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Session 1
– Contributed Reports

Marquis A 
Prospective teachersÕ evaluations of studentsÕ proofs by
mathematical induction Hyejin Park This
study examines how prospective secondary teachers validate several proofs by
mathematical induction (MI) from hypothetical students and how their work
with proof validations relates to how they grade their studentsÕ proofs. When
asked to give criteria for evaluating a studentÕs argument, participants
wished to see a correct base step, inductive step, and algebra. However,
participants prioritized the base step and inductive step over assessing the
correctness of the algebra when validating and grading studentsÕ arguments.
All of the participants gave more points to an argument that presented only
the inductive step than to an argument that presented only the base step. Two
of the participants accepted the studentsÕ argument addressing only the
inductive step as a valid proof. Further studies are needed to determine how
prospective teachers evaluate their studentsÕ arguments by MI if many
algebraic errors are present, especially in the inductive step. 1 
Marquis B 
Analyzing studentsÕ interpretations of the definite
integral as concept projections Joseph F. Wagner This
study of beginning and upperlevel undergraduate physics students extends
earlier research on studentsÕ interpretations of the definite integral. Using
WagnerÕs (2006) transferinpieces framework and the notion of a concept
projection, finegrained analyses of studentsÕ understandings of the definite
integral reveal a greater variety and sophistication in some studentsÕ use of
integration than previous researchers have reported. The dual purpose of this
work is to demonstrate and develop the utility of concept projections as a
means of investigating knowledge transfer, and to critique and build on the
existing literature on studentsÕ conceptions of integration. 9 
Marquis C 
Organizational features that influence departmentsÕ uptake
of studentcentered instruction: Case studies from inquirybased learning in
college mathematics Sandra Laursen Active
learning approaches to teaching mathematics and science are known to increase
student learning and persistence in STEM disciplines, but do not yet reach
most undergraduates. To broadly engage college instructors in using these
researchsupported methods will require not only professional development and
support for individuals, but the engagement of departments and institutions
as organizations. This study examines four departments that implemented
inquirybased learning (IBL) in college mathematics, focusing on the
question, ÒWhat explicit strategies and implicit departmental contexts help
or hinder the uptake of IBL?Ó Based on interview data and documents, the four
departmental case studies reveal strategies used to support IBL instructors
and engage colleagues not actively involved. Comparative analysis highlights
how contextual features supported (or not) the spread and sustainability of
these teaching reforms. We use Bolman and DealÕs (1991) framework to analyze
the structural, political, human resource and symbolic elements of these
organizational strategies and contexts. 62 
Grand Ballroom 5 
An interconnected framework for characterizing symbol sense Margaret Kinzel Algebraic
notation can be a powerful mathematical tool, but not all seem to develop
Òsymbol sense,Ó the ability to use that tool effectively across situations.
Analysis of interview data identified three interconnected viewpoints:
looking at, with, and through the notation. The framework and implications
for instruction will be presented. 27 