Development of Curriculum for Learning Fractions based on the Idea of Mathematics as a Science of Patterns

2022 Fiscal Year Final Research Report

• Project/Area Number: 20K03271
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 09080:Science education-related
• Research Institution: Joetsu University of Education
• Principal Investigator: Nunokawa Kazuhiko 上越教育大学, 大学院学校教育研究科, 教授 (60242468)
• Project Period (FY): 2020-04-01 – 2023-03-31
• Keywords: 算数教育 / 分数 / パターンの科学 / 量と数

Outline of Final Research Achievements

In order that students can not only calculate fractions fluently but also understand fractions as numbers, this study attempted to develop a curriculum framework for learning fractions of elementary school students. The initial framework was constructed on the basis of some mathematicians’ analysis of the relationships between quantities and numbers as well as the idea of mathematics as a science of patterns. This framework was further elaborated after 3rd-, 5th- and 6th-grade lessons on fractions were analyzed from the viewpoint of this framework. The elaborated framework came to include explicit introduction of fractions as numbers by teachers and inner development of the discourse of numbers by learners as well as teachers’ narratives promoting the transition to the discourse of numbers.

Free Research Field

数学教育学

Academic Significance and Societal Importance of the Research Achievements

現行の小学校算数の教科書や授業、先行研究においては、「量分数」概念が重要な役割を果たしており、これが量を用いた分数の導入を支えると同時に、量と数の関係を曖昧にして数としての分数の認識を十分に育成できていないと考えられる。本研究で構築された枠組みは、量と数の関係を明確化した形での分数の導入や展開の方向性、そのために必要な教師の役割などを柱に据えるものであり、従来とは全く異なるアプローチの可能性を示すものである。このアプローチに基づいて学習活動系列などを具体化していくことで、分数をある種の数として明確に位置づけた形での分数学習の展開や、従来と異なる視点での分数学習の研究が可能になると考えられる。