PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
First Semester Calculus Students’ Understanding of the Intermediate Value Theorem
Page: 2-537
In our calculus courses, we often see students perform poorly on problems involving the Intermediate Value Theorem (IVT), despite being a fairly basic concept. Thus, we designed a study to analyze students' conceptual understanding of the IVT and their ability to express the theorem in their own words. Two groups of students were video-taped while working on an activity designed to guide their construction of an initial understanding of the IVT, and fifty-four students were later asked to state the IVT in their own words. Both video data and student responses on the written work were analyzed to identify common themes. It was found that even though students were able to understand the concepts behind the Intermediate Value Theorem, they were unable to correctly describe the IVT in their own words, largely due to confusing the independent and dependent variables and issues with the if/then structure in a theorem.