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A description of student problem solving using a heuristic in a cooperative group setting

Kim Pitts-Hill, Education Department of WA
Kevin Barry and Leonard King, Edith Cowan University
Scott Zehnder, Allenswood Primary School
This descriptive study examined the use of a problem solving heuristic in a series of cooperative learning lessons and built upon the work of King, Barry, Maloney and Tayler (1994) in analysing student talk in small group work. The research participants were four students in a target group and their teacher, in a class of 29 year seven students, in a government primary school.

Seven problem solving lessons formed the content for the study which was based on a cognitive psychological framework. The study employed both qualitative and quantitative data collection to analyse the relationship between the teacher's instructional talk and student talk during the problem solving.

Results of the study provide a greater understanding of the relationship between the teacher's instructional goals and the students' perception of, and use of this instruction, in small group cooperative learning. In turn this has implications for teacher educators and the professional development of teachers in small group cooperative learning techniques.


Research into teacher influences on student cognitive processes during small-group cooperative learning is emerging as a growing domain of inquiry. Such a move has occurred against a background of research that has predominantly focussed on social psychological aspects of cooperative learning. Now research attention is beginning to focus on different aspects of cooperative learning that are more cognitive psychological in nature. This paper reports research that reflects such a redirection of enquiry. The general objective of the study was to establish the nature and degree of connection between the intent and form of small-group cooperative learning set by the teacher (conditions) and the kind of peer group interactions and talk (discussion). In more specific terms this was narrowed down to the following focus question.

To what extent is teacher instruction in a problem solving heuristic reflected in a group of four students' talk during the activity phase of seven problem solving lessons?

Theoretical framework

Recent work in the study of teaching world-wide has resulted in strong support for cooperative learning. Most product studies suggest that students attain academic learning gains equivalent or better than those attained in more traditional learning situations (Bennett & Dunne, 1991; Davidson, 1990; Slavin, 1992). According to Slavin (1992) much current research into small-group cooperative learning has focussed on social psychological outcomes such as group composition, group member roles, decision making processes, evenness of group member contributions, and learning of other group process skills along with kinds of accountability and reward structures.

While the social psychological perspective of small-group learning has been the focus for most researchers a small group of researchers have been focussing on cogitive psychological outcomes (Bennett & Dunne, 1991; 1992; Cohen 1991,1996; Davidson, 1990; Galton & Williamson, 1992; Meloth, Deering & Sanders, 1993; Noddings, 1989). For example, Bennett and Dunne (1991) discussed how teacher verbal behaviour and use of particular teaching skills influenced the quality of student talk and probably the quality of student learning. Meloth et al. (1993) discussed a number of studies about the kinds of teacher behaviours and influence before and during the small group phase of cooperative learning lessons. King, Barry Maloney and Tayler (1993b, 1994) found the quality of teacher talk appeared to be related to the quality of student 'task enhancing' talk such as offering ideas and suggestions, discussing and clarifying, thinking aloud, and verbalising agreed answers and solutions work tasks or problems. Overall, the reported research is suggesting that teacher influences on the cognitive processes of students in cooperative learning is significant.

However, as Bossert (1989) has indicated, any number of factors might also have contributed to the achievement gains reported. Therefore, in Bossert's view there was a need in researching cooperative learning for a "fine grained analysis of students' cognitive processing ...[for]... this would allow the researchers to document how peer interactions ... shape the thinking and processing skills of group members" (p.239). In developing this line of research Meloth, Deering and Sanders (1993) called for the need to refocus the research effort to clarify the nature and degree of connection between the cognitive intent and form of small group cooperative learning set by the teacher and the kind of peer group interaction and talk held by the students. Meloth (personal communication, July 1995) suggests a cognitive psychological perspective, shown in figure 1, in which the teacher's cognitive intent for a lesson ought to shape the cooperative learning task (conditions) and the kind and quality of student talk (discussion) during the small group interaction phase.

