A fundamental study on teaching throght mathematical problem solving focusing on corresponding between pre-formal representations
| Project/Area Number |
17K00968
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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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| Research Field |
Science education
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| Research Institution | Aichi University of Education |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
清水 紀宏 福岡教育大学, 教育学部, 教授 (50284451)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 数学的問題解決 / プリフォーマルな表現 |
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| Outline of Final Research Achievements |
The purposes of this study were to clarify the students' understanding for various pre-formal mathematical representations(representations that support the meaning of formal representations based on students' own informal representations) introduced in arithmetic and mathematics classroom and their roles in problem-solving classes, and to examines the way of teaching for the representations based on the findings.
The results were as follows: It is possible that the understanding of the kind of tape diagram that represents the "ratio of the part to the whole" is low because of the low frequency of the appearance in the context of learning of proportion, while even the children who have not learned the mutual relationship between adition and subtraction are likely to be able to interpret the same type of diagram. Furthermore, it was pointed out that it is important to agree on the functional roles of the diagrams when designing lessons for introducing such diagrams.
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| Academic Significance and Societal Importance of the Research Achievements |
部分-全体関係を表すテープ図に類するプリフォーマルな表現は，加減の相互関係が未習の児童でも，一定程度解釈し使用することができるようであるということを調査によって確かめた。その結果は，そうした調査の少なさからも学術的意義があると考えられる。その結果を踏まえると，そうした図を授業で教師側から導入することも可能だと考えられるが，一方では，関係を表現するというそれらの図の機能的役割についての合意が無い場合，児童は別の目的を持つインフォーマルな図に留まってしまうということを授業分析から指摘もしている。その指摘は授業デザインに対しては重要な示唆であるため，社会的な意義があると考えられる。
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Report
(4 results)
Research Products
(3 results)
