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A Research on "Imaging" of Basic Mathematical Terms

Research Project

Project/Area Number 12680168
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Science education
Research InstitutionSaitama University

Principal Investigator

OKABE Tsuneharu  Saitama University, faculty of Economics, Professor, 経済学部, 教授 (80087080)

Co-Investigator(Kenkyū-buntansha) SUZUKI Toshio  Yamanashi University, Department of Cultural Studies, Professor, 人間教育学部, 教授 (20020472)
IITAKA Shigeru  Gakushuin University, Faculty of Science, Professor, 理学部, 教授 (20011588)
MATSUMOTO Yukio  University of Tokyo, Graduate School of Mathematics, Professor, 大学院・数理科学研究科, 教授 (20011637)
YAMAUCHI Kazunari  Asahikawa Medical college, School of Medicine, Professor, 医学部, 教授 (60041787)
NISHIMURA Kazuo  Kyoto University, Institute of Economic Research, Professor, 経済研究所, 教授 (60145654)
三島 健稔  埼玉大学, 工学部, 教授 (30245310)
Project Period (FY) 2000 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2002: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2000: ¥2,200,000 (Direct Cost: ¥2,200,000)
Keywordsimaging / mathematics education / CG teaching material / Animation / CG教材
Research Abstract

We made a careful choice of mathematical terms in each field to be imaged and compiled information concerning those terms from various sources.
The chosen terms from elementary mathematical concepts are : "angle", "center of gravity", "area", "volume", "set", "cardinality" , "map" , "equivalence relation", "Pythagorean theorem" and "congruence/similarity" ; from analysis : "sequence" , "arithmetic progression", "geometric progression", "limit(ε-δ)", "differential coefficient", "derived function", "tangent line", "extreme value", "convexity", "partial differential", "integral" and "fundamental theorem of calculus" ; from geometry : "topology", "fixed point theorem", "Euler characteristic", "curvature", "tangent plane" and "manifold" ; and from algebra : "group/ring/field", "fundamental theorem of algebra" and "homomorphism/isomorphism".
A larger number of terms have been chosen from the field of analysis more than from the other fields because many of the professors surveyed suggested that the imaging of the mathematical terms, especially of analysis, would be useful for those university students who belong to departments of humanities and social sciences.
We set our goal at describing those terms, without distorting their conceptual contours, so that even those with only basic knowledge junior high school students are thought to have will be interested in and can understand them. Part of the production of our research has been introduced in Worldly Mathematics as a record of lecture at Shinagawa Women' s Junior High School in which was used the teaching material we collaborated with "topology", "angle", "center of gravity", "arithmetic progression", "geometric progression" and "Pythagorean theorem", as its main topics. We have also completed a prototype of an animation cartoon featuring "differential coefficient", "derived function", "tangent line" and "integral".

Report

(4 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • 2000 Annual Research Report
  • Research Products

    (37 results)

All Other

All Publications (37 results)

