Teaching problem-solving strategies in mathematics

Eva Fülöp

doi:10.31129/lumat.v3i1.1050

Abstract

This study uses the methodology of design-based research in search of ways to teach problem-solving strategies in mathematics in an upper secondary school. Educational activities are designed and tested in a class for four weeks. The design of the activities is governed by three design principles, which are based on variation theory. This study aims to contribute to an understanding of how the teaching of problem-solving strategies and strategy thinking in mathematics can be organized in a regular classroom setting and how this affects students´ learning in mathematics. We start by discussing the nature of the concept strategy in relation to the concepts of method and algorithm. Using pre- and post-tests, we compare the development of the students´ conceptual and procedural abilities with a control group. In addition, we use the post-test to investigate the students´ use of problem-solving strategies. The results suggest that these designed activities improve students’ ability to use problem-solving strategies. Moreover, significant differences were found in conceptual and procedural abilities in mathematics, the experimental group improving more than the control groups.

Highlights

Problem-solving and strategy thinking play a crucial role in both everyday and professional life, in a world that is becoming more and more turbulent and characterized by rapid technological innovations, shifting political alliances and emerging economies (NCSM, 1977; Mason, 1982; Sloan, 2006; Goldman, 2012)
This study uses the methodology of design-based research in search of ways to teach problem-solving strategies in mathematics in an upper secondary school
This study aims to contribute to an understanding of how the teaching of problem-solving strategies and strategy thinking in mathematics can be organized in a regular classroom setting and how this affects studentslearning in mathematics

Summary

Introduction

Problem-solving and strategy thinking play a crucial role in both everyday and professional life, in a world that is becoming more and more turbulent and characterized by rapid technological innovations, shifting political alliances and emerging economies (NCSM, 1977; Mason, 1982; Sloan, 2006; Goldman, 2012). The teaching intervention was designed to fit into the regular teaching, without altering the mathematical content but adding learning of strategy thinking This text summarizes the results after the first four weeks of a year-long experiment. In mathematical problem-solving situations, Schoenfeld (1983) describes two different types of decision making, the “what to do” and the “how to” do decisions. The first of these types, the strategic decisions, includes selecting goals and deciding to pursue courses of action. One of the most important responsibilities of educators should be to facilitate the development of proper problem-solving skills, which include knowledge about strategies (Posamentier & Krulik, 1998)

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