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Research of Evaluation and Learning of Mathematics based upon "The New View of Learning Ability"

Research Project

Project/Area Number 07680281
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 教科教育
Research InstitutionYasuda Women's University (1996-1997)
Hiroshima University (1995)

Principal Investigator

HASHIMOTO Masatsugu (1996-1997)  Faculty of Literature, Yasuda Women's University Associate Professor, 文学部, 助教授 (00189507)

岩崎 秀樹 (1995)  広島大学, 大学院・国際協力研究科, 助教授 (50116539)

Co-Investigator(Kenkyū-buntansha) YAMAGUCHI Takeshi  Fukuoka University of Education, Faculty of Education, Associate Professor, 教育学部, 助教授 (60239895)
IWASAKI Hideki  Hiroshima University, Graduate School for International Development and Cooperat, 大学院・国際協力研究科, 助教授 (50116539)
TAKESHITA Masanori  Faculty of Literature, Yasuda Women's University Professor, 文学部, 教授 (80188177)
橋本 正継  安田女子大学, 文学部, 助教授 (00189507)
岡田 よし雄  広島大学, 学校教育学部, 教授 (70093739)
Project Period (FY) 1995 – 1997
Project Status Completed (Fiscal Year 1997)
Budget Amount *help
¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1997: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1996: ¥700,000 (Direct Cost: ¥700,000)
KeywordsNew View of Learning Ability / Generalization / Dorfler's Generalization Model / Learning of Mathematics / Evaluation / Skemp's Director System / Expanded Metacognitive Model / Wittmann's Teaching Units / 算数科 / 数学科 / 課題学習 / メタ認知 / 認識論 / 関心・意欲・態度 / ディレクターシステム / 問題解決学習
Research Abstract

The ultimate purpose of this research is to propose the adequate theory of teaching and learning mathematics based upon "The New View of Learning Ability, " which emphasizes children's interests, will, and attitude. As a first step to achieve this purpose, we have noted on the generalization process which seems to be one of the specific and essential matures of mathematical thinking and learning. For the analysis of the generalization process, Dorfler's generalization model provides us the fruitful suggestions. This model, however, has some issues about the explanation of the cognitive process promoting the generalization. Therefore, in this research, we have firstly set up a theoretical framework for the analysis of cognitive activities in generalization in terms of critical consideration on Dorfler's model from the metacognititive viewpoint and Skemp's director system.
Secondly, in order to illustrate the advantage of our theoretical framework, we have designed two mathematics classes which are both problem-solving oriented, and normal. One is "Numbers on the Calendar" to examine the change of forms in algebraic signs in generalization. The other is "The Sum of Five Angles in Pentagram" to research the change of meaning in geometric figures in generalization. A close observation, comparison, and analysis of these two practice based upon the above framework, especially focusing on "Symbols as Objects" in Dorfler"s model, has shown that there are two types of generalization : one is the generalization of objects, the other is that of method.
Thirdly, we have designed and evaluated new teaching materials, which aim to develop "The New View of Learning Ability", by incorporating Wittmann's Teaching Units into our theoretical framework. To put it concretely, we have developed a teaching experiment "Star Patterns" based on the above theoretical framework and have proved its effectiveness.

Report

(4 results)
  • 1997 Annual Research Report   Final Research Report Summary
  • 1996 Annual Research Report
  • 1995 Annual Research Report
  • Research Products

    (20 results)

All Other

All Publications (20 results)

