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2:05  2:35 pm 
Session 2
– Contributed Reports

Marquis A 
StudentsÕ explicit, unwarranted assumptions in ÒproofsÓ of
false conjectures Kelly Bubp Although
evaluating, refining, proving, and refuting conjectures are important aspects
of doing mathematics, many students have limited experiences with these
activities. In this study, undergraduate students completed proveordisprove
tasks during taskbased interviews. This paper explores the explicit,
unwarranted assumptions made by six students on tasks involving false
statements. In each case, the student explicitly assumed an exact condition
necessary for the statement in the task to be true although it was not a
given hypothesis. The need for an ungiven assumption did not prompt any of
these students to think the statement may be false. Through prompting from
the interviewer, two students overcame their assumption and correctly solved
the task and two students partially overcame it by constructing a solution of
cases. However, two other students were unable to overcome their assumptions.
Students making explicit, unwarranted assumptions seems to be related to
their limited experience with conjectures. 11 
Marquis B 
Physics: Bridging the symbolic and embodied worlds of
mathematical thinking Clarissa Thompson, Sepideh
Stewart and Bruce Mason Physics
spans understanding in three domains – the Embodied (Real) World, the
Formal (Laws) World, and the Symbolic (Math) World. Expert physicists fluidly
move among these domains. Deep, conceptual understanding and problem solving
thrive in fluency in all three worlds and the facility to make connections
among them. However, novice students struggle to embody the symbols or
symbolically express the embodiments. The current research focused on how a
physics instructor used drawings and models to help his students develop more
expertlike thinking and move among the worlds. 41 
Marquis C 
Inquirybased learning in mathematics: Negotiating the
definition of a pedagogy Zachary Haberler and
Sandra Laursen Inquirybased
learning is one of the pedagogies that has emerged in mathematics as an
alternative to traditional lecturing in the last two decades. There is a
growing body of research and scholarship on inquirybased learning in STEM
courses, as well as a growing community of practitioners of IBL in
mathematics. However, despite the growth of IBL research and practice in
mathematics, wide uptake of IBL remains hamstrung in part by the lack of a
sophisticated discussion of its definition. This paper offers a first step
toward addressing this problem by describing how a group of IBL practitioners
define IBL, how they adopt IBL to fit their specific teaching needs, and how
differences in definitions and perceptions of IBL have constrained and
enabled its diffusion to new instructors. 55 
Grand Ballroom 5 
Student resources pertaining to function and rate of change
in differential equations George Kuster While
the importance of student understanding of function and rate of change are
themes across the research literature in differential equations, few studies
have explicitly focused on how student understanding of these two topics grow
and interface with each other while students learn differential equations.
Extending the perspective of Knowledge in Pieces (diSessa, 1993) to student
learning in differential equations, this research explores the resources
relating to function and rate of change that students use to solve
differential equations tasks. The findings reported herein are part of a
larger study in which multiple students enrolled in differential equations
were interviewed periodically throughout the semester. The results culminate
with two sets of resources a student used relating to function and rate of
change and implications for how these concepts may come together to afford an
understanding of differential equations. 124 