Updated on 2024/12/26

写真a

 
OKAZAKI Masakazu
 
Organization
Faculty of Education Professor
Position
Professor
Homepage
http://ed-www.ed.okayama-u.ac.jp/~suugaku/oka/index.htm
External link

Degree

  • Master of Educaiton ( Hiroshima University )

  • Doctor of Philosophy in Education ( Hiroshima University )

Research Interests

  • Mathematics Education

Research Areas

  • Humanities & Social Sciences / Science education

  • Humanities & Social Sciences / Education on school subjects and primary/secondary education

Education

  • Hiroshima University   大学院教育学研究科   教科教育学（数学科教育）専攻, 博士課程後期

    1994.4 - 1997.3

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    Country： Japan

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  • Hiroshima University   大学院教育学研究科   教科教育学（数学科教育）専攻, 博士課程前期

    1992.4 - 1994.3

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    Country： Japan

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  • Hiroshima University   教育学部   教科教育学科数学教育学専修

    1988.4 - 1992.3

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    Country： Japan

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Research History

  • Okayama University   Faculty of Education   Professor

    2021.4

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    Country：Japan

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  • Professor, Graduate School of Education, Okayama University   Graduate School of Education, Okayama University   Professor

    2015.4 - 2021.3

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    Country：Japan

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  • Associate Professor, Graduate School of Education, Okayama University   Department of Mathematics Education   Associate Professor

    2008.4 - 2015.3

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    Country：Japan

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  • Joetsu University of Education   Graduate School of Education

    2007.4 - 2008.3

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  • Joetsu University of Education   College of Education, Joetsu University of Education   Associate Professor

    2006.4 - 2007.3

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    Country：Japan

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  • Vanderbilt University   Peabody College   Visiting Researcher

    2005.1 - 2005.7

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    Country：United States

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  • Joetsu University of Education   College of Education   Research Associate

    1998.4 - 2006.3

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    Country：Japan

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  • Junior high school teacher   Kurose Junior High School

    1997.4 - 1998.3

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Professional Memberships

  • Society of Japan Science Teaching

    2020.11 - 2024.6

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  • Japan Society for Science Education

    2011.2

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  • Okayama University Society of Mathematics Education

    2008.6

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  • Japan Curriculum Research and Development Association

    2000.4

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  • Japan Society of Mathematical Education

    1995.5

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  • PME in Japan

    1993.7

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  • International Group for the Psychology of Mathematics Education

    1993.7

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  • Japan Academic Society of Mathematics Education

    1992.4

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Committee Memberships

  • Japan Curriculum Research and Development Association   Subject Committee  

    2024.4   

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  • Japan Society for Studies on Educational Practices   editorial committee  

    2023.4   

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  • Japan Society of Mathematical Education   Director  

    2022.9   

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  • Okayama University Society of Mathematics Education   President  

    2021.6   

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  • Japan Curriculum Research and Development Association   National Committee  

    2021.4 - 2024.3   

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    Committee type：Academic society

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  • Japan Society of Mathematical Education   Editorial Board of Research Journal of Japan Society of Mathematical Education  

    2020.9   

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  • Japan Society of Mathematical Education   Delegate  

    2020.6 - 2021.6   

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  • Mathematics Education Society in Okayama Prefecture   President  

    2019.6   

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  • PME in Japan   Vice President  

    2019.4   

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    Committee type：Academic society

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  • Japan Academic Society of Mathematics Education   President  

    2019.4   

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  • Japan Academic Society of Mathematics Education   Chief, Editorial Committe of English Academic Journal  

    2017.4 - 2019.3   

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  • Japan Academic Society of Mathematics Education   Vice President  

    2017.4 - 2019.3   

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  • Japan Society of Mathematical Education   Program Committee of Centennial History of Japan Society of Mathematical Education  

    2017.1 - 2018.8   

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  • Japan Society of Mathematical Education   Deputy Chief of External Affairs  

    2016.9 - 2022.8   

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  • Japan Academic Society of Mathematics Education   Director  

    2015.4   

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  • Japan Society of Mathematical Education   Editorial Committee of Centennial History  

    2015.4 - 2018.3   

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  • International Group for the Psychology of Mathematics Education   International Program Committee  

    2014.7 - 2015.7   

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  • Japan Society for Science Education   Editorial board  

    2014.6 - 2018.6   

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  • Japan Academic Society of Mathematics Education   Deputy Chief, Editorial Committee of English Academic Journal  

    2014.4 - 2017.3   

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  • Japan Society of Mathematical Education   Program Committee of Autumn Research Conference  

    2013.4   

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  • Japan Society of Mathematical Education   Committee of External Affairs  

    2012.9 - 2016.8   

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  • International Group for the Psychology of Mathematics Education   International Committee  

    2012.7 - 2016.7   

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  • Psychology of Mathematics Education in Japan   secretariat  

    2012.4 - 2019.3   

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  • Okayama University Society of Mathematics Education   Vice President  

    2011.6 - 2021.6   

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  • Okayama University Society of Mathematics Education   Director  

    2010.6   

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  • Japan Society of Mathematical Education   Delegate  

    2010.6 - 2017.6   

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  • Japan Society of Mathematical Education   Editorial board of Research Journal of Japan Society of Mathematical Education  

    2009.9 - 2020.8   

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  • 24th Conference of International Group for the Psychology of Mathematics Education   Executive Committee  

    1999.6 - 2000.7   

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    Committee type：Academic society

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Papers

  • A Study of Teacher Intervention Using Reflection in an Arithmetic Classroom: From the Perspective of the Theory of Didactical Situations Reviewed

    Shinya Nakao, Masakazu Okazaki

    48 ( 4 )   2025

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    Language：Japanese   Publishing type：Research paper (scientific journal)  

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  • Prospective teachers’ understanding of the indirect proof of the converse of the inscribed angle theorem Reviewed

    Masakazu Okazaki, Keiko Watanabe

    Proceedings of the 47th Conference of the International Group for the Psychology of Mathematics Education   3   265 - 272   2024.7

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    Authorship：Lead author   Language：English   Publishing type：Research paper (international conference proceedings)  

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  • 正四角柱の切断の学習で育成されうる論理的説明の様相

    岡崎正和

    日本数学教育学会, 第12回春期研究大会論文集   12   19 - 26   2024.6

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    Authorship：Lead author   Language：Japanese   Publishing type：Research paper (other academic)  

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  • A study for the reconstruction of mathematical literacy in school mathematics: From the perspective of functional literacy and critical literacy Reviewed

    Ryouna BEPPU, Masakazu OKAZAKI

    Journal of Japan Academic Society of Mathematics Education   29 ( 2 )   1 - 14   2024.4

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  • 教職大学院教科教育領域における教育実践力の向上と実践研究の推進との架橋：学部新卒院生によるリフレクションを促す場の構想 Reviewed

    池田匡史, 石橋一昴, 詫間千晴, 服部裕一郎, 岡崎正和, 宮本浩治, 山田秀和, 川崎弘作

    日本教育大学協会研究年報   42   141 - 152   2024.3

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  • 中学１年生の空間図形における論理的な思考の様相－正四角柱の側面の切断を題材とした授業分析から－

    清家純一, 岡崎正和

    日本数学教育学会第56回秋期研究大会論文集   317 - 320   2023.11

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  • 探究型空間図形カリキュラムの構成原理とその具体化

    岡崎正和

    日本数学教育学会, 第11回春期研究大会論文集   11   173 - 180   2023.6

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  • 高校数学の微分係数の理解を促す深い学びに関する研究―教授学的状況理論とAPOS理論を用いて―

    林田崚, 岡崎正和

    岡山大学算数・数学教育学会, パピルス   ( 29 )   1 - 7   2023.3

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    Language：Japanese   Publishing type：Research paper (bulletin of university, research institution)  

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  • 探究型空間図形カリキュラムの構成原理に関する研究

    岡崎正和

    日本数学教育学会第10回春期研究大会論文集   10   175 - 182   2022.6

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  • 正負の数の単元において式の関係の意識を高める学習場面を捉える

    岡崎正和, 大西修司, 横林慎也, 高田誠, 猪木実奈子, 川本芳弘

    岡山大学算数・数学教育学会パピルス   ( 28 )   46 - 55   2022.3

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    Authorship：Lead author   Language：Japanese   Publishing type：Research paper (bulletin of university, research institution)  

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  • The reciprocal understanding of theorems and proofs through generating of and reflecting on the language for proving: Focusing on proofs with dividing in some cases Reviewed

    Keiko Watanabe, Masakazu Okazaki

    Journal of JASME: Research in Mathematics Education   27 ( 1 )   33 - 46   2021.12

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    Language：Japanese   Publishing type：Research paper (scientific journal)  

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  • Implementing a Science Class Promoting Cross-Curriculum Learning with Mathematics: Focusing on Density, Including Function Concepts Reviewed

    Takayuki YAMADA, Yoshihiko INADA, Masakazu OKAZAKI, Jun-ichi KURIHARA, Tatsushi KOBAYASHI

    Journal of Research in Science Education   62 ( 2 )   559 - 576   2021.11

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    Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Society of Japan Science Teaching  

    DOI： 10.11639/sjst.20082

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  • Enhancing the level of geometric thinking through learning the inscribed angle theorem Reviewed

    Masakazu Okazaki, Keiko Watanabe

    Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education   3   420 - 430   2021.7

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    Authorship：Lead author   Language：English   Publishing type：Research paper (international conference proceedings)  

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  • 探究型幾何カリキュラムの構成原理に関する研究－数学第二類の分析を通して－ Reviewed

    岡崎正和, 影山和也, 和田信哉, 渡邊慶子

    日本数学教育学会, 第9回春期研究大会論文集   137 - 144   2021.6

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  • Research on the mutual construction process of operational and formal proofs of algebraic expression in 8th Grade Reviewed

    Wataru Nishiyama, Masakazu Okazaki

    Journal of JASME: Research in Mathematics Education   26 ( 2 )   83 - 93   2021.3

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  • Learning about amount of substance (mol) to understand quantitative relations in chemical change: Adopting a ratio perspective to improve lessons

    Takayuki Yamada, Takayuki Matsumoto, Kenichi GOTO, Yoshihiko Inada, Masakazu Okazaki, Tatsushi Kobayashi

    40 ( 2 )   615 - 629   2021.3

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    Language：Japanese   Publishing type：Research paper (bulletin of university, research institution)  

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  • 平面図形と空間図形の連動による小中一貫の空間図形カリキュラムを構成する為の視座 Reviewed

    岡崎正和

    日本数学教育学会, 第8回春期研究大会論文集   97 - 104   2020.6

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  • 「関数的な見方・考え方」を働かせた理科授業の改善に関する一考察－数学と理科の教科等横断的な視点から－

    山田貴之, 稲田佳彦, 岡崎正和, 小林辰至

    上越教育大学研究紀要   39 ( 2 )   555 - 575   2020.3

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  • Exploring sixth graders' logical development for spatial figures Reviewed

    Shohei Ono, Masakazu Okazaki

    Journal of JASME: Rearch in Mathematics Education   25 ( 2 )   37 - 53   2019.12

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  • Constituting the theoretical framework for examining proof for understanding: focusing on the pragmatic view of proof

    Keiko Watanabe, Masakazu Okazaki

    439 - 442   2019.11

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  • Characterizing the quality of mathematics lessons in Japan from the narrative structure of the classroom: Mathematics lessons incorporating students' questions as a main axis as a leading case Invited Reviewed

    Masakazu Okazaki, Koji Okamoto, and Tatsuo Morozumi

    Hiroshima Journal of Mathematics Education   12   49 - 70   2019.2

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  • Revealing the assumptions through generating and reflecting on the language of proof

    Keiko Watanabe, Masakazu Okazaki

    503 - 506   2018.11

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    Language：Japanese  

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  • Perspectives needed to examine the quality of a structured problem-solving lesson for teachers’ professional development Invited Reviewed

    Masakazu Okazaki

    Proceedings of the 8th East Asia Regional Conference on Mathematics Education   1   123 - 135   2018.5

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  • Research on children's construction of division concepts and improving its teaching based on the multi-world paradigm

    Tadao Nakahara, Kazushige Maeda, Takeshi Yamaguchi, Masakazu Okazaki, Kazuya Kageyama

    ( 12 )   237 - 249   2018.3

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  • 教科内容構成による中学校の授業づくりと教員養成プログラムの改善(1) ー国語科, 数学科, 理科, 社会科を事例として－

    土屋聡, 岡崎正和, 宇野康司, 飯田洋介, 桑原敏典

    岡山大学教育学部研究集録   ( 167 )   111 - 119   2018.2

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  • 岡山大学教育学部における教員養成のための「教科内容構成」研究－小・中学校教員養成カリキュラムにおける教科内容構成の展開と評価－

    佐藤園, 岡崎正和, 宇野康司, 斉藤夏来, 土屋聡, 尾島卓, 三島知剛, 後藤大輔, 佐藤大介, 高塚成信

    岡山大学教育学部研究集録   ( 167 )   79 - 89   2018.2

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  • 教科内容構成による小学校の授業づくりと教員養成プログラムの改善(1) －国語科, 算数科, 理科を事例として－

    土屋聡, 岡崎正和, 宇野康司, 桑原敏典

    岡山大学教育学部研究集録   ( 167 )   91 - 99   2018.2

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  • Research on the roles of gesture in the process of constructing geometric proofs Reviewed

    Kenta Shishido, Masakazu Okazaki

    Journal of JASME, Rearch in Mathematics Education   23 ( 2 )   141 - 149   2017

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  • The analysis on results of the survey of "Partitive Division and the Extension of lts Meaning'' Reviewed

    Takeshi Yamaguchi, Kazuya Kageyama, Tadao Nakahara, Masakazu Okazaki, Kazushige Maeda

    Journal of JASME, Rearch in Mathematics Education   23 ( 1 )   1 - 20   2017

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  • The underlying principles for constructing mathematics lessons possessed by experienced teachers: Interviews by using the document of a mathematics lesson made in early Showa period Reviewed

    Keiko Kimura, Masakazu Okazaki, Keiko Watanabe

    Journal of JASME, Rearch in Mathematics Education   23 ( 2 )   15 - 29   2017

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  • 発展・拡充期における日本数学教育学会の研究動向

    岩崎秀樹, 岡崎正和

    日本数学教育学会第4回春期研究大会論文集   339 - 346   2016.6

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  • 我が国の「授業づくり」の特色に関する反省的記述

    山田篤史, 影山和也, 岡崎正和, 松浦武人

    日本数学教育学会第4回春期研究大会論文集   265 - 270   2016.6

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  • Analysis of mathematical thinking through interactions with a diagram in mathematics education: The meaning of a diagram obtained from the networking between semiotics and embodiment Reviewed

    Kazuya Kageyama, Shinya Wada, Koji Iwata, Atsushi Yamada, Masakazu Okazaki

    Journal of JASME, Research in Mathematics Education   22 ( 2 )   163 - 174   2016

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  • 倍に関わるわり算の位置づけに関する研究－小学５年から中学１年に対するわり算調査をもとにして－

    岡崎正和, 前田一誠, 中原忠男, 山口武志, 影山和也

    日本数学教育学会, 第49回秋期研究大会発表集録   161 - 164   2016

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  • Types of interaction that promote or hinder the narrative coherence of a mathematics lesson Reviewed

    Masakazu Okazaki, Keiko Kimura, Keiko Watanabe

    Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education   3   395 - 402   2016

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  • Brunerの文化心理学を視座とした数学授業の文化性の探究－「問い」を軸とした数学授業との関連－

    岡崎正和

    日本数学教育学会，第5回春期研究大会論文集   181 - 188   2016

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  • Theoretical perspective for examining qualities of a mathematics lesson in terms of students' narrative thinking Reviewed

    Keiko Watanabe, Masakazu Okazaki, Keiko Kimura

    Journal of Japan Society of Mathematical Education, Research Journal of Mathematical Education   98 ( 臨時増刊 )   49 - 56   2016

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  • Theoretical perspective for examining qualities of a mathematics lesson in terms of the philosophy of narrative Reviewed

    Masakazu Okazaki, Keiko Kimura, Keiko Watanabe

    Journal of Japan Society of Mathematical Education, Research Journal of Mathematical Education   97 ( 臨時増刊 )   49 - 56   2015.11

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  • 算数の事前学習を通した子どものめあての構想が算数の学びに与える効果の検証

    太田誠, 岡崎正和

    日本数学教育学会第48回秋期研究大会発表収録   47 - 50   2015.11

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  • A hermeneutic study on defining the emergence in mathematics education: For activating school mathematics classroom leading to the emergence

    Naomichi Yoshimura, Takeshi Yamaguchi, Tadao Nakahara, Masataka Koyama, Masakazu Okazaki

    The Bulletin of Japanese Curriculum Research and Development   38 ( 2 )   47 - 56   2015

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    Language：Japanese   Publisher：Japan Curriculum Research and Development Association  

    It has been noted that there is an important aspect in an emergence of mathematical knowledge and concepts for all children in a mathematics classroom. It is, however, difficult for an observer to visualize the abstract concept, and whether the emergence is for children or for all participants including the teacher in the classroom. The purpose of this study is to clarify the concept of the emergence in mathematics education in order to develop lessons that activate students' and/or teachers' emergence. Based on the review of previous works on emergence and findings of our study, we define emergence, and proposed five required elements of the emergence: (E1) fundamental property, (E2) subjects, (E3) methods, (E4) mathematical ideas, (E5) newness/valueness of mathematical ideas. We then demonstrate the appropriateness of these five requirements with a reported case and two additional cases of elementary school mathematics classes, and created a framework with four different types of emergences identified in terms of who and what, i.e. the difference between emergences for children and for all participants including the teacher, and the difference between the mathematical knowledge and concepts and the mathematical view and thinking. Finally, we proposed to define the emergence in mathematics education in terms of characteristic, requirements, and types of emergence. The results will be useful for an observer to define emergence, and describe and analyze the dynamic function of social interactions leading to the emergence in school mathematics classrooms.

