Southern California Conferences for Undergraduate Research

Southern California Conferences for Undergraduate Research

Model Analysis in Proof Schemes


Kelly Hartmann


Todd CadwalladerOlsker, Assistant Professor, California State University Fullerton

In this research, we use model analysis to examine students' knowledge of proof, specifically, their beliefs as to what types of proof are most appropriate. This method of analysis gives more information on students' consistency than basic statistics. We distributed a questionnaire to students in an introductory proof class in Spring 2012. As part of this questionnaire students to were asked to pick a result closest to how they would solve the proof themselves, one they would use to help a peer comprehend the proof, and the most mathematically rigorous for each proof. Each of the given proof responses falls into one of four models: empirical-visual, empirical-numeric, deductive-narrative, and deductive-symbolic. It is important for students of mathematics to adopt deductive proof schemes, as these proof schemes constitute proof for mathematicians. Model analysis allows us to examine students’ self-consistency in choosing from these models. For example, if 70% of a class chooses the deductive-symbolic proof, model analysis allows us to distinguish between the case where 70% of the class consistently chooses the expert proof, and that where all of the students pick the expert proof 70% of the time. Model analysis also allows us to create a class density matrix, and find eigenvectors and eigenvalues. These eigenvectors and eigenvalues contain information about the models held by the majority of students in the class

Presented by:

Kelly Hartmann


Saturday, November 17, 2012




Broome Library

Presentation Type:

Poster Presentation