Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem?

By Annie Selden, J. Selden. 2003

373 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/14e5ad3a547cf7128bbbe4256ed9fb735e1978d9

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Citations in the corpus

An assessment model for proof comprehension in undergraduate mathematics (2011, positive): “This finding is consistent with calls from other researchers (e.g., MamonaDowns & Downs, 2005; Selden & Selden, 2003) who have suggested that more research on proof reading is needed.”
Why and how mathematicians read proofs: further evidence from a survey study (2014, background): “However, research has shown that when reading proofs, students find them to be confusing or pointless (e.g., Harel, 1998; Porteous, 1986; Rowland, 2001) and cannot distinguish a valid proof from an invalid argument (Selden & Selden, 2003; Weber, 2009).”
Mathematics Majors' Perceptions of Conviction, Validity, and Proof (2010, background): “…who made these errors did so because (a) they did not check if the assumptions used in a proof were appropriate (a finding also reported in Selden and Selden, 2003), (b) they focused on the correctness of the assertions within the proof but not on what mathematical principles were used to…”
How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition (2014, background): “Selden and Selden (2003) remarked on “the unusual degree of agreement about the correctness of arguments and the truth of theorems arising from the validation process” (p. 7); they also claimed that validity is a function only of the argument and not of the reader: “Mathematicians say that an…”
The Mathematical Nature of Reasoning-and-Proving Opportunities in Geometry Textbooks (2014, background): “Furthermore, it is noteworthy that much of this research was conducted with students in or beyond secondary geometry (e.g., Chazan, 1993; Herbst & Brach, 2006; Selden & Selden, 2003; Soucy McCrone & Martin, 2009).”
Lectures in Advanced Mathematics: Why Students Might Not Understand What the Mathematics Professor Is Trying to Convey. (2016, background): “Students' propensity to focus on calculation rather than the overarching ideas of the proof has been documented in the proof reading literature (e.g., Inglis & Alcock, 2012; Selden & Selden, 2003).”
Doctoral students’ use of examples in evaluating and proving conjectures (2008, background): “…they did not (and would not be expected to) encounter any of the well-known problems with unpacking the logic of mathematical statements cited by Selden & Selden (1995; 2003) and, unlike the preservice teachers studied by Zazkis (2001), had no problem using formal mathematical terms to express…”
A research framework for creative and imitative reasoning (2008, background): “questions, assenting to claims, constructing subproofs, remembering and interpreting other theorems and definitions, complying with instructions, and feelings of rightness or wrongness (Selden and Selden 2003).”
Undergraduate Students’ Understanding of Proof: Relationships Between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof (2015, background): “, Knuth 2002a, b; Martin and Harel 1989), and undergraduate students’ ability to judge validity of proofs (e.g., Morris 2002; Selden and Selden 2003).”
Proof in School Mathematics: Insights from Psychological Research into Students' Ability for Deductive Reasoning (2008, neutral): “…2000; Knuth, Choppin, Slaughter, & Sutherland, 2002) and university students (see, e.g., Epp, 1987; Harel & Sowder, 1998; Martin & Harel, 1989; Selden & Selden, 2003; Simon & Blume, 1996; Stylianides, Stylianides, & Philippou, 2004, 2007; Weber, 2001) face with proof, thereby proposing that…”