CAREER: Understanding the Processes to Comprehend and Evaluate Argument Proofs

New Jersey
Descriptive
Causal
Math
Higher Education
Principal Investigator: 
Keith Weber
Project Overview
Background & Purpose: 

This study has three goals: (a) to understand the reasoning processes necessary to understand and evaluate written mathematical arguments; (b) to design instruction to teach students to use these processes effectively; and (c) to assess this instruction in a controlled teaching experiment.

Setting: 

This project has a higher education research setting and the population of interest is mathematics majors in their third year of college.

Research Design: 

This research project uses a comparative design to generate descriptive [observational] and causal [experimental] evidence. The data from the students reading the arguments consists of quantitative data (numbers from 1 to 5 indicating how convincing they found the arguments, categories for whether the argument was a proof or not), and interview data (they were thinking aloud as they did this). The latter were analyzed using an open-coding scheme. The teaching experiment will be analyzed using videotape analysis, using the methodologies common in design research. The controlled experiment will first code students responses to the pre- and post-test, and then analyze these results using traditional methods from quantitative statistics, primarily repeated measures ANOVAs.

Findings: 

One study compared the reading and learning strategies of successful and unsuccessful students. Successful students spend more time processing the definition by describing it in their own words and relating it to other concepts they are learned, understanding what a theorem is asserting prior to reading its proof, and understanding what a statement is asserting and why it is true prior to writing a proof. Less successful students are more likely to view the arguments they read as “templates” for solutions to be produced at a later time.

Publications & Presentations: 

K. Weber, A. Brophy, and K. Lin (2008). How do Undergraduates Learn about Advanced Mathematical Concepts by Reading Text? In Proceedings of the 11th Conference for Research in Undergraduate Mathematics Education. (http://www.rume.org/crume2008/weber_long.pdf)
(This paper was awarded the honorable mention as the second best paper of the conference).

K. Weber (2009). Mathematics Majors' Evaluations of Mathematical Arguments and Their Conceptions of Proof. To Appear in Proceedings of the 12th Conference for Research in Undergraduate Mathematics Education.

K. Weber (2009). Proving is not Convincing. To Appear in Proceedings of the 12th Conference for Research in Undergraduate Mathematics Education.

On the Web: 
Conference on Research in Undergraduate Mathematics Education