How Mathematicians Determine if an Argument Is a Valid Proof

By Keith Weber. 2008

183 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e86ae14f1d9ded0ecef7deeb5c39aaf572fa71f6

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Citations in the corpus

The Effect of Authority on the Persuasiveness of Mathematical Arguments (2009, background): “However, as discussed earlier, Weber (2008) noted that some mathematicians claimed that they might use different methods to evaluate a student-generated proof compared to a proof written by a mathematician.”
Mathematicians’ perspectives on their pedagogical practice with respect to proof (2012, background): “Regardless of the cause, there is a paucity of research on the processes that students should engage in when reading proofs [27,28] and more research in this area is needed.”
Lectures in Advanced Mathematics: Why Students Might Not Understand What the Mathematics Professor Is Trying to Convey. (2016, background): “While this is clearly an important function of proof, de Villiers (1990) emphasized that this was not the primary function of proof in mathematics (c.f., Mejia-Ramos & Weber, 2014; Weber, 2008; Weber & Mejia-Ramos, 2011).”
Why and how mathematicians read proofs: an exploratory study (2011, methodology): “Using the data from this study, as well as data from a separate study (Weber, 2008) and the philosophical literature on mathematical proof, we identify three general strategies that mathematicians employ when reading proofs: appealing to the authority of other mathematicians who read the proof, line”
How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition (2014, background): “Weber (2008) presented eight mathematicians with six to eight arguments and asked them to determine if these proofs were correct.”
Mathematics Majors' Perceptions of Conviction, Validity, and Proof (2010, background): “Several researchers (e.g., Hazzan & Zaskis, 2003; Mamona-Downs & Downs, 2005; Selden & Selden, 2003; Weber, 2008) have noted that although there have been many studies in which students were asked to construct proofs, the literature on how students read proofs has been comparatively sparse.”
Doctoral students’ use of examples in evaluating and proving conjectures (2008, background): “Mason and Pimm (1984) noted that treating an example as generic requires seeing the general in the particular, and Weber (2008) again offered illustrations of cases in which mathematicians use generic examples in their validation of possibly incorrect proofs.”
Expert and Novice Approaches to Reading Mathematical Proofs (2012, methodology): “More generally, theorists have proposed two possible drawbacks with verbal protocol methods such as those adopted by Selden and Selden (2003) and Weber (2008).”
Beauty Is Not Simplicity: An Analysis of Mathematicians' Proof Appraisals (2015, background): “Unfortunately, a great deal of empirical research has conclusively shown that humans are extremely bad at accurately reporting their thought processes (Dutton & Aron, 1974; Hoffman, 1992; Horsey, 2002; Nisbett & Wilson, 1977), including in mathematics (Inglis & Alcock, 2012; Weber, 2008).”
Why and how mathematicians read proofs: further evidence from a survey study (2014, methodology): “For instance, in Weber (2008), one mathematician was confident that an assertion was correct after checking for several examples, but indicated that he only did this since these types of checks were reliable in the context of number theory; he would not do the same in topology, his area of research.”
The Need for Proof and Proving: Mathematical and Pedagogical Perspectives (2011, background): “Often mathematicians undertake a proof because they are personally convinced of the truth or validity of a mathematical assertion, having explored it empirically and through its structure (de Villiers 1990, 2010 ; Weber 2008 ) .”
Research-based interventions in the area of proof: the past, the present, and the future (2017, background): “At the core of all seven contributions in this Special Issue is the fundamental mathematical concept of proof whose meaning has been the subject of different perspectives in the mathematics education literature (for a summary of some of these perspectives, see: Balacheff, 2002; Stylianides et al., 2”
What Do We Mean by Mathematical Proof (2011, background): “For example, the graphical argument 8It is to this context that Weber [58] adds two other uses of proof in the mathematics classroom: proofs that justify the use of a definition or axiomatic structure, and proofs that illustrate a technique.”