Beyond Proving and Explaining: Proofs That Justify the Use of Definitions and Axiomatic Structures and Proofs That Illustrate Technique.

By Keith Weber. 2002

68 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/131640d2791246edc072d3343dea4fcdadb96d37

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Citations in the corpus

Approaching Proof in a Community of Mathematical Practice (2008, methodology): “Further, intuitive is the opposite of rigorous, intuition is holistic or integrative as opposed to detailed or analytic (ibid., pp. 61-62).”
An assessment model for proof comprehension in undergraduate mathematics (2011, unknown): “The methodology and results of this study are discussed in detail by Weber and Mejia-Ramos (2011) and Weber (2010).”
Making the Connection: Overcoming Students' Difficulties in Learning to Understand and Construct Proofs (2007, unknown): “20 It has been suggested that proofs have various functions within mathematics: explanation, communication, discovery of new results, justification of a new definition, developing intuition, and providing autonomy (e.g., Hanna, 1989; de Villiers, 1990; Weber, 2002).”
Students' Conceptions of a Mathematical Definition (2005, background): “…(Klausmeier & Feldman, 1975; Sowder, 1980; Vinner, 1991; Wilson, 1990); (3) establishing the foundation for proofs and problem solving (Moore, 1994; Weber, 2002); and (4) creating uniformity in the meaning of concepts, which allows us to communicate mathematical ideas more easily (Borasi, 1992).”
What Do We Mean by Mathematical Proof (2011, background): “It is to this context that Weber [58] adds two other uses of proof in the mathematics classroom: proofs that justify the use of a definition or axiomatic structure, and proofs that illustrate a technique.”
Mathematicians’ perspectives on their pedagogical practice with respect to proof (2012, background): “Because of this, students are likely to think proofs that systematize theories have little value [21].”
Lectures in Advanced Mathematics: Why Students Might Not Understand What the Mathematics Professor Is Trying to Convey. (2016, result): “In some cases, proof can be used not to verify new results, but rather to verify, or show how, new definitions or axiom systems can account for results that are known to be true (c.f., Weber, 2002).”