Figure 1

Figure 1: Diagram of a cognitive psychological perspective for small group learning

Our study is based on the cognitive psychological model outlined by Meloth and shown in figure 1. The teacher's cognitive intent was to teach a problem solving heuristic, to a group of four 12 year old students, under set conditions for cooperative learning. The study concentrated on the teacher's instruction in the problem solving heuristic and whether this heuristic was reflected in the students' talk, the learning outcomes and the students' perception of the lesson(s). The problem solving heuristic used involved students responding to a problem by generating or proposing an idea, then negotiating and reacting to that suggestion before coming to a final recommendation about whether it should be included in the group's response to the task. Once this had been done, students worked the last two steps of the heuristic recording and reviewing the appropriateness of the product. The problem solving heuristic is shown in figure 2 on page 6. As indicated in the introduction to this paper a single question guided the study:

To what extent is teacher instruction in a problem solving heuristic reflected in a group of four students' talk during the activity phase of seven problem solving lessons?
Not only did this question have the potential to provide insights on the connection between teacher intent and student's talk in a small group cooperative learning setting but it could also provide data on how students learn and use heuristics, and go about problem solving in a group. The literature in these fields is extensive but in this study particular note was taken of the work of Brown and Palin (1987), Hart (1990) on teacher behaviours and King (1993) on student passivity. Studies that involved heuristics included Leighton, Slavin and Davidson (1989), Polya (1945), Thomas and Robinson (1982), and Roth and Roychoudhury (1993). Authors including Chan (1994), Garner (1990), Lindow, Peterson and Wilkinson (1985), and Wong (1985) that had undertaken studies relating to student knowledge, strategy use and questioning were also consulted as were studies on problem solving procedures conducted by Ross, Rolheiser and Hogaboam-Gray (1996), Ahmid, Tarmizi and Sweller (1988) and Sweller and Low (1992). These studies will be considered in more detail in the Findings and Discussion section of this paper.

Methodology

This research was a descriptive study of one target group and a teacher in a year seven class. The study focussed on the student use of a problem solving heuristic while engaged in small group problem solving lessons. The study involved seven teaching and learning lessons, one lesson per week for seven weeks.

Sample group

The four students in the target group formed part of a class of 27 year seven students (turning 12 years of age) in a metropolitan government primary school. The group consisted of one high achiever, one low achiever and two average achievers, and was mixed for gender, two boys and two girls. Achievement levels used for determining group membership were determined by the teacher prior to the study commencing. The target and class groups were newly formed for the study and generally were not familiar with small group cooperative learning methods. The male teacher volunteered to participate in the study. The teacher had used small group methods but had not had any formal training in small group cooperative learning.

Lessons

Each lesson was approximately 40 minutes in duration and held at the same time on the same day each week. Each of the first three lessons were in different curriculum areas. The remaining four lessons were in a curriculum area chosen by the teacher in conjunction with the researchers and after reflection on the earlier lessons. The curriculum area chosen was mathematics and the lessons involved problem solving activities suitable for small group work.

Each lesson followed a similar format of introduction, student work and conclusion. This involved:

Students would begin work on the problem through such activities as: At some stage during the lesson the teacher would intervene:
Figure 2

Figure 2: Diagram of the problem solving heuristic

The teacher introduced the terms and held a brief class discussion on the meanings of the terms and how the heuristic could be used. This was done prior to the beginning of the activity stage of each lesson. The heuristic diagram remained on the board for the entire lesson in full view of all students.

Data

Several sources of data were used for this study. The teacher's cognitive intent for each lesson, the problem solving processes and procedures to be emphasised and the heuristic for guiding student talk were shared in meetings with the observers before and after lessons. Narrative notes were made of these meetings.

During the lessons students were audio and video recorded. Observers made narrative notes to supplement the audio and video records particularly where non verbal, quiet or gestural communication would have been difficult to interpret from the video records. Following the lessons, individual stimulated recall interviews were held with each student. These interviews were audio recorded.

Data analyses

The recorded student talk in peer group discussions and the recorded student responses to the stimulated recall interviews were transcribed and analysed through reading of the scripts, use of a low inference small group learning interaction analysis system (MAKITAB) (see table 1) and a non numerical unstructured data, indexing searching and theorizing tool (NUD*IST).

MAKITAB analysis

The data were analysed for evidence of student use of the problem solving heuristic. Using the MAKITAB system each separate utterance made by each student, was isolated and coded. The coding categories that describe the problem solving heuristic were:

NUD*IST analysis

Transcribed talk from each of the seven lessons was analysed for each student and for evidence of the student use of the problem solving heuristic during the activity session of the lessons. Student use of the problem solving heuristic was undertaken through text searches for the heuristic terms, and synonyms of the heuristic terms, in all of the text units.

