Student difficulty in constructing proofs: The need for strategic knowledge

By Keith Weber. 2001

479 citations recorded by the source corpus.

Subfields: Education, Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/e7683dc21d5438f1f552f0c87aa11ae3eb3be777

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In Education

In Geometry and Topology

In Theoretical Computer Science

Citations in the corpus

MATHEMATICS TEACHERS’ CONCEPTIONS OF PROOF: IMPLICATIONS FOR EDUCATIONAL RESEARCH (2010, background): “Hart, 1994; Moore, 1994; Selden & Selden, 2003; Weber, 2001 ) or lack understanding of the necessary mathematical language (e.g.”
Mathematics Majors' Perceptions of Conviction, Validity, and Proof (2010, background): “Like the mathematicians in Weber’s (2008) proof validation study, P10 appears to argue that the level of detail that needs to be provided for an argument to be sanctioned as a proof depends on the audience of the proof and community in which it is couched.”
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.”
Proof in School Mathematics: Insights from Psychological Research into Students' Ability for Deductive Reasoning (2008, background): “…a role in facilitating students’ use of deductive reasoning in the context of proof (e.g., Balacheff, 1991; Ball & Bass, 2003; Boero et al., 1996; Herbst, 2002a; Jones, 2000; Lampert, 1992; Mariotti, Bussi, Boero, Ferri, & Garutti, 1997; Stylianides, 2007b, 2007c; Weber, 2001; Yackel & Cobb, 1996).”
Enacting proof-related tasks in middle school mathematics: Challenges and opportunities (2010, background): “The nature of the didactical situation of teaching students to do proofs in school mathematics, however, may unintentionally support a dichotomy between the mathematically rigorous proofs that teachers expect from students and the empirically based arguments that students believe are sufficient for ”
Identifying Kinds of Reasoning in Collective Argumentation (2014, background): “Two of the most prevalent results in the literature on proof and proving are that proving is difficult for students at all levels (e.g., Weber, 2001), and that many school and beginning undergraduate students accept empirical evidence (which would often be characterized as inductive reasoning) as…”
Cognitive Development of Proof (2011, background): “Evidence for this further development was given by Weber (2001) who investigated how four undergraduates and four research students responded to formal problems, such as the question of whether there is an isomorphism between the group of integers under addition and the group of rational numbers…”
A local instructional theory for the guided reinvention of the group and isomorphism concepts (2013, background): “Students struggle not only with proving heorems in abstract algebra (Weber, 2001), but also with the level of abstraction (Hazzan, 1999) and complexity (Leron t al.”