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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. 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. 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. 120 |