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9:15 – 9:45 am |
Session 20
– Preliminary Reports |
Marquis A |
Calculus students' understanding of logical implication and
its relationship to their understanding of calculus theorems Joshua Case and Natasha
Speer In
undergraduate mathematics, deductive reasoning is an important skill for
learning theoretical ideas and is primarily characterized by the concept of
logical implication. This plays roles whenever theorems are applied, i.e.,
one must first check if a theoremÕs hypotheses are satisfied and then make
correct inferences. In calculus, students must learn how to apply theorems.
However, most undergraduates have not received instruction in propositional
logic. How do these students comprehend the abstract notion of logical
implication and how do they reason conditionally with calculus theorems?
Results from our study indicated that students struggled with notions of
logical implication in abstract contexts, but performed better when working
in calculus contexts. Strategies students used (successfully and unsuccessfully)
were characterized. Findings indicate that some students use Ņexample
generatingÓ strategies to successfully determine the validity of calculus
implications. Background on current literature, results of our study, further
avenues of inquiry, and instructional implications are discussed. 28 |
Marquis B |
Service-learning in a precalculus class: Tutoring improves
the course performance of the tutor. Ekaterina Yurasovskaya We
have introduced an experiment: as part of a Precalculus class, university
students have been tutoring algebra prerequisites to students from the
community via an academic service-learning program. The goal of the
experiment was to improve university studentsÕ mastery of basic algebra and
to quantitatively describe benefits of service-learning to studentsÕ
performance in mathematics. At the end of the experiment, we observed 59%
decrease of basic algebraic errors between experimental and control sections.
The setup and analysis of the study have been informed by the theoretical
research on service-learning and peer learning, both grounded in the
constructivist theory of John Dewey. 46 |
Marquis C |
How well prepared are preservice elementary teachers to
teach early algebra? Funda Gonulates, Leslie
Nabors Olah, Heejoo Suh, Xueying Ji and Heather Howell This
study aims to investigate undergraduate preservice teachersÕ knowledge in the
domain of early algebra. We conducted 90-minute clinical interviews with 15
preservice teachers in their fourth year of a five-year teacher preparation
program. These interview sessions collected preservice teachersÕ responses to
a series of assessment items designed to measure their content knowledge for
teaching early algebra, with follow up questions probing their content-based
reasoning. We also collected self-report of their preparation in this content
area. We found that the participants had difficulty on the items targeting
the meaning and use of operational properties and also in evaluating the
appropriate use of the equal sign when presented with different uses in
student work. They reported that they had few opportunities to learn about early
algebra as mathematical content and as a topic to teach. These findings can
inform the development of teacher-education curricula and support materials. 79 |
Grand Ballroom 5 |
Undergraduate students proof-reading strategies: A case
study at one research institution Eyob Demeke and Mateusz
Pacha-Sucharzewski Weber
(2015) identified five effective proof-reading strategies that undergraduate
students in proof-based courses can use to facilitate their proof
comprehension. Following WeberÕs (2015) study, we designed a survey study to
examine how undergraduate studentsÕ proof-reading strategies relate to what
proficient learners of mathematics (mathematics professors and graduate
students in mathematics) say undergraduates should employ when reading
proofs. Our preliminary findings are: (i) Majority of the professors in our
study claimed that undergraduates should use the strategies identified in
WeberÕs (2015) study, (ii) ProfessorsÕ response significantly differed from
undergraduatesÕ in only two of the five proof-reading strategies described in
WeberÕs (2015) study (attempting to prove theorem before reading its proof
and illustrating confusing assertions with examples), and finally (iii)
Undergraduate students, for the most part, tend to agree with their
professorsÕ preferred proof-reading strategies. 106 |
City Center A |
Beyond procedures: Quantitative reasoning in upper-division
Math Methods in Physics Michael Loverude Many upper-division physics courses have
as goals that students should Ōthink like a physicist.Õ While this is not well-defined, most would agree that thinking like a
physicist includes quantitative reasoning skills: considering limiting cases,
dimensional analysis, and using approximations. However, there is often
relatively little curricular support for these practices and many instructors
do not assess them explicitly. As part of a project to investigate student
learning in math methods, we have developed a number of written questions
testing the extent to which students in an upper-division course in
Mathematical Methods in Physics can employ these skills. Although there are
limitations to assessing these skills with written questions, they can
provide insight to the extent to which students can apply a given skill when
prompted. 112 |
City Center B |
A case for whole class discussions: Two case studies of the
interaction between instructor role and instructor experience with a
research-informed curriculum Aaron Wangberg, Elizabeth
Gire, Brian Fisher and Jason Samuels This
paper presents case studies of two instructors implementing a research
informed multivariable calculus curriculum. The analysis, structured around
social constructivist concepts, focuses on the interactions between the roles
of the instructor in facilitating student discussions and the instructorsÕ
experiences with the activities. This study is a part of an effort to
evaluate and improve the projectÕs effectiveness in supporting instructors in
implementing the activities to promote rich discussions with and among
students. We find these instructors to be focused on their roles as
facilitators for student-centered small-group discussion and that they choose
not to have of whole class discussions. We argue that initiating whole class
discussions would address concerns and negative experiences reported by the
instructors. 109 |