‘The Area of a Triangle is 180⁰C’—An Analysis of Learners' Idiosyncratic Geometry Responses through the Lenses of Vygotsky's Theory of Concept Formation

Abstract

In this paper, we focus specifically on Vygotsky's theory of concept formation to gain initial insights into seemingly garbled and incoherent connections we observed in learners' responses to a geometry task. While acknowledging research that is supportive of the van Hiele model as being useful when analysing concept formation in geometry, in this paper we use empirical evidence to argue that today's geometry requires learners to reason with many tools which the van Hiele model does not seem to accommodate. Working with 470 written responses of 12–14-year-old learners to a geometry task, we then explored the potential of Vygotsky's theory of concept formation as an alternative framework. We conclude by discussing the paper's contribution both to theory and to classroom practice.

Keywords:

• Vygotsky
• van Hiele
• idiosyncratic responses
• geometry
• concept formation

Acknowledgement

The research reported in this paper was funded through the FRF Mathematics Chair at Rhodes University. However, the views and opinions expressed in this article do not reflect those of the funders. We also acknowledge the valuable comments we got from the reviewers which helped to reshape this paper.