, both MR and RM made significant contributions. Upon reading the transcript, one sees MK making many statements related to her role as the Recorder. She is very conscientious about checking for consensus among the group members before continuing to the next step. For example, she says at one point, "OK, so don't we draw this here...we draw tension here, right?" (Line 108, Table 3-2, p. 78) This is a part of the role of the Recorder/Checker. Although RM is the least involved of the three, and although he identifies himself as the Energizer for the group, it is clear he adopts the role of Skeptic through the types of questions he asks of the other two students. His skeptical statements can be as simple as "Not like that, do you?" (Line 111, Table 3-2). Group member MR expresses her discomfort with the problem when she says, "Not real confident [about] what's going on in class." 

This group worked very well together. In fact, it was one of the best functioning groups observed in this study. This assessment of the group was initially made when viewing the videotape for purposes of annotating and correcting the transcript. The transcription assistant, who by this time had transcribed several groups' problem sessions, also commented that this was a very good group. It was clear that Group 4A would be the prototype "well-functioning" group. There are the instances where one student completes another student’s thought. These observations eventually lead me to believe there is a co-construction of their problem solution.  (Interestingly enough, about one year after this data was collected, MK worked as a part-time student assistant in the science education group.)

Example of Group 4C

Group 4C consisted of two men and one woman and provides a stark contrast to Group 4A. Members JV and EW are males, SV is a female, foreign student. (This was determined from her name on the log sheet and her slight accent from the videotape audio. Her “King’s English” was impecable and there was no difficulty communicating with her group mates.) EW was identified as the recorder, JV as the Skeptic, and SV as the Manager. Their cumulative exam scores at the time of this group problem indicate JV and EW are from the middle third of the class and SV is from the lower third. Compared to the class mean at the time of this problem, their aggregate standing was very close to the class average (z = .06). Their written solution to Problem 4 was given 7 points by the teaching assistant, slightly below the class mean of 7.46 (z = -.26).

The students in Physics 1041/1042 were introduced to the roles of the manager, recorder, and skeptic. Probably because this aspect of cooperative learning was not stressed in the course, most groups were somewhat cavalier about using the roles. This group is very casual about their group roles, and do not take time to sort out who is doing what, as is seen in Table 3-6 (p. 84; lines 21-23). This casualness also subverts the step by step process of the problem-solving strategy. Instead of stopping after each step, and checking on their progress, they tended to jump around. Although they seem to follow the steps of the problem solving strategy, they are "backfilling" at some places. In this example (Table 3-6), they try to include pictures so as to better their score (Line 27). All cooperative groups will, at times, use humor. Here, (lines 30-34) humor is injected to alleviate their frustration with the problem. This does, however, prohibit any physics from being discussed.
Even with one viewing of the video tape, it becomes clear that SV is a forceful leader of the group and essentially dominates the process. She is more than a manager in the way it was defined for the students, as is seen in Table 3-7 (page 85). She effectively took charge of the group and made sure the group followed the problem-solving strategy. Her commanding presence is best seen in line 39. The off-task talk may have been a reaction of the others to her order giving. Her dialog with EW in the lines that follow (Table 3-7, page 85) are typical of how he was shut out of the solution.

Throughout the first half of this session, members JV and SV tended to hold their own two-way conversation exclusive of EW. When there was a three-way conversation, frequently, SV acted as a mediator between JV and EW. That is, she talks to JV and EW more than JV and EW talk to one another. The effect of this is that EW, the recorder is left to solve the problem by himself without any significant input from SV or JV. For a brief time near the end of the problem session, EW moved to the middle position at the table where both SV and JV could see what he was writing.
When this research was in the planning stage, much thought was given as to how one would recognize a poorly functioning group. When all four groups that made up the fourth taping session initially were viewed, it was clear that Group 4C was an excellent example of a poorly-functioning group. The contrast with Group 4A is remarkable. The transcription assistant made an initial comment on the poor functioning. He noted the difficulty in transcribing this session due to the rapid fire nature of their conversation.

The segment of their dialog in Table 3-9 (page 87) also illustrates how problematic it is to define episodes for this group. It is difficult to determine if a new episode begins in line 90 or 92. Member SV’s thoughts come so fast, they do not seem to connect with what comes before or after. Member JV’s comment in line 93 doesn’t clarify the situation. If lines 90 to 93 comprise one episode, then they are an episode in which there is minimal co-construction occuring.

Several factors may have contributed to this group’s dysfunctional situation. Based on cooperative learning research and practice, I can hypothesize three specific factors: First, the seating arrangement prohibited true face-to-face interaction. Second, the gender imbalance may have caused EW (male) to tune out SV (female). Third, the relatively homogeneous ability of the group may have inhibited skeptical questioning. An interesting question about this is, why, despite such poor functioning, does the group still produce a partially correct, only slightly below-average written solution to the problem? One reason may be that their written solution is largely the work of EW who probably had the best grasp of the three group members of the physics of the problem.

Group 4C provides an excellent example of the lack of co-construction. In Table 3-9 (page 87), the group illustrates how they jump from thought to thought. There is no resolution of which diagram they are constructing and which forces belong on the diagram. The discourse is disorderly and does not flow from person to person or from thought to thought. The Claims often are not supported with appropriate Grounds, Warrants, and Backings. Hence I came to the conclusion that Group 4C is the one group of the 14 that did not consistently engage in co-construction. Their lack of co- construction will be seen in discussing the other research questions as well. We came to refer to Group 4C as “the different group.” These kinds of observations led me to believe that this group is not co-constructing their argument.

Example of Group 4B

Group 4B consisted of one woman (KJ) and two male students (LP and JH).

Based on their individual cumulative exam scores at the time of this problem session, this was a below average group. (z = -.81). All three students were full-time, residential students at the University. JH was the Recorder. Due to an audio problem, the usable portion of the videotape began as they were starting the “Plan” section of the problem solution. However, several portions of the physics description are contained in the analyzed segment. Students frequently retroactively worked on the physics description.

This group’s free-body diagram was not clearly drawn. Although the tension, weight of the mug, weight of the sign, and normal vectors are indicated, the diagram is very cluttered and it is not clear which label is attached to which vector or vector component (cf. Table 3-10, page 92). This group did not draw idealized, free-body and force-vector diagrams. This omission hindered their proper identification of the variables.
In the “Physics Description”, they wrote only one quantitative relationship: Weight x distance = torque

They neglected to also write Newton’s Second Law. However, in the approach section, they wrote S F = 0 and S i = 0, which of course is a mathematical statement of the basic principles of statics. They identified target variables i1 and i2. The vector identified as i1 clearly refers to the tension in the support cable. It is not clear if the other target variable i2 refers to the normal force or a vertical component of a resultant force at the point of contact between the strut and the wall.

They proceed to solve these two equations for the two unknowns and find the answers in units of newton-meters, which of course is not a unit of force but of torque. (i1 = 1500 N•m and i2 = -150 N•m) In other words, they find the torques, but not the forces on the bar, which was the question posed in the problem statement. Although in the dialog seen in Table 3-10 they say “t”, on their diagram they drew “i” which only compounded their confusion.
Despite some poor physics, Group 4B managed to interact well with one another.

The dialog in Table 3-11 (page 93) illustrates how they request and give clarification of ideas. The motioning with the pen (Line 105 ff.) serves to visually clarify the idea. Of the 22 statements in this section, KJ makes 8, JH makes 8 and LP makes 6 statements. That is, their conversation is well-balanced and all students are participating equally.
Their group functioning is rather good. The reason for this can be seen in the manner in which they elaborate on ideas. Each student is an equal partner in the solution. Although there is co-construction of the argument, they are basing the construction on some erroneous physics, and that resulted in a poorer grade on the problem.

Example of Group 4D

Group 4D consisted of one woman (CB) and two male students (ME and ST).

Based on their individual cumulative exam scores at the time of this problem session, this was a below average group (z = -.81). All three students were full-time, residential students at the University. ST was identified as the Recorder. This group also lacked some physics knowledge due to ST being the only one in class the day before when the instructor did another similar problem as an example.

ST:    Were you, you were in class yesterday, weren't you? ME:    No.
CB:    You're the only one. [i.e., who was in class]
ST:        Oh, and I don't remember this. [covers face with palms] ME:    I was drained, I was drained two days...

Such self-disclosures were useful in identifying poorly prepared groups. Their lack of physic knowledge influenced their approach to solving the problem. In the dialog segment in Table 3-12 (page 96), the students coax the teaching assistant into giving a hint. Although the teaching assistants were discouraged from directly answering questions, they would occasionally intervene to make a point about the physics. Dialog sections in which there was considerable teaching assistant intervention were not included in the analysis procedure. This segment is included here as an example of a teaching assistant intervention.

An error in the construction of the free-body diagram eventually led to a mistake in the writing of the equations for the equilibrium condition. They neglected to place the weight of the strut in the center of the strut. Later, when finding the torques, they used a moment arm of 2 meters instead of 1.5 meters.

One reason this group produced a fairly acceptable solution to this problem was because they interacted very well as a group and despite the lack of physics knowledge, and the previously mentioned error, managed to get several portions of the problem correct. The section of dialog in Table 3-14 (page 99) illustrates their attention to the details of the physics description. The difficulty with this diagram, of course, is that the tension, normal force and weights of the mug and strut do not act all at the same place as they have drawn it. In their “Plan”, they thus made a error when applying Si = 0, and as has been noted, use a moment arm of 2 meters instead of 1.5 meters. Even so, there is a good use of warrants to support their argument. Their fatal error was the perpetual problem with novice problem solvers: an improperly drawn free-body diagram! Later, they drew an incorrect force-vector diagram because of this error in the free-body diagram.

