Definitions : dealing with categories mathematically.

Keywords

Mathematics education, Mathematical logic, Computer science, Management science, Mathematics

References

• Visualisation in High School Mathematics.Norma Presmeg — 1986
• Cognitive versus Situational Analysis of Problem-Solving Behaviors.Nicolas Balacheff — 1986
• Intelligence, Learning, and Action: A Foundation for Theory and Practice in EducationRichard R. Skemp — 1979
• The General, the Abstract, and the Generic in Advanced MathematicsGuershon Harel, David Tall — 1991
• Three-dimensional geometry and topologyWilliam P. Thurston, Silvio Levy — 1997
• Cognitive models and prototype theory.George Lakoff — 1987
• Categories, definitions and mathematics : student reasoning about objects in analysisLara Alcock — 2001
• The Warwick analysis project: Practice and theoryDouglas L. Holton — 2001
• A study of pupils' proof-explanations in mathematical situationsAlan Bell — 1976
• On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coinAnna Sfard — 1991
• Making the transition to formal proofRobert C. Moore — 1994
• Unpacking the logic of mathematical statementsJohn Selden, Annie Selden — 1995
• Concise Oxford Dictionary of Current EnglishM. P. Ravenel — 1960
• Proofs and RefutationsBruce Lercher — 1978
• Proofs and Refutations: The Logic of Mathematical DiscoveryDouglas Quadling — 1977
• Heuristic Presentations: The Role of Structuring.Uri Leron — 1985
• Knowledge construction and diverging thinking in elementary & advanced mathematicsEddie Gray, Márcia Maria Fusaro Pinto, Demetra Pitta‐Pantazi — 1999
• Principles of CategorizationE. Rosch — 1978
• A framework for representing knowledge" in the psychology of computer visionM. Minsky — 1975
• The Role of Definitions in the Teaching and Learning of MathematicsShlomo Vinner — 2002

Cited by

• Pre-service elementary school teachers' experiences with interpreting and creating proofsSoheila Gholamazad — 2006
• Teaching Calculus using Dynamic Geometric ToolsTheodosis Zachariades, Keith Jones, Efstathios Giannakoulias — 2007
• Non-traditional Socio-mathematical Norms In Undergraduate Real AnalysisPaul Christian Dawkins — 2009
• Using example generation to explore undergraduates conceptions of real sequences: a phenomenographic studyAntony W. Edwards — 2011
• Comportamiento de estudiantes universitarios al usar definiciones matemáticasValeria Aguirre Holguín — 2015
• Proposição de problemas colaborativos online: um estudo preliminarArthur D. Powell, Leo Akio Yokoyama — 2011
• A transição do cálculo para a análise: uma resenha de três trabalhos de Márcia Maria Fusaro PintoSílvio César Otero-Garcia — 2012
• Explication as a lens for the formalization of mathematical theory through guided reinventionPaul Christian Dawkins — 2015
• Metaphor as a possible pathway to more formal understanding of the definition of sequence convergencePaul Christian Dawkins — 2012
• Transition from secondary to tertiary mathematics: McMaster University experienceAnn Kajander, Miroslav Lovrić — 2005
• Dual processes in mathematics : reasoning about conditionalsMatthew Inglis — 2006
• Student evaluation of mathematical statements using dynamic geometry softwareJeff Connor, Laura J. Moss, Barbara W. Grover — 2007
• Understanding secondary–tertiary transition in mathematicsMegan Clark, Miroslav Lovrić — 2009
• Proof validation in real analysis: Inferring and checking warrantsLara Alcock, Keith Weber — 2005
• Semantic and Syntactic Proof ProductionsKeith Weber, Lara Alcock — 2004
• Ideas from mathematics education: an introduction for mathematiciansLara Alcock, Adrian Simpson — 2009
• A case study on high school students’ mental image in the process of solving regular polyhedron problemsGap Lyung Hong, Won Kyung Kim — 2014
• The Transition from Everyday Definitions to Mathematical Definitions -Gifted Middle School Students` Conceptions of Point and Line definitions-Jihyun Lee — 2011
• How students interpret and enact inquiry-oriented defining practices in undergraduate real analysisPaul Christian Dawkins — 2014
• The role of affect in learning Real Analysis: a case studyKeith Weber — 2008

Related papers

• Concept image and concept definition in mathematics with particular reference to limits and continuityDavid Tall, Shlomo Vinner — 1981
• Traditional instruction in advanced mathematics courses: a case study of one professor’s lectures and proofs in an introductory real analysis courseKeith Weber — 2004
• Convergence of Sequences and Series 2: Interactions Between Nonvisual Reasoning and the Learner’s Beliefs about their own RoleLara Alcock, Adrian Simpson — 2004
• Unpacking the logic of mathematical statementsJohn Selden, Annie Selden — 1995
• Making the transition to formal proofRobert C. Moore — 1994
• Advanced Mathematical ThinkingHuw Griffiths — 1994
• The Role of Logic in Teaching ProofSusanna S. Epp — 2003
• Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem?Annie Selden, John Selden — 2003