Supporting collaborative problem solving: supporting collaboration and supporting problem solving
Christine Pauli & Kurt Reusser, University of Zurich
Abstract
The interpretation of empirical evidence in the area of collaborative learning and problem solving is difficult, because the numerous studies differ greatly with respect to the conceptualization of collaboration and the function of support provided to the learners in the examined learning environments. We propose to distinguish between two types of support: sozio-cognitive and task-specific support structures. (1) Based on different theoretical perspectives on collaborative learning, descriptions of productive conversations have been identified. One important way of socio-cognitive support for collaborative learning is to introduce tools for communication, aimed at fostering such productive conversation patterns in the social interaction of collaborating peers. The design of these tools is based on theoretical considerations related to the social foundations of cognition, and to conversation analysis. (2) Task-specific support structures aim at fostering the construction of specific domain-knowledge, understanding and skill acquisition. This type of support should be based on an underlying task analysis and on a theory of learning and instruction. The evaluation of environments for computer-supported collaborative learning should focus on both of these support structures. In order to illustrate the distinction we refer to a representational tool for collaboratively solving mathematical problems, called Heron. We demonstrate how the central features of the tool relate to both the task-specific and socio-cognitive aspect of supporting collaborative problem solving. The effectiveness of the tool with respect to both types of support was examined by means of detailed analyses of 4 student pair's conversations. A summary of the results is presented. 

1.	Collaborative learning and problem solving: Descriptions of successful peer collaboration 
The research question addressed in our paper concerns possible ways of supporting or facilitating peer collaboration. Starting from the area of research on collaborative learning in general, the role of computers in collaborative learning environments is considered as a special case of possible support structures in educational environments for collaborative learning. Our analysis refers to collaborative learning only, which should be distinguished from cooperative learning (Cohen, 1994; Dillenbourg, 1996; Pauli, 1994). Cooperative learning refers to a small group of learners - usually about 4 learners - who work together as a team to solve a problem, complete a task, or accomplish a common goal (e.g. Cohen, 1994). While in cooperative learning settings it is also possible that the task is distributed among the students of the team so that each student contributes to the common goal by working on a distinct subtask, in collaborative learning environments students have to work all the time on one and the same problem collaboratively. Collaboration in this sense may be described as  "mutual engagement of participants to solve the problem together" (Teasley & Roschelle, 1995, p. 70). Collaboration by these authors is further described as "coordinated, synchronous activity that is the result of a continued attempt to construct and maintain a shared conception of a problem". 
We believe that the distinction between cooperative and collaborative learning is important with respect to the interpretation of results of empirical studies, because these studies differ in substantial aspects. For example, empirical studies in cooperative learning most often focus on the variation of important variables influencing the outcomes of cooperation, and most frequently from a motivational perspective. In contrast to research on cooperative learning, research on collaborative learning has a a greater interest in cognitive processes as compared to motivational ones. Moreover, cooperative learning studies often are classroom interventions, usually covering a longer period of time, collaborative learning studies often are laboratory studies and of short duration, including only a few or even only one collaborative session.
Research on collaborative learning is still based on different theoretical perspectives (see, for recent overviews, e.g. Azmitia, 1996; Dillenbourg, 1996; O'Donnell & O'Kelly, 1994). In correspondence to the theoretical point of view, different socio-cognitive processes or patterns of dialogues have been suggested to be crucial for successful collaborative learning. Some of these constructs and examples of empirical studies are summarized in table 1. It is assumed, that the probability of some group-to-individual-transfer, or cognitive change, as a result of peer collaboration, is higher, if such processes or dialogue patterns are present in peer interaction during collaboration. There is, in fact, some empirical evidence supportig each of these constructs. 
Table 1: Socio-cognitive processes and patterns of peer conversation assumed to be related to successful collaboration
-	Socio-cognitive conflict 
	Nature of conflicts (social vs socio-cognitive) as well as nature of conflict resolution seem to be important (e.g. Mugny, de Paolis & Carugati, 1984; Nastasi & Clements, 1992; Joiner, 1995)
-	(Co-)construction 
	'Transactive discussion' („reasoning that operates on the reasoning of another“. Studies in moral and scientific reasoning, e.g. Azmitia & Montgomery, 1993; Berkowitz & Gibbs, 1983; Kruger, 1993)
-	Articulation 
	Articulation of metacognitive (monitoring and self-regulating) behavior assumed to be followed by individual appropriation of these skills (e.g. Artzt, 1996; Artzt & Armour-Thomas, 1992; Rogoff, 1991)
-	Elaboration
	Giving detailed, elaborate explanations correlates with amount of learning (Webb, 1991). (Results from cooperative learning studies; not clear how these results relate to collaborative learning in the narrower sense)
-	'Establishing a shared problem interpretation' (conversation analysis)
	Structure of turn-taking sequences as indicator of the degree to which students share common problem conceptions or taken-as-shared interpretations (e.g. Cobb, Yackel& Wood, 1992; Crook, 1994; Roschelle & Teasley, 1995).
