A Teaching Method for Facilitating Learners Appreciation of Cultural Aesthetic Qualities of Mathematics

2021 Fiscal Year Final Research Report

• Project/Area Number: 19K14229
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 09040:Education on school subjects and primary/secondary education-related
• Research Institution: Miyagi University of Education (2020-2021); University of Tsukuba (2019)
• Principal Investigator: Hanazono Hayato 宮城教育大学, 教育学部, 准教授 (60816495)
• Project Period (FY): 2019-04-01 – 2022-03-31
• Keywords: 数学の美 / 文化 / 教授方法 / 数学的証明 / 数学的体系 / 数学的定義（条件） / 感得

Outline of Final Research Achievements

In order to elucidate teaching methods that allow learners to perceive the " cultural aesthetic qualities" of mathematics, this empirical study focused on mathematical proofs, mathematical definitions (conditions), and mathematical systems as mathematical objects that reflect this kind of aesthetic qualities.
In the research on mathematical definitions (conditions) and mathematical systems with university students, it was found that when it is difficult to identify the "form" that constitutes the entire system, it is beneficial to structure a part of the system with a graphical representation, and that the experience of learning mathematical relations that function as the "forms" plays an important role.
A study with middle school students on mathematical proofs revealed that the comparison of formal and informal proofs can facilitate appreciation of the " cultural aesthetic qualities" of mathematical proofs that are implicit in them.

Free Research Field

数学教育学

Academic Significance and Societal Importance of the Research Achievements

理論的に基礎づけられた数学の「文化的な美」及びその感得の促進方法を数学的対象と関連づけて具体化し，さらにその促進方法の有効性を実証的に提示したことは，本研究独自の研究成果である。この成果は，これまで主観的な実践に陥りがちであった「数学の美しさ」に関する教育活動に対して，科学的な基礎を与えるものである。
この「数学の美しさ」に関する実践が広く行われることによって，論理のみでは説明できない数学的証明や定義などの特性を学習者が理解することを助けるとともに，数学学習に関する日本の学習者の最重要課題の一つである学習意欲の低迷の改善に大いに寄与することが期待される。