Instructional approach and acquisition of mathematical proficiency: Theoretical insights from learning by comparison and cognitive load theory

Abstract

Quality mathematics learning is more than just the acquisition of mastery in different topical themes; rather, it involves successful acquisition of mathematical proficiency, which espouses a number of cognitive attributes—for example, a student's critical insight of a mathematical concept (e.g., productive disposition). Despite the pivotal role of mathematical proficiency in mathematics curriculum, syllabus requirements fall short of highlighting the design of appropriate instructional approaches that could specifically facilitate the acquisition of different mathematical proficiency strands. The present conceptual analysis article discusses the design of comparative instructional approaches that are based on two well-documented learning theories: (1) learning by comparison theory, such as the active comparison of isomorphic example pairs, and (2) cognitive load theory, such as the use of worked examples to reduce the negative impact of cognitive load imposition on learning. We premise that appropriate instructional approaches, informed by the use of both learning by comparison theory and cognitive load theory, may help to facilitate successful acquisition of multifaceted proficiency strands in mathematics learning. As revealed in the latter sections of the article, our proposed theoretical contention is significant, potentially establishing grounding for future research development and to help complement constructivist learning in the acquisition of mathematical proficiency strands.