Descriptions of conversation:
-	'Exploratory talk' (as opposed to disputational talk and cumulative talk) (Mercer, 1995)
-	Negotiation and argumentation (Baker, 1993; Dillenbourg et al., 1996; Joiner, 1995)
-	: „... dialogues in which turn transitions are smooth, and the sequence of talk follows a cooperative pattern. In periods of successful collaborative activity, students’ conversational turns build upon each other and the content contributes to the joint problem solving activity“ (Roschelle & Teasley, 1995, p. 76)
2.	Supporting collaborative learning: socio-cognitive and task-specific support structures
Classroom observation studies have shown that students' interactive behavior differs in various ways from such productive dialogue patterns  as mentioned in table 1 (a summary of disappointing findings of classroom studies is given by Cohen, 1994). Therefore, one important way of supporting collaborative learning is to make sure that in the social interaction of collaborating peers such conversation patterns and particular socio-cognitive processes emerge. An increasing group of reseachers designing educational learning environments for computer supported collaborative learning adopt a 'shared cognition approach' (Dillenbourg et al., 1996) of collaboration. From this point of view, a main function of educational computer software is to serve as a tool for communication aimed at supporting conversation of collaborating peers, through facilitating processes of sharing understanding, such as negotiation and argumentation. These processes in some sense include what from other perspectives is described as co-construction and conflict resolution as well as articulation. 
Yet, sociogognitive conflict resolution has also been observed to have no or even detrimental effects on individual cognition (e.g. Tudge, 1989), and it is also possible to construct a new misunderstanding of the problem (e.g. Forman & McPhail, 1993). A second, and complementary way of supporting collaborative learning and problem solving is therefore to provide learners with task-specific support structures. This second level of support should be based on a cognitive task analysis as well as on a theory of learning and instruction. 
Table 2 summarizes some ways of supporting collaborative learning in advance (through activities prior to the critical task), on-line, when pairs or groups are at work, and through follow-up activities. We believe that the design of educational learning environments for collaborative learning requires a careful coordination of supportive conditions with respect to each field. Due to limited space, we concentrate on on-line support structures. These include the establishment of optimal conditions, socio-cognitive support structures aimed at facilitating collaboration, and task-specific and/or strategic support and guidance (task-specific support structures). 
Table 2: Supporting collaborative learning
Activities prior to the critical task	On-line	Follow-up activities	
-	Establishing norms of collaboration and problem solving
-	Explicit training for collaboration: 
e.g. for sharing ideas and information, explanation skills... 	-	Establishing conditions for collaboration
-	Task-specific support structures
-	Socio-cognitive support structures 	Reflection on...
-	task-specific aspects of learning and problem solving 
-	task-independent aspects of learning and problem solving (e.g. reflection on monitoring and regulating behavior) 
-	group/dyad interactions: social, motivational and emotional aspects of collaboration	
Conditions for collaboration include individual differences among members of groups (group composition), the goal and incentive structure and the nature of the task (O'Donnell & Danserau, 1992). The influence of goal and incentive structures is in the centre of interest in cooperative learning studies. Studies in collaborative learning tend to neglect these motivational issues. Effects of group composition have been observed with respect to gender of group members (Littleton et al., 1993), to relative ability and/or task specific expertise as well as to perceived expertise or academic status of members (Goos & Galbraith, 1996; Messer et al., 1993; Verba & Vinnykamen, 1992), and to friendship between group members (e.g. Azmitia and Montgomery, 1993) . 
Socio-cognitive support structures, as mentioned above, are mainly directed at improving students' interaction in the sense of supporting the processes of establishing and maintaining a joint problem conception (Roschelle & Teasley, 1995). In addition, socio-cognitive support structures are supposed to improve collaborators' mutual monitoring and regulating of their problem-solving and learning activities by means of the facilitation of reciprocal understanding. Examples of such support structures are collaboration scripts such as  O'Donnell and Danserau's (1992) 'Scripted cooperation', as well as worksheets or explicit instructions that guide the cognitive and metacognitive activities of students. The design of socio-cognitive support structures is based on theoretical considerations concerning the social foundations of cognition on the one hand, and on conversation analysis on the other hand.
