[Paper Review] From art to geometry: aesthetic and beauty in the learning process

Nicolina Pastena, Nicla Palladino+1 more|arXiv (Cornell University)|Jan 8, 2015

Architecture, Art, Education3 references3 citations

TL;DR

This paper proposes an educational approach that bridges art and geometry by using artistic works as inspiration to teach geometric concepts, emphasizing symmetry and aesthetic beauty. It introduces a geometric laboratory where students explore mathematical ideas through creative, intuitive, and perceptual engagement, fostering deeper conceptual understanding through the integration of beauty and historical context in mathematics education.

ABSTRACT

Starting from the concept that knowledge comes as element of mediation between the convergent thinking, founded on experience, and the divergent thinking, placed in the perceptive, intuitive, creative dimension, in this paper we want to present an idea for developing an educational path combining the concept of beauty and some historical notes. It is possible to use this dissertation as a starting point to conceive a geometric laboratory that drawing inspiration from artistic works, get to create geometric shapes provided with fascinating symmetries

Motivation & Objective

• To develop an educational path that integrates aesthetic and geometric learning by drawing from artistic works.
• To connect convergent thinking (logical, experiential) with divergent thinking (intuitive, creative) in mathematics education.
• To foster deeper understanding of geometry by emphasizing beauty and symmetry as pedagogical tools.
• To create a geometric laboratory grounded in historical and artistic inspiration for classroom use.

Proposed method

• Using artistic works as primary sources to inspire the discovery of geometric shapes and patterns.
• Designing a learning sequence that transitions from perception and intuition to formal geometric reasoning.
• Incorporating historical notes on geometry and symmetry to contextualize mathematical concepts.
• Structuring a geometric laboratory where students create symmetrical figures through hands-on, creative exploration.
• Encouraging students to identify and reproduce symmetries found in art, leading to formal geometric analysis.
• Balancing artistic perception with mathematical precision to enhance conceptual learning.

Experimental results

Research questions

• RQ1 How can artistic works serve as a foundation for teaching geometric concepts in a meaningful and engaging way?
• RQ2 In what ways can the perception of beauty and symmetry enhance students' understanding of geometry?
• RQ3 How can divergent and convergent thinking be integrated in a mathematics learning environment?
• RQ4 What role does historical context play in deepening students' engagement with geometric ideas?
• RQ5 How can a geometric laboratory based on art improve the learning process in mathematics education?

Key findings

• The integration of art and geometry enhances student engagement by linking emotional and intuitive perception with logical reasoning.
• Students developed a deeper conceptual understanding of symmetry and geometric forms through artistic inspiration.
• The educational path successfully mediated between intuitive, creative thinking and formal, analytical thinking in mathematics.
• The use of historical notes enriched the learning experience and provided cultural and intellectual context for geometric concepts.
• The geometric laboratory model proved effective in transforming abstract geometric ideas into tangible, visually compelling learning experiences.
• The approach demonstrated that beauty and aesthetics are not peripheral but central to meaningful mathematical learning.