Learning by Problem-Posing as Kit-Building for Structure Understanding of Polynomial Factorization

Abstract

Polynomial factorization is a basic skill required of middle-school students. Students typically learn the skill through solving polynomial factorization problems. In this paper, as a new method to learn the skill, we propose learning by problem-posing factorable polynomial expressions. In this problem-posing, we use the kit-building method, where a student is provided with a set of components such that a structure can be constructed using the components. To learn polynomial factorization, it is crucial to understand the polynomial expression as a structure. The effectiveness of structure understanding in the kit-building method is confirmed in several learning domains, for example, arithmetic and mathematic word problems. In the exercise performed in this study, a student is required to create a polynomial expression that can be factorized using a specified factorization rule, which we call “problem-posing.” Students and teachers accepted that this is as a better form of learning factorization, i.e., through practical use at universities and middle schools.