Students' understandings of logical implication

By Celia Hoyles, D. Küchemann. 2002

109 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9c857bc16b713b08a72200f3895d8d3d24aafa40

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Citations in the corpus

Truth versus validity in mathematical proof (2008, background): “…Inglis & Simpson 2006) and researchers in mathematics education (Radford 1985; Arsac et al. 1992; Legrand 1993; Selden & Selden 1995; Dubinsky & Yiparaki 2000; Hanna 2000; Hoyles & Küchemann 2003; Rogalski & Rogalski, 2004) emphasize the difference between common sense and mathematical logic.”
Research-based interventions in the area of proof: the past, the present, and the future (2017, background): “…the misconception that a single counterexample is insufficient to refute a false mathematical generalization (e.g., Mason & Klymchuk, 2009; Simon & Blume, 1996) or the misconception that a conditional statement is equivalent to its converse (e.g., Hoyles & Küchemann, 2002; Yu, Chin, & Lin, 2004).”
‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation (2012, unknown): “These studies (e.g.: Krummheuer, 1995, 2007; Yackel, 2001, 2002; Whitenack & Knipping, 2002; Stephan & Rasmussen, 2002; Evens & Houssart, 2004; Hoyles & Küchemann, 2002; Weber & Alcock, 2005; Pedemonte, 2005, 2007) span across educational levels, focus largely on arguments produced collectively and…”
Identifying Kinds of Reasoning in Collective Argumentation (2014, background): “Many researchers (e.g., Hoyles & Kuchemann, 2002; Yackel, 2002) followed Krummheuer in using only the core.”
Modelling mathematical argumentation: the importance of qualification (2007, background): “This approach has been adopted by, amongst others, researchers studying basic number skills (Evens and Houssart, 2004), logical deduction (Hoyles and Küchemann, 2002; Weber and Alcock, 2005), geometry (Knipping, 2003; Pedemonte, 2005; Pedemonte, in press), and general proof (Yackel, 2001).”
Proof in School Mathematics: Insights from Psychological Research into Students' Ability for Deductive Reasoning (2008, background): “…(2) descriptions of common difficulties that students face in using deductive reasoning in the context of proof (e.g., Chazan, 1993; Galbraith, 1981; Hoyles & Küchemann, 2002; Knuth et al., 2002; Porteous, 1990); and (3) insights into pedagogical factors (including teachers’ instructional…”
Reasoning-and-proving opportunities in elementary mathematics textbooks (2014, background): “…proficiency to engage in reasoning and proving indicate significant weaknesses in students’ abilities to reason deductively and abstractly at all grade levels (Chazan, 1993; Harel & Sowder, 1998; Healy & Hoyles, 2000; Hoyles & Küchemann, 2002; Knuth, Choppin, & Bieda, 2009; Lannin, 2005).”