Task-specific support structures include specific equipment and resources for tasks that require the performance of concrete procedures, and explicit instructions and/or modelling with respect to task specific problem-solving strategies and formats for problem representation. The main goal of these support structures is to improve students' domain knowledge construction, understanding, and skill acquisition. Support structures of this type have to be based on an underlying domain and task analysis (Reusser, 1993; 1996). According to a 'distributed cognitions' model (Salomon, 1993) of collaboration, guidance may be provided by different 'members' of an interactive learning environment, such as computers, peers, or a participating teacher. With respect to the conceptualization of the distribution and the quality and quantity of explicit procedural and domain conceptual assistance, a theoretical view of teaching and learning is needed (Reusser, 1996). Useful conceptual frameworks are the 'cognitive apprenticeship' model of learning and teaching (Collins, Brown & Newman, 1989), which allows to describe various forms and amounts of assistance in terms of, e.g. modelling, scaffolding and coaching, as well as the cognitive instructional theory developed by Aebli (1987), especially his conceptualization of instructional sub-goals
Within a 'shared cognition approach' to collaborative learning, computer support in collaborative learning and problem solving focussing on the level of socio-cognitive support, is mainly conceptualized in terms of the computer as a mediational resource for shared language, situations and collaborative learning (O'Malley, 1992). It is argued, that the abstract and complex nature, which is typical for school tasks or problems, makes it particularly difficult to establish and maintain a joint problem-space (Crook, 1994). The computer screen may provide learners with visible and manipulable objects of joint reference by means of flexible representation, and may in this way support the construction of a shared problem conception (Roschelle & Teasley, 1995). At the same time, according to the 'cognitive apprenticeship' approach, educational software may guide students' strategic approaches in problem solving by modelling and scaffolding strategic behavior and task specific problem representation (e.g. Katz & Lesgold, 1993; Reusser, 1993). Therefore, with their potential to facilitate and cultivate task related communication and to provide task specific modeling and guidance, computers can represent both, socio-cognitive and task-specific support structures for collaborative learning (O'Malley, 1992; Reusser, 1993; 1996). 
Consequently, the evaluation of computer supported educational environments for collaborative learning may focus, with varied emphasis, on both the socio-cognitive support and/or the task-specific assistance and guidance. A difficult task emerges, namely, to develop instruments of analysis which allow to describe both, the quality of collaboration in terms of conversational processes, as well as task-specific aspects of the joint activity related to domain knowledge construction, understanding, and skill acquisition. 
It follows, as an illustration of the proposed distinction, a short description of some features of a representational tool for collaboratively solving mathematical story problem, called Heron, and some results from a first evaluation study referring to effects of both types of support.
3.	Heron - a representational tool for collaboratively solving mathematical word problems
What is Heron? 
Heron is a mouse-driven, graphics-based problem-solving tool for facilitating and fostering self-directed understanding and solving of a wide class of mathematical story problems. Heron helps students from grades 3 through 9 to identify, conceptualize, and express the relevant pieces of information in a problem, and supports the planning and construction of a mathematical problem model, including the derivation of an equation (see, for a more extended description of Heron, Reusser, 1993, 1996). 

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Task analysis and task-specific support provided by Heron
Heron is based on a task analysis on both, an epistemological level and the level of modelling the psychological processes of understanding and solving word problems (due to limited space, it is not possible to present the task analysis; see Reusser, 1993; Reusser et al., 1996). Based on the task analysis, the task specific support provided by Heron may be conceptualized as scaffolding the collaborating learners in their efforts to understand and solve the story problems, namely through the system's assistance in constructing problem models using the format of solution trees, a graphically based network formalism for dynamic problem representation and planning.
The crucial aspects of solution trees, which allow the simultaneous grasping of both the episodic (situational) and the mathematical structure of word problems, are the following: They
-	offer non-directive assistance in the translation of verbal descriptions of problem situations into mathematical representations, 
-	are tools for both quantitative and qualitative reasoning
-	invite students not only to focus on the latent mathematical structure of a problem, but to base their quantitative reasoning on the qualitative understanding of the problem situation.
-	provide students with a constraining scaffold to learn the mapping between text, situation, and equation,
-	ultimately provide students, by the obligation of their repeated construction, with a strategic approach on mathematization and problem solving. 
Control is left to the learners: Beside the obligation to construct solution trees, HERON acts as a non-directive tool. According to the principle of variable control and of minimal help (Aebli, 1987), the system provides as much learner control as possible: It invites but does not force students to take certain decisions in the problem-solving process. It is up to the user which comprehension path (under the many possible paths) to follow. Students who are using HERON to solve story problems collaboratively may provide each other with additional help. The reciprocal helping may be facilitated through the socio-cognitive support aspect of Heron. 
