Original Research

Learners’ algebraic and geometric connections when solving Euclidean geometry riders

Hans Bila, Kgaladi Maphutha, Paul Mutodi
Pythagoras | Vol 45, No 1 | a810 | DOI: https://doi.org/10.4102/pythagoras.v45i1.810 | © 2024 Hans Bila, Kgaladi Maphutha, Paul Mutodi | This work is licensed under CC Attribution 4.0
Submitted: 06 March 2024 | Published: 26 August 2024

About the author(s)

Hans Bila, Department of Mathematics, Science and Technology Education, Faculty of Humanities, School of Education, University of Limpopo, Polokwane, South Africa
Kgaladi Maphutha, Department of Mathematics, Science and Technology Education, Faculty of Humanities, School of Education, University of Limpopo, Polokwane, South Africa
Paul Mutodi, Department of Mathematics, Science and Technology Education, Faculty of Humanities, School of Education, University of Limpopo, Polokwane, South Africa

Abstract

In this article, we explored Grade 11 learners’ algebraic and geometric connections when solving Euclidean geometry riders. A qualitative interpretive case study design was followed. Thirty Grade 11 learners from a non-fee-paying secondary school in the Capricorn North district of South Africa were conveniently sampled to participate in this study. Data were collected through learners’ responses to classwork, homework exercises, and task-based interviews. Data were analysed thematically. The findings revealed that to solve Euclidean geometry riders successfully, learners need to establish the feature connections embedded in the given figure or diagram. The ability to make feature connections provides a point of departure in the solution process of a geometric problem.

Contribution: Once the feature connection is established, other connections will subsequently emerge. In addition, the reversibility connections become a form of feature connection when solving Euclidean geometry riders. Therefore, we recommend that mathematics teachers emphasise and use mathematical connections in their daily teaching of mathematics.


Keywords

algebraic connections; geometric connections; deductive thematic analysis; Euclidean geometry riders

Sustainable Development Goal

Goal 4: Quality education

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