Reading of the transcripts

The transcripts were also read for evidence of the problem solving heuristic. This was done to confirm the analysis achieved using the MAKITAB system and the NUD*IST analysis. MAKITAB codings, or NUD*IST search strings of the transcripts may not have clearly identified the nature or evidence of the problem solving heuristic or the manner in which students demonstrated the use, if any, of the heuristic. Alternatively the way in which students went about solving the problem may have been different to that sought by the framework of the MAKITAB analysis, the NUD*IST analysis or the problem solving heuristic itself. The reading of the transcripts aimed to provide further insight into the connection between the small group cooperative learning conditions set by the teacher and the kind of discussions held by students, with particular reference to the student use of the problem solving heuristic.

Stimulated recall interviews

The data collected from students in the stimulated recall interviews after the lessons was analysed for indications of the cognitive intent of the teacher and the student use of the problem solving heuristic. Student reports of an idea, discussion, acceptance, rejection, writing and checking were analysed for evidence of the heuristic, portions of the heuristic or cycles of the heuristic.

Table 1: Summary chart of MAKITAB small group learning interaction analysis system

Table 1 image

Findings and discussion

The achievement of the teacher's intent

The data revealed that the teacher's behaviours during the small group cooperative learning were consistent with a cognitively oriented set of conditions. It is clear that the students operated in a cooperative group, on tasks set by the teacher, and did so with success. The students responded positively to the direction of the teacher in cooperating and working within a group to produce a group product by implementing a range of problem solving strategies in a series of open and closed problems. In terms of problem solving skill, the group was quite successful in effecting satisfactory solutions to each task. However, the connection between the teacher's instructional intent, in the form of teaching a problem solving heuristic, and the kind of interaction and talk within the group was not so clear.

In lessons one to three there was no attempt by the teacher to instr uct students in the use of the heuristic but a considerable amount of evidence was found of heuristic related student talk being used naturally, and covertly. The NUD*IST analysis indicated that in these three lessons an average of 30% of all student talk was heuristic related talk (i.e. terms and synonyms) and in the remaining lessons heuristic talk accounted for an average of approximately 38%. It should be noted, however, that the percentage of heuristic talk was affected by the total quantity of student talk in a lesson.

Factors that appeared to impact on the teacher's intent to teach a problem solving heuristic in a small group cooperative setting

After the heuristic had been introduced by the teacher in the fourth lesson there was continuing strong evidence of the use of heuristic associated talk by three of the four students but there was little evidence that students consciously, or overtly, invoked the use of the heuristic. The overt use of the steps in the problem solving heuristic was limited and incidental, and mainly associated with the high achiever and hardly at all with the low achiever. The exception to this trend was lesson six where in a low interest-level problem there was evidence that student use of the heuristic by the high achiever may well have provided the necessary guide to successful problem solving. In post-lesson interviews there was generally an awareness of the heuristic, and its place in the lesson, but little understanding of how it could have been explicitly applied to the problem solving process.

In seeking to explain the limited overt use of the heuristic by these students in the small group cooperative learning setting, the study provided evidence of nine mitigating factors. The factors are presented in four groups. Factors pertaining to the heuristic, factors pertaining to the student group, factors pertaining to the content of the lesson and factors pertaining to the teacher.

Factors pertaining to the heuristic

Factor One

Portions of the heuristic were occurring naturally in student talk both before and after the introduction of the heuristic and students may not have seen the relevance of the model. As one student stated, "we always do that anyway".

The student discussions in lessons one, two and three exhibited as much, if not more, evidence of the elements of the problem solving heuristic than the lessons that followed. This clearly cannot be attributed to the teaching of the heuristic and may provide an insight into the untrained processes used by the students. The evidence indicates that in conditions that did not explicate a problem solving heuristic or framework, students can demonstrate effective problem solving through verbal discussions, however, this is affected by the lesson content among other things.

As was apparent in the post lesson interviews of lessons five, six and seven, most students indicated that there was nothing more to learn about the problem solving heuristic yet there seems little can be done to make the heuristic more relevant. If students understand the essential elements of "idea", "discussion", "acceptance", "rejection", "writing" and "recording" and the interaction among those elements, then there may be little else that can be highlighted that will help students to solve problems. As one student stated "we always do that anyway".

