# Ferris wheels and filling bottles: a case of a student’s transfer of covariational reasoning across tasks with different backgrounds and features

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## Abstract

Using an actor-oriented perspective on transfer, we report a case of a student’s transfer of covariational reasoning across tasks involving different backgrounds and features. In this study, we investigated the research question: How might a student’s covariational reasoning on Ferris wheel tasks, involving attributes of distance, width, and height, influence a student’s covariational reasoning on filling bottle tasks, involving attributes of volume and height? The student transferred covariational reasoning that she employed on Ferris wheel tasks to filling bottle tasks; yet, her covariational reasoning on filling bottle tasks was less advanced. When designing a sequence of tasks intended to engender students’ covariational reasoning, we recommend that researchers begin by using situations consisting of “simpler” attributes, such as height and distance, which students may more readily conceive of as being possible to measure. By taking into account students’ conceptions of task features, researchers can promote transfer of complex forms of mathematical reasoning, such as covariational reasoning.

## Keywords

Variational Reasoning Individual Quantity Ninth Grade Student Smooth Image Covariational Reasoning## Notes

### Acknowledgements

This research was supported in part by a Faculty Development Grant from the University of Colorado Denver. Opinions, findings, and conclusions are those of the authors. We thank Patrick Thompson and Reviewers for their comments on previous versions of this manuscript.

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