A System that Supports Learners’ Strategic Thinking for Solving Highschool Mathematics Problems

Abstract

In high-school mathematics, learners sometimes cannot solve problems well even if they remember formulas. At other times, learners cannot solve similar problems well even if they see a sample answer of the original problem. These cases indicate that mathematical knowledge, such as knowledge of the formulas and definitions in high school math textbooks, is insufficient to solve problems. Past studies have shown that it is important to plan which formula should be used in problem solving. The knowledge necessary to determine which formula should be used in problem-solving is called knowledge of the problem-solving strategy. In the past researchers on educational support systems, there is no established method for mathematics education support systems to construct a problem-solving process with the knowledge of the problem-solving like a human doing. In this study, we analyze problemsolving process in which learners use the knowledge of problem-solving strategy from specific examples. After that, we construct a system with problem-solving ability using the knowledge of the problem-solving strategy. Our system can also verbalize problem-solving processes constructed by itself and let learners read the generated commentary. We conducted a preliminary experiment comparing the commentary with sample answers in usual reference books. In this preliminary experiment, we evaluated the correct answer rate of similar questions and the acquisition rate of the knowledge of problem-solving strategy. As a result, subjects reading the commentary by the system mark better correct answer rate of similar problems, and they can reproduce the knowledge of problem-solving strategy better than ones reading reference books.