Ideas from mathematics education: an introduction for mathematicians

Keywords

Mathematics education, Computer science, Mathematics

References

• Definitions : dealing with categories mathematically.Lara Alcock, Adrian Simpson — 2002
• I Want to be a MathematicianPaul R. Halmos — 1985
• Teaching Mathematical Induction I.Ed Dubinsky — 1986
• Beyond Proving and Explaining: Proofs That Justify the Use of Definitions and Axiomatic Structures and Proofs That Illustrate Technique.Keith Weber — 2002
• Building Formal Mathematics on Visual Imagery: A Case Study and a Theory.Márcia Maria Fusaro Pinto, David Tall — 2002
• An Accompaniment to Higher MathematicsGeorge R. Exner — 1997
• MATHEMATICIANS AND THE SELECTION TASKMatthew Inglis, Adrian Simpson — 2004
• A Framework for Research and Curriculum Development in Undergraduate Mathematics EducationjpegAsiala, A. H. F. Brown, David DeViries — 2009
• Mathematics Teaching Practice: Guide for University and College LecturersJohn Mason — 2002
• Problems with the Language of Limits.John Monaghan — 1991
• Student difficulty in constructing proofs: The need for strategic knowledgeKeith Weber — 2001
• Facilitating Learning Events Through Example GenerationRandall P. Dahlberg, David Housman — 1997
• An Alternate Route to the Reification of FunctionDavid Slavit — 1997
• Mathematics as a Constructive Activity: Learners Generating ExamplesAnne Watson, John Mason — 2005
• Key Ideas: What are they and how can they help us understand how people view proof?Murali Raman — 2003
• Reducing Abstraction Level When Learning Abstract Algebra ConceptsOrit Hazzan — 1999
• The Notion of Limit: Some Seemingly Unavoidable Misconception Stages.Robert B. Davis, Shlomo Vinner — 1986
• Hypothetical Thinking: Dual Processes in Reasoning and JudgementJonathan St. B. T. Evans — 2007
• Cognitive Empathy and the Transition to Independent Graduate Study in MathematicsJanet Duffin, Adrian Simpson — 2005
• On learning fundamental concepts of group theoryEd Dubinsky, Jennie Dautermann, Uri Leron — 1994

Cited by

• Using example generation to explore undergraduates conceptions of real sequences: a phenomenographic studyAntony W. Edwards — 2011
• Where learning starts? A framework for thinking about lectures in university mathematicsDavid Pritchard — 2010
• Example generation exercises in an introductory analysis courseNuala Curley, Maria Meehan — 2010
• Factors mathematicians profess to consider when presenting pedagogical proofsYvonne Lai, Keith Weber — 2014
• Have you seen this?… Students and Proof: Bounds and Functions. A DVD for MathematiciansLara Alcock — 2009
• What’s right with lecturing?David Pritchard — 2010
• Definitions are important: the case of linear algebraAbraham Berman, Ludmila Shvartsman — 2016
• Media Enhanced Teaching and Learning: case studies and evidence of effective usePeter Rowlett — 2012
• Didactics of Mathematics in Higher Education as a Scientific DisciplineRobin Göller, Rolf Biehler, Reinhard Hochmuth — 2017
• Designing a short course for graduate teaching assistants (GTAs) in mathematics: principles and practiceCosette Crisan, Melissa Rodd — 2017
• Investigating students' learning of differential equations in physicsDiarmaid Hyland — 2018
• Mental constructions in linear algebraAsuman Oktaç — 2019
• Errors In Using Convergence Tests In Infinite SeriesMurat Genç, Mustafa AKINCI — 2020
• The mathematical background of proving processes in discrete optimization—exemplification with Research Situations for the ClassroomSylvain Gravier, Cécile Ouvrier-Buffet — 2022
• Developing ‘deep mathematical thinking’ in geometry with 3- and 4-year-olds: a collaborative study between early years teachers and university-based mathematiciansRachel H. Oughton, Kathryn Nichols, David Bolden — 2022
• Example Generation with STACKJie Xin Ng — 2022
• Transitions and Proof and Proving at Tertiary LevelAnnie Selden — 2011
• The National Institute of Education and Mathematics Teacher Education: Evolution of Pre-service and Graduate Mathematics Teacher EducationE. G. Tay, W. Ho, Lu Cheng — 2019
• Explaining Infinite Series: An Exploration of Students' ImagesDanielle Champney — 2013
• Developing mathematics teaching: What can we learn from the literature?Stephanie Treffert-Thomas, B. Jaworski — 2015

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