Epistemological and semiotic research on the design of mathematical lessons based on Mutual Development Model

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K04703
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Education on school subjects and activities
• Research Institution: Kagoshima University
• Principal Investigator: YAMAGUCHI TAKESHI 鹿児島大学, 法文教育学域教育学系, 教授 (60239895)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: 相互発達モデル / 社会的相互作用 / かけ算

Outline of Final Research Achievements

This research aims to develop the theoretical framework for designing teaching and learning process of mathematics which focuses on significant roles of social interactions: negotiation of meaning and negotiation of representation. Main findings of this research are summarized as the following two points.
Firstly, current issues of lessons of ‘multiplication’ which is taught at the third grade in the elementary school was considered in terms of ‘model of mutual development of mathematical meaning and mathematical representation (Mutual Development Model)’ proposed in the previous research. And an alternative new plan of ‘multiplication’ was also designed. Secondly, the teaching experiment based on the alternative new plan was conducted for the third graders. As the result of both qualitative analysis of the teaching experiment and the analysis of the post-test, the effectiveness of both the new plan and ‘Mutual Development Model’ were verified respectively.

Free Research Field

数学教育学

Academic Significance and Societal Importance of the Research Achievements

多くの教師は，授業の「練り上げ」段階における社会的相互作用の重要性を認識してはいるものの，その具体化において悩みやジレンマを抱えている。こうした課題に対して，本研究成果の学術的意義や社会的意義は，「数学的意味の協定」と「数学的表現の協定」の２つを社会的相互作用の重要な機能ととらえた上で，「相互発達モデル」に基づく具体的な授業改善を提起した点にある。本研究によって，多くの教師が苦慮している社会的相互作用に基づく授業デザインの具体的あり方を提言することが可能になる，と考えている。また，今日強調されている「言語活動の充実」に関する示唆も得ることができる，と考えている。