Exploring the Affordances of Using Various Approaches to Mathematics Tasks

Tin Lam TOH

National Institute of Education
Nanyang Technological University
Singapore

Published in The Mathematician Educator, 2025, Vol 6, No. 1, pp 20-32.

Abstract

In this paper, complementing the usual way of finding alternative solutions to a mathematical task as part of the problem-solving process, the affordances of various solution approaches to a given mathematical task are examined. Through examining three solution approaches of the task to find the sum of the first n positive integers and three teaching approaches of binomial theorem, it is illustrated how these solution approaches could lead to the learning of further mathematics beyond the constraint of the task. Finally, by presenting three tasks of the same genre but different nature of solution, it is argued that a careful examination of the plausible solution approaches could provide students the opportunity to strike a balance between selecting an efficient solution approach and a robust solution approach, thereby developing procedural fluency and flexibility.

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