Proof constructions and evaluations

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How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition (2014, background): “Mathematics educators sometimes express concern that students believe things that are untrue based on empirical evidence (e.g., G. Stylianides & Stylianides, 2009).”
The Need for Proof and Proving: Mathematical and Pedagogical Perspectives (2011, background): “General arguments aim to cover appropriately the entire domain of a generalisation (which can have infi nite cardinality; cf. Stylianides and Stylianides 2009a ), whereas empirical arguments can be satisfi ed with the examination of only a subset of that domain.”
MATHEMATICS TEACHERS’ CONCEPTIONS OF PROOF: IMPLICATIONS FOR EDUCATIONAL RESEARCH (2010, background): “Given the important role played by elementary school mathematics teachers, it is necessary to provide more opportunities for them to validate purported arguments(Gholamazadetal.,2004;MartinH Gholamazad et al., 2004; Knuth, 2002a; Martin & Harel, 1989; Stylianides & Stylianides, 2009 ).”
Mathematics Majors' Perceptions of Conviction, Validity, and Proof (2010, result): “In a recent study, Stylianides and Stylianides (2009) found a similar result, with pre-service teachers justifying a proposition with an empirical argument even though many were aware that such a justification was not fully convincing.”