This group did not engage in any overt summarizing, consensus checking or skeptical questioning activities. This may be due to the lack of identifying the role of skeptic with a specific individual. However, their discussion proceeds from one thought to another in an orderly fashion. This is seen in their discussion of the free-body diagram where individual thoughts in the discussion of the forces are connected to one another (lines 18-22, Table 3-13, page 97). The discussion of where to locate the weight connects to the next thought about the existence of a torque due to this weight. In all of the previous examples, there are several references to the surface features of the problem, that is, the observable data. These data, such as the weight of the strut or mug, are used by the students to construct the free-body and force-vector diagram. While constant reference to these features may seem redundant, they actually are an important facet of their solution.
 
Although Group 4D made some fundamental errors in constructing their force- vector diagram, they equally shared in the solution of the problem. Their use of humor, which on the surface seems to alleviate tension, also serves to encourage the group and keep the solution progressing. Their grade on this problem was 6 points. (Although their force-vector diagram was in error, their plan and execution correctly translated the diagram they drew into two equations. An incorrect force-vector diagram correctly translated received more points than an incorrect translation of an incorrect diagram.)

Extension to The Remaining Groups

The procedure just described in detail for these four groups was next extended to include the remaining 10 groups. Several quantitative “data” and qualitative “descriptions” help to form a picture of each group. These data and descriptions are a form of triangulation, but not in the strict sense of using different data to explore the same hypothesis. Rather these measures and descriptions allow viewing the groups from slightly different perspectives. They also helped me to think about the issue of validity. Note again that the four basic “reference points” from which I made these descriptions are: (1) The videotapes and transcripts, (2) quantitative data from the video log sheets and course records, (3) written problem solutions, and (4) the subjective observations by myself, the transcription assistant, and my advisor.
I analyzed each remaining transcript in the manner just described. I examined the group solutions through the “Plan” because I discovered that often some important aspect of the physics surfaced during this portion of the solution. The most difficult aspect of the task was defining episodes. These principles were followed:

New episodes begin with a new thought and/or a new speaker.

Code about 15 to 20 episodes per group solution, if possible.

Examine the solution through the “Plan” portion of problem-solving strategy.

When a single-factor ANOVA was run on the number of lines per episode for each of the 14 groups, a small significant difference was found (F = 1.94; p = .03, Fcrit = 1.76). I ran this test to check whether or not my episode definition may have changed in time. While statistically significant, I decided this was not meaningful in terms of the definition of episodes. It rather reflects the slight difference between “talkative” (e.g., 2A and 5C, o >1) and “untalkative” (e.g., 3A, 6B, 7A, o < 1) groups. Thus looking at which groups had a o > ±1 convinced me that I had not significantly changed my episode delineation during the several months in which I did this.

Summary

The results of this initial analysis provided evidence that these groups are engaging in argument co-construction. The criteria I stated for argument co-construction were largely met in at least 13 of the 14 groups on a consistent basis.

 Does this occur?             Answer    
Claims are supported by Grounds, Warrants, and Backings    YES
Grounds, Warrants, and Backings appear in repeating patterns    YES
Group members listen to each other and discuss the same claim    YES
Claim-making role shifts among group members    YES

Moreover, the groups’ discussions are episodic, that is, statements are not isolated from each other and there is a logical flow to the discussion. More compelling evidence for co-construction became clear later as I looked at other aspects of these groups. Since argument co-construction is occurring, it made sense to move ahead to the second research question and to look for patterns in the argument co-construction within a group.

The basis of this question is the finding that the students in these groups are co- constructing an argument. It could also be stated as “Does a group adopt a particular, persistent manner in which they co-construct their argument?” This suggests looking for repeating patterns across several of their episodes. To determine a group’s pattern of argument co-construction, I flowcharted all of a group’s episodes that focused on the physics description. Then I looked for features common in all their episodes. These features then became the pattern for that group. As will be seen, there are discernible patterns. The following discussion will illustrate the flowchart process.

Episodes that dealt primarily with group functioning (“Who wants to be the recorder?”) or tangential discussions (“Wasn’t that last quiz something else!”) were omitted from this analysis. In many cases, these kinds of statements are embedded in episodes that deal with the physics and these episodes were not a priori omitted. In some sessions, the teaching assistant interrupted the whole class or the group being taped.
These episodes were omitted from the analysis if the intervention or interruption was a major part of the episode.

Episode Flowcharts

Many statements related to the steps of the problem-solving strategy. Although these appear to be procedural, they usually contain important physics. For example, Group 4A paid close attention to the strategy as is seen in the episode in Table 3-16 (p. 104). Their statements about the Target Variable and the Question being asked in the problem are integral parts of the problem-solving strategy (For a summary of the problem-solving strategy, refer to page 33 in Chapter 2). These steps are designed to help the group determine what variables they are to solve. Hence they do relate to the construction of an adequate physics description, and I decided they should not be excluded from the analysis.
The flowchart of this episode (Figure 3-1, page 105) contains a set of symbols, one for each statement type. Each symbol is numbered and the number is the same as a line number in the corresponding episode transcript. The statement abbreviations are the same as those in the transcripts and the speaker’s initials are also included. The arrows indicate the “flow” of the argument. There are some important points to be made about the interpretation of the flowcharts. First, the lines indicate a connection with what preceeds or follows a given symbol. If the thought was left “dangling,” the arrow would not terminate on another symbol. Second, if a statement refers to back to a prior, non- sequential statement, a dotted arrow is drawn to show the connection. That is, if the Support in line 36 referred back to the Claim in 31, a dotted arrow would connect those symbols.

This episode flowcharting procedure was followed for all 14 groups, giving me a collection of approximately 120 flowcharts (out of 291 coded episodes). Some flowcharts were later combined or subdivided as further analysis indicated either a continuation or change in the thought. I excluded a priori any episodes in which the teaching assistant was a speaker in the group, or in which the teaching assistant interrupted the entire class with information on the problem. I also excluded episodes in which the students digressed to talk about everything from their grade on the last quiz to the weekend hockey games. In the end I had 112 flowcharts for the 14 groups. Then, armed with both episode transcripts and the flowcharts, I tried to look for repeating patterns within each groups episodes.

Prototype Flowcharts

To determine if a group had a self-consistent pattern of argument construction, I decided to determine if it was possible to characterize a group in terms of a “prototypical pattern.” That is, on the average, what does this group do?  When attempting to determine a “prototypical pattern” for a group, the focus was on their use of Claims, and their support for Claims with Grounds, Warrants and Backings. In most groups where there was a consistent use of such statements as Clarification or Support, those statements were considered to be secondarily important, but still diagramed. Few groups in this study used Skeptical or Summarizing statements, and so these statements tend to be prominent in the groups (2A, 4A, 5C) that use them more consistently.

Another important factor in determining the pattern and drawing the prototype was a subjective reading of the group’s discussion. Early on in the research, before I ever drew a flowchart, I characterized each group with one short phrase and wrote a brief descriptive paragraph for each group (See Table 2-9, page 65). I readily acquired a feel for the personality of a group, the kinds of statements they prefer, and the order in which they use them. In a sense the transcripts, and the video tapes functioned much like an anthropologist’s “informants.” Table 3-17 summarizes the number of physics description episodes coded and flowcharted for each group.  It was my intention for about eight to ten episodes to determine a prototype, but the case of five groups, less than eight were available and the reasons for this are noted in the table. I excluded episodes in which there was a lengthy off-task discussion or the teaching assistant intervened or interrupted the class. These kinds of discussions tended to occur at the beginning or end of the class period.

Multiple Claims in an Episode

When looking at the 14 prototype flowcharts, I discovered something perplexing. There were multiple claims in some prototypes. This is seen the in the prototype example from Group 4D (Figure 3-3, page 109). I went back to the transcripts and examined them with reference to the episode flowcharts. I found that episodes had multiple, additional claims that seemed to change the essence of the initial claim. In other words, these additional claims were elaborating the original claim. I realized I needed a better way to handle additional claims that would somehow discern differences between the various claims. Group 4B provides an excellent example of the problem (Table 3-18, page 111). The claims in 107, 111, 112, and 114 seemed to be slightly modifying what went before. Moreover, the claim in 113, has an inherent challenge within it. I had expected to find challenges (for example, line 119), but I could not determine how to handle the implicit challenge in 113. This challenge was imbedded in a claim.
A flowchart of this episode (Figure 3-4, page 112) did not reveal any direct clues. The flowchart does reveal a succession of claims, all slightly related, but still new claims. I gradually came to the realization that I was seeing two additional types of claims, one slightly modifying the prior claim, the other (e.g., line 113) giving a new, alternate idea.

With the idea of modifying and alternate claims in mind, I returned to all the fourteen groups and examined the transcripts and the flowcharts for every episode. I examined each additional claim in an episode as to its function within the episode. There were indeed two types of additional claims. Considering how they were used, I named them the Alternate Claim and the Modified Claim.

The Alternate Claim and Modified Claim have several distinctive features. Their characteristics, which will be discussed in more detail, are:

An Alternate Claim follows a Claim or a Modified Claim and presents a contradictory or alternate idea to the initial claim. Either an explicit Challenge precedes an Alternate Claim, or a challenge is implicit within the Alternate Claim. Alternate Claims are sometimes stated as a question. Other verbal cues include “Perhaps we should consider..,” “On the other hand..,” “I think it’s...”

A Modified Claim follows a Claim or an Alternate Claim. A Modified Claim offers an additional, non-contradictory idea(s) to the initial claim, and serves to clarify, extend or elaborate upon the initial claim. A Modified Claim is usually stated in a non-confrontational manner compared to an Alternate Claim.

I also revised the flowchart symbology to reflect this new insight. In addition to symbols representing the Modified Claim and Alternate Claim, I added dotted lines to show the connection of the Modified Claim or Alternate Claim to the original Claim if the connected statements were not sequential. Figure 3-5 (page 114) illustrates the new symbology. In this key flowchart, the dotted line from the Support statement in 26 to the Challenge in 24 indicates the support was for the challenge. It is not uncommon to find these intervening statements. I did not draw a dotted line if a statement relates to the immediately preceding statement. Table 3-19 (page 114) summarizes the abbreviations used for the statement types. These appear in the flowcharts in the abbreviated form.