    DOI： 10.18993/jcrdajp.38.2_47

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  • Examining the coherence of mathematics lessons in terms of the genesis and development of students' learning goals

    Masakazu Okazaki, Keiko Kimura, Keiko Watanabe

    Proceedings of the 7th East Asia Regional Conference on Mathematics Education   1   401 - 408   2015

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  • Research on development of the prescriptive model for designing social interactions in elementary school mathematics classroom

    Takeshi Yamaguchi, Masataka Koyama, Masakazu Okazaki

    Proceedings of the 7th East Asia Regional Conference on Mathematics Education   1   607 - 615   2015

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    Language：English  

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  • Examining the coherence of mathematics lessons from a narrative plot perspective

    Masakazu Okazaki, Keiko Kimura, Keiko Watanabe

    Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education   4   351 - 364   2014

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  • Research on development of the prescriptive model for designing social interactions in an elementary mathematics class based on the multi-world paradigm (II): Verification of its effectiveness through teaching and learning of 'number of outcomes'

    Tadao Nakahara, Masakazu Okazaki, Masataka Koyama, Takeshi Yamaguchi, Naomichi Yoshimura, Hisae Kato, Hajime Katayama

    ( 8 )   105 - 114   2014

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    Language：Japanese   Publisher：International Pacific University  

    This study aims at constructing the prescriptive model which has the theoretical background of social interactions in elementary mathematics classrooms and at the same time which is effective and applicable to teaching practices at elementary school level. In this paper we verify the effectiveness of this model through a teaching experiment on six grade classes of' number of outcomes'. As a result of analysis, we found that the fundamental process of being conscious, solving by the individuals, solving by small group, being reflective, and then making agreement, in particular the small group activity, contributed to the development of the children's understanding of' number of outcomes'. Also, it was suggested that the children's solving activities progressed from their 'individual' solution to' quasi-general', and' general' ones. We also identified the types of intentions of the social interaction: Share of the premise, having and devising their own ideas, sharing the ideas with others, reflecting on the merit and limit of the ideas, abstracting and generalizing from the ideas, finding the commonality, characteristics, and limits among the representations. Moreover, as to the interaction with representations, we found that the children could devise their own representations in order to prevent the overlap and omission, and also recognize that the representations by polygon and table equipped such devices. These findings demonstrate the effectiveness of the prescriptive model for teaching practices.

    DOI： 10.24767/00000406

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    Other Link： http://id.nii.ac.jp/1634/00000406/

  • Research on the learning process of function from the semiotic perspective: a focus on the meaning and the roles of gesture

    Ai Onoda, Masakazu Okazaki

    Journal of JASME, Research in Mathematics Education   20 ( 2 )   197 - 207   2014

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  • Study on the development of autonomy centered on goal setting through learning elementary mathematics based on the RPDCA cycle

    Makoto Ohta, Masakazu Okazaki

    Journal of JASME, Research in Mathematics Education   20 ( 2 )   21 - 29   2014

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  • Study on the development of autonomy by making use RPDCA cycle in arithmetic learning -With a focus on aspects of the stage of looking back-

    Makoto Ohta, Masakazu Okazaki

    Journal of Japan Society of Mathematical Education, Research Journal of Mathematical Education   96   25 - 32   2014

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  • Exploring how a mathematics lesson can become narratively coherent by comparing experienced and novice teachers’ lessons

    Masakazu Okazaki, Keiko Kimura, Keiko Watanabe

    Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education   3   313 - 320   2014

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  • Research on Development of the Prescriptive Model for Designing Social Interactions in an Elementary Mathematics Class Based on the Multi-world Paradigm (Ⅲ): Verification of Its Effectiveness through Teaching and Learning of 'Fractions' in Fourth Grade

    YAMAGUCHI Takeshi, NAKAHARA Tadao, KOYAMA Masataka, OKAZAKI Masakazu, YOSHIMURA Naomichi, KATO Hisae, WAKISAKA Ikufumi, SAWAMURA Masaharu

    Journal of JASME : research in mathematics education   20 ( 2 )   93 - 112   2014

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    Language：Japanese   Publisher：Japan Academic Society of Mathematics Education  

    <p>  The purpose of this study is to develop the prescriptive model for designing social interactions in an elementary mathematics class which is effective and applicable to teaching practices at elementary school level. In this paper we verify the effectiveness of this model through a teaching experiment of 'fractions' conducted for two fourth-grade classrooms in a school.  The teaching experiment had four characteristics: a teaching material focusing on meanings of fractions, recall of the definition of fractions learned in third grade, illustrative representations of tapes, and an applied problem which promotes mathematical generalization.  As a result of analysis, we found out the following four results.</p><p> Firstly the fundamental process of being conscious, solving by the individuals, solving by small group, being reflective, and then making agreement, in particular the small group activity, contributed to solving the problem.  Also, it was suggested that the children's solving activities progressed from their 'individual' solution to 'quasi-general'.</p><p>  Secondly the intentional support of illustrative representations by a teacher was quite effective.  Namely some children in one classroom were able to solve the problem of fractions for themselves and explain the  reason why their answer was correct clearly by using two kinds of illustrative representations of tapes.  In addition, the children negotiated that the length of one-third of a tape whose length was two meters was twothirds meter, as the solution of a problem, by differentiating two kinds of meanings of fractions.  Furthermore, it was confirmed that the children also explained such reason by translating illustrative representations into symbolic representations and generalized their solution of the original problem when they solved an applied one.</p><p>  Thirdly three kinds of social interactions such as social interaction with others, social interaction with the self and social interaction with representations, were activated by setting small groups. These kinds of social interactions contributed to developing the children's deeper understanding of fractions.</p><p> Lastly we could have two concrete suggestions for the improvement of teaching fractions by a comparative analysis of children's activities in two classrooms.  It was so crucial for the children to have an additive view of the definition of fractions in order to solve the problem.  It was important for the children to realize two kinds of the structure which were embedded in illustrative representations of tapes.</p><p>  These four findings demonstrate the effectiveness of the prescriptive model of social interactions for teaching practices in elementary school mathematics.</p>

    DOI： 10.24529/jasme.20.2_93

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  • Identifying situations for fifth graders to construct definitions as conditions for determining geometric figures

    Masakazu Okazaki

    Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education   3   409 - 416   2013

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  • Development from empirical to deductive reasoning in the learning of inclusion relations between geometric figures

    Masakazu Okazaki

    Proceedings of the 6h East Asia Regional Conference on Mathematics Education   3   30 - 40   2013

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  • Teaching and Learning connecting between students and mathematics from the cultural perspectives

    Mari Akiyama, Masakazu Okazaki

    Journal of JASME: Research in Mathematics Education   19 ( 2 )   89 - 99   2013

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  • Research on students' development of functional concepts during the transitional period from elementary to secondary school mathematics

    Takuya Kubo, Masakazu Okazaki

    Journal of JASME: Research in Mathematics Education   19 ( 2 )   175 - 183   2013

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  • Research on the understanding process through transforming the representations in the learning of function: Based on a semiotic approach and a theory of conceptual blending

    Ai Onoda, Masakazu Okazaki

    95   81 - 88   2013

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  • 算数・数学科教材研究に含まれる教師の知識の様相について―数学教育学研究の課題にする為に―

    岡崎正和

    日本数学教育学会第1回春期研究大会論文集   195 - 200   2013

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  • 論証への接続を目指した算数の図形指導に関する研究 (2)－図形の包含関係の学習における推論発達の様相－

    岡崎正和

    第45回数学教育論文発表会論文集   839 - 844   2012

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  • Exploring the nature of the transition to geometric proof through design experiments from the holistic perspective

    Masakazu Okazaki

    ICME 12 Pre-Proceedings   2012

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  • Influences of the epistemologies in mathematics education on practices, teaching and learning, and research methodologies

    Masakazu Okazaki

    Journal of JASME: Research in Mathematics Education   18 ( 2 )   1 - 12   2012

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  • 多世界パラダイムに基づく算数授業における社会的相互作用の規範的モデルの研究（I） －規範的モデルの第１次案－

    中原忠男, 岡崎正和, 山口武志, 吉村直道, 小山正孝, 加藤久恵, 杉田郁代

    第45回数学教育論文発表会論文集   779 - 784   2012

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  • Revealing the structures of geometric dynamic views in terms of figurative recognitions

    Masakazu Okazaki, Hideki Iwasaki, Kazuya Kageyama, Shinya Wada

    The Bulletin of Japanese Curriculum Research and Development   35 ( 2 )   53 - 62   2012

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    Language：Japanese   Publisher：JAPAN CURRICULUM RESEARCH AND DEVELOPMENT ASSOCIATION  

    This study aims at clarifying how students' recognitions of geometric figures in the elementary school can be connected to deductive geometry, and in this paper as a part of the study we will try to reveal the structures of geometric dynamic views that we have already identified in the learning of geometric shapes using the operative sheets and that may be considered to be premises for understanding the logical and relational natures of geometry. We transcribed the aspects of the geometric dynamic views as combinations of simple sentences, characterized each sentence using metaphor, metonymy, or synecdoche, and analyzed them in terms of the compositeness of the figurative recognitions. In our analysis, we found that the dynamic views were consolidated into five views: 1) Producing the different figure based on perceptual analogy, 2) Conceiving the movement of whole figure by the constitutive point, 3) Recognizing the invariants, 4) Reversible views, and 5) Simultaneous identification of invariants and variables. These may suggest the hierarchical nature among the dynamic views when we examine the degrees of compositeness for each dynamic view, which will be investigated in more detail in our future research.

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  • 数学教育学の理論とその形成に関する課題 －認識論，研究方法論との関わりを視点として－

    岡崎正和

    第45回数学教育論文発表会論文集   21 - 26   2012

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  • FIFTH GRADERS' ARGUMENTS FOSTERED IN THE LEARNING OF INCLUSION RELATIONS BETWEEN GEOMETRIC FIGURES

    Masakazu Okazaki

    PROCEEDINGS OF THE 35TH CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION, VOL. 3: DEVELOPING MATHEMATICAL THINKING   3   281 - 288   2011

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    Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：INT GRP PSYCHOL MATH EDUC  

    This study explores the process of transition from elementary to secondary geometry through design experiments. We aim at clarifying the types and characteristics of fifth graders' mathematical arguments, which can be fostered in the learning of inclusion relations between geometric figures. In our analysis, we identified three types of arguments: similarity or difference between properties of figures, suggestion of general-special relations, and consistency among relations and conviction of others. Our examination of their characteristics may imply a process in which each argument connects with each other based on some dynamic views and leads eventually to the last argument.

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  • 数学教育における認識論が実践，学習指導，研究方法論に与える影響について

    岡崎正和

    第44回数学教育論文発表会論文集   21 - 30   2011

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  • 探究的活動としての証明を実現するために： 形式的証明導入前の活動を充実させる

    岡崎正和

    第43回数学教育論文発表会，「課題別分科会」発表収録   39 - 44   2010

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    Language：Japanese   Publisher：公益社団法人日本数学教育学会  

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  • Development of reasoning ability towards proof using seventh grade Plane Geometry

    Masakazu Okazaki

    Proceedings of the 5th East Asia Regional Conference on Mathematics Education   2   188 - 195   2010

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  • WHAT ARE DYNAMIC VIEWS IN GEOMETRY? A DESIGN EXPERIMENT IN A SIXTH GRADE CLASSROOM

    Masakazu Okazaki, Kazuya Kageyama

    PME 34 BRAZIL: PROCEEDINGS OF THE 34TH CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION, VOL 4   4   1 - +   2010

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    Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：INT GRP PSYCHOL MATH EDUC  

    This study explores the process of transition from elementary to secondary geometry through design experiments. We aim to clarify those dynamic views that enhance student recognition of geometric relationships acquired during the experiment. As a result of our analysis, we identified seven dynamic views: concrete manipulation, idealization and mental operation, gesture, grasping the whole movement in terms of points, recognition of invariants and variables, reverse operation, and simultaneous identification of the movement and the figure transformation. Furthermore, we conceived them mainly from the viewpoint of the image schemata and specified their places.

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  • Substantiating the dynamic views in learning geometry: From the viewpoints of image schemata

    Masakazu Okazaki, Hideki Iwasaki, Kazuya Kageyama, Shinya Wada

    Journal of JASME   16 ( 2 )   1 - 10   2010

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    Language：Japanese   Publisher：Japan Academic Society of Mathematics Education  

    This research aims at clarifying the transition process from elementary mathematics to secondary one through the design experiment methodology. In this paper, we sorted out students' dynamic views which enabled them to enhance their understanding of inclusion relations between figures through analyzing our data of classroom lessons "constructing the figures using the operative sheets" based on the grounded theory approach. We could find the follwoing seven dynamic views as a result of our analysis. (A) Concrete manipulation, (B) Idealization and mental operation, (C) Gesture, (D) Grasping the movement of some point during the whole figure change, (E) Recognition of invariants, (F) Reverse operation, and (G) Simultaneous identification of invariants and variables. Then, we characterized the dynamic views of (A) concrete manipulation and (B) idealization and mental operation as the figurative image schema, the dynamic views of (C) gesture, (D) grasping the movement of some point during the whole figure change and (E) recognition of invariants as the opeartive image schema, and (E) reverse operation and (G) simultaneous identification of invariants and variables as the relational image schema. We consider that these characterizations may suggest the possible categories of the image schemata for the recognition of geometry, although we don't claim that these are all cases. Also, we may know why some students could learn the inclusion relations between figures and the others not, if we observe children's thinking in geometry in terms of the framework.

