Problem solving beyond the logic of things: contextual effects on understanding and solving word problems

Arguments are put forward in this paper that classroom word problem solving is more-and also less-than the urgent analysis of a factual structure, in the sense that it is essentially a species of a social-cognitive activity. Word-or story-problems, presented in classroom contexts, represent textual and pragmatic patterms of a certain grammaticality. To present a problem verbally to a student means to organize a fact in some way for the attention of a problem solver. There is not only the structure of the problem text itself by which situations are denoted, but there is also the stimulative nature of the social-pragmatic context which shapes the student's textbook-problem solving behavior over a long period of time.The present paper discusses the results of several studies showing, for example, that subject matter related attitudes towards a problem frequently do not play an important part in the problem solving efforts; that students often solve problems correctly without understanding them; and that false contextual expectations can lead to abstruse errors of understanding and to peculiar solution attempts.The studies indicate that students can become sensitive and skilful in perceiving and capitalizing on subtle textual and contextual signs pointing to the solution and anticipating its pattern. It seems that usual textbook problems let students get accustomed to certain courses of processing where a simple fact, like whether an equation works out evenly or does not, can stop the process or push it further. It is argued that the deeper reason for the observed textual and contextual influences on understanding and problem solving lies in a fundamental weakness of the student's epistemic control behavior. The psychological and instructional significance of the studies is discussed.