Student Understanding and Generalization of Functions from Single to Multivariable Calculus

Students struggle with the concept of functions and the notation associated with it in various mathematical contexts. This thesis investigates student understanding of function notation through their generalization of single variable functions to multivariable functions in a variety of situations. Semi-structured student interviews were conducted and analyzed through a framework using concept image and concept definition coupled with an actor-oriented generalization taxonomy. The findings suggest that students relate back to forms and situations from single variable to assign meaning to multivariable functions. Several teaching implications are suggested based on the trends that emerged in how students understand functions and notation