Title

A covariational understanding of function: Putting a horse before the cart

Document Type

Article

Publication Date

2018

Journal Title

For the Learning of Mathematics

Abstract

Supporting students developing understandings of function has been a notoriously elusive task in mathematics education. We present Thompson and Carlson’s (2017) description of a covariational meaning of function and provide an example of a student who maintains meanings compatible with this description. We use this student’s activity to illustrate nuances in a covariational meaning of function and to highlight how such meanings can be powerful for students. In doing so, we argue that a student who has develop meanings compatible with the covariational meaning of function presented by Thompson and Carlson has the foundational meanings needed to understand a formal definition of function (i.e. the horse needed to pull the cart).

Published Citation

Paoletti, T. & Moore, K. C. (2018) A covariational understanding of function: Putting a horse before the cart. For the Learning of Mathematics, 38(3), 37–43.

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