小学校算数科における児童の「計算のきまり」に関する理解の変容の分析―初期段階の代数的構造の理解の解明を通して―

抄録

The purpose of this paper is to clarify the changes and processes in children’s understanding of “properties of operation” in elementary school mathematics. As a research method, we designed a survey based on “the theoretical framework for the process of understanding the algebraic structure in the set” shown by Kurihara (2023), and conduct a questionnaire survey and an interview survey.

As a result of this paper, based on “the theoretical framework shown by Kurihara (2023), a “lower phase”, “observational level”, “insightful level”, “formal level”, and “higher phase” were defined. We also clarified changes in children’s understanding levels. In addition, when the level of understanding of individuals after solving a problem is the same in a pair, a change in understanding does not likely to occur during the problem-solving process by the pair. When the level of understanding of individuals after solving a problem differs between pairs, a change in understanding is observed, indicating that understanding can be promoted. In an analysis of the understanding process based on cases of pairs in which significant changes in understanding are observed, one child goes back and forth from the “observational level” to the “insightful level” and is then transformed to the “insightful level”.