Group 4A, a single prototype group, had a very predictable pattern, and their pattern will be discussed later in this chapter. Figure 3-8 is their prototype flowchart. In one episode, they used a Modified Claim, but it was not typical of them. Group 4A was so predictable, that I could have drawn this prototype based on only a few of their episodes. Group 4A’s most predictable feature is their end of episode summarization. In the prototype flowcharts, the statements are numbered sequentially, and the statement type is written out, instead of being abbreviated.

Co-Construction of the Argument Revisted

A major theme of this research is that the students in a cooperative problem- solving group are co-constructing the solution to the problem. There is preliminary evidence that this is occurring in at least 13 of these 14 groups: It is possible to use the Toulmin argument structure to analyze the discussion, the conversations proceed episodically, and the flowchart analysis shows connected discourse. Although in Group 4C, the individual episodes are somewhat coherent, their episodes typically do not connect logically to one another and thus their prototype flowchart shows an arrow leading to nothing (Figure 3-9, page 120). One of the things I noticed when drawing the flowcharts was that particular students made particular kinds of statements. For example, in Group 4D, member ST made all of the Modified Claims. To explore co-construction of the argument further, I examined the pattern of who is making the Alternate Claims and Modified Claims. Does the same person make the Modified or Alternate Claim as the original Claim, or is it someone different? Four patterns were noticed.

Who makes Claims Shifts among Members

The claim-making role shifts between students. That is, the maker of a Modified Claim is usually not the maker of the original claim as is seen Group 4B’s Episode 16, Table 3-21 (page 116). Members JH and KJ make Modified Claims and Alternate Claims following LP’s original Claim (see Table 3-26, page 128, Group 2D, for an additional example). However, when the Alternate or Modified claimant is the same person as the original claimant, other students had intervening supporting statements, as this example from Group 4A (Table 3-22, p. 123) illustrates:

Active Members Make Claims

The making of claims is fairly uniformly distributed among the “active” students in a group. Students who make an overall high percentage of the statements, also tend to make most of the claims. Also, members who make original claims, tend to make Modified or Alternate Claims. Students who are “quiet” tend to make fewer claims.

Table 3-23 (p. 125) illustrates these points. Only the flowcharted episodes are considered. The “Statements” column tallies the number of flowchart symbols for each member of the group. The percentage is the percent that number of statements is of the whole. It should be noted that the “Total Claims” are a part of the “Statements” column. That is, member TD in Group 2A, made 15 statements, six of which were claims. If statements and Claims were uniformly distributed, one would expect to see each student making 33% of the statements in a group of three, or 25% of the statements in a group of four. This is seldom the case. A qualitative analysis of the groups can explain the departures from this norm.

Although in Group 5C, member MP makes only 49% of the overall statements, she makes 77% of the Claims. This is because MP, a dominant member of the group, makes a lot of Claims, but she does not support them with other statements. Group 4A member DC was a very quiet student who rarely contributed Claims. He and member MK made statements supporting MP’s Claims. Likewise, in Group 4D, student CB makes no claims. He missed class the day before this problem session and was poorly prepared. In Group 2D, member SU made 21% of the overall statements, but made no claims. Group 2D member SU is an Asian student, and there may be a cultural-based “deferring” to the other two non-Asian students. There was only one person (out of the 45 members, 40 unique individuals) in one group (out of the 14 groups) where a student, AW in Group 5A, made only Modified Claims or Alternate Claims, and no original Claims.

Six of the students appear in two different taping sessions, one from the first quarter (Physics 1041) and one from the second quarter (Physics 1042). Are students consistent in their group participation or do they agree to a group dynamic? As seen in Table 3-24 (page 126), these six students appear to have a fairly consistent degree of participation in terms of the percentage of total claims compared to total statements.
Student KF in particular is very consistent by making no claims in either session. (The table is sorted by Member and then by the session and quarter in which they were taped.)

“Quiet” Students Do Contribute

What about the students who make fewer claims in proportion to their overall statements? Their contributions to the group frequently are a Request for some sort of support or Clarification. This frequently takes the form of skeptical questioning. No one illustrates this point better than member RM of Group 4A. An example (Table 3-25, p.
127) from their discussion shows how his question serves to initiate a clarification of the point MR and MK make about the location of the vectors on the free-body diagram. While his skepticism does not correct an obvious error, it does serve to reinforce the point MK and MR make about the location of the vectors. This is an important function when supporting claims.

Role of a Dominant Student

If there is a dominant student in the group, that person tends to make most of the claims, either original or Modified and Alternate. Groups 2D, 5A, and 5C can be classified as having a dominant student where one person made more than 60% of the total claims. It is important to note that this definition of dominance is in terms of the number of claims a student makes within the group. Another type of dominance I observed is what I would call “social” dominance. That certainly was the case in Group 4C, where SV effectively dominated the group and frequently made sequential claims. In this example from Group 4C, EW tries to make a claim, but JV and SV sidetrack the discussion. This group is my example of an absence of co-construction. It may be that the social interaction among the three students was a contributing factor to this.

SUMMARY

The theme of this chapter has been the patterns of argument co-construction within individual groups. I can now make four major claims related to the first two research questions.

First, students discussed the problem in an episodic manner and episodes were used as a unit of analysis. The group members’ statements are not isolated from each other and there is a logical flow to the discussion.

Second, four criteria for argument co-construction were found in 13 of these 14 groups on a consistent basis, and in one group, 4C, only occasionally. These criteria are:

Claims are supported by Grounds, Warrants, and Backings

Grounds, Warrants, and Backings appear in repeating patterns

Group members listen to each other and discuss the same claim

Claim-making role shifts among group members

Statements of Support, Acknowledgment and Encouragement keep the conversation moving forward and allow students to “transfer” the conversation to another student.

Third, these 14 problem-solving groups appear to adopt not only a group “personality,” but a group dynamic that leads to predictable, or at least repeating, patterns of argument co-construction. The differences in these patterns is evident in the manner the groups further explain, elaborate and defend their ideas. Twelve of the 14 groups had a single prototype pattern and two groups had dual patterns.

Fourth, additional Claims within a group’s episodes can be accounted for by defining the Alternate Claim and Modified Claim.

An Alternate Claim follows a Claim or a Modified Claim and presents a contradictory or alternate idea to the initial claim. Either an explicit Challenge precedes an Alternate Claim, or a challenge is implicit within the Alternate Claim. Alternate Claims are sometimes stated as a question. Other verbal cues include “Perhaps we should consider..,” “On the other hand..,” “I think it’s...”

A Modified Claim follows a Claim or an Alternate Claim. A Modified Claim offers an additional, non-contradictory idea(s) to the initial claim, and serves to clarify, extend or elaborate upon the initial claim. A Modified Claim is usually stated in a non-confrontational manner compared to an Alternate Claim.

These are the argument co-construction patterns within individual groups. The next step is to look at commonalities between the groups. In the next chapter, I will discuss how the groups are similar to each other. That analysis will particularly focus on the Alternate Claim and Modified Claim.
 

CHAPTER 4 PATTERNS BETWEEN GROUPS


Overview

The “answers” to the research questions are somewhat interactive. For example, in discussing the second question (Chapter 3), I came to some partial conclusions about the Modified Claims and Alternate Claims. A more comprehensive examination of the role of Modified Claims and Alternate Claims is given in this chapter which addresses Research Question 3. This chapter examines additional patterns common to all 14 groups. The emphasis in this chapter is on the groups’ use of the Alternate Claims and Modified Claims. Although there are 16 prototype patterns of argument co-construction in the 14 groups, I will show there are several common features between those 16 patterns and the 14 groups.

It may be helpful to quickly review the definition of the episode, since it is the persistent feature of this analysis. An episode is “defined as one or more exchanges which comprise a completed verbal transaction between two or more speakers. A new episode is determined by a shift in what the speakers are talking about, which may be a new aspect, or part of a topic or a complete change of topic” (Sandefur and Bressler, 1971). Tables 2-4 (page 58) and 2-5 (page 59) summarize the statement types used in the episode coding. When the fourteen groups were analyzed, it was found that twelve of them could be characterized individually with a unique prototypical episode, and two groups exhibited two prototypical patterns. That is, I was able to reduce each of the groups to predictable patterns for a particular group.

QUESTION 3. ARE THERE SIMILARITIES IN THE ARGUMENT CO-CONSTRUCTION PATTERNS BETWEEN THE FOURTEEN GROUPS?

To answer this question, I looked at various aspects of the group’s argument construction, and thus this research question has several important sub-questions. First, since the heart of the Toulmin structure is the Claim, I closely examined the process of making a claim, specifically the order of events in an episode. Secondly, as has been noted, Modified and Alternate Claims are important statement categories, and thus I looked at how these additional claims elaborate the original claim. The discussion of Modified Claims and Alternate Claims includes several important subsections, including an analysis of the role of requests, as well as discussions of creative controversy and conflict avoidance. Finally, in the Toulmin argument structure, Ground, Warrants and Backings provide support for Claims, and I will illustrate how these are used to support the claims.

QUESTION 3A. DO THEIR ARGUMENT CONSTRUCTIONS BEGIN OR END WITH A CLAIM?

In a strict Toulmin analysis of an argument, the Grounds, Warrants and Backings lead to the claim. Hence the first sorting of the groups’ prototypes asked where in the process the claim occurs. Of the 16 patterns, only two patterns lead to the claim (Figure 4-1, page 135). Both groups 3B and 7A used supporting statements before and after their claim. Groups 3B and 7A were both groups of four. On the other hand, most groups (12 groups, 14 patterns) begin with the claim and then support it.

It should be noted this “beginning with the claim” may be in part due to the manner in which the episodes were defined. A new episode was defined to begin when a new thought occurs. In general, a claim introduces a new thought, and this new thought begins the new episode. I asked, “Is it natural for a group to begin with a claim?” Group 4A provided an insight into this question. Their episodes were very easy to code and define, in part because they usually ended with a summarizing statement. The next statement after summarizing statement was a new claim, and a new thought, and hence a new episode began.

