Instructional approach and acquisition of mathematical proficiency: Theoretical insights from learning by comparison and cognitive load theory
Open accessAbstract
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.
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Ngu and Phan examine how instructional guidance and cognitive load influence the development of mathematical proficiency.
“Ngu and Phan [40] examine how instructional guidance and cognitive load influence the development of mathematical proficiency.”
From Fluency Illusion: A Review on Influence of ChatGPT in Classroom Settings (2026) · cites this paper as [40]
Although Ngu and Phan's study does not directly investigate ChatGPT or other generative AI tools, it offers relevant theoretical insights into how external instructional supports may shape learners' engagement with complex problem-solving tasks.
“Although their study does not directly investigate the use of ChatGPT or other generative AI tools, it offers relevant theoretical insights into how external instructional supports may shape learners' engagement with complex problem-solving tasks.”
From Fluency Illusion: A Review on Influence of ChatGPT in Classroom Settings (2026) · cites this paper as [40]
Recognizing a correct explanation is not always the same as developing the ability to construct the solution independently.
“These findings suggest that recognizing a correct explanation is not always the same as developing the ability to construct the solution independently [13,14,40].”
From Fluency Illusion: A Review on Influence of ChatGPT in Classroom Settings (2026) · cites this paper as [40]
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References 62 · Cited by 10
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- Authors
- Ngu, B. H., & Phan, H. P.
- Affiliations
- University of New England (AU)
- Corresponding author
- Ngu, Bing Hiong
- Venue
- Asian Journal for Mathematics Education
- Publisher
- SAGE Publications
- Published
- 2024-07-26
- Volume
- 3
- Issue
- 3
- Pages
- 357-379
- ISSN
- 2752-7271 (ISSN-L)
- 2752-7263
- OpenAlex
- W4401033786
- Cited by
- 10
- References
- 62
- Citations by year
- 2026: 9 · 2025: 1
- FWCI
- 7.55
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- Locations
- Asian Journal for Mathematics Education (publishedVersion, cc-by-nc)
- RUNE (Research UNE) (submittedVersion, cc-by-nc)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Visual and Cognitive Learning Processes
- Keywords
- mathematics proficiency, cognitive load theory, worked examples, instructional design, productive disposition, constructivist learning, mathematics learning
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