David Tall

Q: What Schools Are Affiliated With David Tall

David Tall is affiliated with the following schools: University of Warwick, University of Oxford

David Tall's AcademicInfluence.com Rankings

David Tall

Mathematics

#1147

World Rank

#1931

Historical Rank

Measure Theory

#655

World Rank

#895

Historical Rank

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Mathematics

Why Is David Tall Influential?

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According to Wikipedia, David Orme Tall is Emeritus Professor in Mathematical Thinking at the University of Warwick. One of his early influential works is the joint paper with Vinner "Concept image and concept definition in mathematics with particular reference to limits and continuity". The "concept image" is a notion in cognitive theory. It consists of all the cognitive structure in the individual's mind that is associated with a given concept. Tall and Vinner point out that the concept image may not be globally coherent, and may have aspects which are quite different from the formal concept definition. They study the development of limits and continuity, as taught in secondary school and university, from the cognitive viewpoint, and report on investigations which exhibit individual concept images differing from the formal theory, and containing factors which cause cognitive conflict.

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David Tall's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Concept image and concept definition in mathematics with particular reference to limits and continuity (1981) (1819)
Advanced Mathematical Thinking (1994) (997)
Ambiguity and flexibility: A proceptual view of simple arithmetic (1983) (540)
The transition to formal thinking in mathematics (2008) (275)
The Psychology of Advanced Mathematical Thinking (2002) (257)
Functions and Calculus (1996) (218)
Group representations, λ-rings and the J-homomorphism (1969) (207)
THINKING THROUGH THREE WORLDS OF MATHEMATICS (2004) (202)
Conflicts in the Learning of Real Numbers and Limits. (1978) (166)
What is the object of the encapsulation of a process (1999) (164)
Encouraging versatile thinking in algebra using the computer (1991) (146)
The General, the Abstract, and the Generic in Advanced Mathematics (1991) (143)
Knowledge construction and diverging thinking in elementary & advanced mathematics (1999) (140)
Symbols and the Bifurcation Between Procedural and Conceptual Thinking (2001) (137)
Students' Mental Prototypes for Functions and Graphs (1992) (117)
Algebraic Number Theory (1979) (117)
Algebraic Number Theory and Fermat's Last Theorem (2015) (105)
Concept Image and Concept Definition (1988) (99)
Procedural embodiment and magic in linear equations (2008) (99)
How Humans Learn to Think Mathematically: Exploring the Three Worlds of Mathematics (2013) (98)
Duality, Ambiguity and Flexibility in Successful Mathematical Thinking (1991) (98)
Abstraction as a natural process of mental compression (2007) (97)
Definitions and Images for the Definite Integral Concept (1997) (95)
Using Technology to Support an Embodied Approach to Learning Concepts in Mathematics (2004) (94)
Diagnosing Students' Difficulties in Learning Mathematics (1993) (94)
Intuition and rigour: the role of visualization in the calculus (1991) (93)
Understanding the calculus (1985) (92)
Cognitive Growth in Elementary and Advanced Mathematical Thinking (1995) (91)
Building Theories: The Three Worlds of Mathematics. (2004) (91)
Building Formal Mathematics on Visual Imagery: A Case Study and a Theory. (2002) (90)
Natural and Formal Infinities (2001) (90)
