Mathematical Representations in the Teaching and Learning of Geometry A Review of the Literature from the United States

Main Article Content

Siddhi Desai
Sarah Bush
Farshid Safi


This paper presents a synthesis of the literature exploring the teaching and learning of geometry and the role that mathematical representations can play in enriching geometry experiences for our students. Geometry is the only content domain to be taught in all PK-12 grades, however, from historical trends in international assessment data, it continues to be a low scoring area for students in the United States. This paper is organized by the following: (1) theories guiding the teaching and learning of geometry in the U.S.; (2) teaching and learning of geometry in the U.S.; and (3) the role of mathematical representations in geometry. In order for students to appreciate and experience the wonder, joy, and beauty of geometry in a consistent and coherent manner, they need geometry learning experiences that leverage high quality tasks with opportunities in translating between and within multiple representations, and engage them in discovering connections within geometry, between geometry and the other mathematics content domains, and between geometry and their world.


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Research / Empirical
Author Biographies

Siddhi Desai, University of Central Florida

Siddhi Desai,, is a doctoral student at the University of Central Florida. Her research focuses on studying the integration of mathematics, art, history, and modeling to engage students in rich mathematical experiences. She also researches the role of historical perspectives in understanding the evolution of the field of mathematics education.

Sarah Bush, University of Central Florida

Dr. Sarah B. Bush,, is an Associate Professor of K-12 STEM Education at the University of Central Florida. Her research and scholarship focuses on deepening student and teacher understanding of mathematics through transdisciplinary STE(A)M instruction. She is a member of the board of directors of the National Council of Teachers of Mathematics.

Farshid Safi, University of Central Florida

Dr. Farshid Safi,, is an Assistant Professor of Mathematics Education in the School of Teacher Education at the University of Central Florida. His research and teaching focuses on developing conceptual understanding of PreK–12 mathematics for students and teachers through equitable teaching practices while enhancing connections and coherence.