Preservice teachers’ knowledge of proof by mathematical induction

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Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving (2008, background): “This body of research has shown that teachers of all levels tend to have weak knowledge about the logico-linguistic structure of proof (e.g., Harel, 2002; Jones, 1997; Knuth, 2002; Martin & Harel, 1989; Movshovitz-Hadar, 1993; Simon & Blume, 1996; Stylianides et al., 2004, 2007 ), thereby suggestin”
MATHEMATICS TEACHERS’ CONCEPTIONS OF PROOF: IMPLICATIONS FOR EDUCATIONAL RESEARCH (2010, methodology): “ Stylianides et al. (2007) used two items to examine 70 prospective elementary and 25 prospective secondary school mathematics teachers’ conceptions ofproof bymathematical induction in Cyprus.”
Proof in School Mathematics: Insights from Psychological Research into Students' Ability for Deductive Reasoning (2008, background): “One such ability is to recognize that a proof guarantees the truth of a statement for all the elements in the domain covered by the proof (Fischbein, 1982) but does not imply anything about the truth of the statement for elements outside that domain (Stylianides et al., 2007).”
Proof constructions and evaluations (2009, background): “The influence of this factor on prospective elementary teachers’ evaluations of given arguments was suggested by several studies (e.g., Martin & Harel, 1989; Stylianides et al., 2004, 2007; Winicki-Landman, 1998).”