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  • Qualitative study of teacher's teaching act for promoting the learning of proof

    Yuko Sumitomo, Masakazu Okazaki

    1   289 - 294   2010

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  • The recognition of geometric figures cultivated through geometric transformations: The design experiment aimed at the transition towards proof

    Masakazu Okazaki, Seijiro Komoto

    Journal of Japan Society of Mathematical Education: Mathematics Education   91 ( 7 )   2 - 11   2009

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  • Process and means of reinterpreting tacit properties in understanding the inclusion relations between quadrilaterals

    Masakazu Okazaki

    Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education   4   249 - 256   2009

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  • The transition process towards logical proofs through synthesizing geometric transformations and geometric constructions: A design experiment of 7th grade unit "Plane Geometry"

    Masakazu Okazaki, Seijiro Komoto

    Journal of JASME : Research in Mathematics Education   15 ( 2 )   67 - 79   2009

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    Language：Japanese   Publisher：Japan Academic Society of Mathematics Education  

    We conducted a design experiment for clarifying the transition process from geometry in primary mathematics to geometric proof in secondary school for the seventh grade's teaching unit "plane geometry" which was designed as three subunits of (1) the discovery game of geometric figures, (2) the jintori game, and (3) the discovery game of geometric constructions and the geometric proof. In this paper we examined the students' thought processes when they could develop the geometric constructions through the discovery game and explore the geometric proof on the superposition of two triangles which are placed at the arbitrary positions, and aimed at abstracting the factors of students' development towards geometric proofs. The factors of the transition towards logical proofs that we abstracted from our analysis of the design experiment are the following points. 1. Cognitive aspects are ・to find the geometric constructions by using and combining the figures and their properties, ・to confirm and limit the extent where the law works using inductive reasoning and empirical explanation, ・to make the proposition so that inductive reasoning can be changed to deductive reasoning, and ・to reinterpret the procedures of geometric constructions as the conditions for justification. 2. Aspects of the recognition of figure and shape are ・to find out figures and use them for geometric constructions and inferences, ・to conceive shapes included in the figure in terms of various relations and correspondences, ・to see figures as the variables which can be transformed dynamically, and ・to see figures as the representations of relations through showing reasonings diagrammatically. 3. Social aspects are ・to learn based on conjectures, refutations, and consensus among the participants, ・to make conjectures while assuming the criticism by the other students, ・to develop conjectures by examining the criticism and the counter-example by the other students, and ・to reinterpret and express the others' explanations more explicitly. 4. Aspects of the teaching unit structure are ・to envision the fundamental situation and the unit structure as a series of the situation for action, the situation for formulation and the situation for validation in the theory of didactical situation, ・to pose a proof problem so that the learned procedures of geometric constructions can be reconstructed as the conditions for justification, and ・to make geometric transformations and geometric constructions interact with each other at the final stage of the unit.

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  • 論証への接続を目指した算数の図形指導に関する研究 (1) : 図形の包含関係の理解を促す動的な見方の具体化

    岡崎正和, 岩崎秀樹, 影山和也, 和田信哉

    数学教育論文発表会論文集   42   325 - 330   2009

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    Language：Japanese   Publisher：公益社団法人日本数学教育学会  

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  • Initial aspects of logical justification in learning geometric figures: Design experiment of 7th grade unit "Plane Geometry" towards the transition to geometric proof (1)

    Seijiro Komoto, Masakazu Okazaki

    Journal of JASME : Research in Mathematics Education   14   41 - 50   2008

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    Language：Japanese   Publisher：Japan Academic Society of Mathematics Education  

    We conducted the design experiment in the teaching unit "plane geometry" which was concieved as the transitional material from geometry in primary mathematics to geometric proof in secondary school, and designed as three subunits of (1) the discovery game of geometric figures, (2) the jintori game, and (3) the discovery game of geometric constructions. This paper reprorts 7th grade students' initial aspects of logical justification of geometric figures in the first subunit "the discovery game of geometric figures". The findings in this paper are the following four points. ・Students first tended to attend to the larger figures visually in the hemp leaf situation of the discovery game of geometric figures. However, when they began to consider the criticism by others and the counter examples in their minds, they could change their object of justification to the smaller figures, with their consciousness of insufficiency of the empirical explanations. They then developed their idea of trying to justify the constituent geometric figures by using the smaller figure (the right triangle). ・Therefore, we may indicate that the idea of placing the constituent figures by the right triangle was produced in the situation of formulation in which the assumption of the others' criticism was added to the situation of action. ・When students tried to justify the constituent figures by one geometric figure (right triangle), they began to consider the order of placing the figures and the justification of the right triangle itself. The justification could be successful when they reconstructed steps of geometric construction as conditions of proof. Furthermore, we suggest that the logical proof was produced as a feedback of the others' criticism and based on the logic of justification of the right triangle. ・We also found students' tendencies of complementing their logical explanation with the empirical means and of approving the empirical explanation in some cases, although they enhanced their abilities of explaining the geometric figures in the logical manner.

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  • Semiotic chaining in a substantial learning environment aimed at the transition from arithmetic to algebra

    Masakazu Okazaki

    International Journal of Curriculum Development and Practice   10 ( 1 )   13 - 24   2008

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    In the transition from arithmetic to algebra, it is important to create a learning environment which develops the way in which students view mathematical expressions. This paper reports how students may develop their views through an expression constructing activity. We first constructed the activity from a viewpoint of substantial learning environment, next implemented the teaching experiment in a 7th grade class, and analysed the students' actual activities from a perspective of semiotic chaining. As the result of our analysis in terms of semiotic chaining, we identified four states of sign combinations and chaining for students' progress in their view of mathematical expressions, and discussed the important role of the use of brackets in viewing an expression structurally.

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  • Learning of division with decimals towards understanding functional graph

    Masakazu Okazaki

    Proceedings of the Joint Meeting of the 32nd PME and 30th PME-NA Conference   4   65 - 72   2008

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  • 小数除法における算数から数学への移行研究(2)－純小数倍の理解をめぐって－

    岡崎正和

    数学教育論文発表会論文集   41   273 - 278   2008

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  • PROTOTYPE PHENOMENA AND COMMON COGNITIVE PATHS IN THE UNDERSTANDING OF THE INCLUSION RELATIONS BETWEEN QUADRILATERALS IN JAPAN AND SCOTLAND

    Masakazu Okazaki, Taro Fujita

    PME 31: PROCEEDINGS OF THE 31ST CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION, VOL 4   4   41 - 48   2007

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    Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：KOREAN SOC MATH EDUC  

    This study explores the status and the process of understanding of &apos;the inclusion relations between quadrilaterals&apos;, which are known to be difficult to understand, in terms of the prototype phenomena and the common cognitive paths. As a result of our analysis of data gathered in Japan and Scotland, we found that the students&apos; understanding was significantly different for each inclusion relation, and that there were strong prototype phenomena related to the shapes of the square and rectangle in Japan, and related to angles in Scotland, the factors which prevent students from fully grasping inclusion relations. We also confirmed the existence of common cognitive paths in Japan and Scotland, and based on these paths discussed a possible route to teach the inclusion relations between quadrilaterals by analogy.

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  • The place and the tasks of a design experiment methodology in mathematics education -From a viewpoint of a balance between scientific status and practical usefulness-

    Masakazu Okazaki

    Journal of JASME: Research in Mathematics Education   13   1 - 13   2007

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    This paper focuses on a design experiment methodology in mathematics education which has been developed as a methodology for establishing a close and dynamic relationship between theory and practice, and discusses the comprehensive characteristics of the methodology. The design experiment methodology intends to develop (local) theories in mathematics education through designing, practicing and systematically analyzing daily classroom lessons over a relatively long period, where a researcher is responsible for students' mathematical learning in collaboration with a teacher. However, the methodology has also been questioned as to its scientific quality by the positivist scholars, since it explicitly deals with classroom practices that can be characterized as complex phenomena. Thus, this paper tries to place the design experiment methodology especially from a scientific point of view. The points discussed in this paper are the following. 1. The design experiment is an effective methodology for realizing mathematics education as a design science, and it intends to create a fruitful relationship between theory and practice. 2. The design experiment aims to construct a class of theories about the process of learning and the means that are designed to support that learning through (a) designing and planning the learning environments, (b) experimenting the design and the ongoing analysis, and (c) the retrospective analysis. 3. The design experiment is an interventionist methodology that goes through an iterative design process featuring cycles of invention and revision. 4. The design experiment has its intention of producing a theory which premises a social and cultural nature of the classroom, active roles of teacher and students, and learning ecologies and complexities of the community. Thus, it is opposed to an orientation of theory-testing that the positivist studies adopt. 5. The design experiment has been critically discussed in terms of the traditional scientific criteria like generalizability, reliability, replicability and others. 6. We can indicate four points as our tasks for enhancing the scientific qualities of the design experiment; ・Implementing consciously both processes from scholarly knowledge to teaching, and conversely from craft knowledge to researching and scholarly knowledge, ・Analyzing practical data in a systematic way and unfolding a logic of the analysis, ・Assessing and evaluating the design experiment using the revised scientific criteria, and ・Placing some philosophy which the design experiment is based on.

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  • 教授学的状況論に基づく移動による図形の探究 : 図形の論証への接続を目指した教授実験の報告（その２）

    髙本誠二郎, 岡崎正和

    第40回数学教育論文発表会論文集   40   427 - 432   2007

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  • 小数除法における算数から数学への移行研究－傾きの探究を視点として－

    岡崎正和

    第40回数学教育論文発表会論文集   385 - 390   2007

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  • 一つの教室の継続的観察を通してみたアメリカ第7学年の数学授業の特徴

    岡崎正和

    上越数学教育研究   21 ( 21 )   21 - 30   2006

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  • Characteristics of 5th graders' logical development through learning division with decimals

    Masakazu Okazaki, Masataka Koyama

    Educational Studies in Mathematics   60 ( 2 )   217 - 251   2005.10

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

    When we consider the gap between mathematics at elementary and secondary levels, and given the logical nature of mathematics at the latter level, it can be seen as important that the aspects of children's logical development in the upper grades in elementary school be clarified. In this study we focus on the teaching and learning of "division with decimals" in a 5th grade classroom, because it is well known to be difficult for children to understand the meaning of division with decimals, caused by certain conceptions which children have implicitly or explicitly. In this paper we discuss how children develop their logical reasoning beyond such difficulties/misconceptions in the process of making sense of division with decimals in the classroom setting. We then suggest that children's explanations based on two kinds of reversibility (inversion and reciprocity) are effective in overcoming the difficulties/ misconceptions related to division with decimals, and that they enable children to conceive multiplication and division as a system of operations. © Springer 2005.

    DOI： 10.1007/s10649-005-8123-0

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  • A Study on Semiotic Chaining in Mathematics Education : Through the Analysis of Wittmann's "Teaching Unit"

    Bulletin of the Faculty of Education, Ehime University   52 ( 1 )   139 - 152   2005

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  • 代数の導入過程としての正負の数の乗除の単元開発における授業展開の様相

    岡崎正和, 黒田匠

    第37回数学教育論文発表会論文集   37   241 - 246   2004

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  • 図形領域における算数から数学への移行過程について : 図形の相互関係から図形の作図への系統性

    岡崎正和

    第36回数学教育論文発表会，「課題別分科会」発表収録   144 - 149   2003

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  • Geometric construction as an educational material mediating between elementary and secondary school mathematics: Theory and practice to promote transformation from empirical to logical recognition

    Masakazu Okazaki, Hideki Iwasaki

    Japan Society of Mathematical Education: Research in Mathematical Education   80   3 - 27   2003

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  • 算数の式から代数の式への転換を促す正負の数の乗除の単元の再構成に関する研究

    岡崎正和, 黒田匠

    第36回数学教育論文発表会論文集   157 - 162   2003

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  • 全体論的な立場からの文字と式の単元構成について

    岡崎正和

    上越数学教育研究   18 ( 18 )   49 - 58   2003

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  • Study in the structure of the teaching unit of addition and subtraction with positive and negative numbers from the holistic perspective: From the viewpoints of the theory of didactical situations and the algebraic cycle of thinking

    Masakazu Okazaki

    Journal of JASME: Research in Mathematics Education   9   1 - 13   2003

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  • 代数の導入過程における正負の数の加減の学習指導と，それに託される教育理念

    岡崎正和, 黒田匠

    第35回数学教育論文発表会論文集   35   193 - 198   2002

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  • A study on the developmental process from empirical to theoretical conception: Focusing on the process of geometric construction and its justification

    Masakazu Okazaki

    The Bulletin of Japanese Curriculum research and development   24 ( 1 )   11 - 19   2001

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    Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：JAPAN CURRICULUM RESEARCH AND DEVELOPMENT ASSOCIATION  

    This study aims at clarifying the process by which 7th grade students develop their empirical conceptions into theoretical ones. In particular, this paper explores how they develop their geometric conceptions by analyzing two kinds of classroom teaching practices concerning geometric construction. In the first classroom teaching practice study, it is suggested that students can interactionally develop their geometric concept of a kite as well as their way of constructing it. Initially, students conceived a kite as its shape and its collection of properties. They then began to use it as a tool for their geometric constructions, and gradually started to understand the relationship between the procedure of construction and the properties of the geometric figure. Finally, they could not only use the tool explicitly and mentally, but also become aware of the relationships between the properties of the kite itself. That is, their conception of the geometric figure sustained their construction activity and at the same time the activity promoted their understanding of the properties of the geometric figure. However, although we also intended in our teaching plan that students could eventually prove their construction procedure, they were unable to do so. As a result of this, we observed classroom lessons at the university-attached school and analyzed some factors for students to succeed in finding this proof. The results and implications for teaching about geometric construction are as follows. Firstly, students naturally use geometric figures as their cognitive tools in construction. Therefore we think that in the classroom lessons teachers should encourage students to become conscious of and reflect on their own cognitive activities. Secondly, in order to succeed in justifying the construction procedure, students need to not only differentiate it from the product, but also to use this procedure as a condition of proof. Thirdly, if we admit the existence of empirical proof, students have the potential to find some proof and justify it by activating their own image schema.

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  • Geometric Construction as a Threshold of Proof : The Figure as a Cognitive Tool for Justification

    Iwasaki Hideki, Okazaki Masakazu

    International journal of curriculum development and practice   3 ( 1 )   57 - 64   2001

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    Geometric construction is usually considered as the procedure of drawing a figure bounded by a straightedge ruler and a compass. It, however, could be didactical intermediate between a cause-effect and an assumption-conclusion explanation because it is not only a series of systematic activities using only two tools but also mathematical proof of existence in itself. We, therefore, consider it as a educational threshold of proof in system although most mathematics teachers emphasize its procedural aspect. We analyzed the justification of the geometric constructions made by seventh grade students in the classroom lessons in terms of image schema. Image schema was developed for a meaning-making function by Dorfler(1991). It was made available for us to clarify the logical or cognitive base of the students' justification and change of thought. This research finally showed some factors for the transition from construction to proof in geometry.