Dynamic mathematics and the blending of knowledge structures in the calculus (2009) (80)
Students' Difficulties in Calculus Plenary presentation in Working Group 3, ICME, Québec, August 1992 (1993) (75)
Relationships between embodied objects and symbolic procepts: an explanatory theory of success and failure in mathematics (2004) (75)
Student constructions of formal theory: giving and extracting meaning (1999) (74)
The fundamental cycle of concept construction underlying various theoretical frameworks (2005) (73)
Cognitive Units, Connections and Mathematical Proof (1997) (72)
Advanced Mathematical Thinking and the Computer (2002) (70)
Looking at graphs through infinitesimal microscopes, windows and telescopes (1980) (67)
A THEORY OF MATHEMATICAL GROWTH THROUGH EMBODIMENT, SYMBOLISM AND PROOF (2006) (66)
Metaphor or Met-Before? The effects of previouos experience on practice and theory of learning mathematics (2010) (64)
Cognitive development in advanced mathematics using technology (2000) (64)
Inconsistencies in the Learning of Calculus and Analysis (1990) (64)
The notion of infinite measuring number and its relevance in the intuition of infinity (1980) (63)
Success and Failure in Mathematics: The Flexible Meaning of Symbols as Process and Concept (1992) (63)
Building and testing a cognitive approach to the calculus using interactive computer graphics (1986) (62)
Operable Definitions in Advanced Mathematics: The Case of the Least Upper Bound (1998) (60)
Changing Attitudes to University Mathematics Through Problem Solving (1998) (59)
Objects, actions, and images: a perspective on early number development (2000) (56)
The Cognitive Development of Proof: Is Mathematical Proof For All or For Some? (1998) (56)
Professional development through lesson study: teaching the derivative using GeoGebra (2015) (56)
Facets and Layers of the Function Concept (1996) (55)
Mathematical Intuition, with Special Reference to Limiting Processes (1980) (50)
How Humans Learn to Think Mathematically: Set-Befores, Met-Befores and Long-Term Learning (2013) (50)
Concept Images, Generic Organizations, Computers, and Curriculum Change (1989) (50)
Introducing Three Worlds of Mathematics (2004) (49)
Cognitive Development of Proof (2011) (48)
Reflections on APOS theory in Elementary and Advanced Mathematical Thinking (1999) (44)
Constructing the Concept Image of a Tangent (1999) (43)
Technology and Calculus (2001) (43)
Complex Analysis: The Hitchhiker's Guide to the Plane (1983) (41)
Gender and the versatile learning of trigonometry using computer software (1991) (40)
Cognitive Conflict and the Learning of Mathematics (1977) (39)
The blancmange function: Continuous everywhere but differentiable nowhere (1982) (38)
Developing a theory of mathematical growth (2007) (37)
Cognitive aspects of proof, with special reference to the irrationality of √2 (1979) (36)
The Function Machine as a Cognitive Root for the Function Concept. (2000) (36)
Computer Environments for the Learning of Mathematics (1993) (35)
Evolving a three-world framework for solving algebraic equations in the light of what a student has met before (2014) (34)
Concept Maps & Schematic Diagrams as Devices for Documenting the Growth of Mathematical Knowledge (1999) (33)
THE COMPLEXITIES OF A LESSON STUDY IN A DUTCH SITUATION: MATHEMATICS TEACHER LEARNING (2013) (31)
Infinity – The never-ending struggle (2001) (31)
Using the computer as an environment for building and testing mathematical concepts: A Tribute to Richard Skemp (1986) (30)
Differing Modes of Proof and Belief in Mathematics (2002) (29)
A MISMATCH BETWEEN CURRICULUM DESIGN AND STUDENT LEARNING: THE CASE OF THE FUNCTION CONCEPT (2005) (28)
