Review Article

Exploring the relationship between commognition and the Van Hiele theory for studying problem-solving discourse in Euclidean geometry education

Sfiso C. Mahlaba, Vimolan Mudaly
Pythagoras | Vol 43, No 1 | a659 | DOI: https://doi.org/10.4102/pythagoras.v43i1.659 | © 2022 Sfiso C. Mahlaba, Vimolan Mudaly | This work is licensed under CC Attribution 4.0
Submitted: 15 October 2021 | Published: 29 July 2022

About the author(s)

Sfiso C. Mahlaba, Department of Mathematics Education, Faculty of Education, North-West University, Mafikeng, South Africa
Vimolan Mudaly, Department of Mathematics Education, Faculty of Education, University of KwaZulu-Natal, Pinetown, South Africa


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Abstract

This article is an advanced theoretical study as a result of a chapter from the first author’s PhD study. The aim of the article is to discuss the relationship between commognition and the Van Hiele theory for studying discourse during Euclidean geometry problem-solving. Commognition is a theoretical framework that can be used in mathematics education to explain mathematical thinking through one’s discourse during problem-solving. Commognition uses four elements that characterise mathematical discourse and the difference between ritualistic and explorative discourses to explain how one displays mastery of mathematical problem-solving. On the other hand, the Van Hiele theory characterises five levels of geometrical thinking during one’s geometry learning and development. These five levels are fixed and mastery of one level leads to the next, and there is no success in the next level without mastering the previous level. However, for the purpose of the Curriculum and Assessment Policy Statement (CAPS) we only focused on the first four Van Hiele levels. Findings from this theoretical review revealed that progress in the Van Hiele levels of geometrical thinking depends mainly on the discourse participation of the preservice teachers when solving geometry problems. In particular, an explorative discourse is required for the development in these four levels of geometrical thinking as compared to a ritualistic discourse participation.

Keywords

commognition; Van Hiele theory; Euclidean geometry; geometrical thinking; visual mediators

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