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Development of a framework for teaching data modelling in mathematics education and its demonstration in schools and teacher education

Research Project

Project/Area Number 21K02513
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 09040:Education on school subjects and primary/secondary education-related
Research InstitutionUtsunomiya University

Principal Investigator

川上 貴  宇都宮大学, 共同教育学部, 准教授 (90709552)

Co-Investigator(Kenkyū-buntansha) 佐伯 昭彦  金沢工業大学, 基礎教育部, 教授 (60167418)
Project Period (FY) 2021-04-01 – 2025-03-31
Project Status Granted (Fiscal Year 2023)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2024: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2023: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2022: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2021: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordsデータ駆動型モデリング / STEM/STEAM教育 / 社会的意思決定 / 規範的モデリング / 数学的モデル / 統計的モデル / データモデリング / 非形式的な統計的推測 / 統計教育 / 数学教育 / モデルの役割 / 学校教育 / 教師教育
Outline of Research at the Start

よりよい予測や意思決定を志向して,データのばらつきの振る舞いを記述・説明するモデル(表現)を構成・評価・改良する営みとして,データモデリングがある。将来の不確実な状況への対応力がすべての市民に求められる現代社会において,数学教育におけるデータモデリング指導の実現化と実装化は,国内外の数学教育研究や統計教育研究が抱える喫緊の課題である。こうした課題に対して,本研究では,学校教育(子どもを対象)と教師教育(教員養成系大学生や現職教師を対象)の両方を射程に入れ,数学教育におけるデータモデリングの体系的な指導枠組みの構築とその指導枠組みの学校教育・教師教育での有用性の実証に取組む。

Outline of Annual Research Achievements

3年次は,数学的モデリング研究や統計的モデリング研究などの知見に基づいて,数学的モデルと統計的モデルに焦点をあてた学校数学におけるデータ駆動型モデリング(DDM)を捉える枠組みを設定した.この枠組みは,以下の3つから成る:(a)DDMのプロセスにあたる,データ/文脈,数学的モデル,統計的モデルの相互作用を捉える枠組み,(b)DDMの成果にあたる,予測の進展とデータの見方の進展を捉える枠組み,(c)DDMのプロセスと成果の間の媒介にあたる,予測の進展における数学的モデル・統計的モデルの役割を捉える枠組み.そして,設定したDDMを捉える枠組みを3つの授業事例に基づいて例証した.さらに,構築した枠組みを,学校数学におけるDDMの教材や授業の開発に活用する可能性について明らかにした.具体的には,枠組みに基づいてDDMの4つの基本的な活動タイプを導出した:数学・応用指向の活動,統計・応用指向の活動,数学・構造指向の活動,統計・構造指向の活動.また,構築した枠組みに基づいて,DDMにおける教師の6つの介入場面と5つの介入方法を導出した.これらの研究成果は,国際学会の査読付Proceedings(Kawakami, 2023)として公刊された.
さらに,本研究のDDMの枠組みを,STEM教育や社会的な意思決定の学際的な文脈にも拡張を試みることができた.これらの研究成果は,複数の査読付きBook chapterや国際学会の査読付Proceedingsに投稿し,採択が決まっている.

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

本研究のDDMの枠組みを,STEM教育や社会的な意思決定の学際的な文脈にも拡張を試みることができ,その研究成果が,複数の査読付きBook chapterや国際学会の査読付Proceedingsに採択されたことが理由である.

Strategy for Future Research Activity

今後の研究の推進の方策は,以下の通りである.①ICTを取り入れたDDMの教材・授業の開発・実践を通して,本研究で構築した枠組みを精緻化していくこと,②本研究の枠組みを生かして,DDMの課題設計の枠組みを開発すること,③多様で学際的なDDMの活動の可能性を実証的に明らかにしていくこと.

Report

(3 results)
  • 2023 Research-status Report
  • 2022 Research-status Report
  • 2021 Research-status Report
  • Research Products

    (38 results)

All 2024 2023 2022 2021 Other

All Int'l Joint Research (4 results) Journal Article (15 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 14 results,  Open Access: 5 results) Presentation (19 results) (of which Int'l Joint Research: 11 results,  Invited: 1 results)

  • [Int'l Joint Research] Linkoping University(スウェーデン)

    • Related Report
      2023 Research-status Report
  • [Int'l Joint Research] Kassel University(ドイツ)

    • Related Report
      2023 Research-status Report
  • [Int'l Joint Research] Linkoping University(スウェーデン)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] Linkoping University(スウェーデン)

    • Related Report
      2021 Research-status Report
  • [Journal Article] Investigating the role of data in the teaching of statistical modelling: a literature review2024

    • Author(s)
      Takashi Kawakami, Jonas Bergman Arleback
    • Journal Title

      Proceedings of the fourteenth research conference of the Swedish society for research in mathematics education (MADIF14)

      Volume: -

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Advancement of in-service teacher’s pedagogical content knowledge when teaching mathematical modelling: Through interpretation and design of modelling lessons2024

