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4:20 – 4:50 pm |
Session 5 – Preliminary
Reports |
Marquis A |
Use of strategic knowledge in a mathematical bridge course:
Differences between an undergraduate and graduate Darryl Chamberlain Jr. and
Draga Vidakovic The
ability to construct proofs has become one of, if not the, paramount
cognitive goal of every mathematical science major. However, students
continue to struggle with proof construction and, particularly, with proof by
contradiction construction. This paper is situated in a larger research
project on the development of an individualÕs understanding of proof by
contradiction in a transition-to-proof course. The purpose of this paper is
to compare proof construction between two students, one graduate and one
undergraduate, in the same transition-to-proof course. The analysis utilizes
Keith WeberÕs framework for Strategic Knowledge and shows that while both
students readily used symbolic manipulation to prove statements, the graduate
student utilized internal and flexible procedures to begin proofs as opposed
to the external and rigid procedures utilized by the undergraduate. 7 |
Marquis B |
Classifying combinations: Do students distinguish between
different types of combination problems? Elise Lockwood, Nicholas
Wasserman and William McGuffey In
this paper we report on a survey designed to test whether or not students
differentiated between two different types of problems involving combinations
– problems in which combinations are used to count unordered sets of
distinct objects (a natural, common way to use combinations), and problems in
which combinations are used to count ordered sequences of two (or more)
indistinguishable objects (a less obvious application of combinations). We
hypothesized that novice students may recognize combinations as appropriate
for the first type but not for the second type, and our results support this
hypothesis. We briefly discuss the mathematics, share the results, and offer
implications and directions for future research. 30 |
Marquis C |
A case study of developing self-efficacy in writing proof
frameworks Ahmed Benkhalti, Annie
Selden and John Selden This
case study documents the progression of one non-traditional individualÕs
proof-writing through a semester. We analyzed the videotapes of this
individualÕs one-on-one sessions working through our course notes for an
inquiry-based transition-to-proof course. Our theoretical perspective
informed our work with this individual and included the view that proof
construction is a sequence of (mental, as well as physical) actions. It also
included the use of proof frameworks as a means of initiating a written
proof. This individualÕs early reluctance to use proof frameworks, after an
initial introduction to them, was documented, as well as her later acceptance
of, and proficiency with, them. By the end of the first semester, she had
developed considerable facility with both the formal-rhetorical and
problem-centered parts of proofs and a sense of self-efficacy. 44 |
Grand Ballroom 5 |
Results from the Group Concept Inventory: Exploring the
role of binary operation in introductory group theory task performance Kathleen Melhuish and Jodi
Fasteen Binary
operations are an essential, but often overlooked topic in advanced
mathematics. We present results related to student understanding of operation
from the Group Concept Inventory, a conceptually focused, group theory
multiple-choice test. We pair results from over 400 student responses with 30
follow-up interviews to illustrate the role binary operation understanding
played in tasks related to a multitude of group theory concepts. We conclude
by hypothesizing potential directions for the creation of a holistic binary
operation understanding framework. 56 |
City Center A |
Online calculus homework: The student experience Andrew Krause The
MAA advertises that the online homework system WeBWorK is used successfully
at over 700 colleges and universities, and the institution selected for my
study has implemented WeBWorK universally across all calculus courses. I used
a mixed method approach to examine how students experience online calculus
homework in order to provide insights as to how online homework might be
improved. In particular, I examined the behaviors, perceptions, and resources
associated with online homework. A survey was administered to all students in
the mainstream calculus course that provides quantitative information about
general trends and informs further questioning. For example, more than half
of students reported that they never study calculus with classmates nor in
office hours. In tandem with the large survey, I also closely studied the
online homework experience of 4 students through screen recordings and
interviews. 68 |
City Center B |
StudentsÕ symmetric ability in relation to their use and
preference for symmetry heuristics in problem solving Meredith Muller and Eric
Pandiscio Advanced
mathematical problem solving is marked by efficient and fluid use of multiple
solution strategies. Symmetric arguments are apt heuristics and eminently
useful in mathematics and science fields. Research suggests that mathematics
proficiency is correlated with spatial reasoning. We define symmetric ability
as fluency with mentally visualizing, manipulating, and making comparisons
among 2D objects under rotation and reflection. We hypothesize that symmetric
ability is a distinct sub-ability of spatial reasoning which is more
accessible to students due to inherent cultural biases for symmetric balance.
Do students with varying levels of symmetric ability use or prefer symmetric
arguments in problem solving? How does symmetric ability relate to insight in
problem solving? Results from a pilot study indicate that, among
undergraduates, there is high variation in symmetric ability. Further,
students with higher symmetric ability tend towards more positive attitudes
about mathematics. Methods, future research, and implications are discussed. 49 |