It is feasible then to suggest that students may already hold a framework for solving problems. If a problem solving heuristic is specified by the teacher, students may have difficulty in reconciling or assimilating two models, however, there was no evidence in the literature reviewed that focussed on student difficulty reconciling similar or competing heuristic frameworks. Consequently, problem solving heuristics and frameworks developed by students could provide rich information on how students perceive the problem solving process.

The first three lessons indicated that in the absence of the problem solving heuristic, students tackled the problem enthusiastically and unintentionally echoed the steps of the heuristic. It is also not surprising that portions of the heuristic were seen to occur naturally. The heuristic was developed from the MAKITAB Small group Interaction Analysis categories and followed a similar reflective cycle to other problem solving heuristics (Polya, 1945) and the MAKITAB categories were in turn, inductively developed through the observation of student interactions in small groups (King, Barry, Maloney & Tayler, 1993). Overt use of the problem solving heuristic was more evident in the later lessons when it was used intentionally as a supportive and guiding framework.

Factor Two

The lineal steps in the heuristic model did not reflect the rapid, naturally occurring portions and micro-cycles of heuristic talk within the group discussions. Several steps of the heuristic appeared to be occurring in combination and almost simultaneously.

At times, several steps of the heuristic appeared to be occurring simultaneously. This may have been due to a weakness of the heuristic itself, however, students naturally seemed to employ complex combinations of ideas, discussion, acceptance, rejection, writing and checking in order to arrive at suitable solutions. Garner (1990) has argued that learners who have high or adequate background knowledge do not need to employ general learning strategies when solving problems. Garner (1990) argued that effective problem solving occurs when a student monitors their own learning, holds a sufficient knowledge base, recognises that effort and performance are valued and is able to transfer and adapt strategies from earlier contexts. The findings of this current study would suggest that some or all of these conditions were met in the early lessons and hence generated the student activity evident of the problem solving heuristic. This would imply that the heuristic was a product of effective problem solving rather than a tool to assist problem solving.

Rigid adherence to the steps of the problem solving heuristic could be problematic for students. If students had rigidly adhered to the problem solving heuristic steps, the natural flow of ideas and discussions may have been disrupted. In addition the students would have had to maintain their own reflective capacity to acknowledge the steps of the heuristic as they were passed. This would seem to be an impractical imposition for students if they are already broadly aware of the problem solving process.

The structure of heuristics (Robinson, 1946; Thomas & Robinson, 1982; Bransford & Stein, 1984; Roth & Roychoudhury, 1993) appears to imply lineal relationships among the terms. Each step of the heuristic would be completed prior to the next step and so to the completion of a problem. Given the evidence, the concept of a lineal model does not always seem appropriate.

Evidence in the transcripts of student talk, the MAKITAB analysis and the NUD*IST analysis all seemed to show that the heuristic elements occurred in both random micro-cycles and larger macro-cycles. For example, students would propose an idea only to have the idea rejected in a single line of discussion. Small cycles of ideas, proposals, counter proposals, discussion agreements, disagreements, rejections, acceptances, making written records and checking would be nested within the larger cycle represented by the problem solving heuristic. The data suggested that any element of the problem solving process may trigger any other element or series of elements. The concept of order in the elements did not appear as important as the worth and validation of ideas. Students were not discouraged, if after recording an apparently worthwhile idea, further discussion resulted in the idea being rejected. The group moved generally from the initial setting of the problem to a group consensus of a suitable solution, or a solution that appeared suitable at that time.

This would imply that if the heuristic model is linear, it is linear only in a very broad sense and that the current structure does not truly reflect the prob lem solving processes occurring at the micro level. Although the heuristic model elements are part of the descriptive terminology of the MAKITAB instrument it should be noted that the instrument does not indicate a lineal relationship among the elements. An alternative model diagramming the micro level processes might be constructed on a wheel concept such as shown in Figure 3. Figure 3 shows a dynamic relationship among the elements of the problem solving process.

Figure 3

Figure 3: Dynamic problem solving heuristic

Each point on the model can be accessed from any other point. No direction or order is specified and no starting point or finishing point is specified. In this way the essential elements of the problem solving heuristic are maintained yet the flexibility within the model is improved and is more likely to reflect the actions of good problem solvers.