  • [Publications] 岩崎 秀樹・田頭 かおり: "新しい学力観に基づく数学指導の課題-課題学習における一般化の研究-" 広島大学学校教育学会 学校教育学会紀要. 2号. 39-46 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 岩崎 秀樹・山口 武志・田頭 かおり: "数学教育における課題学習の課題-一般化の学習に関するメタ認知概念の拡張に関する考察-" 日本数学教育学会,第28回数学教育論文発表会論文集. 65-70 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 岩崎 秀樹・山口 武志・田頭 かおり: "一般化の過程における「記号の対象化」に関する考察-代数教材と図形教材の比較-" 日本数学教育学会,第29回数学教育論文発表会論文集. 49-54 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 岩崎 秀樹・田頭 かおり: "図形指導における記号の対象化の考察-課題学習の授業実践を例にして-" 全国数学教育学会,数学教育学研究. 3巻. 127-135 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 岩崎 秀樹・山口 武志・田頭 かおり: "Teaching Vnits(TV)の設計と評価-TV「Star Patterns」の分析を中心に-" 日本数学教育学会,第30回数学教育論文発表会論文集. 289-294 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Hideki Iwasaki & Takeshi Yamaguchi: "The Cegnitive and Symbolic Analysis of the Generalization Process:TheComparisen of Algebraic Signs with Geometric Figures" Proceeding of the 21st conference of the International Group for the Psychology of Mathematics Education. Vol.3. 105-112 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Hideki Iwasaki and Kaori Tagashira: "Some Issues of Mathematics Teaching Based upon "The New View of Learning Ability" : The Analysis of Generalization in the "Problem Situation Learning" (In Japanese)" Bulletin of the Academic Society of School Education. Vol.2. 39-46 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Hideki Iwasaki, Takeshi Yamaguchi, and Kaori Tagashira: "Some Issues of the "Problem Situation Learning" on Mathematics Education : On the Extension of the Conception of Metacognition in Generalization Process (In Japanese)" Proceedings of the 28th Annual Meeting of JSME. 65-70 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Hideki Iwasaki and Kaori Tagashira: "On Symbols as Objects in Geometry Teaching : Geometrical Figures as Valuable (In Japanese)" Journal of JASME Research in Mathematics Education. Vol.3. 127-135 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Hideki Iwasaki, Takeshi Yamaguchi, and Kaori Tagashira: "The Cognitive and Symbolic Analysis of the Generalization Process : The Comparison of Algebraic Signs with Geometric Figures" Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education. Vol.3. 105-112 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Hideki Iwasaki, Takeshi Yamaguchi, and Kaori Tagashira: "Design and Evaluation of Teaching Units : On the analysis of TU "Star Patterns" (In Japanese)" Proceedings of the 30th Annual Meeting of JSME. 105-112 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Masatsugu Hashimoto: "Gender Differences on Attitudes and Other Affective Variables in Mathematics Learning : the Case of Pre-service Teachers (In Japanese)" Childhood Education Research Journal. No.5. 99-112 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 岩崎秀樹・田頭かおり: "図形指導における記号の対象化の考察-課題学習の授業実践を例にして-" 全国数学教育学会,数学教育学研究. 3巻. 127-135 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 岩崎秀樹・山口武志・田頭かおり: "Teaching Units (TU)の設計と評価-TU^+Star Patterns」の分析を中心に-" 日本数学教育学会,第30回数学教育論文発表会論文集. 289-294 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hideki Iwasaki & Takeshi Yamaguchi: "The Congnitive and Symbolic Analysis of the Generalization Process : The Comparison of Algebraic Signs with Geometric Figures" Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education. Vol.3. 105-112 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 岩崎秀樹: "一般化の過程における「記号の対象化」に関する考察" 第29回数学教育論文発表会論文集. 49-54 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 橋本正継: "数学に対する女性の意識について-教員養成系における大学生のばあい-" 児童教育研究. 第5号. 99-112 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 岩崎秀樹: "新しい学力観に基づく数学指導の課題" 学校教育学会紀要. 2. 39-46 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 岩崎秀樹: "メタ認知は教授-学習の成因か成果か" 日本科学教育学会年会論文集. 19. 77-78 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 岩崎秀樹: "一般化の学習に関するメタ認知概念の拡張に関する考察" 数学教育論文発表会論文集. 28. 65-70 (1995)

    • Related Report
      1995 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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