Presenting a Model for Integrating the Commutative Property with Components of Algebraic Thinking in Iranian Elementary Mathematics Textbooks

Document Type : Original Article

Authors

Department of Mathematics and Computer Science, University of Zanjan, Zanjan, Iran.

10.48310/reek.2026.5266

Abstract

Background and Objectives: This study aims to move beyond mere critical analysis toward providing a practical model for the systematic integration of the commutative property with the four key components of algebraic thinking (word problems, patterning, conceptualization of the equal sign, and generalization of arithmetic rules) in Iranian elementary mathematics textbooks.
Method: Employing a mixed-methods explanatory sequential design, the research first conducted a quantitative and qualitative content analysis of all mathematics textbooks for Grades 1 to 6 (2023 edition). To further assess the depth of imbalances in the distribution of components, the Shannon entropy technique was utilized as a complementary quantitative analysis.
Findings: Findings revealed a significant imbalance, with 31.34% of all identified instances concentrated in Grade 3 and only 5.97% in Grade 6.  A complementary Shannon entropy analysis also revealed this imbalance. Qualitative analysis uncovered structural weaknesses: a predominant operational view of the equal sign, the reduction of patterning to sequence completion, and an excessive focus on "generalization of arithmetic rules" (59.7%) at the expense of exploratory and relational understanding. In response, this study proposes the design and presentation of a developmental, grade-by-grade integrative model. This model specifies learning objectives, core instructional strategies, and sample activities for each grade and algebraic thinking component, emphasizing continuity, depth, and application.
Conclusion: The study concludes that the current textbook representation lacks a coherent developmental trajectory for fostering algebraic thinking and that the proposed model can serve as a conceptual framework for curriculum revision, teacher guidance, and the design of complementary learning resources.

Keywords

Research and Innovation in Primary Education
Volume 8, Issue 3
October 2026
Pages 172-147

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