Factor Three

Students did not have a range of suitable learning strategies for actioning the heuristic. For example, there was little evidence of the use of effective strategies for actioning the "check" step of the heuristic and this in turn hindered the finding of "correct" solutions to problems.

The results of the data analysed indicated that the heuristic term "check" and its synonyms was often found in the students' talk, however, reading of the transcripts showed that students did not regularly and thoroughly use alternative checking strategies. Instead, students merely repeated the strategy used in solving the problem to check the solution found. If students have little opportunity or lack skills in the examination of disconfirming evidence, either through the group discussions, the checking process or the actions of the teacher, they will unwittingly arrive at incorrect solutions having acted in accordance with the problem solving heuristic. If students have suitable strategies for effective checking of a solution then it is more likely that appropriate solutions will be found.

Heuristic models described in the literature exhibit different levels of support for students. For example the Polya (1945) model of understand the problem, devise a plan, carry out the plan and look back, provides high level overview support similar to the problem solving heuristic used in this study. The SQ4R (Thomas & Robinson, 1982) model provides a far more strategic level of support directing students to study, question, read, recite, review and reflect. The difference in the two levels, overview and strategy, will affect the model's utility for both teachers and students. Lesson four data indicated that even if students followed the heuristic steps it was still possible to conclude the problem solving process with a result that was incorrect. Incorrect solutions imply that there is insufficient checking occurring at that stage of the heuristic.

The heuristic used in this study assumed that a group's corporate wealth included the strategies that enable problem solving. That is, strategies for ideas generation, discussion strategies, strategies for determining acceptance or rejection of an idea, writing or recording strategies and strategies for checking solutions. A total lack of any one subset of these strategies would cause the problem solving process to falter. Conversely, where there exists at least one strategy the problem solving process would continue. This strategy may be a naturally occurring one as found by Lindow, Peterson and Wilkinson (1985) in their study of verbal disagreements when they found that students spontaneously used conflict resolution and consensus agreement strategies.

Factor Four

In the case of low student motivation or low levels of task talk, the problem solving heuristic could act as a framework to facilitate, guide and prompt discussion and problem solving.

In lesson six it appeared that the students were less motivated to state ideas, propositions and discuss insights as possible solutions to the problem. The student behaviour on this occasion seemed to imply that getting the answer to a problem could be more straight forward with no excursions into error, retrial, rethink or reject. This attitude was contrary to the attitude displayed in lessons one, two and three where students employed numerous approaches to solving problems with little or no hesitation. The apparent lack of motivation seemed to be linked with the problem content and the personal motivations of the students. In this lesson, however, the NUD*IST analysis indicated that a higher proportion of the student talk could be attributed to the problem solving heuristic terms and synonyms. This would suggest that in the case of low student motivation or low levels of task talk, the problem solving heuristic could act as a framework to facilitate, guide and prompt discussion and problem solving.

The teacher's specific actions in lesson six to redirect leadership roles toward some students and away from the high achiever may have been an attempt to reduce the reliance of lower achievers on higher achievers, which in turn hold back the high achievers (Perry, Geoghegan, Owens & Howe, 1995). If this was the case, the evidence suggesting higher proportions of heuristic use in lesson six could possibly be attributed to the high achieving student continuing to model the problem solving heuristic, or lower achievers using the heuristic steps as a result of modeling by other students in the earlier lessons. Further, the express direction of the teacher to use the problem solving heuristic may have directed students to extend discussions beyond that which may have occurred (Deering & Meloth, 1991).

Factors Pertaining to the Student Group

Factor Five

Students preferred to use their own procedures and prior knowledge in problem solving.

The heuristic was first overtly used in lesson four, however, the attempt to guide the problem solving process by students was confused. In later situations where use of the heuristic may have aided the problem solving process students did not attempt to utilise the model. In situations where the solution to a problem was reached early in the lesson, the students did not appear to have a clear recollection of the process by which the solution was obtained. These findings are supported by Ross, Rolheiser and Hogaboam-Gray (1996) who found that students preferred to use their own procedures and instruments, rather than those developed by exemplar teachers. Given a choice, students may prefer to follow their instincts in solving problems.

Factor Six

Group discussion during problem solving took place at high speed with many tacit, nonverbal understandings, half completed sentences and changes of direction where a single idea or proposal was followed by a burst of ideas, counter suggestions and negotiations.

