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8 - The Role of Domain Knowledge in Creative Problem Solving

Published online by Cambridge University Press:  19 January 2010

By
Richard E. Mayer
Edited by
James C. Kaufman  and
John Baer
Richard E. Mayer
Affiliation:
Department of Psychology, University of California at Santa Barbara, Santa Barbara, California
James C. Kaufman
Affiliation:
California State University, San Bernardino
John Baer
Affiliation:
Rider University, New Jersey
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Summary

Consider the word problems presented in Table 8.1. Some people are able produce solutions to these problems, whereas others make errors, get frustrated, and fail to generate a correct answer. What do successful mathematical problem solvers know that less successful mathematical problem solvers do not know? This seemingly straightforward question motivates this chapter.

A review of research on mathematical problem solving supports the conclusion that proficiency in solving mathematical problems depends on the domain knowledge of the problem solver (Kilpatrick, Swafford, & Findell, 2001). In this chapter, I examine the research evidence concerning five kinds of knowledge required for mathematical problem solving: (1) factual knowledge, (2) conceptual knowledge, (3) procedural knowledge, (4) strategic knowledge, and (5) metacognitive knowledge.

Table 8.2 provides definitions and examples of each of the five kinds of knowledge relevant to mathematical problem solving. Factual knowledge refers to knowledge of facts such as knowing that there are 100 cents in a dollar. Conceptual knowledge refers to knowledge of concepts such as knowing that a dollar is a monetary unit and knowledge of categories such as knowing that a given problem is based on the structure (total cost) = (unit cost) = (number of units). Strategic knowledge refers to knowledge of strategies such as knowing how to break a problem into parts. Procedural knowledge refers to knowledge of procedures such as knowing how to add two decimal numbers.

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Creativity and Reason in Cognitive Development , pp. 145 - 158
Publisher: Cambridge University Press
Print publication year: 2006

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