This paper explores students' ways of thinking about the average rate of change of a multivariable function and how they generalize those ways of thinking from rate of change of single-variable functions. I found that while students thought about the average rate of change of a multivariable function as the change in the independent quantity with respect to the changes in the dependent quantities, they had difficulty determining a process to assign a value to that rate of change. Most tried to represent the average rate of change as a singular expression, generalizing the ?y/?x expression to create expressions of the form ?z/[?x and ?y], yet did not appear to have a sense of what they believed they were measuring. This suggests that quantitative reasoning, or lack thereof, was at the heart of the students' generalizations. A pedagogical implication of this research is that students' natural tendency to try to determine a singular expression for the average rate of change of a multivariable function could serve as useful as motivating the need to hold a variable fixed. [For the complete proceedings, see ED583989.]