PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
How Does Undergraduates’ Understanding Of The Function Concept Evolve During The Course Of A Semester?
Page: 557
Functions are a crucial topic in the study of mathematics. Research has found that a lack of deep understanding of functions is one of the main reasons why students struggle in calculus (Eisenberg, 1991; Ferrini-Mundy & Graham, 1991; Lauten, Graham, Ferrini-Mundy, 1994; McDonald, Mathews, & Strobel, 2000; Monk, 1994). In light of these studies, we investigate – using traditional paper- and-pencil assessments, concept maps, and an interview – what pre-calculus students’ understanding of functions is, to what extent students have a repertoire of functions at their disposal, how students’ understanding evolves over a semester, and what non-traditional assessments can tell us about this understanding. We found that (1) As Williams (1998) suggested, concept map assessments do reveal something that traditional assessments do not; (2) participants have trouble giving non-examples of functions, and (3) there does not seem to be a major change in participants’ understanding of functions over time.