Quite often only half sentences were spoken and yet other students seemed to know what was meant, and quite often responded with more suggestions, ideas and propositions. Furthermore, talking in the group activity seemed to occur in strings or runs. A single idea or proposal would often be followed by a burst of ideas, counter suggestions and negotiations. On occasions when use of the heuristic apparently was covert or unintentional, it appeared that the students moved through the steps very quickly. Most often the shift from one step to the next was very smooth. It was also evident that unintentional use of the heuristic occurred with no clear adherence to the order of the steps as diagrammed for the students (see Figure 2).

Lindow, Peterson and Wilkinson (1985) found that in a cooperative group setting higher achieving students, and boys in particular, provided a greater number of demonstrations and answers to the discussion points. It is clear that in this study, most of the group discussions occurred at high speed and more often involved greater participation by the boys. This was particularly obvious in lessons one to four where students spoke relatively quickly in stating ideas, propositions or engaging in negotiation.

Factor Seven

The lower achieving student was disadvantaged not only by having little understanding of the heuristic but also by a lack of knowledge of how the steps in the heuristic might be actioned. However, the lower achieving student appeared to be well aware of the status of the discussion and the group activity.

It is possible that lower achieving students could be unaware that the solving of a problem involved a framework of ideas generation, discussion, acceptance or rejection of ideas and the recording and checking of a solution. If so, it would be unlikely that they could effectively self-monitor and assess the point at which the group was having difficulty. For example, a group's inability to discuss their ideas will not be helped by reference to the problem solving heuristic that indicates discussion should follow the generation of ideas. The group will need strategies for developing discussion such as taking turns, stating opinions or looking for positive and negative aspects of an idea.

A lack of strategies available to an individual, particularly in respect to the discussion of ideas may have significant impact on a student's participation. In contrast to active students in the target group, the passive student appeared much less involved in all discussions but still appeared to follow the ideas, reactions and counter-ideas of the group members. Although the transcripts, MAKITAB and NUD*IST analyses indicate low levels of input to most discussions, video evidence suggested that the passive student was well aware of the status of the discussion and the group activity. She did not often put forward her ideas, however, it may be incorrect to assume that her quieter involvement implied less thinking, or less problem solving ability.

One explanation could be that she lacked the confidence and skills to participate (King,1993). This would include group social skills, discussion skills and negotiation skills to make her contributions heard, as for example in lesson one. In lesson two, however, personal experience of camping or outdoor activity seemed to boost her confidence and resulted in higher levels of verbal involvement. It is possible that teacher expectation effects and self-fulfilling prophecies may have exacerbated the situation, particularly if the teacher had assumed that student passivity could not be addressed within the classroom environment. If the student thought that the researcher held low expectations of her recall ability these effects may have also been present in the stimulated recall interviews.

However, effective problem solving is most likely a function of the student and the model among other variables. If a student's understanding of the elements of the model and the nature in which those elements interact, affects the quality of the problem solving, then it is clear that students need to develop this understanding. It appears unlikely that students would hold a strong understanding of the heuristic if they were unable to describe how the element of the heuristic could be actioned. Such would be the case if a student attempted to rote learn the elements of the heuristic. The data examined supports the view that the passive student held the weakest understanding of the problem solving heuristic and was least likely to have contributed strategies for inclusion in the problem solving process. If the problem solving heuristic is to be of greatest use to low achieving students then skills in self-monitoring of cognitive activity (Hart, 1990), management of unproductive beliefs (Hart, 1990) and knowledge of useful strategies (Garner, 1990; Wong, 1985) seem important.

Factors pertaining to the content of the lesson

Factor Eight

Students were overloaded with information and tasks in the problem solving lessons and found it difficult to focus on more than one process at a time.

Sweller (1990), Ahmad, Tarmizi and Sweller (1988) and Sweller and Low (1992) have argued that students could be overloaded in problem solving situations. This assertion is supported by the data from the post lesson interviews. The interviews suggested that students thought the heuristic model was a useful aide, but were unable to provide clear examples of their use of it. Some interview data indicated that the heuristic model was seen more as another framework in which the problem should be solved, but not an effectual aide to reaching the solution. In interviews following lessons five, six and seven, students sometimes claimed that they had "done it last week". This suggests that students considered that learning from the model was complete, there was nothing else to be learned from it and therefore the overload experienced could be reduced by ignoring the heuristic.

