Prospective Secondary Mathematics Teachers' Understanding of ℜ2-to-ℜ Functions as Seen Through Multiple Representation Registers

• In Event: Mathematics Teacher Education Across Professional Roles

Abstract

Prospective secondary mathematics teachers’ (PSMTs’) understanding of ℜ2-to-ℜ functions was investigated using a task-based interview that required reasoning within and across registers (physical, graphical, symbolic). They were asked to: (a) describe graphs that represented given symbolic representations of functions of two variables; (b) choose the symbolic rules represented by sets of given three-dimensional graphs; and (c) connect their experience with the physical representation to the graphical and symbolic representations. Nuances of their conversations and treatments (Duval, 2006, 2017) involving ℜ2-to-ℜ functions included (a) flexibility in executing treatments within symbolic and graphing registers treating literal symbols as variables and as parameters) and (b) tendency to generalize conclusions of simpler examples rather than generalizing the conversion procedures.

Authors

• Mary Kathleen Heid, The Pennsylvania State University

• Matthew Black, Pennsylvania State University

• Rose Mary Zbiek, The Pennsylvania State University