Students' Conceptions of a Mathematical Definition

By Annie Selden, J. Selden, O. Zaslavsky, Karni Shir. 2005

167 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ded911f1a3e2c6d90af79d293b73fd39e7dc087d

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Citations in the corpus

Exemplifying definitions: a case of a square (2008, methodology): “We further acknowledge that there is no consensus on the minimality requirement for a definition among mathematicians as well as among mathematics educators (Linchevsky, Vinner and Karsenty 1992; Vinner, Linchevski and Karsenty 1993; Zaslavsky and Shir 2005).”
Proofs and refutations in the undergraduate mathematics classroom (2008, background): “Many mathematics educators have made brief reference to Lakatos’ (1976) historical case studies and his description of processes of mathematical discovery (e.g., Alcock and Simpson 2004; Mariotti and Fischbein 1997; Zaslavsky and Shir 2005).”
Eigenvalues and eigenvectors: embodied, symbolic and formal thinking (2011, background): “Hence, it is not surprising that many students have real difficulties with definitions of such concepts, which are considered to be fundamental as a starting point for concept formation and deductive reasoning in advanced mathematics (Vinner 1991; Zaslavsky and Shir 2005).”
LEARNERS’ UNDERSTANDING OF THE DEFINITIONS AND HIERARCHICAL CLASSIFICATION OF QUADRILATERALS: TOWARDS A THEORETICAL FRAMING (2007, background): “…and of classification, given that a range of studies is indicating that learners have difficulties both with defining (see, for example, de Villiers, 1998; Vinner, 1991; Zaslavsky and Shir, 2005) and classifying (see, for instance, Currie and Pegg, 1998; de Villiers, 1994; Monaghan, 2000).”
Proof in School Mathematics: Insights from Psychological Research into Students' Ability for Deductive Reasoning (2008, background): “An important ability required for successful performance in this process is to understand the role of assumptions (e.g., definitions, axioms) that underlie a mathematical argument or a proof (Ball & Bass, 2000; Mariotti & Fischbein, 1997; Stylianides, 2007a; Vinner, 1991; Zaslavsky & Shir, 2005).”
A framework for mathematical thinking: the case of linear algebra (2009, background): “These definitions are considered to be fundamental as a starting point for concept formation and deductive reasoning in advanced mathematics [2,3].”