The socio-cognitive support provided by Heron
Implemented as a tool for peer collaboration, HERON's potential to externally represent normally unobservable knowledge-construction activities is particularly important, because these activities can then be identified, inspected and analyzed by both  collaborating students. The visualized and manipulable objects of thinking on the screen - a growing hierarchical structure consisting of meaningfully related, qualitatively and quantitatively described boxes - facilitate the learners' co-reference on crucial aspects of the problem and thus the negotiation of a shared understanding at any point in the problem solving process. In this way the system provides continued access of both collaborators to the crucial operations and actions of the problem solving process - operations and actions that are already completed as well as operations and decisions actually under discussion. Maintaining mutual involvement in the joint problem solving process is thereby facilitated. Moreover, continued access to an external representation of one's own as well as the collaborator's 'mental model' of the problem should in turn facilitate the reciprocal monitoring of problem solving. 

4.	Evaluating Heron
As a first evaluation, we observed 4 student pairs (grade 5) collaboratively solving complex mathematical story problems. 6 story problems were solved with paper and pencil, and 6 structurally isomorphic story problems were solved at the computer (Heron). Conversation was transcribed from audio- and videotapes, and then analyzed with respect to Heron's task-specific assistance (e.g. focus of reasoning not only on the latent mathematical structure of the problem, but on the qualitative understanding of the problem situation), and socio-cognitive support of collaboration (mutual involvement in problem-centered conversation and reciprocal monitoring of problem solving). 
Summary of main results of the evaluation study
Socio-cognitive suppport aspect:
-	Students solving story problems with Heron were generally involved in longer discussions on problem-relevant issues. 
-	The extension of the dialogues of all student pairs working with Heron, compared with dialogues while working with paper and pencil, includes an extension of discussions related to metacognitive activities or problem solving regulation. The supplementary turns refer foremost to the two categories questioning and confirming the procedure and (retrospective) evaluation, and thus to some form of monitoring the collaborative problem solving process. 
-	Comparison of quantity and quality of questions and rejections under both conditions (Heron vs PP) shows an increase of task-relevant questions and rejections when students work with Heron. 
Task-specific support aspect 
-	Students working with HERON verbalized numbers more often with explicit reference to the problem situation and less often without any interpretation, whereas in the PP condition the contrary is true. Student pairs using HERON, thus, talked to a greater extent about the meaning of the numbers on which they operated.
-	These effects are present in all 4 pairs' dialogues; with gradual differences.
-	Analyses of conversations and of students' written solutions and of solution trees show that students used the system in different - and, at least with respect to one of the four pairs not always adequate - ways.

5.	Conclusion
Based on our results we conclude that HERON encourages students to more extensively share their qualitative understanding of the story problems as well as problem solving monitoring. That means, that with respect to these four student pairs the task-specific support provided by Heron as well as a certain facilitation of collaboration seem to have worked. Since HERON was explicitely designed as a non-directive cognitive tool with a lot of learner control, the optimal use by the students is not guaranteed. With respect to the control aspect, our results clearly show that at least for some students there is a need for more help or control taken over by either the system or a participating teacher or expert. As a consequence, the newer version of Heron now available includes some more control by the system, namely, a feedback component which is still designed in correspondence with the 'principle of minimal help' (Aebli, 1987). We expect that this on-line help function now included in Heron should optimize the joint problem solving activities, ant thus the user's profit from working with the system.
The instrument of analysis used in our study focused primarily on the task-specific aspect of support. The analysis of questions and oppositions gives only a rough outline of the way students interacted. Therefore, content analysis was complemented with qualitative descriptions of conversation sequences and with analyses of the solution paths. The construction of instruments of analysis, which allow, with acceptable time costs, to analyze both, the quality of collaboration and the quality of problem solving behavior related to specific knowledge structures and cognitive skills, remains a problem still to be solved.
In correspondence with the integration of different possibilities to support collaborative learning proposed in this paper, we believe that the need of more help or external control of Heron inferred from our results, may interact with some factors mentioned above as conditions of collaboration. Specifically, the relative expertise of collaborating students, and foremost perceived competence (or academic status) should be considered. In addition, optimal implementation of a system such as Heron would require more attention to the components of supporting collaborative problem solving before and after the collaborative learning event, as mentioned above. For example, with respect to activities prior to working with Heron, more attention should be paid to the culture of problem solving maintained in the target classroom. With respect to follow-up activities, the potential of Heron as a tool for reflection has not yet been studied. The next question to be investigated with respect to Heron thus will not only refer to some 'pure' effects of tool enriched with feedback, but also to different ways of embedding Heron as an element in interactive learning environments, including both relatively self-regulated collaborative problem solving as well as more tutorial-like sessions with the participation of the teacher. 

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