Mathematics and art: Ideas to use in teacher education

Abstract

Throughout history, there have always been connections between mathematics and various forms of art, such as music, dance, painting, sculpture, and architecture, which can be effectively used in mathematics classes with highly positive implications for students’ learning. In particular, geometry emerges as a central field in this relationship. These connections not only motivate students and promote mathematical learning but also foster creative thinking and an esthetic sense, both of which are intrinsic to many mathematical concepts. Furthermore, they enable students to recognize and understand the mathematics embedded in numerous visual artistic works. While art provides an esthetic experience for those who study mathematics, it also establishes a connection between thought and emotion, giving deeper meaning to what we perceive. However, this relationship is not always immediately visible. Therefore, both mathematics and art teachers need to use various connections to develop both the student’s “geometric eye” and “artistic eye”. This manuscript aims to discuss ideas about this connection between mathematics/geometry and art. In addition, it presents examples of tasks implemented during the initial training of elementary school teachers, along with some of the works produced by these future teachers.

Keywords

Connections / Elementary teacher education / Visual arts / Mathematics education / Geometry

Funding

This work was financially supported by Portuguese national funds through the Foundation for Science and Technology (FCT) within the framework of the Research Centre on Child Studies of the University of Minho projects, CIEC (UIDB/00317/2020 and UIDP/00317/2020), and Centre for Research and Innovation in Education projects, in ED (UIDP/05198/2020).

Conflict of interest

The authors declare no conflicts of interest.

References

[1] Kline M. Mathematics in Western Culture. United Kingdom: Oxford University Press;1964.

[2] Diego-Mantecón JM, Blanco TF, Búa Aresc JB, Sequeiros PG. Is the relationship between art and mathematics addressed thoroughly in Spanish secondary school textbooks? J Math Arts. 2019; 13(1-2):25-47. doi: 10.1080/17513472.2018.1552068

[3] ME-DGE. Aprendizagens Essenciais: Matemática [Essential Learnings: Mathematics]. Ministério da Educação/Direção- Geral da Educação; 2021. Available from: https://www.dge.mec.pt [Last accessed on 2024 Sep 30].

[4] European Commission. Proposal for a Council Recommendation on Key Competences for Lifelong Learning. EU; 2018. Available from: https://ec.europa.eu/education/sites/education/files/recommendation-key-competences-lifelong-learning.pdf [Last accessed on 2024 Sep 15].

[5] Vale I, Barbosa A, Peixoto A, Fernandes F. Solving problems through engineering design: An exploratory study with pre-service teachers. Educ Sci. 2022; 12:12. doi: 10.3390/educsci12120889

[6] Hardy GH. A Mathematician’s Apology. University of Alberta Mathematical Sciences Society; 1940. Available from: https://web.njit.edu›-akansu›papers›ghhardy-amathematiciansapology.pdf [Last accessed on 2024 Jul 12].

[7] Stix A. The Link between Art and Mathematics. In: Proceedings of the Annual Conference of the National Middle School Association. NMSA; 1995.

[8] CMUP. Arte e Matemática [Art and Mathematics]. Centro de Matemática da Universidade do Porto; 2010. Available from: https://cmup.fc.up.pt/Steecmup/arte/plasticas/index.html [Last accessed on 2024 Sep 15].

[9] Sawyer W. Prelude to Mathematics. United Kingdom: Penguin Books;1955.

[10] Steen L. The science of patterns. Science. 1988; 240:611-616. doi: 10.1126/science.240.4852.611

[11] Durer A. The Complete Engravings, Etchings and Drypoints of Albrecht of Dürer. United States: Dover Publications; 2000.

[12] Bastos R. Notas sobre o ensino da geometria do grupo de trabalho de geometria da APM - simetria [Notes about the teaching of geometry of the group work of geometry of APM - symmetry]. Educ Mat. 2006; 88:9-11.

[13] Veloso E. Simetrias e Transformações Geométricas [Symmetry and Geometric Transformations]. Lisboa: APM; 2012.

[14] Serra M. Discovering Geometry - An Investigative Approach. California: Key Curriculum Press; 2008.

[15] Gimenez J. La proporción: Arte y Matemáticas [The Proportion: Art and Mathematics]. Barcelona: Editorial Graó; 2009.

[16] Vale I, Pimentel T. Padrões e conexões matemáticas no ensino básico [Patterns and connections in elementary education]. Educ Mat. 2010;110,33-38.

[17] Sylviani S, Permana FC, Azizan AT. Enhancing mathematical interest through visual arts integration: A systematic literature review. Int J Educ Math Sci Technol. 2024; 12(5):1217-1235. doi: 10.46328/ijemst.4118

[18] Robbins D. Cubism and Abstract Art: Piet Mondrian. Guggenheim Museum Archives Reel-to-Reel Collection - The Solomon R. Guggenheim Foundation (SRGF); 1962 Available from: https://www.guggenheim.org›wp-content›uploads›2018›08›615214t29_01_piet-mondrian [Last accessed on 2024 Jul 20].

[19] Schapiro M. Mondrian - A Dimensão Humana da Pintura Abstrata [On the Humanity of Abstract Painting]. Brazil: Cosac and Naify; 2001.

[20] Schleicher A. Teaching Excellence through Professional Learning and Policy Reform: Lessons from Around the World. Paris, France: OECD; 2016. doi: 10.1787/9789264252059-en

[21] Vale I. Matemática e arte: Uma conexão a explorar no ensino da matemática [Mathematics and art: A connection to explore in mathematics teaching]. Diálogos Arte. 2017; 7:223-242.