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3:25 – 3:55 pm |
Session 16
– Preliminary Reports |
Marquis A |
Effect of teacher prompts on student proof construction Margaret Morrow and Mary
Shepherd Many
students have difficulty learning to construct mathematical proofs. In an
upper level mathematics course using inquiry based methods, while this is
some research on the types of verbal discourse in these courses, there is
little, if any, research on teachersŐ written comments on studentsŐ work.
This paper presents some very preliminary results from ongoing analysis from
one teacherŐs written prompts on studentsŐ rough drafts of proofs for an
Abstract Algebra course. The teacher prompts will initially be analyzed
through a framework proposed by Blanton & Stylianou (2014) for verbal
discourse and the framework will be modified in the course of the analysis.
Can we understand if a type of prompt is ŇbetterÓ in some sense in getting
students to reflect on their work and refine their proofs? It is anticipated
that teacher prompts in the form of transactive questions are more effective
in helping students construct proofs. 64 |
Marquis B |
Secondary teachers confronting mathematical uncertainty:
Reactions to a teacher assessment item on exponents Heejoo Suh, Heather Howell
and Yvonne Lai Teaching
is inherently uncertain, and teaching secondary mathematics is no exception.
We take the view that uncertainty can present opportunity for teachers to
refine their practice, and that undergraduate mathematical preparation for
secondary teaching can benefit from engaging pre-service teachers in tasks
presenting uncertainty. We examined 13 secondary teachersŐ reactions to
mathematical uncertainty when engaged with concepts about extending the
domain for the operation of exponentiation. The data are drawn from an
interview-based study of items developed to assess mathematical knowledge for
teaching at the secondary level. In our findings, we characterize ways in
which teachers either denied or mathematically investigated the uncertainty.
Potential implications for instructors include using mathematical uncertainty
to provide an opportunity for undergraduates to learn both content and
practices of the Common Core State Standards. The proposal concludes with
questions addressing how undergraduate mathematics instructors could use
uncertainty as a resource when teaching preservice teachers. 70 |
Marquis C |
StudentsŐ concept image of tangent line compared to their
understanding of the definition of the derivative Brittany Vincent and Vicki
Sealey Our
research explores first-semester calculus students' understanding of tangent
lines and the derivative concept through a series of three interviews
conducted over the course of one semester. Using a combination of Zandieh's
(2000) derivative framework and Tall and Vinner's (1981) notions of concept
image and concept definition, our analysis examines the role that students'
concept image of tangent lines plays in their conceptual understanding of the
derivative concept. Preliminary results seem to indicate that students are
more successful when their concept image of tangent includes the limiting
position of secant lines, as opposed to a tangent line as the line that
touches the curve at one point. 89 |
Grand Ballroom 5 |
Unraveling, synthesizing and reweaving: Approaches to
constructing general statements. Duane Graysay Learning
progressions for the development of the ability to look for and make use of
mathematical structure would benefit from understanding how students in
mathematics-focused majors might construct such structures in the form of
general statements. The author recruited ten university students to
interviews focused on tasks that asked for the reconstruction of a general
statement to accommodate a broader domain. Through comparative analysis of
responses, four major categories of approaches to such tasks were identified.
This preliminary report describes in brief those four categories. 102 |
City Center A |
Student conceptions of definite integration and
accumulation functions Brian Fisher, Jason
Samuels and Aaron Wangberg Prior
research has shown several common student conceptualizations of integration
among undergraduates. This report focuses on data from a written assessment
of studentsŐ views on definite integration and accumulation functions to
categorize student conceptualizations and report on their prevalence among
the undergraduate population. Analysis of these results found four
categorizations for student descriptions of definite integrals:
antiderivative, area, an infinite sum of one dimensional pieces, and a limit
of approximations. When asked about an accumulation function, student
responses were grouped into three categorizations: those based on the process
of calculating a single definite integral, those based on the result of
calculating a definite integral, and those based on the relationship between
changes in the input and output variables of the accumulation function. These
results were collected as part of a larger study on student learning in
multivariable calculus, and the implications of these results on
multivariable calculus will be considered. 113 |
City Center B |
Supporting students in seeing sequence convergence in
Taylor series convergence Jason Martin, Matthew
Thomas and Michael Oehrtman Virtual
manipulatives designed to increase student understanding of the concepts of
approximation by Taylor polynomials and convergence of Taylor series were
used in calculus courses at multiple institutions. 225 students responded to
tasks requiring graphing Taylor polynomials, graphing Taylor series, and
describing relationships between different notions of convergence. We detail
significant differences observed between students who used virtual manipulatives
and those that did not. We propose that the use of these virtual
manipulatives promotes an understanding of Taylor series supporting an
understanding consistent with the formal definition of pointwise convergence. 115 |