Proof, Explanation and Exploration: An Overview

By G. Hanna. 2000

514 citations recorded by the source corpus.

Subfields: Education, Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/483e72d6a81dcfb295298e8933ff389ef57fe7c3

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Citations in the corpus

Students' understandings of logical implication (2002, background): “Hanna (2000) lists eight different functions of proof and proving, of which she regards verification and explanation as the most fundamental.”
Deficit or Difference? the Role of Students' Epistemologies of Mathematics in their Interactions with Proof (2006, unknown): “Mis-match between expert and student perceptions of the nature and role of proof, authority and certainty in mathematics are detailed further by a number of researchers (Dreyfus, 1999; Almeida, 2000; Hanna, 2000; Recio and Godino, 2001).”
Seizing the Opportunity to Create Uncertainty in Learning Mathematics (2005, background): “More specifically, in terms of Hanna (2000), it enhanced an inner need for proofs that explain.”
Approaching Proof in a Community of Mathematical Practice (2008, methodology): “All but Transfer have been dealt with in the earlier models about the functions of proof (de Villiers, 1990, 1996).”
Preservice teachers’ knowledge of proof by mathematical induction (2007, background): “First, proof is essential for deep learning in mathematics (e.g., Hanna, 2000 ) and within the conceptual reach of even young children in supporting classroom environments (e.g., Maher and Martino, 1996).”
MATHEMATICS TEACHERS’ CONCEPTIONS OF PROOF: IMPLICATIONS FOR EDUCATIONAL RESEARCH (2010, background): “In mathematics classrooms, proof is a vehicle to enhance students’ understanding of mathematical concepts and promote their mathematical proficiency and reasoning ( Hanna, 2000 ) as proof is “involved in all situations where conclusions are to be reached and decisions to be made” (Fawcett, 1938, p.1”
The Mathematical Nature of Reasoning-and-Proving Opportunities in Geometry Textbooks (2014, background): “Although the process of reasoning-and-proving is an integral component of mathematics (Hanna, 1995, 2000; Hersh, 2009), it has not been successfully integrated into students’ school mathematics experiences (Stylianou, Blanton, & Knuth, 2009).”
Proof in School Mathematics: Insights from Psychological Research into Students' Ability for Deductive Reasoning (2008, background): “…have recommended that proof become central to all students’ mathematical experiences throughout the grades (e.g., Ball, Hoyles, Jahnke, & Movshovitz-Hadar, 2002; Hanna, 2000; Hanna & Jahnke, 1996; National Council of Teachers of Mathematics [NCTM], 2000; Schoenfeld, 1994; Yackel & Hanna, 2003).”
What Do We Mean by Mathematical Proof (2011, background): “These software packages allow students to explore geometric objects and environments, test conjectures, and ‘discover’ new properties of geometric objects [21].”
Dragging as a conceptual tool in dynamic geometry environments (2006, background): “In all cases, this transitional leap is the result of dragging activity in DGE (see [2–5]).”
Visualisation and proof: a brief survey of philosophical perspectives (2007, background): “Parts of this paper appeared previously in Hanna (2000).”
Proof and Proving in School Mathematics (2007, background): “In recent years, however, many researchers and curriculum frameworks have recommended that proof and proving become central to students’ school mathematical experiences in all content areas and at all grade levels (e.g., Ball & Bass, 2003; Ball, Hoyles, Jahnke, & Movshovitz-Hadar, 2002; Carpenter, F”
The Need for Proof and Proving: Mathematical and Pedagogical Perspectives (2011, methodology): “Here, we focus on proof’s central roles within mathematics: validation, explanation, discovery, systemisation of results, incorporation into a framework, and conveying mathematical knowledge (de Villiers 1990 ; Hanna 2000 ; Rav 1999 ) .”
Students’ encounter with proof: the condition of transparency (2008, background): “Hanna (2000) emphasises the importance of discussing with students all the functions of proof in mathematics.”
Proofs as bearers of mathematical knowledge (2008, background): “... the cognitive aspects of proof (Tall, 1998); the role of intuition and schemata in proving (Fischbein, 1982, 1999); the relationship between proving and reasoning (Yackel & Hanna 2003; Maher & Martino 1996); the usefulness of heuristics for the teaching of proof (Reiss & Renkl, 2002); the emphas”