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9:15 – 9:45 am |
Session 9 – Preliminary
Reports |
Marquis A |
Perturbing practices: The effects of novel didactic objects
on instruction Krysten Pampel The
advancement of technology has significantly changed the practices of numerous
professions, including teaching. When a school first adopts a new technology,
established classroom practices are perturbed. These perturbations can have
both positive and negative effects on teachersŐ abilities to teach
mathematical concepts with the new technology. Therefore, before new
technology can be introduced into mathematics classrooms, we need to better
understand how technology effects instruction. Using interviews and classroom
observations, I explored perturbations in classroom practice as an instructor
implemented novel didactic objects. In particular, the instructor was using
didactic objects designed to lay the foundation for developing a conceptual
understanding of rational functions through the coordination of relative
magnitudes of the numerator and denominator. The results are organized
according to a framework that captures leader actions, communication,
expectations of technology, roles, timing, student engagement, and mathematical
conceptions. 8 |
Marquis B |
Investigating student-learning gains from video lessons in
a flipped calculus course Cassie Williams and John
Siegfried The
flipped classroom has garnered attention in post-secondary mathematics in the
past few years, but much of the research on this model has been on student
perceptions rather than its effect on the attainment of learning goals.
Instead of comparing to a ŇtraditionalÓ model, in this study we investigated
student-learning gains in two flipped sections of Calculus I. In this
session, we will focus on the question of determining learning gains from
delivering content via video outside of the classroom. In particular, we will
compare student-learning gains after watching more conceptual videos versus
more procedural ones. We will share qualitative and quantitative data
gathered from surveys and quizzes, as well as results from in-class
assessments. 17 |
Marquis C |
StudentsŐ formalization of pre-packaged informal arguments Melissa Mills and Dov
Zazkis We
gave pairs of students enrolled in a graduate analysis class
tasks in which they were provided with a video taped informal argument for
why a result held and asked to produce a rigorous proof of this result. This
provided a lens into studentsŐ formalization process and the various roles
these informal arguments played in each pairŐs proving process. Comparing
across several pairs of participants revealed 3 distinct roles informal
arguments can play in proving, 1) solely as a starting point, 2) as a
reference that can be continually returned to during the proving process, and
3) as a convincing argument that does not inform the proving process. 43 |
Grand Ballroom 5 |
StudentsŐ Perceptions of Learning College Algebra Online
using Adaptive Learning Technology Lori Ogden Adaptive
learning technology was used in the teaching of an online college algebra
course. As students worked on the mastery goals set for them, the technology
helped students identify content that they already understood and other
content that they had yet to master. Goal orientation theory suggests that
when learning is mastery-oriented, a studentŐs motivation to learn may
improve (Ames & Archer, 1988). Qualitative methodology was used to
describe how students perceived the instruction of their college algebra
course and their learning in the course. Preliminary findings suggested that
an adaptive teaching approach may help build studentsŐ confidence because
they can control the pace of instruction and chose where to focus their
effort without drawing negative attention to themselves. 57 |
City Center A |
Effect of emphasizing a dynamic perspective on the formal
definition of limit Jeremy Sylvestre and
William Hackborn We
attempt to determine the efficacy of using an alternate, equivalent
formulation of the formal definition of the limit in a first-year university
calculus course in aiding the understanding of the definition and of
alleviating the development of common misconceptions concerning the limit. 60 |
City Center B |
Eliciting mathematiciansŐ pedagogical reasoning Christine Andrews-Larson,
Valerie Peterson and Rachel Keller Given
the prevalence of work in the RUME community to examine student thinking and
develop instructional materials based on this research, we argue it is
important to document the ways in which undergraduate mathematics instructors
make sense of this research to inform their own teaching. We draw on HornŐs
notion of pedagogical reasoning in order to analyze video recorded
conversations of over twenty mathematicians who elected to attend a workshop
on inquiry-oriented instruction at a large national mathematics conference.
In this context, we examine the questions: (1) How do undergraduate
mathematics instructors engage in efforts to make sense of inquiry-oriented
instruction? (2) How does variation in facilitation relate to instructorsŐ
reasoning about these issues? Preliminary findings suggest that differences
in facilitation relate to how participants engaged in the mathematics, and
that the nature of participantsŐ engagement with the mathematics was related
to their subsequent pedagogical reasoning. 85 |