Constructing Different Concept Images of Sequences & Limits by Programming (1999) (28)
The roles of visualization and symbolism in the potential and actual infinity of the limit process (2015) (28)
Crystalline Concepts in Long-Term Mathematical Invention and Discovery. (2011) (27)
EMBODIMENT, SYMBOLISM AND FORMALISM IN UNDERGRADUATE MATHEMATICS EDUCATION (2007) (27)
Making Sense of Mathematical Reasoning and Proof (2014) (26)
The Foundations of Mathematics (1977) (26)
THE LONG-TERM COGNITIVE DEVELOPMENT OF DIFFERENT TYPES OF REASONING AND PROOF (2007) (26)
Foundations for the Future: The Potential of Multimodal Technologies for Learning Mathematics (2015) (24)
Using the Function Machine as a Cognitive Root. (2000) (24)
Cognitive development, representations and proof (1995) (24)
Algebraic Number Theory and Fermat's Last Theorem : Third Edition (2001) (24)
A Graphical Approach to Integration and the Fundamental Theorem (1986) (24)
USING JAPANESE LESSON STUDY IN TEACHING MATHEMATICS (2009) (23)
A Cauchy-Dirac Delta Function (2012) (23)
Representable Functors and Operations on Rings (1970) (23)
Lesson study: the effect on teachers' professional development (2011) (23)
A cognitive analysis of Cauchy’s conceptions of function, continuity, limit and infinitesimal, with implications for teaching the calculus (2014) (22)
Function : Organizing Principle or Cognitive Root ? (1999) (22)
Intuitions of Infinity. (1981) (22)
Information Technology and Mathematics Education: Enthusiasms, Possibilities and Realities. (2009) (22)
The Nature of the Object as an Integral Component of Numerical Processes 1 (1997) (21)
THE TENSION BETWEEN INTUITIVE INFINITESIMALS AND FORMAL MATHEMATICAL ANALYSIS (2011) (21)
A Versatile Theory of Visualisation and Symbolisation in Mathematics (1994) (19)
A child thinking about infinity (2001) (19)
Visualizing Differentials in Two and Three Dimensions (1992) (19)
The Roles of Cognitive Units, Connections and Procedures in achieving Goals in College Algebra (1999) (19)
Elementary Axioms and Pictures for Infinitesimal Calculus (1982) (19)
PERCEPTIONS, OPERATIONS AND PROOF IN UNDERGRADUATE MATHEMATICS (2010) (18)
Conflicts and Catastrophes in the Learning of Mathematics (1999) (17)
The gradient of a graph (1985) (17)
Understanding the Processes of Advanced Mathematical Thinking 1 (1994) (17)
Descriptions and Definitions in the Teaching of Elementary Calculus (2005) (16)
Technology and Versatile Thinking in Mathematics. (2000) (16)
The transition from embodied thought experiment and symbolic manipulation to formal proof (2007) (16)
Following students' development in a traditional university analysis course (2001) (16)
The Dynamics of Understanding Mathematics (1978) (15)
The Value of the Computer in Learning Algebra Concepts (1986) (15)
LONGER-TERM CONCEPTUAL BENEFITS FROM USING A COMPUTER IN ALGEBRA TEACHING (1988) (15)
Interrelationships Between Mind and Computer: Processes, Images, Symbols (1993) (14)
Concept Images, Computers, and Curriculum Change (1989) (14)
Intuitive infinitesimals in the calculus (1980) (14)
Visualizing Higher Level Mathematical Concepts Using Computer Graphics (1983) (14)
USING THEORETICAL-COMPUTATIONAL CONFLICTS TO ENRICH THE CONCEPT IMAGE OF DERIVATIVE (2003) (13)
ENCOURAGING MATHEMATICAL THINKING THAT HAS BOTH POWER AND SIMPLICITY (2007) (13)
From School to University: the Transition from Elementary to Advanced Mathematical Thinking (1997) (12)
The Transition from Arithmetic to Algebra: Number Patterns, or Proceptual Programming? (1992) (12)
How Humans Learn to Think Mathematically: The Three Worlds of Mathematics (2013) (12)
