Teaching through problem solving
Donaldson, Sarah Elizabeth
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If problem solving is what mathematics is all about, then mathematics teachers should be in the business of helping students develop their problem-solving abilities. One way to help is to teach mathematics through problem solving. In this approach, problems are a means by which students learn new mathematical concepts and synthesize mathematical knowledge. During the last few decades, mathematics education researchers have called for studies that focus on the role of the teacher in problem-solving instruction. The purpose of the present study was to investigate the teaching practices used by those who teach through problem solving. Four high school mathematics teachers participated in the study. Although each teacher was unique, five common practices emerged: (a) teaching problem-solving strategies, (b) modeling problem solving, (c) limiting teacher input, (d) promoting metacognition, and (e) highlighting multiple solutions. These practices were consistent with the advice given by mathematics education experts.