2023 Fiscal Year Final Research Report
Study on the mathematics lesson with proving: with teaching materials for the students 13-18 years old based on the coherent understanding
| Project/Area Number |
20K02855
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 09040:Education on school subjects and primary/secondary education-related
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| Research Institution | Shiga University |
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Principal Investigator |
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | 証明 / 中高一貫 / 授業構成原理 |
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| Outline of Final Research Achievements |
There are two major results of this research.
The first is the clarification of the importance of " proof with cases" in the teaching of proofs for third graders in junior high school, and the principles for structuring such lessons. Specifically, the following two points were clarified: 1) Proofs should not be regarded as statements combining several theorems and properties, but as a single coherent statement; 2) By interrelating the notation and meaning of proofs for each case, the assumptions of the theorem can be deeply understood.
The second is that we have clarified the principle of structuring a lesson that takes into account the fact that there can be various proofs for a single theorem. By comparing various proofs of a theorem from the viewpoints of the part and the whole, we have derived the principle of a lesson in which mathematical inquiry is conducted through proofs.
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| Free Research Field |
数学教育学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究の成果は，数学を探究するための方法としての証明の位置づけを理論的にも実践的にも明確にすることに貢献すると考える。中学2年生で基礎的な証明を学習した後，証明の仕組みへの理解をいかに高め，証明を数学を学ぶための道具とできるのかをテーマとして，特に中学3年生から高等学校数学への架け橋となるような数学科授業の具体的な教材を開発したり，授業の展開をどのようにすべきかなどの授業構成原理を提案することができた。
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