Our prior research showed that groups of three worked better than groups of four for physics problem solving (Heller and Hollabaugh, 1992). Since both 3B and 7A are groups of four, perhaps claim making is inhibited, or slower to take shape, in larger groups. But, the other group of four (2A) did not follow this claim-last pattern. Group 2A had a better ability mix (LLMH) than Groups 3B or 7A (both LLLM). That may have caused an “interaction” between group size and ability mix. Even so, I am reluctant on the basis of only two “samples” to come to a general conclusion that claim making is inhibited in groups larger than three.

QUESTION 3B. WHAT ROLES DO MODIFIED CLAIMS AND ALTERNATE CLAIMS PLAY IN THE ARGUMENT CO-CONSTRUCTION PROCESS OF THESE GROUPS?

The original research question as stated in Chapter 1 (page 11) was: What roles do challenges to the original claim play in the argument construction process of these groups? Two observations of the groups’ patterns prompted an adjustment of the question. First, it is apparent there are very few overt challenges. Second, the Modified Claims and Alternate Claims appear to fulfill the role of challenging and changing the original claims.
When examining the prototype flowcharts, it became apparent that some groups use Alternate Claims and some do not. As is shown in Figure 4-2, seven of the 16 patterns (5 groups) typically contained Alternate Claims, and nine of the 16 patterns (9 groups) do not. I will first discuss the five groups that use the Alternate Claims and then the nine groups that use few Alternate Claims, but do use Modified Claims.
Figure 4-2. Alternate and Modified Claim Use.

Why do Some Groups Use Alternate Claims?

Creative Controversy

There are very few direct challenges in all of the analyzed episodes in all the 14 groups. In fact, the challenge symbol does not appear in any prototypical episode flowchart. That is, direct challenges are rare in these 14 groups. Part of the reason for this lies in the definition of Alternate Claim: A challenge is implicit within the Alternate Claim. What is the challenging aspect of the Alternate Claim in the argument co- construction process?

My hypothesis is that the Alternate Claim is a form of controversy or “creative conflict.” The Alternate Claim affords a means of challenging an idea (claim) without directly challenging the individual stating the idea and hence it is an example of creative controversy (Johnson, Johnson, & Holubec, 1988; Johnson and Johnson, 1992). I found no example in which one student directly and overtly challenged or criticized another student for his or her opinion. There were disagreements over ideas, as is seen in the numerous examples of Alternate Claims, but the disagreements were handled with sensitivity to the other students and without direct personal confrontation.

The Johnson model of cooperation in groups proposes four decision-making processes (Johnson and Johnson, 1987; pp. 224-226):
“Controversy exists when one student’s ideas, information, conclusions, theories, and opinions are incompatible with those of another, and the two seek to reach an agreement.”

“...debate exists when group members argue for positions that are incompatible with one another and a winner is declared on the basis of who presented the best position.”

“Concurrence-seeking occurs when members of a decision-making group inhibit discussion to avoid any disagreements or arguments and emphasize agreement; there is a suppression of different conclusions, an emphasis on quick compromise, and a lack of disagreement with in a decision-making group” “Individualistic decision making occurs when isolated individuals independently decide on a course of action without and interaction or consultation with each other; each decision maker comes to his or her own decision.”

Conflict Avoidance

To understand more fully the role Alternate Claims play in creative conflict, the issue of conflict avoidance must be addressed. In physics, destructive interference of light waves leads to dark patterns on a viewing screen, and constructive interference of light waves causes a bright pattern. “Evidence supports the argument that a cooperative context aids constructive controversy” (Johnson and Tjosvold, 1989, p. 57). Creative activity occurs when controversy or conflict in a group is constructive, and the outcome is greater than any individual contribution. In general, the students in this study engaged in constructive controversy (with Group 4C being the notable exception). The degree of constructiveness, however, was largely dependent on the composition of the group:

Whether there are positive or negative consequences depends on the conditions under which controversy occurs and the way in which it is managed. These conditions and procedures include: 

the goal structure within which the controversy occurs, 

the heterogeneity of decision-makers, 

the amount of relevant information distributed among decision-makers, 

the ability of decision-makers to disagree with each other without creating defensiveness, and

the perspective taking skills of the decision-makers (Johnson and Tjosvold, 1989, p. 56).

Lack of these factors may help explain less adequate physics descriptions.

Prior research showed a general reluctance of students in a physics problem- solving group to make overt challenges or to disagree with each other (Heller and Hollabaugh, 1992). (We have dubbed this “Minnesota niceness,” and it may in part be culturally conditioned. Other college faculty in Minnesota have noticed this phenomena.)

“The second reason is that most organizational personnel seem to lack the interpersonal skills and competencies needed to stimulate controversy and ensure that it is managed constructively.”

“Thirdly, the discussion of conflicting ideas may not be a standard and common practice within decision-making and problem-solving situations due to fear and anxiety most people seem to fear in conflict situations. A general feeling in our society is that conflicts are bad and should be avoided, and consequently many people believe that an effective organization is one in which there are no conflicts among members.”

The avoidance of conflict has been discussed at great lengths in the social psychology literature (cf. Deutsch, 1965; 1973). The overwhelming impression is that people generally do whatever is necessary to avoid direct conflict, particularly when the goal of a group of people is cooperation and they are in a classroom setting. When I discussed conflict avoidance with a colleague who teaches interpersonal communication, he mentioned the interesting idea that the more cohesive a group, the greater the tendency to engage in “conflict” (Gaskill, 1995; Barker, Wahlers, & Watson, 1995). I do not believe these groups were particularly cohesive, and in fact may have experienced more forces of disruption than of cohesion. As I mentioned earlier, the two week residence time in a particular group may not be adequate for good cohesion.

This lack of cohesion can be explained in the context of these 14 groups.

Structuring academic controversies is an integral part of learning to be effective in a cooperative learning group (Johnson, Johnson and Smith, 1990). In an ideal situation, students would experience group activities that build the skills, both interpersonal and problem solving, necessary for effective, constructive controversy. Students in this course were not taught these skills. Thus, when constructive controversy occurs in these groups, it is somehow instinctual or may even arise as a part of the problem-solving strategy and the group roles, which encourage skepticism and critical questioning.

It also may be that these groups avoided conflict because they lacked one or more of the five characteristics of the Johnson model. The attention to the details of structuring these groups fell by the wayside as the teaching assistants attempted to balance their teaching duties with their own academic work. Of the 14 groups, three were groups of four, not three members. The performance heterogeneity of the groups was not balanced in 9 of the 14 groups.  There was a gender imbalance in 9 of the 14 groups.  As seen in the transcripts, fixed furniture greatly inhibited face-to-face interaction in Group 4C. Typically, groups left the room after finishing the problem, without engaging in any group processing. These “structural defects” would all inhibit group cohesion and hence tend to inhibit direct conflict. However, this may also be serendipitous.

Summary

The tendency of these problem-solving groups to avoid direct conflict may help explain the roles of the Modified Claim and Alternate Claim. The isolated Modified Claim may be a lower level of creative controversy. When the Modified Claim leads to an Alternate Claim, the Modified Claim is a first step in the creative controversy process. The Alternate Claim, with the inherent challenge, is a more obvious form of creative controversy. It allows students to disagree with one another without being critical of one another. That is, the Alternate Claim is a crucial step in the process of argument co- construction. This suggests the making of Modified and Alternate Claims are not ends in themselves, but steps in a process of argument construction. They are a high-level form of elaboration. But, conflict avoidance may only be a part of the reason for using Alternate Claims instead of direct challenges. To further explore the reasons for using Alternate Claims, I turned to the groups that do not use them.

Why Do Some Groups Not Use Alternate Claims?

It is apparent from Figure 4-2 (page 136) that seven of the prototype patterns contain Alternate Claims and nine do not typically contain Alternate Claims. In other words, five of the fourteen groups use Alternate Claims and the other nine groups typically do not use Alternate Claims, but do use Modified Claims. In the previous sections Why do Some Groups Use Alternate Claims? and Creative Controversy, I suggested the Alternate Claim and Modified Claim are a form of creative controversy. The view of the Modified Claim in that discussion is that the Modified Claim is a step leading to the Alternate Claim. However, there are Modified Claims that stand isolated from Alternate Claims. Thus, another way to phrase the theme of this section is, “Why are there Modified Claims without Alternate Claims?” The answer appears to lie in the quality, that is the degree of correctness, of the original claim.

Consider this scenario: A student makes a Claim. Two or more other students hear that Claim. One or more of the hearers may interpret the Claim to be correct, ambiguous or “fuzzy” in some aspect, or incorrect. Based on their interpretation, these other students may propose a Modified Claim or an Alternate Claim. One could hypothesize that the prompt for the Modified Claim or Alternate Claim resides in the quality of the original Claim. There are four possibilities. First, original Claims that are correct and completely clear should not need to be modified and they should be accepted by the rest of the group and perhaps followed by Grounds, Warrants, and Backings.

Second, original Claims that are correct, but perhaps incomplete or ambiguous (“fuzzy”), should be followed by a Modified Claim that brings clarity to the original Claim. Third, original Claims that are very ambiguous should be followed by a Modified Claim, or in an extreme case by and Alternate Claim. The Alternate Claim would follow in a case where the original Claim is misunderstood by the hearer(s). Fourth, and finally, original Claims that are totally incorrect should be followed by Alternate Claims that provide the correction to the initial Claim. In all four cases Grounds, Warrants, and Backings should also appear in the episode.

To test this hypothesis relating Claim correctness to the use of Modified Claims and Alternate Claims, I re-analyzed the Claims, Modified Claims, and Alternate Claims of all 14 groups. I rated the original Claims as essentially correct or slightly unclear (+1), very ambiguous or “fuzzy” (0), or totally incorrect (-1).  I also tabulated the type of claim (Modified Claim or Alternate Claim) that follows the original claim. If a Claim was followed by an Alternate Claim or an Alternate Claim and a Modified Claim, I counted that as an Alternate Claim following the Claim. If the original Claim was followed only by a Modified Claim, then that was counted as a Modified Claim following.

