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  1. Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem?Annie Selden - 2003 - Journal for Mathematics Education Research 34 (1):4-36.
    We report on an exploratory study of the way eight mid-level undergraduate mathematics majors read and reflected on four student-generated arguments purported to be proofs of a single theorem. The results suggest that mid-level undergraduates tend to focus on surface features of such arguments and that their ability to determine whether arguments are proofs is very limited -- perhaps more so than either they or their instructors recognize. We begin by discussing arguments (purported proofs) regarded as texts and validations of (...)
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  • Teaching proving by coordinating aspects of proofs with students' abilities.Annie Selden & John Selden - 2009 - In Despina A. Stylianou, Maria L. Blanton & Eric J. Knuth (eds.), Teaching and learning proof across the grades: a K-16 perspective. New York: Routledge. pp. 339--354.
    In this chapter we introduce concepts for analyzing proofs, and for analyzing undergraduate and beginning graduate mathematics students’ proving abilities. We discuss how coordination of these two analyses can be used to improve students’ ability to construct proofs. -/- For this purpose, we need a richer framework for keeping track of students’ progress than the everyday one used by mathematicians. We need to know more than that a particular student can, or cannot, prove theorems by induction or contradiction or can, (...)
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  • Supporting Mathematical Argumentation and Proof Skills: Comparing the Effectiveness of a Sequential and a Concurrent Instructional Approach to Support Resource-Based Cognitive Skills.Daniel Sommerhoff, Ingo Kollar & Stefan Ufer - 2021 - Frontiers in Psychology 11.
    An increasing number of learning goals refer to the acquisition of cognitive skills that can be described as ‘resource-based,’ as they require the availability, coordination, and integration of multiple underlying resources such as skills and knowledge facets. However, research on the support of cognitive skills rarely takes this resource-based nature explicitly into account. This is mirrored in prior research on mathematical argumentation and proof skills: Although repeatedly highlighted as resource-based, for example relying on mathematical topic knowledge, methodological knowledge, mathematical strategic (...)
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