for the learning of mathematics

an international journal of mathematics education

Teo Paoletti ,  Kevin C. Moore - Vol. 38 Num. 3 (2018)
 A covariational understanding of function: putting a horse before the cart


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. We argue a student who has developed meanings compatible with a covariational meaning of function has the foundational meanings needed to understand a formal definition of function (i.e. the horse needed to pull the cart).