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Multiple pathways for developing functional thinking in elementary mathematics textbooks: a case study in China

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Abstract

The mathematics education literature indicates a consensus regarding the importance of developing algebraic thinking in elementary school mathematics. However, the approaches used to implement this concept vary around the world. This study examines how a popular standards-based elementary mathematics textbook series in China provides opportunities to learn about functional thinking, which is a key component of algebraic thinking. Building on the literature, an analytical framework was generated to examine the features of function-related tasks in the textbook series across grades. The results of the fine-grained coding analysis show that four categories of function-related tasks in the textbook provide opportunities to learn about multi-modes of functional thinking. These tasks primarily serve to enhance arithmetic learning, while offering opportunities to learn about functional thinking as an embedded component. Elaborated design and arrangement of the function tasks promote opportunities to learn about multiple modes of functional thinking. In addition, two pathways to support the development of functional thinking are identified. Finally, the implications for task design and textbook development which attempt to develop functional thinking are discussed.

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Notes

  1. There are two textbooks in each grade.

  2. See Appendix 2 for the number of questions in different categories of tasks.

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Acknowledgements

We thank Dr. Dovie Kimmins from Middle Tennessee State for proofreading the manuscript and Dr. Xiaobao Li from Widener University for checking the accuracy of the translation of the function tasks, appreciate Dr. Yiran Ding for drawing Fig. 2, and thank Dr. Dan Zu, Miss Zehua Hou, Miss Bojun Liu, and Mr. Xinqiu Qu for their assistance in coding.

Funding

This study was supported by the Research Program Funds of the Collaborative Innovation Center of Assessment for Basic Education Quality at Beijing Normal University (Grant No. 2022–03-042-BZPK01) and the Entrusted General Education Research Project of the Chinese Society Education in 2021 (Grant No. 2021010301WT2). The opinions expressed do not necessarily reflect the views of the Foundation.

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  1. Faculty of Education, Northeast Normal University, No. 5268 Renmin Street, Changchun, China

    Rui Ding & Xixi Deng

  2. Middle Tennessee State University, Murfreesboro, USA

    Rongjin Huang

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Appendices

Appendix 1

Table 4

Table 4 Sample function tasks for each category
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Appendix 2

Table 5

Table 5 Number of questions in function tasks that offered OTL different modes of FT
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Ding, R., Huang, R. & Deng, X. Multiple pathways for developing functional thinking in elementary mathematics textbooks: a case study in China. Educ Stud Math 114, 223–248 (2023). https://doi.org/10.1007/s10649-023-10237-w

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