In lessons four to seven, extra tasks also appeared to overload students. In lessons one, two and three the students were simply presented with the problem and asked to provide a solution. In later lessons students were required to understand the problem, choose from the list of problem solving strategies, solve the problem, while demonstrating an awareness of the problem solving heuristic and employing cooperative group learning skills. The components listed for the latter lessons appeared to compete for the students' attention and may have had the effect of crowding the learning environment.

Often during the student interviews, on sections concerning the teacher's introduction of the lesson, the respondent would claim that they were "just listening, not thinking anything". The interview data gave no indication as to the meaning of "not thinking anything". It is possible that students found it difficult to focus their thinking on two or more issues simultaneously. That is, students found difficulty in focussing on the information being received through listening, the expected cognitive activity of solving the problem and the metacognitive activity of reflection on effective problem solving (Sweller & Low, 1992). Alternatively, students may have found difficulty in verbalising or recalling the thoughts that had occurred during the lesson (King & Tuckwell, 1983).

A third alternative could be that the thinking most likely to occur, at the time the teacher introduced the problem solving heuristic, was affected by the order of the lesson components. The components introduced were the problem solving heuristic, followed by the group cooperation skills, the list of problem solving strategies and finally the lesson problem. Thinking that focussed on solving the problem would not be encouraged if the problem was last in the series of information delivered by the teacher. In lessons four to seven the problem was presented last out of all the lesson components. It is not surprising that students reported difficulty in thinking about the strategies they should use. Stating the problem as a final part in the lesson introduction, forced students to try and think about strategies and the problem solving heuristic without a problem context in which to apply them. This sentiment was evident in the transcripts of the stimulated recall interviews. Listening, as reported by students, may have been simply taking in information and was a strategy used by students to manage the apparent overload of information.

Factors pertaining to the teacher

Factor Nine

There was insufficient modeling by the teacher of how the heuristic might be used in problem solving tasks. Also group monitoring behaviours to support the use of the heuristic, which on the surface appeared to be effective, were occasionally parried by the group.

The heuristic was modeled by the teacher at the beginning of each lesson through reference to the boarded diagram. Questions about the diagram were directed to each group in the class. The model was also referred to while the teacher was monitoring behaviours and in the conclusion of each lesson. At the time this was thought to be adequate but on reflection, and for the target group of four students, the teacher's modeling does not seem to have been particularly effective.

During the activi ty part of the lessons the teacher asked questions of the target group in relation to the heuristic. The students were required to indicate on the heuristic model where the group was operating, however, generally this did not result in any significant discussion and did not provoke any further reflection from the teacher or the students. Conversely, students were aware that if they did not achieve success in a task the teacher was quite likely to help them with clues or possible strategies. On a few occasions the teacher refocused the students on the problem solving heuristic and the stage at which the students were operating. This had the effect of guiding the students in the solving of the problem, for example, by suggesting that if the group was satisfied they had completed the discussion of an aspect then they should seek agreement to accept or reject the idea.

However, it was apparent that the level of teacher modeling was insufficient. Brown and Palincsar (1987) argue that teacher modeling and the definition of specific roles and strategic tasks, provides a firm foundation for student learners. Results of studies found that long term maintenance, transfer and generalisation of learning was accomplished for students that had received the teacher modeling. Personal experience of the writer in the use of the reciprocal model (Palincsar & Brown, 1989) has found that students easily undertake the specific roles following teacher modeling.

Had the teacher in this study rigidly and frequently modeled the implied processes and strategies of the heuristic, students may have achieved even higher levels of problem solving success. For example, if the teacher had suggested that students ought to monitor their progress according to the heuristic on a regular basis or that students should take an active leadership role in solving the problem through directing the problem solving processes of the group, higher levels of problem solving success may have been achieved by students. Teacher modeling of regular reflection on the group's position on the model may have also encouraged students to take on a group monitoring role. Regular reflection may also have encouraged higher levels of recording and questioning.

Furthermore, it appeared that at times, the group needed to be allocated traditional cooperative group roles (Johnson & Johnson, 1975, 1994; Burns, 1981) such as leader, questioner, recorder and researcher. This was most evident in the sixth lesson where one student was absent and the role of questioner, even though not formally allocated, was missing from the group. This student often appeared to question the answers of other group members and hence promote discussion and reflection. Absence of the student and the role was associated with much less group discussion, lower levels of reflective talk and lower quantities of task talk altogether.