  • [Publications] 岡部 恒治: "イメージを用いた数学教育-特に微分積分について-"日本数学教育学会誌. 83巻3号. 30-34 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] HIRAOKA Kazuyuki, MISHIMA Taketoshi: "Classification of double attributes via mutual suggestion between a pair of classifiers"Proceedings of ICONIP 2002. 1852-1856 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 飯高 茂: "大学生から見た高校数学の改善案"数学教育の会・数学教育研究. 5号. 13-16 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kazuo Nishimura, Koji Shirnomura: "Trade and Indeterminacy in a Dynamic General Equilibrium Model"Journal of Economic Theory. 105. 244-259 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Shinji Fukuhara, Yukio Matsumoto, Noriko Yui: "Non-commutative polynomial reciprocity formulae"International J. Math.. 12巻. 973-986 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] I.Hasegawa, K.Yamauchi: "Infinitesimal conformal transformations on tangent bundles with the lift metric I+II"Scientiae Mathematicae Japonicae. Vol.57No.1. 129-137 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 岡部 恒治, 藤原 和博: "[世の中教科書]数学"新潮社. 238 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] OKABE Tsuneharu: "The Teaching of Mathematics by Using Image ―In the case of Calculus―"Journal of Japan society of Mathematical Education. 83-3. 30-34 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] HIRAOKA Kazuyuki and MISHIMA Taketoshi: "Classification of double attributes via mutual suggestion between a pair of classifiers"Proceedings of ICONIP 2002. 1852-1856 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] IITAKA Shigeru: "A Plan to Improve the Education of High School Mathematics Suggested by a University Student"Study of Mathematics Education ( Association of Mathematics Education ). 5. 13-15 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] NISHIMURA Kazuo, SHIMOMURA Koji: "Trade and Indeterminacy in a Dynamic General Equilibrium Model"Journal of Economic Theory. 105. 244-259 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] FUKUHARA Shinji, MATSUMOTO Yukio and YUI Noriko: "Non-commutative polynomial reciprocity formulae"International J. Math.. 12. 973-986 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] HASEGAWA Izumi, YAMAUTI Kazunari: "Infinitesimal conformal transformations on tangent bundles with the lift metric I+II"Scientiae Mathematical Japonicae. 57-1. 129-137 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] OKABE Tsuneharu: "Worldly Mathematics"Shinchosha. 238 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 岡部 恒治: "イメージでわかる数学(連載)"教育科学・数学教育 (明治図書). 43巻4号-44巻3号. (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] HIRAOKA Kazuyuki, MISHIMA Taketoshi: "Classification of double attributes via mutual suggestion between a pair of classifiers"Proceedings of ICONIP 2002. 1852-1856 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 飯高 茂: "大学生から見た高校数学の改善案"数学教育の会・数学教育研究. 5号. 13-16 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kazuo Nishimura, Koji Shimomura: "Trade and Indeterminacy in a Dynamic General Equilibrium Model"Journal of Economic Theory. 105. 244-259 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Shinji Fukuhara, Yukio Matsumoto, Noriko Yui: "Non-commutative polynomial reciprocity formulae"International J. Math.. 12巻. 973-986 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Yamauchi: "Infinitesimal conformal transformations on tangent bundles with the lift metric I+II"Scientiae Mathematicae Japonicae. Vol.57 No.1. 129-137 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] 岡部 恒治: "自分で考える力をつける算数の本"日本経済新聞社. 238 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] 岡部 恒治, 藤原 和博: "[世の中教科書]数学"新潮社. 238 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] 岡部 恒治: "イメージでわかる数学(連載)"教育科学・数学教育(明治図書). 42巻4号-43巻3号. 110-112 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 岡部 恒治: "イメージを用いた数学教育-特に微分積分について-"日本数学教育学会誌(日本数学教育学会発行). 83巻3号. 30-34 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 飯高 茂: "分数と割り算"数学教育の会・数学教育研究. 4号. 77-105 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 岡部 恒治: "不動点の存在について"数学セミナー. 41巻2号. 19-23 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] 松本幸夫: "韓国の数学教科書"科学(岩波書店). 70巻. 872-877 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] Izumi HASEGAWA, Kazunari YAMAUCHI: "Infinitesimal Projective Transformations on Contact Riemannian Manifolds"J.Hokkaido Univ.of Education. Vol.51,No.1. 1-7 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] 岡部 恒治: "考える力をつける数学の本"日本経済新聞社. 238 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 岡部恒治: "イメージを用いた数学教育-特に微分積分について-"日本数学教育学会誌(日本数学教育学会発行). 83巻3号. 30-34 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] 岡部恒治: "面積から考えてみよう"数学通信(日本数学会発行). 5巻1号. 4-17 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 松本幸夫: "韓国の数学教科書、"科学(岩波書店). 70巻. 872-877 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.Kamada and Y.Matsumoto,: ""Knots in Hellas, 98""Certain racks associated with the braid groups, Proceedings of the International Conference on Knot Theory. 118-130 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Hiraoka,K.,Hidai,K.,,Mizoguchi,H.,MishimaT., 他: ""Online LDA which can per-form both successive learning and incremental learning, ""Proceedings of the World Multicon-ference onCybernetics, & Informatics, International Inst.of Informatics & Systemics, Orland,. SCI-2000. 96-101 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Izumi HASEGAWA,Kazunari YAMAUCHI: ""Infinitesimal Projective Transformatios on Contact Riemannian Manifolds""J.Hokkaido Univ.of Education. Vol.51,No.1. 1-7 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Nishimura: "Optimization and Chaos, (edited with Mukul Mujumdar and Tapan Mitra)"Springer. (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 飯高茂,吉田明史監修,岡部恒治 他: "高等学校学習指導要領の展開(数学編)"明治図書. 356 (2000)

    • Related Report
      2000 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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