Mathematical sense-making through learner choice

Piera Biccard

doi:10.4102/pythagoras.v39i1.424

Abstract

This article explores a conceptual relationship between learner choice and mathematical sense-making. It argues that when learners can exercise choice in their mathematical activities, mathematical sense-making can be enhanced. The literature around mathematical modelling suggests a link between sense-making and learner choice. A three-tiered conceptual analysis allowed ‘purposiveness to thinking’ from the author through engagement with selected literature. Research questions related to a three-tiered analysis: generic, context-specific, and conditional accounts of sense-making in mathematics classrooms were formulated. The analysis resulted in a framework showing how sense-making may be constrained or enhanced in mathematics classrooms through learner choice. This article may add to our holistic understanding of sense-making in mathematics classrooms. It may contribute to mathematics teacher education by proposing that teachers are resourced to facilitate learners’ conceptual and procedural choice in primary or secondary mathematics classrooms.

Highlights

Learners often view learning mathematics as non-sense-making (Dienes, 1971; Schoenfeld, 1991)
Other realistic mathematics education scholars http://www.pythagoras.org.za (Gravemeijer, 1994a; Treffers, 1987) echo the importance of differentiation based on learners using their own methods
A context analysis will answer the question: What features of mathematical modelling support learner choice and contribute to sense-making?

Summary

Introduction

Learners often view learning mathematics as non-sense-making (Dienes, 1971; Schoenfeld, 1991). This article uses a conceptual approach to explore learner choice as a property of sense-making It proposes that choice may elicit enhanced understanding and application of mathematics. Other realistic mathematics education scholars http://www.pythagoras.org.za (Gravemeijer, 1994a; Treffers, 1987) echo the importance of differentiation based on learners using their own methods (which implies learner choice) Terms such as ‘own methods’ are considered to be consistent with learners being allowed to make decisions or have choice when solving problems. The section that follows the method focuses on the occurrence of sense-making in mathematical classrooms generally It is followed by a section looking at a specific mathematical activity, that is, modelling, focusing and descriptively on what features of modelling activities support learner choice to enhance learner sensemaking. The final section concludes with a possible framework provided by the author for understanding sense-making through learner choice in mathematics classrooms

Method and research questions

Conclusion