Promoting Geometric Reasoning through Artistic Constructions

Scott A Courtney,Brittany Armstrong

doi:10.20897/ejsteme/11332

Abstract

In order to promote geometric understanding, teachers frequently use hands-on activities. Such activities can be used to expound upon the declarative statements and theorems of geometry. Using a compass, straightedge, and protractor, students are able to actively build conceptions involving bisectors, midpoints, and perpendicular lines. Additionally, activities that require students to problem-solve and formulate problems, using their construction knowledge and skills, can reinforce and strengthen that which they have learned. This article describes STEAM instruction with high school geometry students designed to productively integrate geometric constructions, digital technology, elements of art, and principles of design to enhance students’ geometric reasoning.

Highlights

Geometry and spatial sense provide students with understandings and ways of thinking that can be applied in a variety of contexts
We describe a high school Geometry teacher’s attempts to promote a STEAM environment by providing her students with opportunities to use geometric constructions, and mathematically challenging and aesthetically pleasing geometric figures in mathematical proofs; the report addresses the following research question: How can a high school Geometry class integrate geometric constructions, digital technology, elements of art, and principles of design to enhance students’ geometric reasoning?
We described a sequence of activities that integrated geometric constructions, digital technology, elements of art, and principles of design to enhance students’ geometric reasoning

Summary

INTRODUCTION

Geometry and spatial sense provide students with understandings and ways of thinking that can be applied in a variety of contexts. We describe a high school Geometry teacher’s attempts to promote a STEAM environment by providing her students with opportunities to use geometric constructions, and mathematically challenging and aesthetically pleasing geometric figures in mathematical proofs; the report addresses the following research question: How can a high school Geometry class integrate geometric constructions, digital technology, elements of art, and principles of design to enhance students’ geometric reasoning?. Integrating hands-on activities and proof through geometric constructions, promotes greater student interest, and provides students with more meaningful learning experiences. We describe the second author’s implementation of a sequence of high school mathematics activities designed to provide students with opportunities to engage in geometric reasoning and develop meaningful understandings involving geometry and proof through artistic compass and straightedge constructions and digital technology. Taking note of Gettings’ (2016) warning regarding the danger of superficially including art in STEM projects, the sequence of activities utilize art to enhance students’ geometric reasoning

METHODS

Make geometric constructions

Findings

DISCUSSION AND CONCLUSION