Progression and Transfer of the Mathematical Modelling Perspective in Junior Secondary Mathematics: The Integrated Unit on Functions and Equations as a Case Study

Xi Yang Corresponding author

doi:10.56201/ijasmt.vol.12.no10.2026pg16.30

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Progression and Transfer of the Mathematical Modelling Perspective in Junior Secondary Mathematics: The Integrated Unit on Functions and Equations as a Case Study

Xi Yang Corresponding author

Abstract

The mathematical modelling perspective is one of the places where school mathematics meets the world beyond the classroom. Yet modelling tasks in many junior secondary classrooms are still compressed into a familiar routine: read the problem, write an expression, and calculate an answer. Students may handle familiar exercises without being able to state the assumptions behind a model, judge whether a result is credible, or decide how the model should change when a condition is altered. To address this fragmentation, the present study draws on a literature review, content analysis, and design research to describe modelling as five connected phases: identifying, constructing, interpreting, validating and revising, and transferring a model. Using the integrated unit on functions and equations, the paper reorganizes related content and proposes tasks that place different models in the same context, carry one model across contexts, vary constraints, infer relationships from data, and compare competing models. The aim is to help students attend to mathematical structure rather than remember only surface-level problem types. Assessment is organized around five dimensions and four developmental levels, with evidence drawn from worksheets, classroom explanations, modelling products, transfer tasks, and reflective notes. The outcome is a design framework rather than evidence of instructional effectiveness. Its practical value lies in making assumptions, domains of applicability, and transfer visible in unit goals, classroom tasks, homework, and assessment, while leaving the framework open to subsequent classroom testing and revision.

Keywords

mathematical modelling perspective; integrated-unit instruction; learning progression; model transfer; functions and equations

References

[1] Ministry of Education of the People's Republic of China. Mathematics Curriculum Standards for Compulsory Education (2022 Edition) [S]. Beijing: Beijing Normal University Press, 2022. [in Chinese] [2] Wang, B. A Study of Teaching to Develop the Mathematical Modelling Perspective among Junior Secondary Students: Using Real-World Problems and Quadratic Equations in One Variable as an Example [D], 2023. [in Chinese] [3] Huang, C. A Study of Junior Secondary Mathematics Homework Design for Developing the Mathematical Modelling Perspective [J], 2026. [in Chinese] [4] Deng, Z. Strategies for Integrating Modelling Ideas into the Teaching of Functions in Junior Secondary Mathematics [J], 2025. [in Chinese] [5] Liu, C. Project-Based Learning in Junior Secondary Mathematics Focused on the Mathematical Modelling Perspective: The Appearance of Suspect X as an Example [J]. [in Chinese] [6] Zheng, P. Interdisciplinary Homework Design in Junior Secondary Mathematics from an Integrated-Unit Perspective: Relationships among the Sides and Angles of Right Triangles as an Example [J]. Journal of Middle School Mathematics, 2024(2). [in Chinese] [7] Huang, L. A Study of Visualization in Junior Secondary Mathematics Based on Core Competencies [D]. [in Chinese] [8] Yuan, M. A Study of the Current Implementation and Development Strategies for Integrated Practice in Junior Secondary Mathematics: Statistics and Probability as an Example [D], 2022. [in Chinese] [9] Hu, S. Core-Competency-Oriented Unit Design in Junior Secondary Mathematics: Algebraic Fractions in the First Semester of Grade 8 in the PEP Edition as an Example [D]. [in Chinese] [10] Bi, Y. A Statistical and Comparative Analysis of Mathematical Core Competencies Assessed in the Shaanxi Senior High School Entrance Examination, 2015–2022 [D]. [in Chinese] [11] Blomhøj M, Jensen T H. Developing mathematical modelling competence: conceptual clarification and educational planning[J]. Teaching Mathematics and its Applications, 2003, 22(3):123-139. [12] Maaß K. What are modelling competencies?[J]. Zentralblatt für Didaktik der Mathematik, 2006, 38:113-142. [13] Galbraith P, Stillman G. A framework for identifying student blockages during transitions in the modelling process[J]. Zentralblatt für Didaktik der Mathematik, 2006, 38:143-162. [14] Kaiser G, Sriraman B. A global survey of international perspectives on modelling in mathematics education[J]. Zentralblatt für Didaktik der Mathematik, 2006, 38:302-310. [15] Lobato J, Rhodehamel B, Hohensee C. “Noticing” as an alternative transfer of learning process[J]. Journal of the Learning Sciences, 2012, 21(3):433-482. [16] Schukajlow S, Kaiser G, Stillman G. Empirical research on teaching and learning of mathematical modelling: a survey on the current state-of-the-art[J]. ZDM Mathematics Education, 2018, 50:5-18. [17] Cevikbas M, Kaiser G, Schukajlow S. A systematic literature review of the current discussion on mathematical modelling competencies: state-of-the-art developments in IJASMT E- ISSN 2489-009X , conceptualizing, measuring, and fostering[J]. Educational Studies in Mathematics, 2022, 109:205-236. [18] Hänze M, Leiss D. Using heuristic worked examples to promote solving of reality-based tasks in mathematics in lower secondary school[J]. Instructional Science, 2022, 50:529- 549. [19] Niss M, Højgaard T. Mathematical competencies revisited[J]. Educational Studies in Mathematics, 2019, 102:9-28.

Progression and Transfer of the Mathematical Modelling Perspective in Junior Secondary Mathematics: The Integrated Unit on Functions and Equations as a Case Study

Abstract

Keywords

References

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