The Experience of Learning Styles and Approaches in Problem-solving

Problem-solving tasks are set as a regular part of the course work on most courses in science, mathematics and technology, and in some social science courses as well. They are seen as an important part of the students’ work because they require the application of knowledge and principles to new situations, thus testing and reinforcing the students’ real understanding of what they have learned. Knowledge without the ability to apply it is rightly seen as a very poor commodity, and teachers therefore regard problem-solving exercises as an important part of learning. We can assume, for the purpose of this chapter, that the problems being set for students have a purely educational value; that it is not so much the solution that is of interest, as the process of reaching that solution. We can thus define a problemsolving task as one which ‘engages the students in thinking about the subject matter in ways designed to improve their understanding of it’. Problems may sometimes be set to give students practice in some procedure, such as solving quadratic equations, but students learn little from this, other than a facility with the procedure itself. Such problems do not fit into our definition. We are concerned only with problems intended to develop in the students at least a greater familiarity with their subject, and perhaps a better understanding as well. The teacher faces a difficult challenge in designing problem-solving tasks that fully serve this educational function. Such tasks should help the students to weave the factual knowledge they have into their own conceptual organisation, by enabling them to elaborate the relationships between concepts and to impose structure on the information they have. If they do less, then the exercise can easily become a meaningless mechanical manipulation, and loses its real educational potential. Naturally, for many teachers the choice of problem-solving tasks is circumscribed by the traditions of their subject, and there is relatively little creative effort involved in designing such tasks. Even when there is, it is more likely to be for the sake of the elegance of the problem, rather than for its educational value. But the design of problems is important because the cognitive activity inherent in a particular problem-solving task determines the way the student will think about the subject matter. ‘Bookwork’ problems will encourage bookwork solutions, requiring very little cognitive effort on the part of the student. A more imaginative problem that challenges the student and invites him to construct new ways of combining information will promote a better understanding. The point is illustrated neatly by Dahlgren’s question to economics students about the cost of a bun (Chapter 2). They were practised at defining the laws of supply and demand, but their lack of basic understanding was revealed by their inability to break out of familiar patterns of thinking to answer a very basic but unusual question. If we can establish the characteristics of a good problem-solving task we must then ask how successful it is in practice. This brings us back to the main theme of this book. Here we ask “what are students’ experiences of learning from problemsolving?” In this chapter, we begin by considering how problem-solving has been studied in the past, and how this relates to recent studies of the students’ experience of problem-solving. We shall find that students’ approaches to problem-solving can be described in terms of the deep and surface approach already introduced in Chapter 3. This categorisation is developed further to include a theoretical analysis of the internal relations between the students’ learning processes and the nature of the subject matter content. The aim overall is to clarify the nature of learning from problem-solving which may then enable us to use it more efficiently as a teaching method.