These results support the hypothesis that the groups’ use of Modified Claims and Alternate Claims is related to the degree of correctness or quality of the original Claim. Modified Claims and Grounds, Warrants, and Backings tend to follow and clarify mostly correct initial Claims (21/28 or 75%). Modified Claims follow and slightly “tweak” an ambiguous initial Claim (30/46 or 65%). Sometimes Alternate Claims follow an ambiguous initial Claim (16/46 or 35%). Alternate Claims follow incorrect initial Claims (15/21 or 71%).

Based on these results, I hypothesized further about why some groups consistently use Alternate Claims and some rarely do: Groups that have a consistent use of Alternate Claims should also have more incorrect original claims. To test this hypothesis, I determined an overall Claim quality rating for each group by averaging the correctness rating for each group’s set of original Claims. An average closer to 1.0 would indicate a majority of correct Claims. A number near 0.0 would indicate either mostly ambiguous Claims or an even mix of correct and incorrect. A number near -1.0 would indicate mostly incorrect claims. In Table 4-12 (page 160), Claim Quality is compared with the groups’ use of Modified Claims and Alternate Claims. Instead of sorting the table by group, or if they use or do not use Alternate Claims, I sorted them by the “Claim Quality.” The MC and AC entries were determined by what the group typically does.

Furthermore, I divided the 14 groups in to three subgroups: The top five, the middle four, and the bottom five in terms of claim quality. An interesting pattern emerges from this ordering.

The top five groups in terms of Claim quality (7A, 4A, 3B, 3A, 5C) use only Modified Claims. Groups 7A and 4A, which have the same claim quality use Modified Claims to extend and elaborate ideas in an original correct Claim (For example, Group 4A, Table 4-17, p. 166). Of the five groups (4B, 2B, 5B, 5A, 2A) that have the lowest Claim quality, four of these groups use Alternate Claims after incorrect initial claims (For example, Group 4B, Table 4-15, page 164). The middle four groups, 2D, 6B, 4C, and 4D were more difficult to interpret. Group 4C was most difficult to classify because this group again exhibited their frenetic behavior by having no persistent pattern of how Alternate Claims followed Claims.
There are some other observations about these three groupings shown in Table 4- 12 (p. 160). First, it is not surprising to find Groups 3A and 7A using only Modified Claims. Their argument construction generally leads to a Claim. The Modified Claims they use immediately follow the original Claim and serve to slightly clarify the original Claim. It is interesting to hypothesize that if their Claims were less correct, their episodes would have extended far beyond the original Claim and would contain more Modified Claims and perhaps Alternate Claims. I probably would not have then found their arguments ending with a Claim, but rather found their episodes beginning with a Claim and followed by elaboration.
Second, it is interesting that groups 3B and 7A are both groups of four and typically do not use Alternate Claims. It may be that the challenging aspect of an Alternate Claim is inhibited in a problem-solving group larger than three. This hypothesis is consistent with prior cooperative group problem-solving research (Heller and Hollabaugh, 1992). However, Group 2A, another group of four, typically does use Alternate Claims and I can not generalize this hypothesis on the basis of two out of three groups. This possible inhibiting of challenges in argument co-construction in groups of four, however, warrants further investigation.

Third, I determined the presence of a “dominant” student in each group by looking at Table 3-23 (page 125). Three Groups (2D, 5A, and 5C) of the fourteen had a student who made the large majority (Š60%) of the claims. These “dominant” students appear in each third of the claim quality ranking (although Group 5C and 2D are essentially identical). That suggests that the presence or absence of a dominant student in the group doesn’t appear to directly influence quality of the original Claims. However, if the groups are sorted by the “Use AC” column, then dominant students are not found in groups that use Alternate Claims. This finding suggests that the making of Alternate Claims may be inhibited in a group with a dominant student. It is important, however, to note that the working definition of “dominant” is based on the overall percentage of claims a student makes. Three factors may contribute to the number of claims a student makes: The group members personalities, their social interaction and their knowledge of physics. I did not find any pattern between the students’ overall class performance (Low, Medium, High) and whether or not they were dominant in the groups. Groups 2D and 5A were balanced (LMH) and Group 5C had a slight imbalance (LMM). In this context, dominance therefore seems to be a personality factor. Group 4C, which had a “socially dominant” member follows this pattern as well. The use of Alternate Claims (usually by SV) after correct Claims (usually by EW) seems to be based more on how these students interacted with each other and not on Claim quality. This may also reflect their lack of co-construction.

This finding means that lower quality initial Claims tend to lead to Alternate Claims, whereas higher quality initial Claims tend to lead to Modified Claims. Thus, the Alternate Claim provides a group with a means to rectify incorrect Claims. This, I believe, is a part of creative controversy: A student disagrees with another student who makes an initially incorrect Claim. The Alternate Claim allows for verbalization of the disagreement and correction of the Claim. The Modified Claim, on the other hand, allows a group to fill in the details of an initially correct claim or to clarify a “fuzzy” initial claim.

The Role of Requests

A very common statement type in this whole study is the Request. I wondered: Are the Modified Claims and Alternate Claims spontaneous, or does a request initiate them?    I found that the answers to Requests may clarify a statement (“Meters?” “Yes, meters.”) or may actually elicit an additional Modified Claim, Grounds, Warrants, and Backings, or other support statements. Table 4-14 summarizes the results of Requests in the 14 groups. The single phrase “What?” was interpreted as a request for clarification, whereas “What force is acting?” was interpreted as a request for a claim.

Summary

There are four general claims I can now make concerning the role of Modified Claims and Alternate Claims in argument co-construction.

The Alternate Claim

generally occurs in a “controversy” model of decision-making,

is a higher form of creative conflict,

generally corrects original claims that are wrong or “fuzzy”,

and allows students in problem-solving groups to disagree while avoiding direct conflict.

The Modified Claim

can elicit another Modified Claim or Alternate Claim; it can serve as a bridge or link to the Alternate Claim,

may prompt the ideas that cause the maker of the Alternate Claim to state the Alternate Claim,

is a lower-level form of creative conflict when it stands in isolation of an Alternate Claim

and refines, clarifies or elaborates original claims that are slightly “fuzzy” or incomplete.

All Claims are steps in a “reconceptualization” process.

Within episodes, the claim-making role shifts between students, that is the Modified Claimant and the Alternate Claimant are not the same as the original Claimant.

The claim-making role is fairly uniformly distributed among the active students in a group. Usually all students make claims.

When there is a dominant student, he or she tends to make most of the claims.

All students in the group are involved in the argument co-construction, that is, even the “quiet” students contribute.

Although groups engage in both types additional claims, they tend to have a typical controversy pattern which uses either Alternate Claims or Modified Claims. This pattern is related to the correctness of the original claim.

The grounds for this finding are:

Direct challenges are rare.

13 of the 14 groups followed a Controversy Model of Decision Making. 

9 of the 13 groups following the Controversy Model did not use Alternate Claims but do use Modified Claims. 7 of these 9 groups have a higher initial Claim quality. Modified Claims are requested in these groups.

5 of the 13 groups following the Controversy Model use Alternate Claims. These 5 groups have a lower initial Claim quality. Alternate Claims are never requested in any group.

At least one Modified Claim and one Alternate Claim are found in every group. 

To summarize, when a Modified Claim stands in isolation from any Alternate Claim, it seems to fulfill a refinement role, what a physicist might call a “tweaking” of the original claim. Again, the very definition of the Modified Claim may be partially responsible for this “tweaking” function: A Modified Claim presents a variation on the prior claim, but does not present a totally new idea. This also seems to be the function when the Modified Claim appears in an episode with an Alternate Claim. Alternate Claims are more likely when the original Claim is somehow erroneous. The presence or absence of a dominant student in a group does not seem to directly influence quality of the original Claim, but the making of Alternate Claims may be inhibited in a group with a dominant student.

QUESTION 3C. DO THE GROUPS HAVE A PREFERENTIAL MEANS TO SUPPORT ARGUMENT CONSTRUCTION?

The previous discussion of Question 3b on the Modified Claims and Alternate Claims lead to the conclusion that these are a fundamental part of the argument co- construction process. Yet, these types of statements are insufficient by themselves.

Argument co-construction also needs substance that connects the co-construction to the statement of the problem as well as the laws and principles of physics. This is the function of the Grounds, Warrants and Backings.

Figure 4-5 (page 171) shows the sorting the 16 argument co-construction patterns into categories based upon the use of the basic Toulmin categories. Whether or not there are additional claims, the groups preferred to use Grounds and Warrants to support their claims. Of the 16 patterns, five predominantly exhibit Grounds and Warrants, and seven show the use of Grounds, Warrants, and occasional Backings. And, Group 4C, of course, tended to not have any further elaboration following the additional claims.

Overemphasis on the surface features of a problem could lead to a heavy use of Grounds. The opposite of this, reliance mainly on Warrants and Backings, leads to an interesting situation where the physics is not adequately described in the context of the particular problem. Important bits of data are omitted and the solution becomes flawed. For example, this is seen in Group 3A. This group attempted to model their solution after other problems they have seen in the textbook, the professor has done in class, or problems the Teaching Assistant has done in recitation. Compared to all 14 groups, they had a much higher use of Backings (z = 2.12) and a much lower use of Grounds (z = - 1.12). Their physics description was initially weak because they did not have an adequate “picture” of the problem. What ultimately “saved” Group 3A, and earned them 10 points on the problem, was following the problem solving strategy in a fairly precise manner. An example shown in Table 4-18 is from early in their solution, and ultimately they did draw upon some “data” in the problem. It might be that this initial discussion about other problems they have seen led them to the inclusion of proper Grounds. Even so, they relied very heavily on modeling their solution after other examples.

Groups like 3A that use many Backings tend to have some lack of physics knowledge, due to inadequate preparation, missing class, or other factors such as lacking the pre-requiste course. When these groups use Backings, they show a hierarchical preference to model their solution after first the professor, then the textbook, then the teaching assistant. Table 3-12 (page 96) illustrates how Group 4D sought intervention from the teaching assistant. One member of Group 4D had missed class the day before the group problem. In general I found that groups that use many Backings are “in trouble” or lack self-confidence. Groups, such as 4A, that use fewer Backings (z = -0.45) seem to be very confident they can solve the problem.

