Saturday

2:30 – 3:00 pm

Session 26 – Contributed Reports

Marquis A

A national investigation of Precalculus through Calculus 2

Chris Rasmussen, Naneh Apkarian, David Bressoud, Jessica Ellis, Estrella Johnson and Sean Larsen

We present findings from a recently completed census survey of all mathematics departments that offer a graduate degree (MasterŐs and/or PhD) in mathematics. The census survey is part of a larger project investigating department-level factors that influence student success over the entire progression of the introductory mathematics courses that are required of most STEM majors, beginning with Precalculus and continuing through the full year of single variable calculus. The findings paint a portrait of studentsŐ curricular experiences with Precalculus and single variable calculus, as well as the viewpoints held by departments of mathematics about that experience. We see that departments are not unaware of the value of particular features characteristic of more successful calculus programs, but that they are not always successful at implementation. However, our data also suggest hope for the future. Our work not only reveals what is currently happening, but also what is changing, how, and why.

Paper

23

Marquis B

When nothing leads to everything: Novices and experts working at the level of a logical theory

Stacy Brown

Building on Antonini and MariottiŐs (2008) theorization of mathematical theorem and research on studentsŐ meta-theoretical difficulties with indirect proof, this study examines mathematics majors and mathematicians: (1) responses and approaches to the validation tasks related to the assertion S*→S, when given a primary statement, S, of the form ∀n, P(n) ⇒ Q(n)) and a secondary statement, S* of the form used in proofs by contradiction; namely, ∄n, P(n) ∧ ~Q(n)); and, (2) selection of a statement to prove given S* and S. Findings indicate that novice proof writers responses differ from advanced students and mathematicians both in their approaches and selections, with novices tending to become entangled in natural language antonyms and to engage in the chunking of, rather than parsing of, quantified compound statements.

Paper

82

Marquis C

Effects of dynamic visualization software use on struggling studentsŐ understanding of calculus: The case of David

Julie Sutton and James Epperson

Using dynamic visualization software (DVS) may engage undergraduate students in calculus while providing instructors insight into student learning and understanding. Results presented derive from a qualitative study of nine students, each completing a series of four individual interviews. We discuss themes arising from interviews with David, a student exploring mathematical relationships with DVS who earns a C in calculus. David prefers to visualize when solving mathematical tasks and previous research suggests that such students, while not the ÔstarsŐ of their mathematics classroom, may have a deeper understanding of mathematical concepts that their non-visualizing peers. Using modified grounded theory techniques, we examine evidence of uncontrollable mental imagery, the need to refocus David on salient aspects of the animations, instances when DavidŐs apparent conceptual knowledge is neither fully connected to nor supported by procedural knowledge, and DavidŐs failure to transfer knowledge when DVS was not offered during assessment.

Paper

120