A VIEW OF MATHEMATICAL PROBLEM SOLVING IN SCHOOL
James G. Greeno Stanford University and the Institute for Research on Learning
The information-processing view of problem solving has achieved several major successes. Among them is the analysis of cognitive processes and knowledge structures involved in solving problems in school mathematics. This paper will begin with a brief review of results that have been obtained in these analyses, considering both the contributions to cognitive science that have been achieved, and some ways in which the resulting theoretical results are beginning to be used in educational practice. We now have clear theoretical pictures of the knowledge that text problems require, and these can be used to teach that problem-solving knowledge more effectively.
We can also use these clear theoretical pictures to ask whether the knowledge needed for text problems is what we want students to learn. In my view, the answer is that knowledge required for solving text problems is unacceptably limited. I will present this opinion and sketch an alternative view of mathematical knowing as an activity, rather than as a set of cognitive structures and processes. If we want students to become knowers of mathematics in this sense, the goals and methods of