The two groups that had dual argument patterns, 4B and 5B, both use Alternate Claims, but in slightly different ways. When Group 4B uses a Modified Claim preceding an Alternate Claim, there is additional elaboration in the form of Grounds, Warrants, and Backings.
However, when there is no Modified Claim preceding an Alternate Claim, there are no additional Grounds, Warrants, and Backings. It seems as if the Modified Claim elicits the Grounds, Warrants, and Backings. Perhaps the more “tentative” nature of the Modified Claim made necessary these support statements.

Group 5B, on other hand, typically used no Modified Claims, and sometimes their Alternate Claims were elaborated and sometimes they were not. In other words, I cannot accurately characterize Group 5B’s use of supporting statements. This lack of elaboration and support may account for a persistent misuse of the terms orbital velocity and escape velocity. 

Summary

Based on this analysis of Grounds, Warrants, and Backings, I can now claim these groups are supporting their argument co-construction with statements that would be expected in a Toulmin argument structure.

The grounds for this claim are:

7 of 16 patterns contain additional Grounds, Warrants and Backings.

5 of 16 patterns contain Grounds and Warrants.

1 pattern contains mostly Warrants and Backings.

3 patterns contain little additional elaboration or support.

Groups that use Backings tend to prefer the professor.

SUMMARY

In this chapter I explored the similarities in the argument co-construction between these 14 problem-solving groups. Chapter Five will discuss the implications of these findings for present and future research and practice in science education. The emphasis was on the use of the Modified Claims and Alternate Claims, the role of requests, as well as creative controversy and conflict avoidance. Since the Toulmin structure includes Grounds, Warrants, and Backings, I also examined how groups use these types of statements. There are three major findings.
 
First, most of the patterns (14 of 16 patterns, 12 of the 14 groups) begin with a claim.

This is different from a strict Toulmin argument pattern where the claim is the end result of the argument construction.
Second, the Alternate Claim and Modified Claim were discussed in Chapter Three in the context of the need to account for additional claims within an episode. In this chapter, the discussion looked more closely at the role these claims played in the argument co-construction process. There are four major claims I can make about the Alternate Claim and Modified Claim.

The Alternate Claim

generally occurs in a “controversy” model of decision-making,

is a higher form of creative conflict,

generally corrects original claims that are wrong or “fuzzy”,

and allows students in problem-solving groups to disagree while avoiding direct conflict.

The Modified Claim

can elicit another Modified Claim or Alternate Claim; it can serve as a bridge or link to the Alternate Claim,

may prompt the ideas that cause the maker of the Alternate Claim to state the Alternate Claim,

is a lower-level form of creative conflict when it stands in isolation of an Alternate Claim

and refines, clarifies or elaborates original claims that are slightly “fuzzy” or incomplete.
 
All Claims are steps in a “reconceptualization” process.

Within episodes, the claim-making role shifts between students, that is the Modified Claimant and the Alternate Claimant are not the same as the original Claimant.

The claim-making role is fairly uniformly distributed among the active students in a group. Usually all students make claims.

When there is a dominant student, he or she tends to make most of the claims.

All students in the group are involved in the argument co-construction, that is, even the “quiet” students contribute.

Although groups engage in both types additional claims, they tend to have a typical controversy pattern which uses either Alternate Claims or Modified Claims. This pattern is related to the correctness of the original claim.

The grounds for this finding are:

Direct challenges are rare.

13 of the 14 groups followed a Controversy Model of Decision Making.

9 of the 13 groups following the Controversy Model did not use Alternate Claims but do use Modified Claims. 7 of these 9 groups have a higher initial Claim quality. Modified Claims are requested in these groups.

5 of the 13 groups following the Controversy Model use Alternate Claims. These 5 groups have a lower initial Claim quality. Alternate Claims are never requested in any group.

At least one Modified Claim and one Alternate Claim are found in every group.

Because all students are involved in the claim-making process, co-construction of the argument is occurring. That is, the solution to the problem is a group solution and not the product of the best individual in the group. This supports prior research (Heller, Keith, and Anderson, 1992). The Modified Claim can be spontaneous or be offered in response to a request for clarification. A lack of group cohesion and conflict avoidance may inhibit direct challenges.

Finally, the Modified Claim and Alternate Claim are one means of supporting a Claim.

Grounds, Warrants, Backings provide “color” and base the problem on the stated parameters and
 
the principles of physics. Most groups use Grounds, Warrants, and occasional Backings to support their arguments. Lack of adequate Grounds leads to an inadequately described problem, and a reliance on Backings for support. Groups that use Backings tend to prefer the professor over the teaching assistant or textbook.
 
CHAPTER 5 DISCUSSION OF RESULTS

RESEARCH SUMMARY

This chapter will briefly summarize the research setting and procedures and then discuss the meaning of the results. The purpose of this research was to undertake a systematic “fine- grained examination” of what students actually do in cooperative problem-solving groups. The research explored the process of argument co-construction, using Stephen Toulmin’s argument structure, in fourteen cooperative problem-solving groups while they completed their qualitative analysis of physics problems. The physics courses used for this study were the algebra-based, introductory two-quarter sequence Physics 1041 and 1042, taught winter and spring quarters 1991, at the University of Minnesota.
Students were taught a problem solving strategy (Heller and Hollabaugh, 1992). They were expected to use this five-step strategy in the recitation period when solving a complex problem as a cooperative group. The students were introduced to the four roles of Manager, Recorder, Skeptic and Engergizer. It was intended that there would be a heterogeneous mix within a group in terms of the students’ performance in the class (high, medium, low). Also, it was intended that there would be all groups of three, and no groups where the number of men was greater than the number of women. However, the teaching assistants only occasionally followed this plan. In reality, of the 14 groups in this study, there were 11 groups of three, only four of these groups met the gender criteria, and of these four, only one met the ability composition criteria.
 
Students in a group worked a “practice” problem one week, and then worked a problem for a grade the following week. Students were then reassigned to new groups for another two- week period. During each of the two quarters, there were four graded problems, offering eight data collection opportunities. Only six of these problems were used in this study.

The data collection and analysis consisted of these procedures:

Videotaping 14 groups solving six physics problems (“raw” data).

Transcribing the videotapes.

Editing the transcripts with annotations to written solutions and the videotapes.

Identifying the Toulmin statements of Claims, Grounds, Warrants, and Backings.

Identifying new statement categories based on the cooperative group roles and the problem-solving strategy.

Characterizing each group qualitatively and their written solutions quantitatively.

This “processed” material comprised the “data” in this research. In order to answer the research questions, another analysis tool was invented, the flowchart.

In order to determine the patterns of argument construction, I flowcharted all of a group’s episodes that focused on the physics description. The flowchart of each episode contains a set of symbols, one for each statement type. Each symbol contains the transcript statement number, statement type, and speaker. Then I characterized a group in terms of a “prototypical pattern”. That is, on the average, what does this group do? When attempting to determine a “prototypical pattern” for a group, the focus was on their use of Claims, and their support for Claims with Grounds, Warrants and Backings. I discovered there were multiple claims in the prototypes. I found that episodes had multiple, additional claims that seemed to change the essence of the initial claim and elaborated the original claim. Based on how they were used, I named them the Alternate Claim and the Modified Claim.
 
I will now make major “claims” related to the research questions. Just as these 14 groups preferred, I will state the claim and then follow it with grounds, warrants and backings, and modified claims. The theme of Chapter Three was the search for self-consistent the patterns of argument co-construction within individual groups.

Claim 1. Thirteen of these fourteen problem-solving groups engaged in argument co- construction as they completed a physics description of a problem. There are two findings that support this. First, students discussed the problem in an episodic manner and episodes were used as a unit of analysis. The group members’ statements are not isolated from each other and there is a logical flow to the discussion. Very few episodes contained statements that did not relate to previous statements by other group members. Second, four criteria for argument co-construction were found in 13 of these 14 groups on a consistent basis, and in the other group, 4C, only occassionally. These criteria are:

Claims are supported by Grounds, Warrants, and Backings

Grounds, Warrants, and Backings appear in repeating patterns

Group members listen to each other and discuss the same claim

Claim-making role shifts among group members

Statements of Support, Acknowledgment and Encouragement keep the conversation moving forward and allow students to “transfer” the conversation to another student.

Claim 2. There are self consistent argument co-construction patterns within a group.

Two findings support this claim. First, these 14 problem-solving groups appear to adopt a group dynamic that leads to predictable, or at least repeating, patterns of argument co-construction.

The differences in these patterns is evident in the manner the Groups further explain, elaborate and defend their ideas. Twelve of the 14 groups had a single prototype pattern and two groups had dual patterns.
 
Second, additional Claims within a group’s episodes can be accounted for by defining the Alternate Claim and Modified Claim.

An Alternate Claim follows a Claim or a Modified Claim and presents a contradictory or alternate idea to the initial claim. Either an explicit Challenge precedes an Alternate Claim, or a challenge is implicit within the Alternate Claim. Alternate Claims are sometimes stated as a question. Other verbal cues include “Perhaps we should consider..,” “On the other hand..,” “I think it’s...”

A Modified Claim follows a Claim or an Alternate Claim. A Modified Claim offers an additional, non-contradictory idea(s) to the initial claim, and serves to clarify, extend or elaborate upon the initial claim. A Modified Claim is usually stated in a non-confrontational manner compared to an Alternate Claim.

All groups contain at least one Alternate Claim and one Modified Claim somewhere in their analyzed episodes. The claim-making role shifts among the students. This also supports the claim of co-construction of an argument.

Chapter Four explored the similarities in the argument co-construction between these 14 problem-solving groups. The emphasis was on the use of the Modified Claims and Alternate Claims, the role of requests, as well as creative controversy and conflict avoidance. Since the Toulmin structure includes Grounds, Warrants, and Backings, I also examined how groups use these types of statements. The general claim in this chapter is: Claim 3. There are similarities in the argument co-construction patterns between the fourteen groups. Three subsequent modified claims support and clarify this initial claim.