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  • Study on the introductory process of algebra from the holistic perspective: On the emergence of algebraic ideas

    Masakazu Okazaki

    7   39 - 49   2001

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  • 全体論的な視座からの授業設計に関する考察 : 中学校1年の文字式・方程式の授業デザインに向けて

    岡崎正和

    上越数学教育研究   16 ( 16 )   47 - 56   2001

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  • 数学授業における場を視点とした代数の導入過程の構成に関する研究

    岡崎正和, 黒田匠

    第34回数学教育論文発表会論文集   37 - 42   2001

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  • 教授単元の考えを普段の授業に実現する一つの試み : 教授学的工学に着目して

    岡崎正和

    第33回数学教育論文発表会論文集   33   31 - 36   2000

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  • 中学1年生の図形の経験的認識と，理論的認識へ高める作図の教授学的機能

    岡崎正和

    上越数学教育研究   15 ( 15 )   29 - 38   2000

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  • Basic study on activities of defining geometrical figures : Referring to an investigation on the understanding of inclusion relations between geometrical figures

    Masakazu Okazaki

    Journal of JASME: Research in Mathematics Education   5   101 - 110   1999

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    Geometrical definitions play important roles in learning geometry. Especially, in demonstrative geometry students need to function well since geometrical logic is constructed based on the definition. In junior high school mathematics, the inclusion relation between geometrical figures is one of relatively simple teaching materials to be understood by using definitions. In this study, firstly we analyze students' understanding of inclusion relations between geometrical figures, as an indication of whether the definitions are functional for junior high school students. The findings are follows; ・Inclusion relations between parallelogram and rhombus, and between rhombus and square are already conceived by more than half of 1st graders. On the contrary, the scores of inclusion relations between parallelogram and rectangle, and between rectangle and square are less than 50 % in 3rd graders. ・On the whole, the degree of achievement of the contents is low. Therefore, we cannot say that learning inclusion relations in demonstrative geometry is effective. Secondly, we discussed activities in which students construct geometrical definitions, from the viewpoints of transition to demonstrative geometry. Geometrical definition is initially used by young children to classify or construct geometrical shapes, and therefore it shows the characteristics of the shape. On the other, the definitions in demonstrative geometry are necessary and sufficient conditions, and they are used as bases and premises for constituting geometrical logic. We suggested that in order to fill the gap, it is important for students to construct definitions as the formalization of geometrical concepts in the level of action. The activities have the following two aims; ・To understand the definition as the condition for determining the geometrical figure ・To understand the definition as a starting point of ordered relations among geometrical properties The former is recognized in the activity of classification among geometrical figures by using operational sheets (Nakahara, 1995), and the latter will be recognized in the activity of geometrical construction of perpendicular bisector, perpendicular line, and bisector of angle based on the geometrical figure of kite or rhombus. Through these activities, student will be able to conceive the geometrical figure as a set of geometrical properties and control the figure using the definition.

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  • The Transition from arithmetic to mathematics (1) : Focusing on algebraic sum and its teaching

    Hideki Iwasaki, Masakazu Okazaki

    Journal of JASME: Research in Mathematics Education   5   85 - 90   1999

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    Language：Japanese   Publisher：Japan Academic Society of Mathematics Education  

    Most of studies on algebraic area in school mathematics are focused on the understanding of meaning or operation of algebraic symbols, notations or equation. They hardly pay attention to the subtraction of a negative number and algebraic sum. In this study our interest is mainly devoted into two sorts of understanding about positive and negative numbers in order to clarify the transition from arithmetic to mathematics. Arithmetic has no necessity to regard subtraction as addition anywhere. Even if mathematics has necessity to develop it, mathematics teaching could not apply the idea of opposite number and inverse operation to understand the subtraction of a negative number as the addition of a positive number before going to algebra. And there is little room to explain it in arithmetic either. Therefore we use a metaphor to understand the change of subtraction to addition under the virtual reality and the language game. Moreover this idea must be formalized clearly and systematically in the algebraic sum. In this article we showed that the metaphorical understanding of the subtraction of a negative number and the systematic formalization of calculation in algebraic sum were a bridge to introduce mathematics teaching from arithmetic teaching.

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  • 図形教育における算数から数学への移行を促す授業開発に関する研究

    岡崎正和, 岩崎秀樹, 板垣政樹

    第32回数学教育論文発表会論文集   32   233 - 238   1999

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  • 算数から数学への移行期における子どもの論理の発達の特徴 : 除法の一般化を事例として

    岡崎正和

    上越数学教育研究   ( 14 )   39 - 48   1998

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  • 均衡化理論に基づく数学的概念の一般化における理解過程に関する研究

    岡崎正和

    日本数学教育学会誌「数学教育学論究」   69   29 - 34   1998

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  • 算数から数学への移行とその指導に関する研究(2) : 図形学習の転換点

    岡崎正和, 岩崎秀樹

    第31回数学教育論文発表会論文集   165 - 170   1998

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  • 算数から代数への移行とその指導に関する研究(1) : 学校数学における代数和の位置づけとその指導

    岩崎秀樹, 岡崎正和

    第30回数学教育論文発表会論文集   391 - 396   1997

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  • Research on the understanding processes in generalization of mathematical concepts : Generalization of parallelogram

    Masakazu Okazaki

    Journal of JASME : Research in Mathematics Education   3   117 - 126   1997

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    Language：Japanese   Publisher：Japan Academic Society of Mathematics Education  

    In this research we approach to the understanding processes in generalization of mathematical concepts based on the "Optimizing Equilibration Model of Mathematical Understanding". In this paper, in particular, we will clarify the processes through which children understand inclusion relations between quadrilaterals and generalize their schema of parallelogram. Difficulties in understanding inclusion relations are not consisted in mathematical logic, but in such children's tacit property that each angle of rectangle is not 90°. We have discussed means that they overcome the difficulties and understand inclusion relations, and indicated that the following means are effective. 1. conceiving geometrical figures dynamically by manipulating on operative material and seeing continual transformations from parallelogram to rectangle or rhombus 2. understanding conservation of properties in the transformations 3. understanding negative properties in the transformations 4. analogy to the inclusion relation between parallelogram and rhombus 5. analogy to the inclusion relation between rhombus and square We also clarified that after understanding the content, children's schema of parallelogram becomes to be in the states of the followings. 1. Properties of a geometrical figure are organized, and children can define a geometrical figure by using those properties. 2. Children conceive properties of a geometrical figure as common properties between geometrical figures. 3. A geometrical figure is a bearer of their properties. These states are effective for children to learn proof in lower secondary school. Therefore, children should learn inclusion relations between quadrilaterals in primary school.

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  • 理解モデルの機能

    岡崎正和

    第30回数学教育論文発表会「テーマ別研究部会」発表収録   41 - 48   1997

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  • 子どもの理解に基づく教材構成に関する研究(1) : 四角形の相互関係の共通概念経路を中心として

    岡崎正和

    第30回数学教育論文発表会論文集   391 - 396   1997

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  • A Basic Study on Cognitive Processes of Mathematical Concepts (XVII) : An Examination of Elementary School Mathematics Classroom Based on the Constructive Approach

    ( 24 )   95 - 101   1996.3

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  • Research on the understanding process in generalization of mathematical concepts based on the equilibration theory : Understanding process in generalization of quotitive division

    Masakazu Okazaki

    Journal of JASME : Research in Mathematics Education   2   91 - 100   1996

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    Language：Japanese   Publisher：Japan Academic Society of Mathematics Education  

    Multiplication and division of decimal fraction is one of the most difficult contents for 5th graders in the primary school. This study focuses on the division of decimal fraction, especially on the generalization from quotitive division to first application of ratio. The purpose of this study is to clarify the understanding process in generalization of quotitive division, especially the factors of difficulties in understanding the division of decimal fraction and the factors for overcoming the diffuculties. The main results are folloing; 1. The generalization of quotitive division is made by extending the idea of 'measurement'. 2. In the generalization, it is effective to use the operative material that can generalize the idea of measurement and that function as the semi-concrete material for number-line expression. 3. The primitive model on quotitive division include the properties of 'quotient is integer' and 'dividend is larger than divisor'. 4. Children feels difficulties in such situations that quotient is decimal fraction and that dividend is smaller than divisor. These situations are related with primitive model. 5. The stages that the idea 'how many times' is abstracted from how many pieces 'are folloing; (a) The idea of 'how many times' is primitively constructed in such a division that dividend is larger than divisor and quotient is decimal fraction. (b) The idea of 'how many times' is realized in such a division that dividend is smaller than divisor. (c) The merit of the idea of 'how many times' is realized when all division of decimal fraction is conceived by the idea.

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  • 拡大均衡化モデルの規範性について : 指導原理含意性を中心として

    岡崎正和

    第29回数学教育論文発表会論文集   229 - 234   1996

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  • 均衡化理論に基づく数学的概念の一般化における理解過程に関する研究 : 暗黙のモデルとネガティブな側面

    岡崎正和

    中国四国教育学会「教育学研究紀要」   41 ( 2 )   148 - 153   1996

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  • Research on the understanding processes in generalization of division concept: Generalization of partitive division

    Masakazu Okazaki

    Bulletin of the Faculty of Education, Hiroshima University. Part 2, Science & culture   45   83 - 92   1996

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  • A Basic Study on Cognitive Processes of Mathematical Concepts (XVI) : Practical Study of Mathematics Classroom Based on the Constructive Approach

    ( 23 )   77 - 86   1995.3

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  • 均衡化理論に基づく数学的概念の一般化における理解の成長に関する研究 : 数学的一般化の理解モデルの構築

    岡崎正和

    第28回数学教育論文発表会論文集   7 - 12   1995

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  • 均衡化理論に基づく数学的理解の成長に関する研究 : 均衡化のプロセスを中心として

    岡崎正和

    中国四国教育学会「教育学研究紀要」   40 ( 2 )   169 - 174   1995

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  • A study on growth of mathematical understanding based on the equilibration theory: Analysis of interviews on understanding of "inclusion relations between geometrical figures"

    Masakazu Okazaki

    Journal of JASME : Research in Mathematics Education   1   45 - 54   1995

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    Language：Japanese   Publisher：Japan Academic Society of Mathematics Education  

    In Japanese primary school geometry, one of the subject matters whose position in curriculum are unstable is "inclusion relations between geometrical figures". The unstableness seems to be due to unclearness about causes of difficulties, ways of teaching, or students' processes of understanding about the subject matter. So, the purpose of this paper is to clarify the causes of difficulties and the growing processes in understanding it, by way of interpreting the data from interviews through "the model of understanding". The findings and implications from the investigation are follows. 1. Students seem to conceive geometrical figures as being static and fixed. 2. There is a tendency that tacit irrelevant properties are added in the students' conception of geometrical figures. For example, in parallelogram there are two irrelevant properties - the lengths of neighboring sides are not equal, and the sizes of neighboring angles are not equal. 3. In order to understand inclusion relations between geometrical figures, it is very useful to use "operational material" that can move a geometrical figure and transform from one figure to the other. 4. Students can recognize the statement like "rhombus is a kind of parallelogram", if they interiorize the common properties of parallelogram and rhombus. 5. But if students take conscious of properties proper to the figure that is inside in inclusion relation, for example, neighboring sides are equal in rhombus, then they also take conscious of tacit property at the same time, for example, the lengths of neighboring sides are not equal in parallelogram, and soon return to their exclusive conception because of their conflict. 6. If students have ever constructed flexible images of the figure that is outside in inclusion relation, i.e. the image that deny the tacit (irrelevant) property, then their images are reflected, coordinated, and they can grow their understanding about inclusion relations between geometrical figures.

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  • 数学教育における理解の深まりに関する研究(IV) : 「規範性」の視点からの均衡化モデルの検討

    岡崎正和

    中国四国教育学会「教育学研究紀要」   39 ( 2 )   186 - 191   1994

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  • 均衡化理論に基づく数学的理解の成長に関する研究 : W. Doerflerの一般化の理論を中心として

    岡崎正和

    第27回数学教育論文発表会論文集   107 - 112   1994

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  • A study on the development of understanding in mathematics education (V): The process of development of understanding the effect of image making

    Masakazu Okazaki

    Bulletin of WJASME: Research in Mathematics Education   20   9 - 16   1994

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  • A Basic Study on Cognitive Processes of Mathematical Concepts (XV) : Practical Study of Mathematics Classroom Based on Constructivism

    ( 22 )   31 - 40   1993.4

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  • A Basic Study on Cognitive Processes of Mathematical Concepts (XIV) : An Analysis of the Fundamental Principles and Experimental Research of Mathematics Education Based on Constructivism

    ( 21 )   31 - 40   1993.3

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  • A study on the development of understanding in mathematics education (I): Framework for grasping the development of understanding

    Masakazu Okazaki

    Bulletin of WJASME: Research in Mathematics Education   19   53 - 59   1993

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  • 数学教育における理解の深まりに関する研究(III) : 均衡化モデルの設定とその有効性について

    岡崎正和

    第26回数学教育論文発表会論文集   43 - 48   1993

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  • 子どもの「問い」を生かす算数授業―「静岡」からの発信－

    岡本光司編, 落合有紗, 永田健翔, 鈴木元気, 佐藤友紀晴, 酒井信一, 横山剛志, 立花千紗子, 岡崎正和, 両角達男, 松島充（ Role： Joint author）

    静岡新聞社  2023.8 

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  • コミュニケーションとしての思考: 人間の発達,ディスコースの成長,数学化

    岡崎 正和, 山田 篤史, 岩﨑 浩, 岩田 耕司, 岡崎 正和, 影山 和也, 加藤 久恵, 清水 紀宏, 山田 篤史, 和田 信哉（ Role： Edit）

    共立出版  2023.5  （ ISBN:4320114914 ）

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    Total pages：410   Language：Japanese

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  • 新編数学Ⅲ

    小山正孝, 岡崎正和（ Role： Joint author）

    第一学習社  2023.4 

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  • イラスト図解ですっきりわかる算数

    新算数教育研究会（ Role： Contributor）

    東洋館出版社  2023.3 

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  • 新編数学（数学Ⅰ，数学A，数学Ⅱ，数学B，数学C）

    小山正孝, 岡崎正和他（ Role： Joint author）

    第一学習社  2022.4 

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  • 算数・数学の授業研究ハンドブック

    日本数学教育学会編（ Role： Joint author ,  第3部第3章コラム）

    東洋館出版社  2021.8 

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  • Japan Society of Mathematical Education/ Centenary History

    Japan Society of, Mathematical Education（ Role： Contributor）

    Toyokan  2021.7 

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  • 中学数学

    重松敬一, 小山正孝, 飯田慎司, 岡崎正和他（ Role： Joint author）

    日本文教出版  2021.4 

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  • 小学算数

    小山正孝, 飯田慎司, 岡崎正和他（ Role： Joint author）

    日本文教出版  2020.4 

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  • 中学数学

    重松敬一, 岡崎正和他（ Role： Joint author）

    日本文教出版  2016.4 

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  • 算数の本質に迫る「アクティブ・ラーニング」

    東洋館出版社  2016  （ ISBN:9784491032849 ）

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  • Selected Regular Lectures from the 12th International Congress on Mathematical Education

    Springer  2015  （ ISBN:9783319171869 ）

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  • 小学算数

    日本文教出版  2015  （ ISBN:9784536180900 ）

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  • Elementary mathematics

    Nihon Bunkyo  2015  （ ISBN:9784536180900 ）

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  • 中等数学教育

    協同出版  2014  （ ISBN:9784319106769 ）

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  • 中学数学

    重松敬一, 岡崎正和他（ Role： Joint author）

    日本文教出版  2012.4  （ ISBN:9784536180764 ）

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  • 新しい学びを拓く算数科授業の理論と実践（共著）

    ミネルヴァ書房  2011  （ ISBN:9784623060436 ）

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  • Elementary mathematics

    Nihon Bunkyo  2011  （ ISBN:9784536180672 ）

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  • Elementary mathematics intructional guide

    Nihon Bunkyo  2011  （ ISBN:9784536280976 ）

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  • 小学算数

    日本文教出版  2011  （ ISBN:9784536180672 ）

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  • 小学算数教師用指導書総論

    日本文教出版  2011  （ ISBN:9784536280976 ）

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  • Theory and practice of the elementary mathematics class "jointly worked"

    Minerva  2011  （ ISBN:9784623060436 ）

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  • 新数学教育の理論と実際＜中学校・高等学校（必修）編＞

    聖文新社  2010  （ ISBN:9784792200992 ）

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  • 数学教育学研究ハンドブック

    東洋館出版社  2010  （ ISBN:9784491026268 ）

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  • 300 basic knowledge of the terminologies in mathematics education

    Meiji Tosho  2000  （ ISBN:4185007183 ）

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  • 算数・数学科重要用語300の基礎知識

    明治図書  2000  （ ISBN:4185007183 ）

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  • 数学的な見方・考え方を働かせられる生徒を育てるために

    岡崎正和

    算数・数学情報誌Root（ルート）   ( 33 )   6 - 7   2024.4

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    Authorship：Lead author   Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)  

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  • 図形の構成の仕方について考察すること Invited

    岡崎正和

    新しい算数研究8月号   629   10 - 15   2023.8

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  • 式と計算の順序（今月の指導4年に対するコメント）

    岡崎正和

    新しい算数研究12月号   ( 623 )   59   2022.12

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  • 商としての分数（今月の指導5年に対するコメント）