    • Author(s)
      Akihiko Saeki, Kosuke Yata, Masafumi Kaneko, Takashi Kawakami
    • Journal Title

      Researching Mathematical Modelling Education in Disruptive Times

      Volume: - Pages: 353-364

    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Journal Article] Roles of mathematical and statistical models in data-driven modelling: A prescriptive modelling perspective2024

    • Author(s)
      Takashi Kawakami, Akihiko Saeki
    • Journal Title

      Researching Mathematical Modelling Education in Disruptive Times

      Volume: - Pages: 595-605

    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Journal Article] Extending data-driven modelling from school mathematics to school STEM education2024

    • Author(s)
      Takashi Kawakami, Akihiko Saeki
    • Journal Title

      The Contribution of Mathematics to School STEM Education: Current Understandings

      Volume: -

    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Journal Article] The Relationships Between Statistics, Statistical Modelling and Mathematical Modelling2023

    • Author(s)
      Arleback Jonas Bergman, Kawakami Takashi
    • Journal Title

      Advancing and Consolidating Mathematical Modelling: Research from ICME-14

      Volume: - Pages: 293-309

    • DOI

      10.1007/978-3-031-27115-1_18

    • ISBN
      9783031271144, 9783031271151
    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] In-Service Teachers’ Transformation of a Mathematised Task into Modelling Tasks2023

    • Author(s)
      Saeki Akihiko, Kaneko Masafumi, Kawakami Takashi, Ikeda Toshikazu
    • Journal Title

      Advancing and Consolidating Mathematical Modelling: Research from ICME-14

      Volume: - Pages: 241-257

    • DOI

      10.1007/978-3-031-27115-1_15

    • ISBN
      9783031271144, 9783031271151
    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Journal Article] A triplet of data/context, mathematical model, and statistical model: Conceptualising data-driven modelling in school mathematics2023

    • Author(s)
      Takashi Kawakami
    • Journal Title

      Proceedings of the Thirteen Congress of the European Society for Research in Mathematics Education (CERME13)

      Volume: - Pages: 1243-1250

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Redesigning a mathematical task to an interdisciplinary modelling task2023

    • Author(s)
      Kosuke Mineno, Takashi Kawakami, Akihiko Saeki
    • Journal Title

      Proceedings of the Thirteen Congress of the European Society for Research in Mathematics Education (CERME13)

      Volume: - Pages: 1297-1298

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] 学校数学におけるデータ駆動型モデリングの学習指導に関する研究2023

    • Author(s)
      川上 貴
    • Journal Title

      兵庫教育大学大学院連合学校教育学研究科博士論文

      Volume: - Pages: 1-358

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Characterising rationales for using statistical modelling in education research from a mathematical modelling perspective: A review2022

    • Author(s)
      Takashi Kawakami, Jonas Bergman Arleback
    • Journal Title

      Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12)

      Volume: - Pages: 1109-1116

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A Framework for Describing and Analysing Data-Driven Modelling Activities in School Mathematics: From the Perspectives of Mathematical and Statistical Models2022

    • Author(s)
      川上 貴, 佐伯 昭彦
    • Journal Title

      Journal of Science Education in Japan

      Volume: 46 Issue: 4 Pages: 421-437

    • DOI

      10.14935/jssej.46.421

    • ISSN
      0386-4553, 2188-5338
    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] 低学年児童の非形式的な統計的推測の促進におけるモデルの役割:データモデリングの過程に着目して2022

    • Author(s)
      川上貴
    • Journal Title

      科学教育研究

      Volume: 46

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] 説明の評価・改善を通した中学1年生の批判的思考の進展の特徴づけ:「図形の移動の活用」の授業における班の話し合いの事例から2022

    • Author(s)
      滝田和徳, 水野高宏, 川上 貴, 牧野智彦, 日野圭子
    • Journal Title

      日本数学教育学会誌 数学教育

      Volume: 104

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Data-Based Modelling to Combine Mathematical, Statistical, and Contextual Approaches: Focusing on Ninth-Grade Students2021

    • Author(s)
      Takashi Kawakami,Kosuke Mineno
    • Journal Title

      Mathematical Modelling Education in East and West, Springer

      Volume: ー Pages: 389-400

    • DOI

      10.1007/978-3-030-66996-6_32

    • ISBN
      9783030669959, 9783030669966
    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] 統計教育からSTEM/STEAM教育の第一歩を2021

    • Author(s)
      川上貴
    • Journal Title

      新しい算数研究10月号

      Volume: 609 Pages: 38-39

    • Related Report
      2021 Research-status Report
  • [Presentation] Teaching and learning statistics with paper helicopters2024

    • Author(s)
      Jonas Bergman Arleback, Takashi Kawakami
    • Organizer
      Matematikbiennalen 2024
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research
  • [Presentation] 学校数学におけるデータ駆動型モデリングの概念化:数学的モデルと統計的モデルを視座として2023

    • Author(s)
      川上 貴
    • Organizer
      日本数学教育心理研究学会令和5年度春期研究集会
    • Related Report
      2023 Research-status Report
    • Invited
  • [Presentation] 数学教科書の教材から学際的なモデリングの教材へ:STEM/STEAM教育を志向して2023

