Proof and Proving in School Mathematics

By Andreas J. Stylianides. 2007

416 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ceacff1db818f1ce8ab3e10b36b320b7edf3053d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Research-based interventions in the area of proof: the past, the present, and the future (2017, methodology): “Although in this Editorial we use the term Bproof^ in line with the conceptualization elaborated in Stylianides (2007) to broadly mean a mathematical argument for or against a mathematical claim that is both mathematically sound and conceptually accessible to the members of the local community…”
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).”
Proof constructions and evaluations (2009, background): “2.1 Clarification of terms In the context of a community of learners, an argument for the truth of a statement that qualifies as a proof is general, valid, and accessible to the members of the community (see Stylianides, 2007, p. 291, for an elaborated version of this definition).”
PROSPECTIVE TEACHERS’ CHALLENGES IN TEACHING REASONING-AND-PROVING (2013, background): “Yet, various domains of research—psychological research (reviewed in Stylianides & Stylianides 2008b), research on exemplary classroom instruction at the elementary school level (e.g. Ball & Bass, 2003; Lampert, 1990; Reid, 2002; Stylianides, 2007; Zack, 1997), and research on typical classroom prac”
Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving (2008, background): “The reader is referred to Stylianides (2007b) for further elaboration on the aforementioned definitions of proof and proving, exemplification of their applicability in school mathematics as early as the elementary grades, and illustration of their utility in studying the role of teachers in engagi”
Undergraduate mathematics majors’ writing performance producing proofs and counterexamples about continuous functions (2009, background): “While a mathematical proof is “neither rigorous nor complete” (Hanna, 1991, p. 59), it should incorporate the important ideas of sets of accepted statements, modes of argumentation, and modes of argument representation in the classroom community (Stylianides, 2007).”
How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition (2014, unknown): “In the United States, much of a nonmathematician’s conceptions of proof are formed in their high school geometry course, as this is typically the only course in which most students have extensive experience with proof (e.g., Moore, 1994; A. Stylianides, 2007).”
Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification (2017, background): “Proving, the activity of making a proof, consists of mathematically arguing by sequencing assertions for or against a mathematical claim (Stylianides 2007).”
The Need for Proof and Proving: Mathematical and Pedagogical Perspectives (2011, background): “In order to convince, a proof has to align with the norms (e. g., forms of reasoning, logical rules of inference, modes of argumentation and modes of argument representation) of the community to which it is presented (Harel and Sowder 2007 ; Siu 2008 ; Stylianides 2007 ) .”
Expert and Novice Approaches to Reading Mathematical Proofs (2012, background): “, Moore, 1994; Weber, 2001; Weber & Alcock, 2004), and on how pedagogy can be designed to develop students’ understanding of proof (e.g., Rowland, 2002; Stylianides, 2007; G. J. Stylianides & A. J. Stylianides, 2009).”
MATHEMATICS TEACHERS’ CONCEPTIONS OF PROOF: IMPLICATIONS FOR EDUCATIONAL RESEARCH (2010, methodology): “2. It employs forms of reasoning (modes of argumentation) that are valid and known to or within the conceptual reach of the classroom community; and 3. It is communicated with forms of expression (modes of argument representation) that are appropriate and known to or within the conceptualreachofthec”