The calculus of leibniz — an alternative modern approach (1979) (12)
How Humans Learn to Think Mathematically: The Historical Evolution of Mathematics (2013) (12)
The Influence of Computers and Informatics on Mathematics and its Teaching: Graphic Insight into Calculus and Differential Equations (1986) (11)
Changing Attitudes to Mathematics through Problem Solving (1994) (11)
Flexible thinking and met-befores : impact on learning mathematics (2013) (11)
Versatile Learning and the Computer. (1989) (11)
Recent developments in the use of the computer to visualize and symbolize calculus concepts (1991) (11)
The Long-Term Cognitive Development of Reasoning and Proof (2010) (10)
Proceedings of the third International Conference for the Psychology of Mathematics Education (1979) (10)
A Versatile Approach to Calculus and Numerical Methods (1990) (9)
1 REFLECTING ON POST-CALCULUS-REFORM (2004) (9)
The Mathematics Curriculum and the Micro. (1984) (9)
Mathematical Processes and Symbols in the Mind (1992) (8)
The Psychology of Advanced Mathematical Thinking: Biological Brain and Mathematical Mind (1994) (8)
Procedural and conceptual aspects of standard algorithms in calculus (1996) (8)
Lies, Damn Lies ... and Differential Equations (1986) (8)
WHAT DO MATHEMATICS AND PHYSICS TEACHERS THINK THAT STUDENTS WILL FIND DIFFICULT? A CHALLENGE TO ACCEPTED PRACTICES OF TEACHING (2005) (8)
From Biological Brain to Mathematical Mind: The Long-Term Evolution of Mathematical Thinking (2019) (8)
THE HISTORICAL & INDIVIDUAL DEVELOPMENT OF MATHEMATICAL THINKING: IDEAS THAT ARE SET-BEFORE AND MET-BEFORE (2008) (8)
The number sense: how the mind creates mathematics , by Stanilas Dehaene. Pp. 274. £20. 1998. ISBN 0 713 99170 4 (Allen Lane: The Penguin Press). (1998) (8)
Complementing supportive and problematic aspects of mathematics to resolve transgressions in long-term sense making (2019) (8)
The Nature of Advanced Mathematical Thinking (2008) (8)
Conceptual and Procedural Approaches to Problem-Solving (1996) (7)
A LIFE-TIME'S JOURNEY FROM DEFINITION AND DEDUCTION TO AMBIGUITY AND INSIGHT (2006) (7)
PERSONAL AND PUBLIC ASPECTS OF FORMAL PROOF: A THEORY AND A SINGLE-CASE STUDY (2005) (7)
SETTING LESSON STUDY WITHIN A LONG-TERM FRAMEWORK OF LEARNING (2007) (7)
EMBODIMENT, SYMBOLISM, ARGUMENTATION AND PROOF (2007) (6)
CONSTRUCTION OF CONCEPTUAL KNOWLEDGE: THE CASE OF COMPUTER-AIDED EXPLORATION OF PERIOD DOUBLING (2001) (6)
Making Sense of Mathematical Thinking over the Long Term: The Framework of Three Worlds of Mathematics and New Developments (2019) (6)
LONG-TERM DEVELOPMENT OF MATHEMATICAL THINKING AND LESSON STUDY (2008) (5)
Graphical Packages for Mathematics Teaching & Learning (1987) (5)
A Comparative Study of Cognitive Units in Mathematical Thinking (2001) (5)
Building Long-term Meaning in Mathematical Thinking: Aha! and Uh-Huh! (2019) (5)
Chords, tangents and the Leibniz notation (1985) (5)
James J. Kaput (1942–2005) imagineer and futurologist of mathematics education (2008) (5)
Long-term principles for meaningful teaching and learning of mathematics (2019) (5)
LONG-TERM DEVELOPMENT OF MATHEMATICAL THINKING AND LESSON STUDY (2008) (5)
Building Long-term Meaning in Mathematical Thinking: Aha! and Uh-Huh! (2019) (5)
Attainment and Potential: Procedures, Cognitive Kit-Bags and Cognitive Units (2001) (4)
Visual Organisers for Formal Mathematics (1995) (4)
Success and Failure in Mathematics: Procept and Procedure 1. A Primary Perspective (1992) (4)
Schemas and processes for sketching the gradient of a graph (2001) (4)
Verbal Evidence for Versatile Understanding of Variables in a Computer Environment (1989) (4)
