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A Procedural Route toward Understanding the Concept of Proof
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Weber, Keith – International Group for the Psychology of Mathematics Education, 2003
In this paper, I describe how undergraduates can develop their understanding of the concept of proof by viewing the act of proving as a procedure. Such undergraduates first understand proof as an algorithm, or a step-by-step mechanical prescription for proving certain types of statements. The students can then condense this algorithm into a…
Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Undergraduate Students
A Framework for Describing the Processes that Undergraduates Use to Construct Proofs
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Weber, Keith – International Group for the Psychology of Mathematics Education, 2004
The purpose of this paper is to offer a framework for categorizing and describing the different types of processes that undergraduates use to construct proofs. Based on 176 observations of undergraduates constructing proofs collected over several studies, I describe three qualitatively different ways that undergraduates use to construct proofs. In…
Descriptors: Undergraduate Students, Cognitive Processes, Mathematics Skills, College Mathematics