2021 Fiscal Year Final Research Report
Clarification and control of the transition of the "modes of expansion of the discourse" in generating "incomplete proofs"
| Project/Area Number |
19K02805
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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 | Utsunomiya University |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2022-03-31
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| Keywords | 証明学習 / 未完成な証明 / 命題の認識値 / 命題のステータス / ディスコースの拡張 / 中学校数学 |
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| Outline of Final Research Achievements |
In the process of generating incomplete proofs, when making an argument using the collected information, if there is enough information to grasp the whole picture of the theory, the reasoning can be understood, and it is not necessary to show the details in detail, so a leap of reasoning is generated.
In addition, two patterns were found for the generation of proofs including inversive inference, and the aspects of understanding the epistemic values and status of the propositions influencing each generation were clarified.
Finally, the key to making a complete proof for a student is to recognize the degree of gap or leap in the step of reasoning and how to organize propositions into the proof. Moreover, since the students' ideas are gradually modified and improved, it is becoming clear how to improve and modify the incomplete proof.
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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 |
本研究で「未完成な証明」の生成過程での「ディスコースの拡張」の転換の「きっかけ」，「ディスコースの拡張」の転換に影響する中学生の認識が解明されることで，「未完成な証明」の生成過程の理解が進み，数学教育研究上大きな価値がある．これらの知見によって，
生徒が「未完成な証明」を改善・修正する手立ての開発に貢献できる．その結果，未完成な証明の生成に留まっていた生徒が，自力で証明を完成させることができるようになる．
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