The complementary roles of prepared software & programming in the learning of mathematics (1986) (4)
New Cognitive Obstacles in a Technological Paradigm (1989) (4)
Conceptual Foundations of the Calculus and the Computer (1992) (4)
Cognitive Units, Connections and Compression in Mathematical Thinking1 (2002) (4)
Metaphorical Objects in Advanced Mathematical Thinking (1997) (3)
Advanced calculus (3rd edition) , by Wilfred Kaplan. Pp 721. £14·95. 1984. ISBN 0-201-11680-4 (Addison-Wesley) (1985) (3)
UNIVERSITY STUDENTS ’ EMBODIMENT OF QUANTIFIERS (2002) (3)
COGNITIVE AND SOCIAL DEVELOPMENT OF PROOF THROUGH EMBODIMENT , SYMBOLISM & FORMALISM (2008) (3)
Computers in the mathematics curriculum : a report of the Mathematical Association (1992) (3)
Visualizing Differentials in Integration to Picture the Fundamental Theorem of Calculus (1991) (3)
Flexible Thinking, Consistency, and Stability of Responses: A Study of Divergence (2001) (3)
Can All Children Climb the Same Curriculum Ladder (1996) (3)
Complex Analysis: Taylor series (1983) (3)
Existence Statements and Constructions in Mathematics and Some Consequences to Mathematics Teaching. (1982) (3)
Mathematicians thinking about Students thinking about Mathematics (1993) (3)
The Anatomy of a Discovery in Mathematics Research (2016) (3)
Construction of Objects through Definition and Proof (1999) (3)
Graphic Insight into Mathematical Concepts 1 (1992) (3)
The Development of Mathematical Thinking: Problem-Solving and Proof (2009) (3)
THE PSYCHOLOGY OF SYMBOLS & SYMBOL MANIPULATORS: WHAT ARE WE DOING RIGHT? (1995) (2)
Comments on the Difficulty and Validity of Various Approaches to the Calculus (2017) (2)
Infinity – the never-ending struggle 1 (2002) (2)
Different Cognitive Obstacles in a Technological Paradigm or A Reaction to: "Cognitive Obstacles Encountered in the Learning of Algebra" 1 (2018) (2)
The effectiveness of lesson study on mathematical knowledge for teaching (2010) (2)
Yes, Virginia, Some Children Do Grow up to Be Mathematicians@@@Advanced Mathematical Thinking (1993) (2)
Blending Ideas in the Calculus (2013) (2)
The Chasm between Thought Experiment and Formal Proof (1999) (2)
Modelling irrational numbers in analysis using elementary programming (1992) (2)
Introducing Algebra on the Computer: Today and Tomorrow. (1983) (2)
Drawing Implicit Functions. (1986) (2)
Computing languages for the mathematics classroom (1987) (1)
A Quartic with a thousand roots (1990) (1)
Essay Review " Mathematics as an Educational Task " (2014) (1)
The Articulation Principle for making long-term sense of mathematical expressions by how they are spoken and heard: Two case studies (2022) (1)
Students' Concept Images for Period Doublings as Embodied Objects in Chaos Theory (2001) (1)
Calculations and Canonical Elements (2005) (1)
The calculus curriculum in the microcomputer age: A Working Group Report from the Ware Conference (1986) (1)
School algebra and the computer (1993) (1)
The Evolution of Technology and the Mathematics of Change and Variation: Using Human Perceptions and Emotions to Make Sense of Powerful Ideas (2013) (1)
What do we "see" in geometric pictures? (the case of the blancmange function) (2000) (1)
W(h)ither calculus (1987) (1)
Minkowski’s theorem (1979) (1)
Calculations and Canonical Elements: Part I. (1979) (1)
MATHEMATICAL AND EMOTIONAL FOUNDATIONS FOR LESSON STUDY IN MATHEMATICS (2010) (1)
Strengthening the 1960s UK Commonwealth Institute hyperbolic paraboloid roof (2020) (1)
Mathematics and Emotion (2013) (1)
Infinitesimals in Real and Complex Analysis (2018) (0)
Sensible mathematics: sense making of trigonometric relationships in the context of lesson study (2013) (0)
