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The Role of Definitions in the Teaching and Learning of Mathematics
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The Role of Definitions in the Teaching and Learning of Mathematics (2002)The Role of Definitions in the Teaching a…Selected Regular Lectures from the 12th International Congress on Mathematical Education (2015)Selected Regular Lectures fro…Defining as a mathematical activity: A framework for characterizing progress from informal to more formal ways of reasoning (2010)Defining as a mathematical ac…Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving (2008)Understanding and describing …Students’ images and their understanding of definitions of the limit of a sequence (2008)Students’ images and their un…Intuitive nonexamples: the case of triangles (2008)Intuitive nonexamples: the ca…Exemplifying definitions: a case of a square (2008)Exemplifying definitions: a c…Doctoral students’ use of examples in evaluating and proving conjectures (2008)Doctoral students’ use of exa…LEARNERS’ UNDERSTANDING OF THE DEFINITIONS AND HIERARCHICAL CLASSIFICATION OF QUADRILATERALS: TOWARDS A THEORETICAL FRAMING (2007)LEARNERS’ UNDERSTANDING OF TH…Surprises from Mathematics Education Research: Student (Mis)use of Mathematical Definitions (2004)Surprises from Mathematics Ed…Images of the limit of function formed in the course of mathematical studies at the university (2004)Images of the limit of functi…Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role (2004)Convergence of sequences and …Mathematical Beliefs — A Search for a Common Ground: Some Theoretical Considerations on Structuring Beliefs, Some Research Questions, and Some Phenomenological Observations (2002)Mathematical Beliefs — A Sear…Development of angle concepts by progressive abstraction and generalisation (2000)Development of angle concepts…Supporting Innovation: The Impact of a Teacher's Conceptions of Functions on His Implementation of a Reform Curriculum (1998)Supporting Innovation: The Im…Unpacking the logic of mathematical statements (1995)Unpacking the logic of mathem…Images of rate and operational understanding of the fundamental theorem of calculus (1994)Images of rate and operationa…Mathematics as an Educational Task (1972)Piaget’s Theory (1976)Thinking and Speech (1987)Conceptualizations and Issues related to Learning Progressions, Learning Trajectories, and Levels of Sophistication (2011)Making sense by measuring arcs: a teaching experiment in angle measure (2012)Learning angles through movement: Critical actions for developing understanding in an embodied activity (2014)Teachers' Beliefs and Educational Research: Cleaning up a Messy Construct (1992)Handbook of educational psychology (1997)The Psychology of Attitudes (1997)Studying the Practical Rationality of Mathematics Teaching: What Goes Into “Installing” a Theorem in Geometry? (2011)Greek-Cypriot elementary teachers’ epistemological beliefs about mathematics (2017)Making the transition to formal proof (1994)Dictionaries: The Art and Craft of Lexicography (2002)Validations of Proofs Considered as Texts: Can Undergraduates Tell Whether an Argument Proves a Theorem? (2003)An Inquiry-Oriented Approach to Span and Linear Independence: The Case of the Magic Carpet Ride Sequence (2012)Two Perspectives on Proportional Relationships: Extending Complementary Origins of Multiplication in Terms of Quantities (2014)Criticism and the Growth of Knowledge (1970)The Body in the Mind (1987)A Calculus Graphing Schema (2000)The Psychology Of Intelligence (2005)Foundational Reasoning Abilities that Promote Coherence in Students' Function Understanding (2008)In the Absence of Meaning… (2013)Advanced Mathematical Thinking, edited by David Tall. Pp 289. £56. 1991. ISBN 0-7923-1456-5 (Kluwer Academic Publishers) (1995)Handbook of research design in mathematics and science education (2000)Reinventing the formal definition of limit: The case of Amy and Mike (2011)A local instructional theory for the guided reinvention of the group and isomorphism concepts (2013)The Process of Education (1960)National Council of Teachers of Mathematics (1979)Those Who Understand: Knowledge Growth in Teaching (1986)Proof constructions and evaluations (2009)PROSPECTIVE TEACHERS’ CHALLENGES IN TEACHING REASONING-AND-PROVING (2013)The Mathematical Nature of Reasoning-and-Proving Opportunities in Geometry Textbooks (2014)Concept image and concept definition in mathematics with particular reference to limits and continuity (1981)Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (2004)Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon (2011)Early-years teachers’ concept images and concept definitions: triangles, circles, and cylinders (2014)Learning How to Learn (1984)The Role of Logic in Teaching Proof (2003)The Uses of Argument (2003)How Mathematicians Determine if an Argument Is a Valid Proof (2008)An assessment model for proof comprehension in undergraduate mathematics (2011)Case Study Research: Design and Methods (1984)Mathematics Teacher Change and Developments (2002)A Conceptual Framework for Learning to Teach Secondary Mathematics: A Situative Perspective (2004)Ethnographic Interview (2017)Standards-Based School Mathematics Curricula (2020)Categorization and naming in children: problems of induction (1990)Second Handbook of Research on Mathematics Teaching and Learning. 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  • 1994Images of rate and operational understanding of the fundamental theorem of calculus366 cited
  • 1995Unpacking the logic of mathematical statements247 cited
  • 1998Supporting Innovation: The Impact of a Teacher's Conceptions of Functions on His Implementation of a Reform Curriculum207 cited
  • 2007LEARNERS’ UNDERSTANDING OF THE DEFINITIONS AND HIERARCHICAL CLASSIFICATION OF QUADRILATERALS: TOWARDS A THEORETICAL FRAMING177 cited
  • 2008Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving166 cited
  • 2004Surprises from Mathematics Education Research: Student (Mis)use of Mathematical Definitions157 cited
  • 2008Exemplifying definitions: a case of a square157 cited
  • 2010Defining as a mathematical activity: A framework for characterizing progress from informal to more formal ways of reasoning130 cited
  • 2000Development of angle concepts by progressive abstraction and generalisation119 cited
  • 2002Mathematical Beliefs — A Search for a Common Ground: Some Theoretical Considerations on Structuring Beliefs, Some Research Questions, and Some Phenomenological Observations117 cited
  • 2004Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role108 cited
  • 2008Intuitive nonexamples: the case of triangles108 cited

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2004
Images of the limit of function formed in the course of mathematical studies at the university
100 cited
  • 2008Doctoral students’ use of examples in evaluating and proving conjectures91 cited
  • 2008Students’ images and their understanding of definitions of the limit of a sequence91 cited
  • 2015Selected Regular Lectures from the 12th International Congress on Mathematical Education90 cited