    • Author(s)
      峰野 宏祐, 川上 貴, 佐伯 昭彦
    • Organizer
      日本数学教育学会第11回春期研究大会
    • Related Report
      2023 Research-status Report
  • [Presentation] Validation in sixth-grade data-driven modelling2023

    • Author(s)
      Takashi Kawakami, Katsuki Akizawa
    • Organizer
      The 21st International Conference on the Teaching of Mathematical Modelling and Applications (ICTMA21)
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research
  • [Presentation] Facilitating problem posing in mathematical modelling: The case of 12th-grade students2023

    • Author(s)
      Kosuke Yata, Akihiko Saeki, Naohiro Minagawa, Takashi Kawakami
    • Organizer
      The 21st International Conference on the Teaching of Mathematical Modelling and Applications (ICTMA21)
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research
  • [Presentation] Designing mathematical modelling involving a simulation with physical experiments2023

    • Author(s)
      Kosuke Mineno, Akihiko Saeki, Takashi Kawakami
    • Organizer
      The 21st International Conference on the Teaching of Mathematical Modelling and Applications (ICTMA21)
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research
  • [Presentation] データモデリングプロセスとデザインプロセスを組み合わせたSTEM/STEAM教育:教員養成の取組み2023

    • Author(s)
      川上 貴, 西村圭一
    • Organizer
      日本科学教育学会第47回年会
    • Related Report
      2023 Research-status Report
  • [Presentation] 小学校中学年における統計的思考の促進を目指した授業:STEMアプローチを通して2022

    • Author(s)
      千葉 将平, 川上 貴
    • Organizer
      第104回全国算数・数学教育研究(島根)大会
    • Related Report
      2022 Research-status Report
  • [Presentation] The Role of Mathematical and Statistical Models in Data-Driven Modelling: A Prescriptive Modelling Perspective2022

    • Author(s)
      Takashi Kawakami, Akihiko Saeki
    • Organizer
      The 20th International Conference on the Teaching of Mathematical Modelling and Applications (ICTMA20)
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] The Development of In-service Teacher's Perspectives for Analyzing Mathematical Modelling Lessons2022

    • Author(s)
      Akihiko Saeki, Kosuke Yata, Masafumi Kaneko, Takashi Kawakami
    • Organizer
      The 20th International Conference on the Teaching of Mathematical Modelling and Applications (ICTMA20)
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] オーストラリアにおけるSTEM教育に関する動向調査:学習評価と教員支援についての数学教育の視点からの示唆2022

    • Author(s)
      川上 貴
    • Organizer
      日本科学教育学会第46回年会
    • Related Report
      2022 Research-status Report
  • [Presentation] Characterising rationales for using statistical modelling in education research from a mathematical modelling perspective: A review2022

    • Author(s)
      Takashi Kawakami, Jonas Bergman Arleback
    • Organizer
      Twelfth Congress of the European Society for Research in Mathematics Education (CERME12)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] 規範的モデリングの観点から見たデータモデリングの特徴:ある大学生によるCOVID-19に関する社会的意思決定の事例から2021

    • Author(s)
      川上貴
    • Organizer
      日本科学教育学会第45回年会
    • Related Report
      2021 Research-status Report
  • [Presentation] 数学的モデリングの学習指導を支える教師教育の在り方:国内外の研究動向の概観からみえる論点2021

    • Author(s)
      川上貴,佐伯昭彦
    • Organizer
      日本科学教育学会第45回年会
    • Related Report
      2021 Research-status Report
  • [Presentation] Young children’s use of previous modelling processes in advancing data modelling2021

    • Author(s)
      Takashi Kawakami
    • Organizer
      44th Conference of the International Group for the Psychology of Mathematics Education (PME44)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] How can novice STEM teachers develop Integrated STEM materials: The first step from mathematics textbooks2021

    • Author(s)
      Takashi Kawakami, Akihiko Saeki
    • Organizer
      43rd Mathematics Education Research Group of Australasia (MERGA43) Conference
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] The rationales of statistical modelling in education research from a mathematical modelling perspective2021

    • Author(s)
      Takashi Kawakami, Jonas Bergman Arleback
    • Organizer
      The 14th International Congress on Mathematical Education (ICME14)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] The development of a modelling teacher education program starting from the transformation of a mathematised task into modelling tasks2021

    • Author(s)
      Akihiko Saeki, Masafumi Kaneko, Takashi Kawakami, Toshikazu Ikeda
    • Organizer
      The 14th International Congress on Mathematical Education (ICME14)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] 数学教育の立場からのSTEM教師教育プログラム構想の提案:算数・数学教科書の教材からSTEM教材への再教材化を中核として2021

    • Author(s)
      佐伯 昭彦, 金児 正史, 川上 貴
    • Organizer
      日本科学教育学会研究会
    • Related Report
      2021 Research-status Report

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Published: 2021-04-28   Modified: 2024-12-25  

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