How Humans Learn to Think Mathematically: Expert Thinking and Structure Theorems (2013) (0)
Mathematical Thinking & the Brain (1978) (0)
How Humans Learn to Think Mathematically: Problem Solving and Proof (2013) (0)
How Humans Learn to Think Mathematically: References (2013) (0)
Technology and Cognitive Growth in Mathematics (1999) (0)
Technology and Versatile Thinking in Mathematics; Proceedings of Society for Information Technology in Teacher Educational Conference. (2009) (0)
Factorization into irreducibles (1979) (0)
The origins of algebraic number theory (1979) (0)
Success and failure in arithmetic and algebra (1992) (0)
The Origins of Complex Analysis, and Its Challenge to Intuition (2018) (0)
The exponential function (1983) (0)
How Humans Learn to Think Mathematically: Compression, Connection and Blending of Mathematical Ideas (2013) (0)
Works for chorus and orchestra (1996) (0)
How Humans Learn to Think Mathematically: Where It All Came From (2013) (0)
Geometric representation of algebraic numbers (1979) (0)
G. Frobentus, The Collected Works of Frobenius (1849–1917) , edited by J.-P. Serre (Springer-Verlag, 1968), 3 vols., $34.00. (1969) (0)
Contemplating the Infinitely Large and Small (2013) (0)
Complex Analysis: Laurent series (1983) (0)
Journeys through Embodiment and Symbolism (2013) (0)
Proceedings of the International Conference for the Psychology of Mathematics Education (3rd, Coventry, England, July 9-14, 1979). (1979) (0)
Algebraic Epic (1969) (0)
Complex Analysis: Homotopy versions of Cauchy's Theorem (1983) (0)
CRYSTALLIZING MATHEMATICS CONCEPTS (2015) (0)
In their critique of “object as a central metaphor in advanced mathematical thinking”, Confrey and Costa (1996) describes members of the Advanced Mathematical Thinking Group, including myself, as “reification theorists”. By selective quation they attibute theores (1999) (0)
The Nature of Advanced Mathematical Thinking a discussion paper for PME - Hungary 1988 (1988) (0)
How Humans Learn to Think Mathematically: Reflections (2013) (0)
Fundamental Deficiencies (1969) (0)
Continuous Mathematics and Discrete Computing Are Complementary, Not Alternatives... (1984) (0)
Significant Changes in University Mathematics Education (2019) (0)
Complex Analysis: Angles, logarithms, and the winding number (1983) (0)
Quadratic and cyclotomic fields (1979) (0)
Cauchy’s Theorem (2018) (0)
Versatile Learning & the Computer (1989) (0)
Complex Analysis: Algebra of the complex plane (1983) (0)
Long-Term Effects of Sense Making and Anxiety in Algebra (2017) (0)
The Transition to Formal Knowledge (2013) (0)
How Humans Learn to Think Mathematically: Expanding the Frontiers through Mathematical Research (2013) (0)
Journeys through three worlds of mathematics (2013) (0)
What Mathematics is Needed by Teachers of Young Children ? (2004) (0)
Lesson Study in secondary education (2021) (0)
Complex Analysis: The origins of complex analysis, and a modern viewpoint (1983) (0)
Promoting versatile learning of higher order concepts in algebra using the computer (1988) (0)
RESPONSE TO THE REACTION BY CZARNOCHA & PRABHU (2004) (0)
How Humans Learn to Think Mathematically: The Foundations of Mathematical Thinking (2013) (0)
How Humans Learn to Think Mathematically: Illustration Credits (2013) (0)
Complex Analysis: Topology of the complex plane (1983) (0)
Complex Analysis: Analytic continuation (1983) (0)
Class-group and class-number (1979) (0)
Enhancing pre-service mathematics teachers’ understanding of function ideas (2022) (0)

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What Schools Are Affiliated With David Tall?

David Tall is affiliated with the following schools: