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Study on training of ability to grasp phenomena mathematically based on modal analysis of learner's function understanding

Research Project

Project/Area Number 17K04823
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Education on school subjects and activities
Research InstitutionBukkyo University

Principal Investigator

Nisawa Yoshiki  佛教大学, 教育学部, 准教授 (60633815)

Project Period (FY) 2017-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords関数の学習モデル / 途上概念 / 数値を用いない学習 / 教育実践 / 関数 / 学習モデル / 論理構造 / 理解研究 / 事象の認識段階 / 抽象化途上の段階 / 抽象的表現の段階 / 変化と対応 / 数理的に捉える力
Outline of Final Research Achievements

The concept of functions is essential when understanding a phenomenon using mathematics, and it also occupies a central position in mathematical learning. Considering the previous challenges faced by students, who are learning functions, this study constructs a scientific “learning model for functions” concerning cognition in mathematical education classes. Furthermore, it empirically demonstrates a new plan to learn functions by developing teaching material.

Academic Significance and Societal Importance of the Research Achievements

本研究では関数の学習モデルを構築し,関数理解のためには途上概念の形成が必要で,途上概念を形成するための学習として「数値を用いない学習」の必要性を示した。教育実践を通して,この新たな学習が関数学習として児童の認知・認識に適したものであることが認められている。従って,小学校の関数学習に新たな指針を示すことになったと考える。また,中学校における関数学習のあり方にも,新たな可能性を見いだすことができた。

Report

(4 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (18 results)

All 2020 2019 2018 2017

All Journal Article (8 results) (of which Open Access: 3 results,  Peer Reviewed: 3 results) Presentation (9 results) (of which Int'l Joint Research: 4 results) Book (1 results)

  • [Journal Article] Basic Research on the Formation of Students’ Concept of Functions2019

    • Author(s)
      Yoshiki NISAWA
    • Journal Title

      Contributions to math lessons 2019 (Original title in German.)

      Volume: 2019 Pages: 1365-1365

    • Related Report
      2019 Annual Research Report
    • Open Access
  • [Journal Article] 関数の学習指導における課題と展望2019

    • Author(s)
      二澤善紀
    • Journal Title

      数学教育学会 2019年度秋季例会 予稿集

      Volume: 2019 Pages: 73-75

    • Related Report
      2019 Annual Research Report
  • [Journal Article] 関数指導における教材開発のための基礎的研究-関数指導の体系に着目して2018

    • Author(s)
      二澤善紀
    • Journal Title

      数学教育学会誌

      Volume: Vol.59 No.1・2 Pages: 1-10

    • NAID

      130007729824

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Applying van Hiele’s Levels to Basic Research on the Difficulty Factors behind Understanding Functions2018

    • Author(s)
      Yoshiki Nisawa
    • Journal Title

      International Electronic Journal of Mathematics Education

      Volume: Volume 13 (2018) Pages: 61-65

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Junior High School Students’ Understanding of Mathematical Functions2018

    • Author(s)
      Yoshiki Nisawa
    • Journal Title

      The 3rd Annual Meeting of the German Mathematical Association (DMV) and the Society for Didactics of Mathematics (GDM)

      Volume: Band III Pages: 1315-1318

    • Related Report
      2018 Research-status Report
  • [Journal Article] 関数指導における教材開発のための基礎研究-関数の指導体系2018

    • Author(s)
      二澤善紀
    • Journal Title

      数学教育学会2018年度春季年会予稿集

      Volume: - Pages: 231-233

    • Related Report
      2017 Research-status Report
  • [Journal Article] 学校数学における関数の理解に関する学習者の様相の分析2017

    • Author(s)
      二澤善紀
    • Journal Title

      日本・中国 数学教育国際会議論文集

      Volume: - Pages: 93-96

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] 中学校における関数理解のための一試み2017

    • Author(s)
      河合真美, 二澤善紀
    • Journal Title

      数学教育学会夏季研究会(関西エリア)予稿集

      Volume: - Pages: 63-66

    • Related Report
      2017 Research-status Report
  • [Presentation] Organized Session 解析教育の課題と展望:関数の学習指導における課題と展望2019

    • Author(s)
      二澤善紀
    • Organizer
      数学教育学会 2019年度秋季例会 Organized Session A
    • Related Report
      2019 Annual Research Report
  • [Presentation] 小学校段階における関数学習の基礎研究2019

    • Author(s)
      二澤善紀
    • Organizer
      2019年度 数学教育学会春季年会
    • Related Report
      2018 Research-status Report
  • [Presentation] Basic Research on the Formation of Students’ Concept of Functions2019

    • Author(s)
      Yoshiki Nisawa
    • Organizer
      The 53rd Annual Meeting of the Society for Didactics of Mathematics (GDM)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] 関数指導における教材開発のための基礎研究 -小学校段階の指導についての一考察-2018

    • Author(s)
      二澤善紀
    • Organizer
      2018年度 数学教育学会秋季例会
    • Related Report
      2018 Research-status Report
  • [Presentation] Function understanding of learners' aspects2018

    • Author(s)
      Yoshiki Nisawa
    • Organizer
      125/5000 The 3rd Annual Meeting of the German Mathematical Association (DMV) and the Society for Didactics of Mathematics (GDM)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] 関数指導における教材開発のための基礎研究-関数の指導体系2018

    • Author(s)
      二澤善紀
    • Organizer
      2018 年度数学教育学会春季年会
    • Related Report
      2017 Research-status Report
  • [Presentation] 中学校における関数理解のための一試み2017

    • Author(s)
      河合真美, 二澤善紀
    • Organizer
      2017年度数学教育学会夏季研究会(関西エリア)
    • Related Report
      2017 Research-status Report
  • [Presentation] Educational Practice on Structural and Systematic Understanding in Mathematical Modelling2017

    • Author(s)
      Yoshiki NISAWA, Masami KAWAI
    • Organizer
      The 18th International Conference on the Teaching of Mathematical Modelling and Applications (ICTMA-18)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] 学校数学における関数の理解に関する学習者の様相の分析2017

    • Author(s)
      二澤善紀
    • Organizer
      日本・中国 数学教育国際会議
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Book] 算数・数学における関数概念の認識発達を培う理論と実践2020

    • Author(s)
      二澤善紀
    • Total Pages
      224
    • Publisher
      ミネルヴァ書房
    • Related Report
      2019 Annual Research Report

URL: 

Published: 2017-04-28   Modified: 2021-02-19  

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