Thursday

1:25 - 1:55 pm

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

Paper

Marquis B

Analyzing studentsÕ interpretations of the definite integral as concept projections

Joseph F. Wagner

This study of beginning and upper-level undergraduate physics students extends earlier research on studentsÕ interpretations of the definite integral. Using WagnerÕs (2006) transfer-in-pieces framework and the notion of a concept projection, fine-grained 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

Paper

Marquis C

Organizational features that influence departmentsÕ uptake of student-centered instruction: Case studies from inquiry-based 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 research-supported 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 inquiry-based 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.

Paper

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.

Paper

27