Schoenfeld (1983) advocates small-group problem solving for several reasons. First, it gives the teacher a chance to coach students while they are engaged in semi-independent problem solving; he cannot really coach them effectively on homework problems or class problems. Second, the necessity for group decision making in choosing among alternative solution methods provokes articulation, through discussion and argumentation, of the issues involved in exercising control processes. Such discussion encourages the development of the metacognitive skills involved, for example, monitoring and evaluating one’s progress. Third, students get little opportunity in school to engage in collaborative efforts; group problem solving gives them practice in the kind of collaboration prevalent in real-world problem solving. Fourth, students are often insecure about their abilities, especially if they have difficulties with the problems. Seeing other students struggle alleviates some of this insecurity as students realize that difficulties in understanding are not unique to them, thus contributing to an enhancement of their beliefs about self, relative to others.
We believe that there is another important reason that small-group problem solving is useful for learning: the differentiation and externalization of the roles and activities involved in solving complex problems. Successful problem solving requires that one assume at least three different, though interrelated, roles at different points in the problem-solving process: that of moderator or executive, that of generator of alternative paths, and that of critic of alternatives. Small-group problem solving differentiates and externalizes these roles: different people naturally take on different roles, and problem solving proceeds along these lines. And here, as in reciprocal teaching, students may play different roles, so that they gain practice in all the activities they need to internalize.
There is one final aspect of Schoenfeld’s method that we think is critical and that is different from the other methods we have discussed: What he calls postmortem analysis. As with other aspects of Schoenfeld’s method, students alternate with the teacher in producing postmortem analyses. First, after modeling the problem-solving process for a given problem, Schoenfeld recounts the solution method, highlighting those features of the process that can be generalized (see math sidebar). For example, he might not the heuristics that were employed, the points in the solution process where he or the class engaged in generating alternatives, the reasons for the decision to pursue one alternative before another, and so on. In short, he provides what Collins and Brown (1988) have labeled an abstracted replay, that is, a recapitulation of some process designed to focus students’ attention on the critical decisions or actions. Postmortem analysis also occurs when individual students explain the process by which they solved their homework problems. Here students are required to generate an abstracted replay of their own problem-solving process, as the basis for a class critique of their methods. The alternation between expert and student postmortem analyses enables the class to compare student problem-solving processes and strategies with those of the expert; such comparisons provide the basis for diagnosing student difficulties and for making incremental adjustments in student performance.
A FRAMEWORK FOR DESIGNING LEARNING ENVIRONMENTS
Our discussion of cognitive apprenticeship raises numerous pedagogical and theoretical issues that we believe are important to the design of learning environments generally. To facilitate consideration of these issues, we have developed a framework consisting of four dimensions that constitute any learning environment: content, method, sequence, and sociology. Relevant to each of these dimensions is a set of characteristics that we believe should be considered in constructing or evaluating learning environments. These characteristics are summarized in the adjacent sidebar and described in detail below, with examples from reading, writing, and mathematics.
Recent cognitive research has begun to differentiate the types of knowledge required for expertise. In particular, researchers have begun to distinguish among the concepts, facts, and procedures associated with expertise and various types of strategic knowledge. We use the term strategic knowledge to refer to the usually tacit knowledge that underlies an expert’s ability to make use of concepts, facts, and procedures as necessary to solve problems and accomplish tasks. This sort of expert problem-solving knowledge involves problem-solving heuristics (or “rules of thumb”) and the strategies that control the problem-solving process. Another type of strategic knowledge, often overlooked, includes the learning strategies that experts use to acquire new concepts, facts, and procedures in their own or another field.
We should emphasize that much of experts’ strategic knowledge depends on their knowledge of facts, concepts, and procedures. For instance, in the math example discussed earlier, Schoenfeld’s students could not begin to apply the strategies he is teaching if they did not have a solid grounding in mathematical knowledge.