Semantic and Syntactic Proof Productions

By Keith Weber, Lara Alcock. 2004

263 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Education, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/4aee65e20386f7a57438797476435a386c288be7

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Citations in the corpus

Expert and Novice Approaches to Reading Mathematical Proofs (2012, background): “…of proof (e.g., Bell, 1976; Harel & Sowder, 1998; Knuth, 2002), on how students construct mathematical proofs (e.g., Moore, 1994; Weber, 2001; Weber & Alcock, 2004), and on how pedagogy can be designed to develop students’ understanding of proof (e.g., Rowland, 2002; Stylianides, 2007; G.…”
How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition (2014, result): “Similar results were found for students at all levels of their education, including mathematics majors completing advanced mathematics courses (e.g., Weber, 2001; Weber & Alcock, 2004).”
Doctoral students’ use of examples in evaluating and proving conjectures (2008, methodology): “ Weber and Alcock (2004) did use the semantic/syntactic distinction in discussing studies of undergraduate students in group theory and real analysis, and they observed similar tendencies in the context of a beginning course on proof (Alcock & Weber 2008; Weber et al. 2005).”
What Do We Mean by Mathematical Proof (2011, background): “Mathematics educators sometimes draw a distinction between “proofs that convince” and “proofs that explain” [20, 31, 63].”
Investigating the secondary–tertiary transition (2008, background): “Weber and Alcock (2004) also distinguish syntactic and semantic proof”
Preservice Elementary Teachers' Conceptual and Procedural Knowledge of Mean, Median, and Mode (2006, background): “Stating definitions correctly can also be considered a syntactic issue (Weber & Alcock, 2004).”
Every unsuccessful problem solver is unsuccessful in his or her own way: affective and cognitive factors in proving (2009, methodology): “In the phase of carrying out the plan, this kind of representation may evoke a treatment such as the syntactic strategy mentioned in (Weber 2001; Weber & Alcock 2004 ), based on unwrapping the definitions and pushing symbols.”
Mathematics Majors' Perceptions of Conviction, Validity, and Proof (2010, result): “However, in several studies that my colleagues and I have conducted with upper-level mathematics majors ( Weber, 2001 ; Weber & Alcock, 2004 ; Weber, Alcock, & Radu, 2005 ), we have found that empirical arguments are relatively rare responses when challenging proof construction tasks are presented”