PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Generalizing Calculus Ideas from Two Dimensions to Three: How Multivariable Calculus Students Think about Domain and Range
Page: 593
We analyzed multivariable calculus students’ meanings for domain and range and their generalization of that meaning as they reasoned about domain and range of multivariable functions. We found that students’ thinking about domain and range fell into three broad categories: input/output, independent/dependent variables, and/or as attached to specific variables. We used Ellis’ (2007) actor-oriented generalizations framework to characterize how students generalized their meanings for domain and range from single-variable to multivariable functions. This framework focuses on the process of generalization – what students see as similar between ideas in multiple contexts. We found that students generalized their meanings for domain and range by relating objects, extending their meanings, using general principles and rules, and using/modifying previous ideas. Our results about how students understand and generalize the concepts of domain and range imply that the domain and range of multivariable functions is a topic instructors should explicitly address.