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Study of the method of evaluating mathematical ability using the Hiille vsl

Research Project

Project/Area Number 07558147
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section展開研究
Research Field 教科教育
Research InstitutionCHIBA University

Principal Investigator

SATO Tuneo  CHIBA UNIV.Facuity of Science, Professor, 理学部, 教授 (60009371)

Co-Investigator(Kenkyū-buntansha) NAGISA Masaru  CHIBA UNIV.Facuity of Science, Associate Professor, 理学部, 助教授 (50189172)
INABA Takashi  CHIBA UNIV.Facuity of Science, Professor, 理学部, 教授 (40125901)
NOZAWA Souhei  CHIBA UNIV.Facuity of Science, Professor, 理学部, 教授 (20092083)
YOSHIDA Hidenobu  CHIBA UNIV.Facuity of Science, Professor, 理学部, 教授 (60009280)
NAKAMURA Yosikuni  CHIBA UNIV.Facuity of Science, Professor, 理学部, 教授 (90110270)
安田 正実 (安田 正美)  千葉大学, 理学部, 教授 (00041244)
田栗 正章  千葉大学, 理学部, 教授 (10009607)
Project Period (FY) 1995 – 1997
Project Status Completed (Fiscal Year 1997)
Budget Amount *help
¥6,000,000 (Direct Cost: ¥6,000,000)
Fiscal Year 1997: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1996: ¥3,600,000 (Direct Cost: ¥3,600,000)
KeywordsMathematical education / Evaluation by the Hiille value / the method of evaluation / Deviation / ヒューレ / 力の習熟度 / 新しい評価法 / 生徒の個性 / 生徒の適性 / 個性値(適性値) / 新しい評価理論
Research Abstract

When solving mathematical problems everyone uses a method based on the following four activities, though there may be some individual differences in the stress placed on the various activities or in the order. The activities are :
1) Read and analyze the problem. (Structure analysis)
2) Restate the problem in one's own words. (Translation)
3) Determine and establish the goal. (Goal-setting)
4) Carry out the solution & write it down. (Execution)
We realize that each activity requires a variety of individual skills in several areas. We have summed up the areas as follows :
1) Structure analysis
a) Analyze the structure of the problem.
b) Comprehend the conditions.
c) Recall definitions and theorems.
2) Translation
a) Handle material written in words.
b) Handling graphs, charts, etc.
c) Transfer information from sentences to mathematical expressions.
3) Goal-setting
a) Proceed logically.
b) Discern the relation with similar problems.
c) Generalize from specific cases of the problem.
4) Execution
a) Choose the method of solution.
b) Actually proceeding towards the goal.
c) Use information from one part of a problem in another part.
The degree of proficiency in each of the four skills above is assigned a value using an evaluation table like Figure 1. This table divides the four skills into subskills a), b), and c) and makes it easy to assign a value. Whether one can carry out activities 1)-4) or not depends on one's proficiency in these skills. We thought that we could evaluate a student's present proficiency (aptitude) if we measure a student's proficiency in each skill separately and see whether he has learned the skills in a balanced way. By using the information from this evaluation we can expect students to become proficient in these skills, learn to solve math problems, and come to like mathematics. Also Questions I and II will disappear.

Report

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

    (25 results)

All Other

All Publications (25 results)

  • [Publications] H.Yoshida and I.Miyamoto: "Solutions of the Dirichlet problem on cone with continuous date" J.Japan Math.Soc.50(1). 71-93 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Yoshida and I.Miyamoto: "Harmonic functions in a cone which vanish on the boundary" Mathematische Nachrichten. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Yoshida and I.Miyamoto: "Particular solutions of the Dinichlet problem on a strip with continuous data" Gakuto Intern.Ser.Math.Sci.Appl.(to apper).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] S.Nozawa: "Remarks on sharp characters of rank three" Technical Reports of Mathematical Sciences. 13(21). 1-14 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] T.Inaba: "An example of a flow on a noncompact syrface without minimal set" Eng Th.and Dyn.Sys.(to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] M.Nagisa: "C^<【symmetry】>-環の自由積のstable rank" 数理解析研究所講究録. 1003. 1-14 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 佐藤 恒雄: "教養の線形代数" 培風館, 193 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Yoshida and I.Miyamoto: "Solutions of the Dirichlet problem on cone with continuous data" J.Japan Moth.Soc.50(1). 71-93 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Yoshida and I.Miyamoto: "Harmonic functions in a cone which vanish on the boundary." Mathematische Nachrichten. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Yoshida and I,Miyamoto: "Particular solutions of the Dirichlet problem on a strip with continuous data" Gahuto Intern.Ser.Math.Sci.Appl.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] S.Nozawa: "Remarks on sharp characters of rank three" Technical Reports of mathematical Sciences. 13(21). 1-14 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] T.Ineba: "An example of a flow on a noncompact surface without minimal set." Erg Th.and Dyn.Sys. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H. Yoshida and I. Miyamoto: "Solutions of the Dirichlet problem on cone with continuous data" J. Japan Math. Soc.50(1). 71-93 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] H. Yoshida and I. Miyamoto: "Harmonic functions in a cone which vanish on the boundary" Mathematische Nachrichten. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] H. Yoshida and I. Miyamoto: "Particular solutions of the Dirichlet problem on a strip with continuous data" Gokuto Intern. Ser. Math. Sci. Sppl.(to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] S. Nozawa: "Remarks on sharp characters of rank three" Technical Reparts of mathematical Sciences. 13(21). 1-14 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] T. Inaba: "An example of a flow on a noncompact surface without minimal set." Eng Th. and Dyn. Sys.(to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] M. Nagisa: "C^+-環の自由積のstable rank" 数理解析研究所講演録. 1003. 1-14 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 佐藤恒雄: "教養の線形代数" 培風館, 193 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Nozawa and D.ALVIS: "Sharp characters with irrational values" Journal of the Mathematical Society of Japan. 第48巻第3号. (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] H.Yoshida: "A type of uniqueness for the Dirichlet problem on a half-space with continuous data," Pacific J.Math.172. 591-609 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] H.Yoshida,I.Miyamoto,: "Solutions of the Dirichlet problem on a cone with continuous data" Journal of the Mathematical Society of Japan. 5(1)(to appear). (1998)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Inaba and P.Walczak: "Transverse Hausdorff dimension of codim-1 C^2-foliations" Fundamenta Mathematicae. Vol.149. 239-244 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Kurano,M.Yasuda,J.Nakagami,Y.Yoshida: "Markov-type fuzzy decision processes with a discounted reward on a closed interval," European Journal of Oprational Research.Vol.92. 649-662 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Nagisa: "C^*-環の自由積のstable rank" 数理解析研究所講究録. (to appear).

    • Related Report
      1996 Annual Research Report

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

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