    岡崎正和

    新しい算数研究9月号   620   67 - 67   2022.9

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  • 数学的な見方・考え方を成長させる資質・能力ベースの単元をいかに設計するか

    岡崎正和

    新しい算数研究12月号   611   4 - 7   2021.12

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  • 新しい時代の数学教育の営みを支える理論的基盤を探究する Invited

    岡崎正和

    日本数学教育学会誌   103 ( 11 )   1 - 1   2021.11

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  • 資質・能力を育む数学指導のあり方

    岡崎正和

    算数・数学情報誌Root（ルート）   ( 27 )   8 - 9   2021.6

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  • Implementing a Science Class Promoting Cross-Curriculum Learning with Mathematics: Focusing on Density, Including Function Concepts

    山田貴之, 稲田佳彦, 岡崎正和, 栗原淳一, 小林辰至

    日本理科教育学会理科教育学研究(Web)   62 ( 2 )   2021

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  • 数学化の過程を意識し，価値ある問いを創り出す授業

    岡崎正和

    新しい算数研究5月号   592   4 - 7   2020.5

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  • 測定領域における教材と授業づくり－数学的な見方・考え方をどうとらえるか－

    岡崎正和

    新しい算数研究1月号   564   4 - 7   2018.1

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  • 移動を通して図形の見方・考え方を深める活動

    岡崎正和

    Root（ルート）   ( 21 )   14 - 15   2017.10

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  • 中学校数学科におけるアクティブ・ラーニング

    岡崎正和

    Root（ルート）   ( 17 )   7 - 9   2015.11

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  • 算数科の授業づくり：確かな教材研究に支えられた指導法開発への期待

    岡崎正和

    学校教育, 広島大学附属小学校学校教育研究会   ( 1174 )   14 - 21   2015.6

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  • 数学的な思考力・表現力の育成：数学的活動や言語活動を通した数学的探究の学び

    岡崎正和

    Root（ルート）   ( 16 )   10 - 11   2015.4

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  • 探究活動としての図形の証明

    岡崎正和

    Root（ルート）   ( 15 )   7 - 9   2014.10

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  • 算数と数学の一貫性を意識した学習指導

    岡崎正和

    第96回全国算数・数学教育研究大会講習会テキスト   37 - 42   2014.7

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  • 知識や事象のつながりの点から学力向上について考える

    岡崎正和

    Root（ルート）   ( 11 )   7 - 9   2013.7

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  • 存在証明としての作図

    岡崎正和

    数学教育   ( 667 )   10 - 11   2013

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  • 数学的な推論の指導を効果的にする実践研究の必要性

    岡崎正和

    数学教育   ( 658 )   10 - 11   2012

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  • 『逆向きに考える力』を豊かにする面白問題

    岡崎正和

    数学教育8月号   64 - 67   2011

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  • 知識の構成と展開の中で活用を考える

    岡崎正和

    Root（ルート）   ( 4 )   16 - 17   2010.10

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  • 子どもの考えを活かす指導と構成主義

    岡崎正和

    日本数学教育学会誌   92 ( 11 )   32 - 33   2010

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  • 算数を数学に接続する一般化に基づく教授単元の計画・実施・評価に関する開発研究

    岩崎 秀樹, 岡崎 正和, 植田 敦三, 山口 武志, 馬場 卓也, 二宮 裕之

    年会論文集;日本科学教育学会   28   127 - 130   2004.8

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    Language：Japanese   Publisher：一般社団法人日本科学教育学会  

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    CiNii Books

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  • ドイツがはじめた東洋的な算数教育

    岡崎正和

    研究と実践   2 - 7   2004

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  • 算数と数学を架橋する図形の学習指導

    岡崎正和

    今こそDo Math!   55 - 64   2003

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  • 人間関係を基盤にした算数授業のデザイン

    岡崎正和

    新しい算数研究7月号   ( 366 )   66 - 68   2001

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  • 子どもの理解に基づいて，算数・数学指導を展開するために

    岡崎正和

    研究と実践, 上越数学教育研究会   2 - 5   1998.11

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  • 定義の役割を実感させよう

    岡崎正和

    中学数学   95 ( 2 )   1995

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  • 数学の授業を捉える認知的，社会的視座 : Paul Cobbの社会的構成主義の理論

    岡崎正和

    新しい算数研究12月号   298   66 - 69   1995

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  • 数学の本質は形式的証明か？

    岡崎正和

    中学数学   93 ( 4 )   1993

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Presentations

  • Examination of the appropriation process through reflection in mathematics education: From the perspective of reflection throughout the unit

    Shinya Nakao, Masakazu Okazaki

    2024.12.14 

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    Event date： 2024.12.14 - 2024.12.15

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Changing process of children's explanatory descriptions in second-grade due to awareness of others: Focusing on explanations in problems about ordinal numbers and cardinal numbers

    Michita Sakai, Masakazu Okazaki

    2024.12.14 

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    Event date： 2024.12.14 - 2024.12.15

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • A study on socio-mathematical values ​​in lessons using social open-ended problems: Aiming to clarify critical thinking in mathematics learning

    Taiki Hanaya, Masakazu Okazaki

    2024.12.14 

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    Event date： 2024.12.14 - 2024.12.15

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Mathematics education policy, the national curriculum and the recent curriculum reforms in Japan Invited

    Masakazu Okazaki

    The Global Forum on Mathematics Education Policy 2024 in South Korea  2024.11.30 

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    Event date： 2024.11.29 - 2024.11.30

    Language：English   Presentation type：Oral presentation (invited, special)  

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  • Characteristics of 1st and 2nd grade students’ expository descriptions in mathematics

    Michita Sakai, Masakazu Okazaki

    The 15th International Congress on Mathematical Education  2024.7.13 

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    Event date： 2024.7.7 - 2024.7.14

    Language：English   Presentation type：Oral presentation (general)  

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  • Transitional aspects of deductive reasoning in the upper elementary school stage

    Masanori OBAYASHI, Masakazu OKAZAKI

    The 15th International Congress on Mathematical Education  2024.7.8 

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    Event date： 2024.7.7 - 2024.7.14

    Language：English   Presentation type：Oral presentation (general)  

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  • A study of interactive reflection activities: From the perspective of the extended focusing framework

    Shinya NAKAO, Masakazu Okazaki

    The 15th International Congress on Mathematical Education  2024.7.8 

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    Event date： 2024.7.7 - 2024.7.14

    Language：English   Presentation type：Oral presentation (general)  

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  • 振り返りに見る学習者の思考変容の把握に関する一考察：小学校第4学年「小数の乗法」の単元を事例にした拡張焦点化分析を視点に

    中尾真也, 岡崎正和

    全国数学教育学会, 第60回研究発表会  2024.6.23 

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    Event date： 2024.6.22 - 2024.6.23

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 小学2年児童の算数における他者意識が記述に与える影響：「なんばんめ」の問題についての児童の説明の特徴

    酒井道太, 岡崎正和

    全国数学教育学会, 第60回研究発表会  2024.6.22 

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    Event date： 2024.6.22 - 2024.6.23

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 平面図形と空間図形の連動を視点とした小中一貫の図形カリキュラムの開発研究－教材の位置づけとその学習過程－

    岡崎正和, 影山和也, 和田信哉, 渡邊慶子, 池田敏和

    日本数学教育学会, 第12 回春期研究大会  2024.6.9 

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    Event date： 2024.6.9

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 小学校高学年段階における演繹的推論への過渡的様相：三角形の内角和における立論を通して

    大林正法, 岡崎正和

    全国数学教育学会, 第59回研究発表会  2023.12.17 

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    Event date： 2023.12.16 - 2023.12.17

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 小学２年児童の算数における説明の記述の様相：「なんばんめ」の問題での読み手を意識した記述の分析を通して

    酒井道太, 岡崎正和

    全国数学教育学会, 第59回研究発表会  2023.12.17 

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    Event date： 2023.12.16 - 2023.12.17

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 倍と割合の学習の系統性について考える

    岡崎正和

    岡山大学算数・数学教育学会令和5年度研究会  2023.11.25 

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    Event date： 2023.11.25

    Language：Japanese   Presentation type：Oral presentation (invited, special)  

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  • 小学校下学年の算数における説明の記述の発達の様相－「なんばんめ」と「図にあらわして考えよう」 における児童の記述の比較を基にして－

    酒井道太, 岡崎正和

    全国数学教育学会, 第58回研究発表会  2023.6.24 

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    Event date： 2023.6.24 - 2023.6.25

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 平面図形と空間図形の連動を視点とした小中一貫の図形カリキュラムの開発研究（4）

    岡崎正和, 影山和也, 和田信哉, 渡邊慶子, 太田伸也

    日本数学教育学会, 第11 回春期研究大会  2023.6.4 

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    Event date： 2023.6.4

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 学校数学における数学的リテラシーの定義の再構成と適用:機能的リテラシーと批判的リテラシーの視点から

    別府凌名, 岡崎正和

    全国数学教育学会第57回研究発表会  2022.12.11 

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    Event date： 2022.12.10 - 2022.12.11

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 若手教員における指導のための数学的知識の変容過程に関する研究：教師間の関わりを通して

    西田健太, 岡崎正和

    全国数学教育学会第57回研究発表会  2022.12.11 

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    Event date： 2022.12.10 - 2022.12.11

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 教職大学院が担うべき学校支援のあり方―教科教育領域教員の学校への関わりの事例分析―

    宮本浩治, 岡崎正和, 石橋一昴, 高旗浩志, 高瀬淳

    令和4年度日本教育大学協会研究大会  2022.10.6 

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    Event date： 2022.10.6

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 算数と数学の一貫性を意図した中学校数学の授業づくり Invited

    岡崎正和

    日本数学教育学会第104回全国算数・数学教育研究大会  2022.8.4 

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    Event date： 2022.8.4 - 2022.8.5

    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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  • 小学校上学年における推論の移行過程：三角形の内角和における立論を通して

    大林正法, 岡崎正和

    全国数学教育学会第56 回研究発表会  2022.6.26 

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    Event date： 2022.6.26 - 2022.6.27

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 平面図形と空間図形の連動を視点とした小中一貫の図形カリキュラムの開発研究（3）

    岡崎正和, 影山和也, 和田信哉, 渡邊慶子, 太田伸也

    日本数学教育学会, 第10 回春期研究大会, 2022年6月5日. 宇都宮大学.  2022.6.5 

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    Event date： 2022.6.5

    Language：Japanese   Presentation type：Symposium, workshop panel (public)  

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  • Kyozaikenkyu as well-formed story making for developing quality mathematics lessons

    Masakazu Okazaki, Keiko Kimura, Keiko Watanabe

    The 14th International Congress on Mathematical Education  2021.7.17 

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    Event date： 2021.7.11 - 2021.7.18

    Language：English   Presentation type：Oral presentation (general)  

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  • 平面図形と空間図形の連動を視点とした小中一貫の図形カリキュラムの開発研究（2）

    岡崎正和, 影山和也, 和田信哉, 渡邊慶子, 太田伸也

    日本数学教育学会, 第9 回春期研究大会  2021.6.6 

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    Event date： 2021.6.6

    Language：Japanese   Presentation type：Symposium, workshop panel (public)  

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  • 中学2年生の数学的アイデンティティの形成の様相：「文字式の証明」の学習後の振り返りを基にして

    中市聖人, 岡崎正和

    全国数学教育学会, 第53 回研究発表会, 2020年12月19, 20日  2020.12.20 

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    Event date： 2020.12.19 - 2020.12.20

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 教職大学院における教科教育のあり方の探究

    高瀬淳, 小林万里子, 宮本浩治, 岡崎正和

    令和2年度日本教育大学協会研究大会  2020.12.6 

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    Event date： 2020.12.6

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 平面図形と空間図形の連動を視点とした小中一貫の図形カリキュラムの開発研究（１）

    岡崎正和, 影山和也, 和田信哉, 渡邊慶子, 太田伸也

    日本数学教育学会, 第8 回春期研究大会  2020.6.7 

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    Event date： 2020.6.7

    Language：Japanese   Presentation type：Symposium, workshop panel (public)  

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  • 証明の仮定の意識化に関する研究－その意義と方法－

    渡邊慶子, 岡崎正和

    全国数学教育学会，第49回研究発表会  全国数学教育学会

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    Event date： 2019.2.9 - 2019.2.10

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：広島大学  

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  • アクションリサーチャーを育成する教育課程の創造―教科教育研究の成果を取り入れた新しい教職大学院カリキュラムの構想

    岡崎正和, 小林万里子, 熊谷愼之輔, 高瀬淳, 平井安久, 藤井浩樹, 宮本浩治, 山田秀和

    平成30年度日本教育大学協会研究集会  2018.10.13 

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    Event date： 2018.10.13

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 小学校高学年における空間的思考の発達の様相－実物，見取り図，展開図，投影図の四者関係を視点とした質的分析研究－

    小野翔平, 岡崎正和

    全国数学教育学会，第47回研究発表会  全国数学教育学会

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    Event date： 2018.1.27 - 2018.1.28

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：広島大学  

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  • 算数学習におけるめあてと振り返りをつなぐ子どもの問い～RPDCAサイクルを活かした算数の学び～

    太田誠, 岡崎正和

    日本教育実践学会第17回研究大会  2014.11.1 

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    Event date： 2014.11.1 - 2014.11.2

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 関数の学習過程を分析するための記号論的アプローチについて

    小野田愛, 岡崎正和

    日本教科教育学会第39回全国大会2013/11/23, 24  2013.11.24 

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    Event date： 2013.11.23 - 2013.11.24

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 算数科授業における社会的相互作用による「創発的見方・考え方」の生起に関する解釈的研究

    吉村直道, 山口武志, 中原忠男, 小山正孝, 岡崎正和, 加藤久恵, 前田一誠, 宮崎理恵

    日本教科教育学会第39回全国大会  2013.11.23 

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    Event date： 2013.11.23 - 2013.11.24

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 見通しと振り返りの連動による自律性の育成に関する研究～PDCA サイクルを活かした算数の学び～

    太田誠, 岡崎正和

    日本教育実践学会第16回研究大会  2013.11.2 

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    Event date： 2013.11.2 - 2013.11.3

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 数学教育における理論と実践の関係性：特に，実践の理論化に焦点をあてて

    岡崎正和

    全国数学教育学会学会第32回研究発表会  2011.6.27 

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    Event date： 2011.6.26 - 2011.6.27

    Language：Japanese   Presentation type：Symposium, workshop panel (nominated)  

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  • Semiotic chaining in an expression constructing activity aimed at the transition from arithmetic to algebra

    Masakazu Okazaki

    The 30th Conference of the International Group for the Psychology of Mathematics Education  2006.7.19 

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    Event date： 2006.7.16 - 2006.7.21

    Language：English   Presentation type：Oral presentation (general)  

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  • 教育大学における算数・数学教育に関する科目内容とその編成： 教育実習と講義，演習との関連から

    布川和彦, 中村光一, 崎浩, 高橋等, 岡崎正和, 渡辺千一, 田村雅人, 中澤和仁

    日本数学教育学会第34回数学教育論文発表会  2001.11.23 

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    Event date： 2001.11.23 - 2001.11.24

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 経験的認識から理論的認識への変容過程に関する研究 －図形の作図とその正当化の過程に焦点を当てて－

    岡崎正和

    日本教科教育学会26回全国大会  2001.11.18 

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    Event date： 2001.11.18 - 2001.11.19

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Development of naive algebraic ideas during solving problems and explaining the solution processes

    Masakazu Okazaki

    The 25th Conference of the International Group for the Psychology of Mathematics Education  2001.7.14 

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    Event date： 2001.7.12 - 2001.7.17

    Language：English   Presentation type：Oral presentation (general)  

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  • 算数科教師に内在する授業構成原理に関する研究―昭和初期の算術授業を対象として―

    全国数学教育学会，第45回研究発表会  2017 

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  • 図形の証明の構成過程におけるジェスチャーの役割に関する研究

