Aspects of Japanese High School Students’ Word Problem Solving from a Probabilistic Modeling Perspective: A Case of Probability of Repeated Trials

Abstract

With the increasing complexity of society, the importance of quantifying uncertainty in decision-making is growing. Alongside the development of technologies such as TinkerPlots and CODAP, and the spread of mathematical modeling research in general, there has been a recent proposal that school education should foster problem-solving skills and abilities by engaging students in real-world problem-solving using probability (probabilistic modeling). However, teaching probabilistic modeling in school education is not easy. In this paper, we aim to clarify whether students can engage in the probabilistic modeling process through solving word problems. The results demonstrate that students can indeed engage in probabilistic modeling through word problem-solving, provided that the class includes at least the following three instructional innovations: (1) Designing teaching materials in a way that causes students to make errors or diverge in their thinking. (2) Creating tasks where students’ expectations differ from simulation results, or where students can intuitively sense the correct outcome but struggle to quantify and explain the degree of accuracy. (3) Including activities that allow students to change the conditions of the problem.