## Abstract

Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions of coordination tasks by chapter and for the type of task demanded (perception vs. construction). Results suggest that different coordination tasks are used earlier and later in learning and for different topics, as well as for specific pedagogical and scaffolding purposes. For example, the algebra-to-text coordination task was more prevalent in the first chapter, suggesting that students are being eased into calculus content. By contrast, requests to construct graphs from algebraic expressions were emphasized in later chapters, suggesting that students are being pushed to think more conceptually about functions. Our nuanced look at coordination tasks in a reform textbook has implications for research in teaching and learning calculus.

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## Acknowledgements

The research reported herein was supported by grant number R305A120471 from the U.S.Department of Education. The opinions are those of the authors and do not represent the policies ofthe U.S. Department of Education. Portions of this study were presented at the 2013 ResearchPresession of the annual meeting of the National Council of Teachers of Mathematics on April 15,2013 in Denver, Colorado. We are grateful to Shaaron Ainsworth, Tim Fukawa-Connelly, WilliamZahner, and Theodore Wills for providing helpful comments in discussions of and on earlier versions of the paper. We also thank the reviewers whose comments helped improve and clarify this manuscript.

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Chang, B.L., Cromley, J.G. & Tran, N. Coordinating Multiple Representations in a Reform Calculus Textbook.
*Int J of Sci and Math Educ* **14, **1475–1497 (2016). https://doi.org/10.1007/s10763-015-9652-3

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### Keywords

- Calculus
- Conceptual understanding
- Functions
- Multiple representations
- Textbooks