Profile: Keith H. Weber

Departments

Department of Learning & Teaching

Education

Ph.D, Carnegie Mellon University

Publications

K. Weber and J.P. Mejia-Ramos (in press). Why and how mathematicians read proofs. To appear in Educational Studies in Mathematics.

K. Weber (in press). Mathematics' majors perceptions of conviction, validity, and proof. To appear in Mathematical Thinking and Learning.

I. Radu and K. Weber (in press). Refinements in students' reasoning on completed infinite interative processes. To appear in Educational Studies in Mathematics.

K. Weber (2009). How syntactic reasoners can develop understanding, evaluate conjectures, and construct counterexamples in advanced mathematics. Journal of Mathematical Behavior, 28, 200-208.

K. Weber (2008). How mathematicians determine if an argument is a valid proof.  Journal for Research in Mathematics Education, 39, 431-459.

K. Weber, C. Maher, A. Powell, and H.S. Lee (2008). Learning opportunities from group discussions: Warrants become the objects of debate. Educational Studies in Mathematics, 68, 247-261.

K. Weber (2006). Investigating and teaching the thought processes used to construct proofs. Research in Collegiate Mathematics Education, 6, 197-232.

K. Weber and L. Alcock (2004). Semantic and syntactic proof productions. Educational Studies in Mathematics, 56, 209-234.

K. Weber (2001). Student difficulties in constructing proofs: The need for strategic knowledge. Educational Studies in Mathematics, 48, 101-119.

Research Inititatives

The central purpose of my research is to understand the processes used in advanced mathematical thinking, particular those with reading, writing, and understanding mathematical proof. I try to specify what understandings, skills, and beliefs undergraduates should develop in their advanced mathematics courses, and compare these with the understandings, skills, and beliefs that undergraduates actually possess. This can be useful in specifying deficiencies in instruction in upper-level mathematics courses.

My current project involves students' evaluation and comprehension of mathematical arguments. The first part of this project consists of identifying the skills and dispositions that mathematics majors often lack that prevent them from reading mathematical arguments appropriately. The second part involves developing instruction to address these difficulties.