    全国数学教育学会，第45回研究発表会  2017 

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  • 量の視点を意識した中学校の関数グラフの読解に関する研究

    全国数学教育学会，第45回研究発表会  2017 

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  • Classroom culture and genre for developing narratively coherent mathematics lessons

    41st Conference of the International Group for the Psychology of Mathematics Education  2017 

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  • 数学教育学研究と教材開発

    全国数学教育学会，第46回研究発表会  2017 

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  • わり算概念の構成過程に関する理論的・実証的研究－「等分除とその拡張」の理解に関する考察－

    全国数学教育学会，第43回研究発表会  2016 

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  • National presentation of Japan

    13th International Congress on Mathematical Education  2016 

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  • Hypothesizing how fifth graders construct geometric definitions based on inclusion relations among geometric figures

    13th International Congress on Mathematical Education  2016 

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  • 算数・数学授業の質を捉える理論的視座に関する研究（２）―「思考様式としての物語」の考察を中心に―

    全国数学教育学会，第44回研究発表会  2016 

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  • 定義の構成過程における例の意味と役割に関する研究

    全国数学教育学会，第43回研究発表会  2016 

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  • 数学教育における図式との相互作用による数学的思考の分析―図式に関わる諸理論の比較検討―

    全国数学教育学会，第43回研究発表会  2016 

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  • 中学１年生での定義の構成に関する実践的検討－算数と数学の接続を視点として－

    全国数学教育学会，第42回研究発表会  2015 

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  • 多世界パラダイムに基づく算数授業における社会的相互作用の規範的モデルの開発研究（Ⅲ）－第5学年「単位量あたりの大きさ」の授業による検証－

    全国数学教育学会，第39回研究発表会  2014 

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  • 多世界パラダイムに基づく算数授業における社会的相互作用の規範的モデルの開発研究（Ⅲ）－第4学年「分数」の授業による検証－

    全国数学教育学会，第39回研究発表会  2014 

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  • 見通しを軸にした自律性の育成に関する研究 ～RPDCAサイクルを活かした算数の学び～

    全国数学教育学会，第39回研究発表会  2014 

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  • 関数学習における記号論的変換プロセスに関する研究－概念ブレンドの理論をもとにして－

    全国数学教育学会，第39回研究発表会  2014 

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  • 小中接続期における関数概念の発達の様相に関する研究

    全国数学教育学会，第37回研究発表会  2013 

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  • 文化的視点から生徒と数学を結ぶ学習指導のあり方に関する研究

    全国数学教育学会，第37回研究発表会  2013 

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  • Exploring the nature of the transition to geometric proof through design experiments from the holistic perspective (Regular Lecture)

    12th International Congress on Mathematical Education  2012 

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  • Exploring the nature of the transition to geometric proof through design experiments from the holistic perspective (一般招待講演)

    第12回数学教育世界会議  2012 

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  • 文化的視点からの数学学習に関する研究(2)－価値と自己効力感に着目して－

    全国数学教育学会，第36回研究発表会  2012 

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  • 数学教育における認識論が学習指導と研究に及ぼす影響－認識論研究の展開と課題を中心として－

    全国数学教育学会, 第35回研究発表会  2012 

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  • 数学教育における認識論が実践，学習指導，研究方法論に与える影響について

    日本数学教育学会，第44回数学教育論文発表会  2011 

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  • 数学的思考を発達させる

    日本数学教育心理研究学会，平成23年度研究集会  2011 

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  • Fifth graders’ arguments fostered in the learning of inclusion relations between geometric figures

    35th Conference of the International Group for the Psychology of Mathematics Education  2011 

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  • 証明の学習を促進する教師の指導行為に関する質的分析研究

    日本数学教育学会，第43回数学教育論文発表会  2010 

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  • Development of reasoning ability towards proof using seventh grade Plane Geometry

    第5回東アジア数学教育国際会議  2010 

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  • What are dynamic views in geometry? A design experiment in a sixth grade classroom

    第34回数学教育心理研究学会  2010 

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  • 図形の動的な見方の構造化：比喩の視点から

    全国数学教育学会，第32回研究発表会  2010 

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  • 図形における動的な見方の具体化：図形におけるイメージ図式の構造化を視野に入れて

    全国数学教育学会，第31回研究発表会  2010 

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  • Development of reasoning ability towards proof using seventh grade Plane Geometry

    5th East Asia Regional Conference on Mathematics Education  2010 

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  • What are dynamic views in geometry? A design experiment in a sixth grade classroom

    34th Conference of the International Group for the Psychology of Mathematics Education  2010 

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  • 探究的活動としての証明を実現するために： 形式的証明導入前の活動を充実させる

    日本数学教育学会，第43回数学教育論文発表会，課題別分科会  2010 

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  • 論証への接続を目指した算数の図形指導に関する研究 (1)－図形の包含関係の理解を促す動的な見方の具体化－

    第42回数学教育論文発表会  2009 

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  • Process and means of reinterpreting tacit properties in understanding the inclusion relations between quadrilaterals

    第33回数学教育心理国際学会  2009 

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  • PME: Research Report への投稿，査読，発表について

    日本数学教育心理研究学会，平成２１年度研究集会  2009 

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  • 小数除法における算数から数学への移行研究(2)－純小数倍の理解をめぐって－

    日本数学教育学会第41回数学教育論文発表会  2008 

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  • Learning of division with decimals towards understanding functional graph

    Joint Meeting of the 32nd Conference of the International Group for the Psychology of Mathematics Education, and the XXX North American Chapter  2008 

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  • 移動と作図のプロセスの顕在化による論証への移行に関する研究－図形の論証への接続を目指した教授実験の報告（その３）－

    全国数学教育学会，第27回研究発表会  2008 

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  • The learning of division with decimals towards understanding the functional graph

    The Sixth International Workshop of Mathematics Education Research  2007 

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  • Semiotic chaining in an expression constructing activity aimed at the transition from arithmetic to algebra

    The Fifth International Workshop of Mathematics Education Research  2006 

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  • 研究としての授業研究の方法と課題－デザイン実験の方法論に焦点をあてて－

    日本数学教育学会，第39回数学教育論文発表会  2006 

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  • 数学教育研究方法論としてのデザイン実験について－科学性と実践性の調和を目指して－

    全国数学教育学会，第24回研究発表会  2006 

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  • Reconstructing the unit “four operations with positive and negative numbers” from the perspective of the transition from arithmetic to algebra

    The Forth International Workshop of Mathematics Education Research  2005 

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  • 数学教育における記号論的連鎖に関する考察 －Wittmannの教授単元の分析を通して－

    全国数学教育学会, 第21回研究発表会  2005 

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  • アメリカの数学教育におけるホットな研究課題－教員養成システムと研究方法論－

    日本数学教育心理研究学会  2005 

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  • Characteristics of 5th graders' logical development through learning division with decimals

    The Third International Workshop of Mathematics Education Research  2004 

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  • 算数を数学に接続する一般化に基づく教授単元の計画・実施・評価に関する開発研究

    日本科学教育学会, 第２８回年会  2004 

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  • 理論と実践の間の有機的な関係の構築に向けて－研究のパラダイムと方法論の視点から－

    全国数学教育学会第19回研究発表会  2004 

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Awards

  • Academic Society Award (Academic Research Division)

    2022.11   Japan Society of Mathematics Education  

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  • Academic Society Encouragement Award

    2018.1   Japan Academic Society of Mathematics Education  

    Takeshi Yamaguchi, Kazuya Kageyama, Tadao Nakahara, Masakazu Okazaki, Kazushige Maeda

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  • Academic Society Encouragement Award

    2004.1   Japan Academic Society of Mathematics Education  

    Masakazu Okazaki

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    Country：Japan

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Research Projects

  • The collaborative research on the development of class lessons and curriculum coherent from elementary to secondary mathematics in terms of the linkage between plane and spatial geometry

    Grant number：20H01745  2020.04 - 2024.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    岡崎 正和, 渡邊 慶子, 和田 信哉, 影山 和也

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    Grant amount：\9490000 （ Direct expense: \7300000 、 Indirect expense：\2190000 ）

    本研究は，図形教育において，算数での図形の直観的・経験的な学習と中等校数学での図形の関係的・論証的な学習のギャップ，及び平面図形の学習と空間図形の学習とのカリキュラム上のギャップの現状に鑑み，小学校と中学校の一貫を縦軸，平面図形と空間図形の連動を横軸とする幾何カリキュラムを構成し，探究的な学びとしての空間図形の授業のあり方を研究するものである．
    2021年度は，まず，探究型幾何カリキュラムの構成原理を明らかにするために，生徒が現象を数学化し，数学を創り出すという視点から作成された戦前の幾何学教科書である数学「第二類」に着目し，問題における問いの文に関する分析を通して，カリキュラム構成の原理を導出することを目的とした。考察の結果，（1）幾何学的現象の理解と命題化，（2）説明や証明を通した論理的な理解，（3）学んだ数学の応用と具体化としてカテゴリー化し，カリキュラム構成原理の一つの軸にすることができた。また，カリキュラム構成のための個別的な理論として，視覚化の機能，記号論の機能，証明の機能について検討した。成果は，日本数学教育学会「第9回春期研究大会論文集」にて発表した。
    第二に，証明を理解することへのアプローチとして，場合分けのある証明を対象として，証明言語の生成とふり返りの連鎖による定理と証明の相互理解が生じる様相について分析を行った。また，それが幾何学的な思考水準を，中学校レベルから高等学校レベルへと押し上げる役割があることを明らかにした。成果は，それぞれ，全国数学教育学会「数学教育学研究」，及び数学教育心理研究国際会議にて公表した。
    第三に，授業づくりのための基礎的考察として，教科横断的な学習のあり方，質の高い数学授業を開発するための教材研究のあり方について検討を行った。成果はそれぞれ，日本理科教育学会誌「理科教育学研究」，数学教育世界会議の中で公表した。

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  • The practical study for the theory of mathematical knowledge for teaching and for developing a teaching unit in terms of the consistency between elementary and secondary mathematics

    Grant number：17K00974  2017.04 - 2021.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    Okazaki Masakazu

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    Grant amount：\4420000 （ Direct expense: \3400000 、 Indirect expense：\1020000 ）

    The study aimed at clarifying theory and practice for mathematics teaching which enables students to overcome the gaps between elementary and secondary mathematics and which can coherently develop the students’ learning through a teaching unit. As a theoretical perspective, I discussed the narrative thinking of mathematics classroom and its culture as the analytical framework of the study. Practically, I conducted the design experiments on division, proof by literal expression, solid figure, and geometric proof and analyzed them particularly in terms of the narrative thinking and the semiotic interpretation. Finally, I tried to conceptualize the theoretical viewpoints as well as clarifying mathematical knowledge for teaching for the bridging between elementary and secondary mathematics.

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  • Development of learning materials with sensation by using virtual reality technology - in the case of three dimensional figures -

    Grant number：15K00921  2015.04 - 2019.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    Irie Takashi

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    Grant amount：\4420000 （ Direct expense: \3400000 、 Indirect expense：\1020000 ）

    The learning materials, which allow learners instinctive handling of three dimensional figures in the virtual reality space and offer them the characteristics of those figures through visual and kinematic sense, were developed by using a haptic device.
    (1) The material to experience the characteristics of basic three dimensional figures. (2) The material to experience the characteristics of regular polyhedrons and semi-regular polyhedrons. (3) The material to experience the transition of regular polyhedrons by truncation. In all materials, learners were able to contact the figures, hold them, move them, rotate them, and observe them from three directional view.

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  • Investigating Japanese teacher's practical knowledge related to elementary school mathematics lesson by using historical approach

    Grant number：15K04466  2015.04 - 2019.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    Kimura Keiko

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    Grant amount：\4420000 （ Direct expense: \3400000 、 Indirect expense：\1020000 ）

    The aim of this study is to clarify the practical knowledge of Japanese elementary school teacher related to math classes. The characteristics of the study method was used to reveal practical knowledge and narrate their own experience by individual interview, pre-war math textbooks and lesson records, and lesson plans prepared by the teachers. Two kinds of pre-war textbooks and lesson records contributed to evoke the teachers’ inner narratives, which are difficult to expose based on the current textbooks. The lesson record by using black covered textbook show us the 9 elements of lesson constructions. The Japanese teachers’ reflection on the lesson record by using green covered textbook lead to their explicit awareness that they try to make their own lesson by helping their children to lead to the conclusion through integrating the children’s ideas among each other. The main study outcome is that using historical materials is effective to elicit teacher narratives of math lessons.

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  • Analysis of mathematical thinking in terms of interactions with a diagram in mathematics education: from the cognitive and cultural perspective

    Grant number：26381211  2014.04 - 2017.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    Kageyama Kazuya

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    Grant amount：\4810000 （ Direct expense: \3700000 、 Indirect expense：\1110000 ）

    The purpose of this research is to understand students' mathematical thinking by supposing that it is related to constructing and using diagrams, which are inscriptions on a paper, such as figures, tables and signs, with certain rules.
    Diagrams are constructed originally through bodily actions or experiences, while these include some useful ideas and are handed on to the next. This research implied that students thought mathematically by reading a pattern or law to make a hypothesis and verifying the range in which they could deal with it as a theory.

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  • Theoretical and Emprical Research on the Construction Process of the Concept of Division based on the Multi-World Paradigm

    Grant number：26285205  2014.04 - 2017.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    Nakahara Tadao

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    Grant amount：\6890000 （ Direct expense: \5300000 、 Indirect expense：\1590000 ）

    This research has three main objectives The first is to develop tests for clarify the actual performance situation and the construtive process of the concept of division. The second is to clarify the construtive process and misconceptions of division by analyzing results of the longitudinal and cross-sectional survey. The third is to propose the improvement of lesson of division in the elementary level. Firstry, we developed six sets of tests of division, for 5th to 7th grader, which could reveal difficulties of understanding the meaning of division. Secondary, we analyzed the results of the tests by three part, that is, dividing division & its extention, including division & its extention, and division using how many times as. Thridy, we proposed the implovement principle, such as interaction of making sence of division and using tools for solving story problem of division, for teaching devision.

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  • A collaborative study of developing curriculum and mathematical knowledge for teaching for connecting between elementary and secondary mathematics

    Grant number：26350194  2014.04 - 2017.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    Okazaki Masakazu

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    Grant amount：\4810000 （ Direct expense: \3700000 、 Indirect expense：\1110000 ）

    This study aimed at developing curriculum and mathematical knowledge for teaching for connecting between elementary and secondary mathematics. As a theoretical perspective, I examined the viewpoint of narrative coherence for analyzing the qualities of a mathematics lesson, and the viewpoint of didactical situation theory for constructing and analyzing mathematical teaching unit. Practically, I conducted the experimental lessons for the contents of area, geometrical definition in elementary mathematics, and proportion and linear function in junior high school with school teachers. As the result of qualitative analysis, I conceptualized mathematical knowledge for teaching bridging between elementary and secondary mathematics through mainly focusing on the narrative construction of a lesson in terms of students’ goals and interactions with teacher, and students’ gesturing for understanding mathematical concepts.

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  • A study on students' own representation and their refinement processes in arithmetic and mathematics classes

    Grant number：25381208  2013.04 - 2017.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    Norihiro Shimizu

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    Grant amount：\4810000 （ Direct expense: \3700000 、 Indirect expense：\1110000 ）

    The purpose of this study is to identify informal representation by students and teachers in arithmetic and mathematics lessons and to clarify their roles in mathematics learning.
    As a result of the study, we constructed a theoretical framework to capture informal representation and clarified the roles played by informal representation in classes for constructing figure concepts and discovering the numerical relations in multiplicative table, using the framework. We pointed out the importance that teachers have a positive stance to take the students' informal representation as the subject of classroom discussion and they examine and analyze the teaching materials to realize such classes.

