Development of a Curriculum Bridging Elementary and Secondary Mathematics on the Basis of the Variable Concept

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K00954
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Science education
• 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)
• Research Collaborator: Isono Masato ; Aoyagi Jun
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: 変数 / 小学校算数 / 中学校数学 / 数量関係 / 文字式 / 方程式 / 関数 / 変量

Outline of Final Research Achievements

The aim of this study was to construct a principle which makes it possible to develop a curriculum bridging learning multiplicative structures at elementary school level and learning algebra at secondary school level. The analysis of previous researches, the current curriculum in Japan, and teaching and learning processes in mathematics lessons from the viewpoint of the variable concept, showed that such curriculum should include (a) to reconceptualize learning multiplicative structures in terms of description of variable quantities of objects-of-thought; (b) to shift from description of variable quantities or the use of variable at meta-level to the use of variable at object-level; (c) to make this shift explicit to students and to maintain the classroom discourse where variables are at object-level.

Free Research Field

数学教育学

Academic Significance and Societal Importance of the Research Achievements

小学校高学年から中学校にかけての算数・数学の指導に関して、学習者の理解の困難については具体的場面を利用することで学習者が取り組みやすくするという方向の提案が多いが、本研究はそうした提案とは方向性を異にし、具体的場面を用いた学習から数学的概念自体を対象とした学習への移行という観点からカリキュラムを吟味したり、そうした移行を意図的に生じさせるようなカリキュラムを構成したりするための原理を提案するという点で意義を有する。