Teaching and learning to develop the ability to solve problems using algebraic expressions:Analysis of difficulty in understanding and lesson study

2023 Fiscal Year Final Research Report

• Project/Area Number: 21K02573
• 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: University of Yamanashi
• Principal Investigator: Shimizu Hiroyuki 山梨大学, 大学院総合研究部, 教授 (80562446)
• Project Period (FY): 2021-04-01 – 2024-03-31
• Keywords: 高校生の文字式の理解 / 式をひとまとまりとみること / 方程式の利用

Outline of Final Research Achievements

The purpose of this research is to clarify where students stumble and have difficulty when trying to solve problems using letter expressions in school mathematics, and based on the results, to learn how to use letter expressions. The aim is to propose learning guidance that aims to solve problems.
In this study, we conducted a questionnaire survey targeting high school students in two districts across the country. This survey revealed that even high school students have difficulty viewing formulas as a whole, and that a certain number of students remain unresolved even as they progress in their studies. Based on this, we decided that instruction that emphasizes viewing equations as a unit is necessary at the junior high school level, and we implemented lessons aimed at understanding the relationships between equal quantities when using equations.

Free Research Field

数学教育学

Academic Significance and Societal Importance of the Research Achievements

高校生に対して式をひとまとまりとみるといった文字式の見方やその理解を明らかにする調査は，これまで行われていなかった。中学校段階では，式をひとまとまりとみることの困難性は明らかとなっているので，その調査と同じ問題で行うことによって，その困難性が高等学校へ進学し数学の学習を進めていくうちに，解消していくのか，それとも解消するために何らかの手をうつ必要があるのかを明らかにすることは，生徒も学びから学習指導を提案するために価値のあることであると考える。本研究で，一定数の生徒に，その困難性が残ることが明らかとなり，中学校段階での指導を充実させることが明らかになったという点で研究の意義があると考える。