Research on instruction of rate and proportion to foster the transition from informal to pre-formal expressions

2022 Fiscal Year Final Research Report

• Project/Area Number: 20K02909
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 09040:Education on school subjects and primary/secondary education-related
• Research Institution: Aichi University of Education
• Principal Investigator: YAMADA Atsushi 愛知教育大学, 教育学部, 教授 (20273823)
• Project Period (FY): 2020-04-01 – 2023-03-31
• Keywords: プリフォーマルな表現 / インフォーマルな表現 / 割合指導

Outline of Final Research Achievements

The purpose of this study is to investigate informal expressions related to rate and proportion that students may have prior to formal instruction of rate and proportion, and to examine the instruction that foster the transition from informal expressions to the use of preformal mathematical expressions.
Based on the investigation, four types of instruction as follows are designed : a) how to draw a "relationship diagram" and making a mathematical expression with □, b) rephrasing problem statements, c) gesture as an alternative of relationship diagram and as a mnemonic of how to construct it, and d) using an informal expression to complement the interpretation of tape diagrams. The results of the post-test showed a high percentage of correct answers to the national test problems and that many children were able to draw accurate relationship diagram using gestures.

Free Research Field

数学教育学

Academic Significance and Societal Importance of the Research Achievements

割合学習の困難は長年にわたり指摘されており，その学習を促す様々なプリフォーマルな表現（例えば，関係図）に基づく割合指導の研究は盛んである。しかし，そうしたプリフォーマルな表現の使用・解釈にも困難があるというのが児童の実態である。本研究は，プリフォーマルな表現の解釈・使用を下支えしうるインフォーマルな表現に着目しているが，そうした研究は少なく，学術的意義は少なくない。また，インフォーマルな表現からプリフォーマルな表現使用への移行を促すと考えられる４つの指導をデザインし，一定程度の効果も確認できたため，学術的にも社会的にも意義があると考えられる。