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  • Reflective Description of Japanese Mathematics Education

    Grant number：24243078  2012.04 - 2017.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (A)

    UEDA ATSUMI

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    Grant amount：\40560000 （ Direct expense: \31200000 、 Indirect expense：\9360000 ）

    We focused on the development of the infrastructure to disseminate Japanese mathematics education internationally in collaboration with JASME. We invited overseas researchers to hold a series of symposiums at JASME and examined the framework to describe mathematics education in Japan. As a result, we were able to extract the viewpoints of “curriculum”, “lesson”, “teacher training”, “values” as a framework describing Japanese mathematics education reflectively. Also, in order to disseminate Japanese mathematics education internationally, we prepared manuscripts based on the framework and translated them to publish in English.

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  • Research on development of the prescriptive model for designing social interactions in an elementary class based on the multi-world paradigm

    Grant number：23330268  2011.04 - 2014.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    NAKAHARA TADAO, KOYAMA Masataka, YAMAGUCHI Takeshi, OKAZAKI Masakazu, YOSIMURA Naomichi, KATOH Hisae

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    Grant amount：\11180000 （ Direct expense: \8600000 、 Indirect expense：\2580000 ）

    Nowadays,mathematics teaching in the elementary school values on students'communicating activities. However,we often observe the situations that children act pretend play of communication or that children's important statements don't be fully utilized. With the aim of improving such problematic situations, we fisrt considered the communicating activities as 'Social Interactions' and clarified the epistemological significances that the social interaction have. Second, we considered the prescriptive model of social interaction for designing and practicing elementary mathematics lessons which make a good use of such significances of social interactions. The model is constructed by (1) the fundamental lessons process, (2) the crucial kinds of social interactions, (3) teacher's main activities, (4) children's main activities, and so forth. Third, we showed several application examples of the classroom lessons which were implemented based on the model.

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  • The developmental study of classroom lessons and curriculums for connecting between elementary and secondary mathematics through design experiments

    Grant number：23501019  2011 - 2013

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    OKAZAKI Masakazu

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    Grant amount：\4160000 （ Direct expense: \3200000 、 Indirect expense：\960000 ）

    This study aimed at developing classroom lessons and curriculum for connecting between elementary and secondary mathematics through a design experiment methodology. We first examined several theoretical viewpoints of the epistemological studies sustaining mathematics classroom practices, the theory building in mathematics education, and the semiotic views. Next, we analyzed the experimental lessons we designed and implemented on inclusion relations between geometric figures, geometrical definitions in the elementary school, and proportion in the junior high school by using the grounded theory approach. Last, we conceptualized our findings from the data analysis towards constituting theory and practice bridging between elementary and secondary mathematics.

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  • A Comparative Study on Teacher Education for "Math for Excellence"

    Grant number：22300268  2010 - 2012

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    NINOMIYA Hiroyuki, IWASAKI Hideki, KUNIMUNE Susumu, SOMA Kazuhiko, SASAKI Tetsuro, BABA Takuya, OKAZAKI Masakazu

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    Grant amount：\14430000 （ Direct expense: \11100000 、 Indirect expense：\3330000 ）

    1) Research and study in America
    Attending to “Confratute 2011", which is organized by Neag Center for Gifted Education and Talent Development, University of Connecticut, mathematics teacher education for gifted and talented students was observed. The long-term field survey had beenconducted at Brigham Young University, Utah, and US Japan Mathematics TeachingSummit had been organized.
    2) Research and study in Japan
    The cases at Misato city in Saitama, and Kokubunji city in Tokyo had been examined.
    3) The Workshop with invited researcher from overseas
    Prof. Peter Sullivan from Monash University, Australia, was invited for our international workshop, and he made key note lecture both in Hiroshima and Tokyo, aswell as exchanging the ideas of the lesson for “Math for Excellence" through the observation about math lessons in Japan.

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  • Fundamental study on lesson design on the basis of the roles of representation in mathematical problem solving

    Grant number：22530963  2010 - 2012

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    YAMADA Atsushi, IWASAKI Hiroshi, SHIMIZU Norihiro, OKAZAKI Masakazu

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    Grant amount：\4290000 （ Direct expense: \3300000 、 Indirect expense：\990000 ）

    The aims of this study was to clarify the patterns of construction/transformation of (problem) representation in mathematical problem solving, to investigate its roles in progress of problem-solving process, and to consider the methodology of lesson design on the basis of the roles. The main results were to identify five types of wide-purpose representations for mathematical problem solving, to investigate three constructional/transformational patterns of problem representation in mathematical problem solving (i.e.; construction/reconstruction, abstraction/concretization, shift), and to analyze the concrete roles of “abstraction/concretization” process of problem representation.Furthermore, a methodology of lesson design on the basis of the roles of abstraction process was considered.

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  • The comprehensive study of developing theory, practice and contents connecting between elementary and secondary mathematics through design experiments

    Grant number：20500750  2008 - 2010

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    OKAZAKI Masakazu, IWASAKI Hideki, KAGEYAMA Kazuya, WADA Shinya

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    Grant amount：\3640000 （ Direct expense: \2800000 、 Indirect expense：\840000 ）

    This study aims at finding the theoretical and empirical bases on the transition from elementary to secondary mathematics through design experiments. We designed two transitional processes in which students developed their recognitions of functional graphs based on their views of rate and in which they enhanced their recognitions of proof through cultivating their dynamic and flexible views of figures, and implemented the experiments. Then, we have extracted and theorized the findings on the transition by analyzing the data qualitatively.

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  • A theoretical and practical research on the effect that quality of mathematics lessons gives to students problem solving process and learning of mathematics

    Grant number：19530792  2007 - 2009

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    IWASAKI Hiroshi, YAMADA Atsushi, SHIMIZU Norihiro, OKAZAKI Masakazu

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    Grant amount：\2470000 （ Direct expense: \1900000 、 Indirect expense：\570000 ）

    本研究では,通常の授業ではなく,主にそのメタレベルにおける学習の効果を意図して計画・実施された2つの授業実践(確率の授業と正負の数の乗除法各10時間)から得られた質的データを対象として,数学の授業の質が生徒の解決過程と学習に及ぼす効果,主にメタレベルの学習への効果を調べた。結果として,数学の授業の質が生徒の数学の(メタレベルの)学習に及ぼす効果として,先行研究では明らかにされてこなかった効果(プラスの効果)がありうることを事例的に明らかにした。

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  • Developmental Research for Construction of Mathematical Literacy in Life Long Learning Society

    Grant number：18330192  2006 - 2009

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    IWASAKI Hideki, UEDA Atumi, BABA Takuya, OKAZAKI Masakazu, NINOMIYA Hiroyuki, YAMAGUCHI Takeshi, GINNSHIMA Fumi, ABE Yoshitaka, SHINNO Yusuke

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    Grant amount：\9300000 （ Direct expense: \7500000 、 Indirect expense：\1800000 ）

    Our group of scientific study compiled a part of 22 published papers, 17 oral presentations, and 5 lectures conducted by eminent researchers of mathematics education coming from the United States as the final report of the research. Every year the group invited the internationally renowned professors as a guest speaker to deliver a keynote speech on the theme, mathematical literacy. In each paper and presentation, the authors discussed on a literacy, which is unique to mathematics education, basic concepts for formation of mathematical literacy, and principles and methods to grow mathematical literacy.

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  • デザインリサーチによる中学校数学へ向けた高学年算数の授業開発に関する研究

    Grant number：18700629  2006 - 2007

    日本学術振興会  科学研究費助成事業  若手研究(B)

    岡崎 正和

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    Grant amount：\1700000 （ Direct expense: \1700000 ）

    本研究の目的は、算数と中学数学との乖離を乗り越える為に、それらを接続する理論的視点を明らかにするだけでなく、接続を実質的に実現する為の授業開発を行うことにある。本年度はまず算数から数学への移行を促す理論を開発する上での研究方法論を整備することから始めた。そして学校現場での比較的長期の授業研究の実施とその体系的分析から数学教育の理論的知見を抽出する方法論であるデザイン実験に注目し、文献研究を通してその位置と課題を明らかにした。[論文は全国数学教育学会誌「数学教育学研究」に掲載]
    次に、図形分野における移行教材となりうるものとして図形の相互関係をとりあげて、日本とイギリスの中学生の質問紙調査によるデータをもとにして、その理解過程を、共通概念経路という視点から統計的分析を通して明らかにした。[論文は数学教育心理国際会議論文集に掲載]
    さらに、小学校5年の小数除法と、中学1年の平面図形の単元について、算数から数学への移行の視点から授業をデザインし、授業実践を行い、それぞれについて分析を行った。[論文はいずれも日本数学教育学会数学教育論文発表会論文集に掲載]前者の小数の除法に関する論文では、崖の傾きを探究の場として、除法の意味を測定活動を通して一般化する活動が、中学の関数のグラフの認識につながりうることが示唆された。また後者の平面図形に関する論文では、図形の移動教材を教授学的状況論の視点から再構成したときに、特に図の認識の面において論証への接続がなされることが明らかになった。

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  • 算数と数学の接続における2つの一般化に関する開発研究

    Grant number：17011049  2005 - 2006

    日本学術振興会  科学研究費助成事業  特定領域研究

    岩崎 秀樹, 植田 敦三, 馬場 卓也, 山口 武志, 岡崎 正和, 二宮 裕之

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    Grant amount：\7400000 （ Direct expense: \7400000 ）

    本研究の課題意識は,数学的認識の質的変換を可能にする教材構成の原理にある。そこに日本独自の制度的視点を加えて,「算数と数学の接続」という形で問題化した。すなわち「教育内容と学習の適時性」について,一般化の視座から教材の構成原理にアプローチした。平成18年度は,2年間の研究の最終年度にあたるが,本年度の研究成果をまとめると下記の2点となる。
    第1は,平成17年度までの研究において提案した「一般化分岐モデル」に基づきながら,算数と数学の接続を促す移行教材を開発したことである。つまり,代数教材としては,「分数の除法」や「負の数の減法」の教材化を提案するとともに,幾何教材としては,「図形の作図」や「包摂関係」の教材化を提案した。特に,算数から代数への接続については,Wittmannの「パターンの科学としての数学」の研究成果をレビューしながら,意味と形式の接続・統合が重要であることを指摘した。また,上述の代数教材および幾何教材に関する教授実験の分析を通じて,その教材の有効性や意義を例証した。
    第2は,平成14〜17年度に引き続き,国際ワークショップを開催したことである。平成18年11月に,Dorfler教授(オーストリア・クラーゲンフルト大学)とWittmann教授(ドイツ・ドルトムント大学)の2名を同時に招聘し,2年間にわたる研究のまとめと総括を行った。
    なお,平成18年度は最終年度にあたるため,最終報告書を作成した。

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  • 全体論の立場からの中学校数学への接続を意図した算数の授業開発に関する研究

    Grant number：16700539  2004 - 2005

    日本学術振興会  科学研究費助成事業  若手研究(B)

    岡崎 正和

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    Grant amount：\1300000 （ Direct expense: \1300000 ）

    本年度は、まず算数を中学校数学に接続する上での実践的授業研究の方法論について検討を行った。具体的には、デザインリサーチの方法論と呼ばれるもので、大学研究者、現場教師、さらには他の研究協力者たちが協働しながら、デザインを開発し、実践し、反省して、再デザイン化を図るとともに即時的・回顧的な質的分析のプロセスの中から、科学的知見を抽出する方法である。この成果は、日本数学教育心理研究学会で発表を行った。
    次に、Educational Studies in Mathematics誌掲載論文において、小学校高学年の教材として、等分除の一般化としての小数の除法をとりあげ、それを算数から数学への移行教材として捉え直し、そのデザインに関して実践した授業過程を分析して、子ども達の中学校数学へ向けた論理的発達の様相を明らかにした。
    さらに、包含除の一般化としての小数の除法に関してデザインリサーチの点から授業開発研究を行い、データを収集した。また、その一部に関して子ども達の学習過程を分析し、算数から数学への移行の様相を検討した。その結果、小数の除法を割合概念の理解を促進するように展開したとき、中学校の関数学習への接続の道が開かれることが示唆された。
    以上のことと昨年度の研究を通して、算数を中学校数学に接続する為の理論的基盤としての教授学的状況論と記号論的連鎖の過程、実証的研究の方法論としてのデザインリサーチの方法論、具体的内容としての等分除の一般化場面と包含除の一般化場面における小数の除法の学習過程および中学校数学へ向けた子ども達の思考の高まりの様相について総括し、研究のまとめとした。

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  • 算数を数学に接続する一般化に基づく教授単元の計画・実施・評価に関する開発研究

    Grant number：15020241  2003 - 2004

    日本学術振興会  科学研究費助成事業  特定領域研究

    岩崎 秀樹, 植田 敦三, 馬場 卓也, 山口 武志, 二宮 裕之, 岡崎 正和

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    Grant amount：\4800000 （ Direct expense: \4800000 ）

    平成16年度の研究の主な目的は,小学算数と中学数学の接続を念頭に置きながら,算数から数学への移行の本質を一般化や記号論の視座から明らかにすることである。研究の結果,アメリカ・イリノイ州立大学のPresmeg博士が提唱する「記号論的連鎖(semiotic chaining)」の枠組みと,その連鎖の上昇を特徴づける比喩の視座から,「図形の作図」に関する授業実践を分析した。その上で,隠喩的,隠喩・換喩的,換喩・隠喩的,換喩的という4つの比喩によって特徴づけられる「四層記号連鎖モデル」を理論的枠組みとして新たに定式化した。この四層記号連鎖モデルの理論化を通じて,「算数的表現を活用し,新たな対象を生じさせる前移行的記号化」と「生じさせた対象をさらに反省し,数学的表現に再変換する後移行的記号化」という2つの記号化が,算数から数学への接続過程において重要であることを指摘した。
    また,平成16年度の研究の一環として,平成16年11月には,ドイツ・ドルトムント大学のWittmann博士を招聘して,第3回国際ワークショップを開催した。Wittmann博士は,本研究の理論的基盤となっている「教授単元(Teaching Units)」の理論を提唱している研究者である。Wittmann博士からは,「教授単元」や「本質的学習場」を理論的背景としながらドイツで精力的に展開されているプロジェクト「mathe2000」について,最新の研究成果をご講演いただいた。同時に,本研究グループの研究成果を発表しながら,それについて適切なコメントをいただき,2年間の研究成果を総括した。

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  • 全体論の立場からの中学校数学の導入過程の構成に関する研究

    Grant number：14780097  2002 - 2003

    日本学術振興会  科学研究費助成事業  若手研究(B)

    岡崎 正和

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    Grant amount：\1500000 （ Direct expense: \1500000 ）

    全体論の立場から中学校1年の代数的内容の単元をデザインするための理論を構築し,正負の数の加減,乗除,文字と式の単元を現場の中学校教師と共同で開発し,実証的に検討した。
    まず,算数から数学への移行に関する理論を学会誌に発表した。そこでは作図を事例として,算数での認識と中学校数学での認識の間に,移行期に相当する活動を適切に想定することによって,算数から数学への移行が成し遂げられ得ることを明らかにした。続いて,正負の数の加減の単元を事例として,全体論の視座からの単元構成のあり方について明らかにし,学会誌に発表した。そこでは教授学的状況論における行為の状況,定式化の状況,妥当化の状況という3つの状況に,代数的思考のサイクルの視点を加味することによって,全体論的に単元が構成されうることを明確にした。
    次に,数学教育の国際会議において,中学校の代数的内容に繋がりうる,算数における小数の除法の理解過程の様相について発表を行った。ここでは小数の除法の理解を阻害するミスコンセプションが,逆と相反という2種類の可逆的思考の統合によって克服され,またその過程で中学校数学の認識へと思考様式が転化しうることを明らかにした。
    さらに,正負の数の乗除と文字と式に関する単元開発を行い,算数の式から代数の式への接続プロセスの様相について学会で発表した。ここでは総合式を作り,分析するという視点から構想された学習活動の中で,式に関する重要なアイデアが生じ,それが数学的に高まる過程において,式が構造的に認識されるようになることを明らかにした。また,正負の乗除の単元で培われる認識を引き継ぎ,高めるような文字と式の単元構成のあり方について検討し,基本的な活動形態を明らかにした。