However, it is also apparent that the students swapped roles frequently and that this swapping of roles was done according to the interaction of numerous factors. These included such aspects as

Detailed discussion of the factors above is beyond the scope of this paper, however, it is evident that there are numerous interrelated and complex factors acting within the cooperative learning situation. Central to each of these factors is the teacher's role within the classroom and the activity of the lesson (King, Barry, Maloney & Tayler, 1993b). In this study the focus has been on the teacher's cognitive intent and specifically in the teaching of a problem solving heuristic. While it has been argued that the teacher's modeling was one aspect that may have led to less effective use of the heuristic, other authors attribute lower achievement in the use of heuristic devices to poor strategy use (Chan, 1994), a lack of student knowledge (Garner, 1990) and low skill levels in question generation (Wong, 1985). Hart (1990) claimed that modeling the problem solving processes of experts for low achievers overloaded the low achieving students. Low achievers were better served by the models from average students.

Alternatively, Leighton, Slavin and Davidson (1989) used heuristics in cooperative groups and consistently found that the cooperative groups out performed the control groups. This could mean that the effectiveness of the problem solving heuristic is maximised for low achieving students through the modeling effect of the average and high achieving students in the cooperative groups. If low achievers receive the heuristic modeling from average and high achieving group members, the heuristic could remain a productive device in the small group learning situation. This would imply that the teacher's modeling would cater more for the needs of the higher achiever in the group and that there exists a flow-on effect from this modeling.

Lesson data in this study suggests that by not frequently refocusing on the problem solving heuristic, and opting to give clues to the solving of the problem, the teacher may have inadvertently regained control of the problem solving process. As a result student ownership and student investment in seeking a justifiable solution may have been weakened by the absence of understanding and the attempts at guessing solutions. In effect the skills required to solve the problem, including use of the heuristic, could have been undermined by teacher hints and clues.

Conclusions

The findings of the study imply that teachers in cooperative learning must work with students in order to develop effective problem solving skills and in this instance the effective use of a problem solving heuristic. Specifically teachers need to determine what pre-existing heuristics and frameworks are held by students. Such questions as "how do people solve problems?" and "what are the steps involved in solving a problem?" may elicit starting points for student discussions on understanding problem solving heuristics and frameworks. The use of a model should be part of a negotiated curriculum rather than a framework provided by the teacher in which students should operate.

Teacher awareness of the students' ability to action the heuristic steps, in a fast moving, complex group, may have to be developed through a two stage learning process. In stage one the teacher could actively test to see if students can recall suitable strategies aligning with various heuristic steps. In stage two of the process the teacher is able to unobtrusively observe the success students have in actioning the steps of the heuristic with suitable strategies while solving problems.

It may be also necessary for teachers to teach and model participation and management strategies as well as discussion and decision making skills. The culture of the group should recognise the listener's responsibility and right to participate in group discussions. Difficulties may arise if the onus for the participation of passive students rests with the passive student. Suitable modeling by the teacher in each of the areas of the heuristic students would promote student understanding and implementation of the model in problem solving contexts.

Fundamental, is the understanding developed from this study and others, that heuristics and frameworks themselves are derived from observations of natural contexts and effective workers in action. The frameworks do not exist of their own right but are generalisations of the processes effected by successful students. It is therefore necessary to remind teachers that it is likely in group work some students will demonstrate both intentional and unintentional use of problem solving frameworks and mandating one framework over another may cause confusion for some students. If teachers neglect to teach each strategy within larger, broader frameworks, a rote learning of strategie s and a concomitant loss in understanding may result. On balance, this research indicated that cooperative learning has considerable potential for the process of teaching and learning heuristics. However, it is a complex process because of the number of factors that impact on the nexus between the cognitive intent of the teacher and the outcomes of students. With further research this process should become clearer.

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Contact person: Kim Pitts-Hill, Education Department of WA
kim.pitts-hill@eddept.wa.edu.au

Please cite as: Pitts-Hill, K., Barry, K., King, L. and Zehnder, S. (1998). A description of student problem solving using a heuristic in a cooperative group setting. Proceedings Western Australian Institute for Educational Research Forum 1998. http://www.waier.org.au/forums/1998/pitts-hill.html


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