Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics

TLDR

The authors argue that, rather than mastering skills, students should engage in problem solving, noting that mathematics has historically distinguished between knowledge acquisition and application, and that common dichotomies acquire new meaning under this perspective. The study proposes that curriculum reform should enable students to problematize the subject, building on Dewey’s reflective inquiry to enhance understanding and contrasting it with other problem‑solving views. The authors develop an alternative principle grounded in Dewey’s reflective inquiry, arguing it facilitates understanding and contrasting it with other problem‑solving perspectives.

Abstract

We argue that reform in curriculum and instruction should be based on allowing students to problematize the subject. Rather than mastering skills and applying them, students should be engaged in resolving problems. In mathematics, this principle fits under the umbrella of problem solving, but our interpretation is different from many problem-solving approaches. We first note that the history of problem solving in the curriculum has been infused with a distinction between acquiring knowledge and applying it. We then propose our alternative principle by building on John Dewey’s idea of “reflective inquiry,” argue that such an approach would facilitate students’ understanding, and compare our proposal with other views on the role of problem solving in the curriculum. We close by considering several common dichotomies that take on a different meaning from this perspective