Claim 3a. The groups’ argument co-constructions usually begin with a Claim. Most of the patterns (14 of 16 patterns, 12 of the 14 groups) begin with a claim. This is different from a strict Toulmin argument pattern where the claim is the end result of the argument construction.
 
Claim 3b. Modified Claims and Alternate Claims play a direct role in the argument co- construction process of these groups and allow groups to engage in creative controversy and to correct initially incorrect or ambiguous claims. The Alternate Claim and Modified Claim were discussed in Chapter Three in the context of the need to account for additional claims within an episode. In Chapter Four, the discussion looked more closely at the role these claims played in the argument co-construction process. There are four major findings about the Alternate Claim and Modified Claim.

The Alternate Claim

generally occurs in a “controversy” model of decision-making,

is a higher form of creative conflict,

generally corrects original claims that are wrong or “fuzzy”,

and allows students in problem-solving groups to disagree while avoiding direct conflict.

The Modified Claim

can elicit another Modified Claim or Alternate Claim; it can serve as a bridge or link to the Alternate Claim,

may prompt the ideas that cause the maker of the Alternate Claim to state the Alternate Claim,

is a lower-level form of creative conflict when it stands in isolation of an Alternate Claim

and refines, clarifies or elaborates original claims that are slightly “fuzzy” or incomplete.

All Claims are steps in a “reconceptualization” process.

Within episodes, the claim-making role shifts between students, that is the Modified Claimant and the Alternate Claimant are not the same as the original Claimant.

The claim-making role is fairly uniformly distributed among the active students in a group. Usually all students make claims.

When there is a dominant student, he or she tends to make most of the claims.

All students in the group are involved in the argument co-construction, that is, even the “quiet” students contribute.
 
Although groups engage in both types additional claims, they tend to have a typical controversy pattern which uses either Alternate Claims or Modified Claims. This pattern is related to the correctness of the original claim. The grounds for this finding are:

Direct challenges are rare.

13 of the 14 groups followed a Controversy Model of Decision Making. (Warrant: Johnson Model, Table 4-10, p. 151)

9 of the 13 groups following the Controversy Model did not use Alternate Claims but do use Modified Claims. 7 of these 9 groups have a higher initial Claim quality. Modified Claims are requested in these groups.

5 of the 13 groups following the Controversy Model use Alternate Claims. These 5 groups have a lower initial Claim quality. Alternate Claims are never requested in any group.

At least one Modified Claim and one Alternate Claim are found in every group. (Table 3-23, page 125)

Because all students are involved in the claim-making process, co-construction of the argument is occurring. That is, the solution to the problem is a group solution and not the product of the best individual in the group. This supports prior research (Heller, Keith, and Anderson, 1992). The Modified Claim can be spontaneous or be offered in response to a request for clarification. A lack of group cohesion and conflict avoidance may inhibit direct challenges.

Claim 3c. The groups have a preferential means to support claims made in argument construction (e.g., Grounds, Warrants, Backings). Grounds, Warrants, Backings provide “color” and base the problem on the stated parameters and the principles of physics. Most groups use Grounds, Warrants, and occasional Backings to support their arguments. Lack of adequate Grounds leads to an inadequately described problem, and a reliance on Backings for support.

Groups that use Backings tend to prefer the professor over the teaching assistant or textbook.
 
RELIABILITY, VALIDITY, AND GENERALIZABILITY REVISITED

It is important to address again the reliability, validity and generalizability of this study now that the results are known. The fundamental issue can be simply summarized: Are the results what a reasonable person would conclude from this data, and would expect to conclude in another situation from similar data?

While there are limited “triangulation” sources in the strict sense of the concept’s usage in qualitative research, there are several “reference points” from which my conclusions were drawn. Figure 1-2 (page 23) can now be made more specific. The primary sources for this study are the videotapes. These led to the coded transcripts. The transcripts gave birth to the flowcharts. Together they form the primary data.
The written solutions to the problems are related to the video, and help to clarify what the students were discussing. These are a separate type of data and due to their written form could be objectively evaluated.

Descriptive data relating to the size, gender and performance mix of the group, as well as quantitative test scores enabled some “statistical” characterization of the groups. It is important to see this data as descriptive and not normative. That is, this data helps to describe the members of a group individually and their group as a whole. One of the most useful pieces of data of this type were the self-disclosure statements such as “I missed class yesterday.” While these statements come from the videos, they really are self-descriptions of the groups.

Finally there are the subjective comments that I, the transcription assistant, and my dissertation advisor made upon viewing the tapes or reading the transcripts. At first glance, all fourteen transcripts look a lot alike. Immediate differences are noted upon comparing different problem sessions. Within one problem session, repeated readings of each group lead me to be able to “feel” what the group was like.

All of these four reference points enabled me to answer the research questions and come to the conclusions I did. Although the videos were the primary source, I do not believe it would have been possible to eliminate one reference point over another. Like the points of a compass, they help to locate the results in a broader picture. A visual representation of these four cardinal directions is depicted in Joseph Maxwell (1992) offers a useful typology for understanding validity. His goal is to provide a checklist of “threats” to validity. He identifies these categories of validity useful in qualitative studies: Descriptive, interpretive, theoretical, generalizability. The categories reformulate the traditional validity, reliability, generalizability categories which actually come from quantitative research. Maxwell’s categories can be useful in analyzing the validity of this study.

Descriptive Validity

Descriptive validity asks if the account of the research is factually accurate. For example, are the transcripts an accurate rendering of the original videotapes? In an attempt to be descriptively valid, I checked the transcripts against the video, not once, but several times. If an interpretive questions arose, I found the episode on the video and carefully watched it while making annotations. Moreover, the transcripts themselves were repeated edited. Where important, I noted the antecedents of pronouns so the reader would know to what “it” refers. The written solutions were the source of drawings incorporated in the annotated transcripts. It was important to reproduce their drawings as accurately as possible. In many cases I watched the video repeatedly to see exactly what they were drawing at a given instant. My comments about Group 4C’s seating was based on observing their seating arrangement on the video as well as my own personal observation of the group when they were solving the problem. The use of a video source as opposed to an audio source for the basic data is the primary guarantor of descriptive validity in this study.
Other descriptive aspects of the data are also accurate. The quiz grades for the students in these two courses were obtained directly from the department’s master spreadsheet containing the grades. The few statistical analyses in this research were made with generally accepted methods with an Excel™ Spreadsheet. A simple check of the video log sheet revealed the gender of the students, and this was cross checked with the video itself.

Interpretive Validity

There is subjectivity in this research. Interpretive validity asks if what is interpreted from the observations is true to the data. That is, what is the meaning of the observations and does it reflect what the participants (i.e., the students in the groups) actually did? Maxwell notes, “Like descriptive validity, then, interpretive validity, while not atheoretical, refers to aspects of accounts for which the terms of the account are not themselves problematic. Interpretive accounts are grounded in the language of the people studied and rely as much as possible on their own words and concepts” (Maxwell, 1992; p. 289; emphasis added). The guarantor of interpretive validity in this study is the manner in which the interpretation developed. There was an interactive process. For example, the flowcharts refer to the transcripts, and indeed one must read the transcript of an episode to understand the flowchart.

Likewise, there was an iteration process. I view the progress through this research as a helix. There is constant forward movement but I continually returned to the same groups or the same ideas. For example, the four groups in session four formed the basis of the coding system. When I was satisfied with the coding, the system was extended to the other 10 groups.

Flowcharts were drawn for Groups 4A, 4B, 4C, 4D. When I was satisfied with the results, I extended the flowcharting to the other 10 groups. Then I faced the question of what to do with the additional claims in an episode. After identifying the Alternate Claims and Modified Claims in the four groups, I went back to the remaining 10 groups. They were recoded to account for the Alternate Claims and Modified Claims. Next, the revised flowcharts were drawn for Groups 4A, 4B, 4C, 4D, and then for the remaining groups. In other words, instead of plowing boldly ahead, I made sure at each step that what I was doing made sense to me and fairly represented the data.  In addition, I had to convince Dr. Heller that what I was doing made sense.  An analogy to this process might be the pilot testing of curriculum materials. After testing, revisions are made prior to releasing the materials to the larger audience. I believe this is a constructivist way of doing research: The process is a part of the product, and meaning is constructed out of what is evident, reasonable, and logical. Even subjective evaluations were are part of this process. We were able to assign highly subjective monikers to groups (“bad”, “good”, “confused”, “dysfunctional”) and know which group we were discussing by its pejorative name. Finally, the independent evaluation of the written solutions supplied another interpretive reality check.

One major interpretive concern was that somehow my coding of the statements or drawings of the flowcharts changed between the beginning and the end of the study. First of all, it is important to note the order in which the sessions were coded: 4, 2, 3, 5, 6, and 7. I saw no “chronological” pattern to such measures as lines per episode. I have already addressed the issue of whether or not the students who appear in more than one group were consistent in their claim making (Table 3-24, page 126). They are relatively consistent.

As a final example of interpretive validity, consider the very use of the Toulmin categories and the additional defined categories. Alternate Claims and Modified Claims are interpretive but also related to the Toulmin category of the Claim. Likewise categories like Consensus Checking grew out of the cooperative groups and the problem-solving strategy. That is, these additional statement types are not atheoretical, to use Maxwell’s term.