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  • 小学算数を中学数学に接続する分数による除法に関する学習指導の開発研究

    Grant number：14022233  2002

    日本学術振興会  科学研究費助成事業  特定領域研究

    岩崎 秀樹, 馬場 卓也, 山口 武志, 植田 敦三, 岡崎 正和

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    Grant amount：\2500000 （ Direct expense: \2500000 ）

    本研究の課題意職は,算数を数学に接続するという「教育内容と学習の適時性」について,一般化の視座から理論的に明確にすると同時に,実践的にも当該教材の意義を明らかにする点にある。いくつかある接続教材の中から,特に問題を含む「分数による除法」(以下「÷分数」)をとりあげ,上記課題に対する解答を試みた。実際,平成6年2月に文部省によって実施された「教育課程実施状況調査」によれば,6学年児を対象とする「分数÷分数」を立式させる問題の通過率は27.2%であり,一方5学年児を対象とする「小数÷小数」(以下「÷小数」)を立式させる問題の通過率は65.9%であった。両問題の数理構造は類似しているにもかかわらず,通過率に40%近くの差が生じるところに,接続を考察する上で,基本的な問題が内包されていると考えた。
    本年度の研究実績の概要をまとめれば,次の3点に集約される。第1点は,上で述べたような「÷分数」に関する低い通過率の要因を一般化の視座から理論的に明らかにした点である。本研究では,「÷分数」と「÷小数」の通過率の差が立式に不可分なアルゴリズムの理解によるものであり,両者のアルゴリズムの理解が「外延的一般化」あるいは「内包的一般化」として質的に異なることを指摘した。第2点は「÷分数」指導の新たな目的を提起した点である。つまり,小学算数を中学数学に接続する教材という視座から,算数を統合し代数へと発展させる出発点として「÷分数」の教材を位置づけるべきことを指摘した。第3点としては,現行の比例的推論に基づく「÷分数」指導に代わって,新たな指導の対案を提案した点である。その対案とは,立式のためには「比較」のスキーマを前提とし,「×逆数」の説明には,既有の数学的知職を仮定する教授学的介入である。本研究では,この対案に基づく教授実験を設計,実施し,その妥当性,有効性を示すことができた。

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  • 算数から数学への移行を支援する授業開発に関する研究

    Grant number：12780112  2000 - 2001

    日本学術振興会  科学研究費助成事業  奨励研究(A)

    岡崎 正和

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    Grant amount：\1300000 （ Direct expense: \1300000 ）

    算数から数学への移行を促す教材として,代数分野からは中学校1年の正負の数,文字と式,方程式を,そして幾何分野からは図形の作図をとり上げ,各教材に関して,現場の中学校教師と共同して,授業開発を行った。
    代数分野に関しては,まず,教材を未習の生徒に対してインタビュー調査を実施した。そこでは,方程式に関わる問題解決の過程の中で文字と式の単元で学習する内容に関わるアイデアが生じることが分かり,さらに,そうしたアイデアが生じる過程について知見を得た。それを,「全体論的な視座からの代数の導入過程に関する研究-代数的発想の生起の様相-」として,学会誌に発表した。
    次に,インタビュー調査で明らかになった内容や,先行研究の文献研究から得られた知見をもとにして,現場教師と共同で2002年4月から10月にかけて,中学校1年の数学の授業開発を行った。授業は毎時間ビデオカメラで録画して,それを分析,検討し,その成果の一部として,代数の導入過程の単元構成について,「数学授業における場を視点とした代数の導入過程の構成に関する研究」と題して論文を発表した。
    幾何分野に関しても,中学校教師と中学校1年の作図の授業開発を実施し,その授業を分析して,学会誌に発表した。一つは,「経験的認識から理論的認識への変容過程に関する研究-図形の作図とその正当化の過程に焦点を当てて-」と題して,生徒の図形認識の様相が作図の学習を通してどのように変容するかを分析・考察した。もう一つは,「Geometric construction as a threshold of proof : The figure as a cognitive tool for justification」と題し,図形の形のイメージ,さらにはその操作的なイメージが,作図の学習や論証への移行をどのように支えているかについて分析した。

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  • Investigation of zeta functions associated with prehomogeneous vector spaces

    Grant number：10640014  1998 - 1999

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    NAKAGAWA Jin, OKAZAKI Masakazu, IWASAKI Hiroshi, NUNOKAWA Kazuhiko

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    Grant amount：\3000000 （ Direct expense: \3000000 ）

    Let L be the lattice of integral binary cubic forms and LィイD4^ィエD4 be the dual lattice of L. The distribution of cubic fields is closely related to the prehomogeneous vector space of binary cubic forms. The zeta functions ξィイD2iィエD2(L, s)(I = 1, 2) associated with this space are expressed as sums of |DィイD2KィエD2|ィイD1sィエD1ηィイD2KィエD2(2s) over all cubic fields K. Here ηィイD2KィエD2(s) =ζ(2s)ζ(3s - 1)ィイD7ζィイD2KィエD2(s)(/)ζィイD2KィエD2(2s)ィエD7. Using this expression and class field theory, I proved Ohno conjecture which statesξィイD21ィエD2(LィイD4^ィエD4, s) = 3ィイD1-3sィエD1ξィイD22ィエD2(L, s) andξィイD22ィエD2(LィイD4^ィエD4, s) = 3ィイD11-3sィエD1ξィイD21ィエD2(L, s). As applications of this result, I obtained certain relations among the number of cubic fields of positive and negative discriminants, and a refinement of Sholz's reflection theorem. These results are published in Inventiones mathematicae. I also gave a talk on the results at International Congress of Mathematicians ICM98.
    I have been studying the prehomogeneous vector spaces of pairs of ternary quadratic forms which is closely related to the distribution of discriminants of quartic fields and 2-torsion subgroups of ideal class groups of cubic fields. In particular, I have obtained certain relations between the set of equivalence classes of pairs of integral ternary quadratic forms and 2-torsion subgroups of cubic fields. I gave a talk on this result at the symposium on number theory at Tsuda College.

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  • Submanifolds in Hyperbolic, Space

    Grant number：09640098  1997 - 1998

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    MORI Hiroshi, IWASAKI Hiroshi, NUNOKAWA Kazuhiko, KUMAGAI Kohichi

    　 More details

    Grant amount：\3000000 （ Direct expense: \3000000 ）

    A fundamental problem in differential geometry is to characterize and determine all the submanifolds in a space form. A complete solution to the problem in the generality as stated above simply seems beyond the reach of the current mathematics. Historically, various conditions were imposed upon so as to make the problem somewhat more feasible, if not more viable. One of such conditions is to restrict submanifolds to being of codimension one and of the same constant curvature as the ambient space. The problem has received considerable attention under this rather restricted state ; indeed, it has seen much progress.
    For example, the problem has long been settled for the Riemannian space forms of non-negative curvature, in the hyperbolic case, only some partial solutions existed until a lengthy but more complete description of the space was recently obtained, In the indefinite case, Graves gave the answer to the problem for the flat Lorentzian space forms. The case involving the de Sitter space forms was treated by Abe.
    In this report, we take up the anti-de Sitter space forms of constant curvature -1. We give a. complete description of the space of the isometric immersions of H^^-_1^n into H^^-_1^<n+1>. Here we denote by H^^-_1^n the universal pseudo-Riemannian covering manifold of the n-dimensional anti-dc Sitter space-time H_1^n.

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  • Special Activities and Integrated Studies Methodology AI （2021academic year） 1st semester  - 月5,月6

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  • Special Activities and Integrated Studies Methodology AI （2021academic year） 1st semester  - 月5,月6

  • Special Activities and Integrated Studies Methodology AI （2021academic year） Second semester  - 月5,月6

  • Special Activities and Integrated Studies Methodology AI （2021academic year） Fourth semester  - 月5,月6

  • Special Activities and Integrated Studies Methodology AI （2021academic year） Second semester  - 月5,月6

  • Special Activities and Integrated Studies Methodology　BⅠ （2021academic year） Third semester  - 月5,月6

  • Special Activities and Integrated Studies Methodology　BⅡ （2021academic year） Fourth semester  - 月5,月6

  • Methodology of Special Activities and Integrated Studies ＣⅠ （2021academic year） Third semester  - 月5,月6

  • Methodology of Special Activities and Integrated Studies ＣⅡ （2021academic year） Fourth semester  - 月5,月6

  • Studies in Extra-curricular Activities A(1) （2021academic year） 1st semester  - 月5,月6

  • Studies in Extra-curricular Activities A(1) （2021academic year） Third semester  - 月5,月6

  • Studies in Extra-curricular Activities A(1) （2021academic year） 1st semester  - 月5,月6

  • Studies in Extra-curricular Activities A(2) （2021academic year） Second semester  - 月5,月6

  • Studies in Extra-curricular Activities A(2) （2021academic year） Fourth semester  - 月5,月6

  • Studies in Extra-curricular Activities A(2) （2021academic year） Second semester  - 月5,月6

  • Studies in Extra-curricular Activities B(1) （2021academic year） Third semester  - 月5,月6

  • Studies in Extra-curricular Activities B(2) （2021academic year） Fourth semester  - 月5,月6

  • Studies in Elementary Mathematical Education A (1) （2021academic year） 1st semester  - 木3,木4

  • Studies in Elementary Mathematical Education A (2) （2021academic year） Second semester  - 木3,木4

  • Arithmetic Lesson Development （2021academic year） Second semester  - 木3,木4

  • Arithmetic Teaching Methodology （2021academic year） 1st semester  - 木3,木4

  • Teaching Practice of Analysing Problems at School for Middle School Leaders （2021academic year） 1st-4th semester  - その他

  • Teaching Practice for Inquiry （2021academic year） 1st-4th semester  - その他

  • Teaching Practice for Verification （2021academic year） 1st-4th semester  - その他

  • Teaching Practice for Problem Finding （2021academic year） 1st and 2nd semester  - その他

  • Teaching Practice for Problem Solving （2021academic year） Summer concentration  - その他

  • Secondary Education Mathematics Content Construction Ⅰ （2020academic year） Third semester  - 金3,金4

  • Secondary Mathematics Education Methodology Development A (1) （2020academic year） 1st semester  - 水3,水4

  • Secondary Mathematics Education Methodology Development A (2) （2020academic year） Second semester  - 水3,水4

  • Secondary Mathematics Education Methodology （BasicⅠ） （2020academic year） Third semester  - 金7,金8

  • Secondary Mathematics Education Methodology （BasicⅡ） （2020academic year） Fourth semester  - 金7,金8

  • Secondary Mathematics Education Methodology B (1) （2020academic year） Third semester  - 金7,金8

  • Secondary Mathematics Education Methodology B (2) （2020academic year） Fourth semester  - 金7,金8

  • Secondary Education Mathematics Teaching Methodology (BasicⅠ) （2020academic year） Third semester  - 金7,金8

  • Secondary Education Mathematics Teaching Methodology (BasicⅡ) （2020academic year） Fourth semester  - 金7,金8

  • Approaches to Education （2020academic year） 1st semester  - 火1,火2

  • Theory and Practice of Educational Evaluation B （2020academic year） Fourth semester  - 木5,木6

  • Development of Teaching-materials and Instructional Design A （2020academic year） Third semester  - 水1,水2,水3,水4

  • Development of Teaching-materials and Instructional Design B （2020academic year） Fourth semester  - 金1,金2

  • Math for math teachers （2020academic year） Summer concentration  - その他

  • The theories of the development of teaching-materials and the instructional desi （2020academic year） 1st semester  - 火3,火4

  • The theories of the development of teaching-materials and the instructional desi （2020academic year） Second semester  - 火3,火4

  • Design and Practice of Subject II(Mathmatics Education) （2020academic year） Second semester  - 金1,金2

  • Design and Practice of Subject (Mathmatics Education) （2020academic year） Second semester  - 金1,金2

  • Seminar in Teaching Profession Practice (Secondary school A) （2020academic year） 1st-4th semester  - 水7,水8

  • Practical Studies in Educational Research (Inquiring Issues/Mathmatics Education （2020academic year） 1st-4th semester  - その他

  • Practical Studies in Educational Research(Verifying Proposals/Mathmatics Educati （2020academic year） 1st-4th semester  - その他

  • Practical Studies in Educational Research I(Analysing Schools) （2020academic year） 1st and 2nd semester  - 金7,金8

  • Practical Studies in Educational Research I (Searching Issues) （2020academic year） 1st and 2nd semester  - 月3,月4

  • Practical Studies in Educational Research II(Proposing Solutions) （2020academic year） 3rd and 4th semester  - 金7,金8

  • Practical Studies in Educational Research II (Solving Issues) （2020academic year） 3rd and 4th semester  - 月3,月4

  • Methodologies of Educational Practical Research IIA(Mathmatics Education) （2020academic year） Third semester  - 木7,木8

  • Methodologies of Educational Practical Research IIB(Mathmatics Education) （2020academic year） Fourth semester  - 木7,木8

  • Special Activities and Integrated Studies Methodology AI （2020academic year） 1st semester  - 月5,月6

  • Special Activities and Integrated Studies Methodology AI （2020academic year） Third semester  - 月5,月6

  • Special Activities and Integrated Studies Methodology AI （2020academic year） 1st semester  - 月5,月6

  • Special Activities and Integrated Studies Methodology AI （2020academic year） Second semester  - 月5,月6

  • Special Activities and Integrated Studies Methodology AI （2020academic year） Fourth semester  - 月5,月6

  • Special Activities and Integrated Studies Methodology AI （2020academic year） Second semester  - 月5,月6

  • Special Activities and Integrated Studies Methodology　BⅠ （2020academic year） Third semester  - 月5,月6

  • Special Activities and Integrated Studies Methodology　BⅡ （2020academic year） Fourth semester  - 月5,月6

  • Methodology of Special Activities and Integrated Studies ＣⅠ （2020academic year） Third semester  - 月5,月6

  • Methodology of Special Activities and Integrated Studies ＣⅡ （2020academic year） Fourth semester  - 月5,月6

  • Studies in Extra-curricular Activities （2020academic year） 1st and 2nd semester  - 月5,月6

  • Studies in Extra-curricular Activities A(1) （2020academic year） 1st semester  - 月5,月6

  • Studies in Extra-curricular Activities A(1) （2020academic year） Third semester  - 月5,月6

  • Studies in Extra-curricular Activities A(1) （2020academic year） 1st semester  - 月5,月6

  • Studies in Extra-curricular Activities A(2) （2020academic year） Second semester  - 月5,月6

  • Studies in Extra-curricular Activities A(2) （2020academic year） Fourth semester  - 月5,月6

  • Studies in Extra-curricular Activities A(2) （2020academic year） Second semester  - 月5,月6

  • Studies in Extra-curricular Activities B(1) （2020academic year） Third semester  - 月5,月6

  • Studies in Extra-curricular Activities B(2) （2020academic year） Fourth semester  - 月5,月6

  • Studies in Elementary Mathematical Education A （2020academic year） 1st and 2nd semester  - 木1,木2

  • Studies in Elementary Mathematical Education A (1) （2020academic year） 1st semester  - 木3,木4

  • Studies in Elementary Mathematical Education A (2) （2020academic year） Second semester  - 木3,木4

  • Arithmetic Lesson Development （2020academic year） Second semester  - 木3,木4

  • Arithmetic Teaching Methodology （2020academic year） 1st semester  - 木3,木4

  • Teaching Practice of Analysing Problems at School for Middle School Leaders （2020academic year） 1st-4th semester  - その他

  • Teaching Practice for Inquiry （2020academic year） 1st-4th semester  - その他

  • Teaching Practice for Verification （2020academic year） 1st-4th semester  - その他

  • Teaching Practice for Problem Finding （2020academic year） 1st and 2nd semester  - その他

  • Teaching Practice for Problem Solving （2020academic year） 3rd and 4th semester  - その他

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