Review article
https://doi.org/10.15516/cje.v27i2.5815
The Cognitive Development of Students and Understanding the Equals Sign: A Review
Lihong Cui
orcid.org/0000-0003-3616-2215
; Capital Normal University School of Mathematical Sciences
Shuo Cui
; Capital Normal University School of Mathematical Sciences
Siqing Lian
; Capital Normal University School of Mathematical Sciences
Jinhai Liu
orcid.org/0009-0004-6187-3750
; Henan Normal University School of Mathematics and Statistics
Abstract
For decades, the cognitive development of the equals sign has attracted attention from scholars, yet comprehensive reviews are lacking. This study aims to review research on four areas: students' understanding of the equals sign, factors influencing their understanding, interventions to promote understanding, and cross-cultural comparisons. It also aims to identify unresolved issues, gaps, and developmental trends. Based on a review of 85 papers from 1932 to 2024 from six databases, this study contributes by (a) summarizing students’ understanding of the equals sign across age groups, various understanding levels, crucial factors influencing students' understanding, theoretical frameworks and measurement items and results widely seen in studies about interventions, and students’ understanding from different countries; (b) recognizing the lack of research on high school and college students' understanding, the developmental paths of different understanding levels, specific influencing factors, and portable interventions to improve both procedural and conceptual knowledge of the equals sign; and (c) suggesting future research to explore the cognitive mechanisms of understanding the equals sign, integrate procedural and conceptual teaching, distinguish between reducing or preventing misunderstandings, develop a unified measurement tool, and examine factors behind cross-country differences in understanding. This study contributes to a more systematic theory and research framework in mathematics education.
Keywords
algebra; equation; mathematical equivalence; understanding.
Hrčak ID:
344783
URI
Publication date:
27.6.2025.
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