Theoretical Validity
 
Theoretical validity ask if the account of the research is valid in terms of the theory of what is happening in these groups. “...the issue is the legitimacy of the application of a given concept or theory to established facts, or indeed whether any agreement can be reached about what the facts are” (Maxwell, 1992; p. 293).  There are two issues in this specific research:  Is the use of Toulmin’s argument structure valid, and do students co-construct a problem solution? One might even ask if constructivism itself is a valid world-view. The theoretical starting point of this research was that Toulmin is valid and that students do co-construct a solution. For nearly 40 years, Toulmin’s argument structure has been use in rhetoric, debate, and logic. Although many have “argued” with some of his ideas, the fundamental assertion that a formal argument structure contains Claims, Grounds, Warrants, and Backings is generally accepted. That acceptance is supported by the number of people and disciplines that have used it. Likewise, there is a vast body of research literature on constructivism in science. It is a view of science learning that is commonplace. In both cases, I believe these theoretical frameworks have stood the test of time because they work.  That is a bit like theories in physics.  Those that survive do so because they are able to describe existing phenomena and predict new behavior.

Generalizability Validity

This type of validity asks if the account can be extended to other persons, times, or settings. What generalizability really asks is if this account can be used to make sense of other situations and settings. Qualitative studies are not usually replicated, but the extension to other settings is important to consider. I will more directly address the issue of generalizability in my discussion of suggestions for future research and suggestions for curriculum and instruction.

SIGNIFICANCE OF THE RESEARCH
 
This was not the first research to use the episode as a unit of analysis. However, as far as I know, it is the first to use episodes in a qualitative case study of cooperative group problem solving. The episode is a valid unit of analysis because a group co-constructs an argument by conversing, and conversations consists of multiple statements and sentences. Thus, it was better, in this case, to use episodes instead of just counting statement types. The use of this technique is further warranted because using episodes revealed important patterns. Even so, the episodes are composed of statements and it was important to carefully classify individual statements. One could see the statements as a micro-context and the episode as a mini-context.

I also feel confident that beginning with the Toulmin categories yielded rich insights. As I found, students in a problem-solving group do not strictly follow the Toulmin argument structure and thus, other statement types must be considered. In addition, their patterns do not always lead to the claim. Even so, the Toulmin structure is a valid and useful analysis tool for studying the process of cooperative group problem solving. Part of the usefulness is the manner in which the additional statement types complement the Toulmin statements.
Students in a problem-solving group are engaged in co-constructing an argument. That means the product, i.e., the problem solution, is a group product and not the work of an individual. This is a finding in this study that supports previous research.  We frequently hear the criticism of cooperative group problem solving, especially from physics professors, that the best student in the group solves the problem. I believe, post research, that this is not the case. Even the least involved student contributed some idea that lead to the solution. I might even argue in the case of Group 4D that ST’s insistence that there is no normal force lead to a much better understanding of the forces acting on the sign. In Group 4A, RM who was very quiet, frequently asked the skeptical questions or requested clarification because he did not understand.
 
The ensuing discussions led to all three students understanding better. It may even be the questions of the least “capable” student that leads to the problem solution. This has implication for how we teach problem solving and how we structure cooperative groups.
Students in a problem-solving group use Modified and Alternate Claims. These additional claims are a means for students to engage in “creative controversy” in order to elaborate claims, correct and clarify initial claims, and to co-construct a problem solution. One of the fundamental tenets of cooperative learning is that when a group member asks a “why” question, someone will have to “explain, elaborate or defend” an idea (Brown and Palincsar, 1989, p. 395). Thus, the use of Alternate Claims and Modified Claims lead me to the conclusion these claims are a means of engaging in the cooperative task of explaining, elaborating and defending ideas. Furthermore, since creative controversy was not explicitly taught to these students, it is interesting that several of the groups none the less practiced it spontaneously. One might ask how much more they would engage in controversy if the groups were more cohesive and if conflict management skills were explicitly taught.
Finally, I believe this research shows that a qualitative case study approach is useful in understanding the nature of cooperative group problem solving. When I started this research I did not know what a systematic “fine-grained examination” of the argument co-construction process even looked like, let alone how I would go about it. Now, I am not only sure of what it looks like, but I believe this is a good example of how to do it. I have attempted to be very clear in my assumptions, methods, and techniques. It should be possible for someone to extend or translate the general approach to another context.
 
SUGGESTIONS FOR FUTURE QUALITATIVE AND QUANTITATIVE RESEARCH

Two important questions in any research are those of generalizability and repeatability.

The very nature of a qualitative study makes broad generalizations tenuous and repetition difficult. It may be, however, possible to generalize or repeat the study in similar contexts. Such a context would be a course where the instructor and teaching assistants knew the basics of cooperative group problem solving but do not strictly follow all the structuring and management guidelines. However, I must agree unequivocally with Schofield that I have no desire “to engage in the relatively unexciting task of conducting a study designed specifically to replicate a previous one” (Schofield, 1990, p. 203). What I believe to be more fruitful is to translate or extend the study to similar contexts. The similar context would be a college physics course, either calculus-based or algebra-based, in which the Johnson model of cooperative learning was employed. Three possible studies come to mind.

First and foremost, it is our hypothesis that the problem-solving strategy seems to give these students a means to “talk physics.” Given some of the less than desirable composition aspects of these groups (number, gender and performance mix), it is amazing to me as a physics teacher that they did as well as they did on these problems. Since the problem-solving strategy is itself a “construction” and provides an outline of the problem solution, the strategy may be partially responsible for the argument co-construction patterns. An interesting study would compare two courses using cooperative learning that are alike except for the use and non-use of the specific problem-solving strategy. One could compare the argument co-construction structures of groups in the two courses.

It would be possible to “control” for some of the “variables.” Because much of what I found is intimately a part of the problem-solving strategy we use at the University of Minnesota and at Normandale Community College, it would be important to use the same strategy, or a very similar one. As I noted, the group management was not ideal. I would attempt to maintain stricter control over group composition, following the size, gender, and performance mix guidelines from our prior research (Heller and Hollabaugh, 1992). I believe it would be useful to have a larger number of groups solving the same problem. Ten groups (five from the course using the strategy, five from the non-using course) would be ideal, but perhaps not practical due to the costs of video equipment and operators. Using more groups solving the same problem helps control the “variable” of the problem itself. Although this is a concept from quantitative research, I believe it is useful to think about this “variable”. Although I didn’t find any qualitative “variability” associated with the problem type (e.g., dynamics or energy conservation), I think it would be better to “control” for it than to ignore it.

Second, if group cohesion indeed fosters creative controversy, then there should be more creative controversy in a more cohesive group.  A way to test this idea would be to videotape two sets of groups. The first set of groups (preferably 10 in number) would be from early in the first term of a two-quarter or two-semester sequence course. These groups would be taped solving a problem in the second week of the groups’ existence. Then, near the end of the second term, groups could be formulated and kept the same for about three weeks. During the third week, the groups could solve a problem. It is almost always the case that by the end of the second term of a course, there are no more “new” combination of members in a cooperative group. Everyone has worked with everyone else by that time. Cohesion should be higher than at the beginning. In such a situation, I would expect to see more controversy and more spontaneous Alternate Claims in response to incorrect Claims.
 
Another means to foster group cohesion would be to specifically teach creative controversy skills. Providing this instruction should lead to more cohesion and hence more Alternate Claims. A means to test this would be to give a group problem, teach controversy skills, an then give another problem. More Alternate Claims should appear. One could even run this as a controlled, quantitative experiment where a control group did not receive instruction in creative controversy.

Third, I did not address the issue of conceptual change. Looking for misconceptions was not the purpose of this research. There are examples of incorrect usage of physics terminology by these groups. The comment of Brown and Palincsar (1989) about the necessity in the group to “explain, elaborate or defend” an idea is actually made in the context of their theorizing about what promotes conceptual change. If I wanted to look for evidence of conceptual change, I would select groups from early in an academic term when concepts like Newton’s Laws of Motion are still a bit unclear and confusing to students. I’d probably give an inclined plane problem and see if that old common misconception of “the force making it go up the plane” surfaces and is corrected by the group process. Based on my experience as a teacher, out of ten groups, some are sure to get it right and some are sure to persist in the misconception.

CURRICULUM AND INSTRUCTION CONCERNS

Although this research had a specific research goal, and very definite research questions, the ultimate goal of research in science education is to improve teaching and learning. I have several suggestions to make concerning the use of cooperative groups in physics problem solving. Some of these suggestions are based on results that support previous research and some are based on this contribution to science education.
 
Suggestions Supported by This Research

Because the groups’ Backings show a preference to model their solution after the professor, modeling the problem-solving strategy in class can be an effective means of fostering physics problem-solving skills. However, the instructor must be cautious that he or she models the “right stuff.” For example, being consistent and thorough when drawing free-body diagrams is very important.

Groups should be explicitly taught creative controversy skills. Because there is a prototype pattern (Group 4B, Type 1) in which there is no Modified Claim preceding an Alternate Claim and there are no additional Grounds, Warrants, and Backings supporting the Claim, it would be important to teach students to support all claims with Grounds, Warrants, and Backings.

Co-construction should be promoted. This might be done by paying very close attention to group participation. Students might then participate more equally and fully in the group. An instructor could monitor groups as they work and intercede to draw in a “quiet” student. It also might be helpful to rotate roles mid-problem. In many of these 14 groups, the Recorder bore the major task of consensus checking. Rotating this role to another student might bring in other ideas. I would recommend this only as a technique to encourage equal participation and not recommend its universal use. Even though all students contribute, it can be important to encourage the student who feels his or her contribution is insignificant.

Skeptical questioning and consensus checking should be overtly built into any problem solving strategy. An instuctor could promote this by asking to see intermediate steps before the group moves along. All the problems in this study were quantitative with numerical answers. My own experience, coupled with the importance of skeptical questioning and consensus checking in this study, suggests giving problems with algebraic answers might foster this in cooperative problem-solving groups.

Suggestions Supported by Previous Research and This Research

Groups should be carefully managed in terms of gender, performance, and number of members. This agrees with prior research. I believe some of the dysfunction observed in some of these groups (e.g., 4C) could be avoided if the instructor becomes acquainted with the students personalities and intervenes in dysfunctional groups.

Group processing, according to the Johnson model, improves group functioning. This should be a part of all problem-solving groups in order to foster group cohesion and functioning.

The explicit problem-solving strategy seems to have helped these groups. Teaching problem solving should be an integral part of all physics courses at all levels of instruction.