Learning Geometry Problem Solving by Studying Worked Examples

Abstract

Research has demonstrated that instruction that relies heavily on studying worked examples is more effective for less experienced learners compared to instruction emphasizing problem solving. However, the guidance associated with studying some worked examples may reduce the performance of more experienced learners. This study investigated categories of guidance using geometry worked examples. Three conditions were used. In the theorem and step guidance condition, students were provided with the solution steps required to reach the answer and the theorems used to justify the steps. In the step guidance condition, learners were only provided with the sequence of steps needed to reach the answer but not with the theorems explaining the steps. The problem-solving condition required learners to solve problems without any guidance. It was hypothesized that for students who had already learned the relevant theorems, the major task was to learn to recognize problem states and their associated solution moves. The step guidance condition should best facilitate such knowledge, compared to a problem-solving or a theorem and step guidance approach. For students who had not yet fully learned the theorems, the theorem and step guidance approach should be superior. Two geometry instruction experiments supported these hypotheses. Information concerning theorems should only be provided if students have yet to learn and automate theorem schemas.