Mathematical Cognition Bibliography

The following bibliography represents a broad selection of readings in the emerging field of mathematical cognition. The selections come from the fields of computer science (with a particular emphasis on knowledge representation and reasoning), linguistics, psychology, education, child development and mathematics. The listing is incomplete and will grow over time. Entries in red are those I consider essential to the field. Click here for a partial index of author homepages. A CiteLine generated version of the final bibliography I used in my dissertation can be found here.

1922:

  1. Thorndike, Edward L. (1922), The Psychology of Arithmetic (New York: Macmillan).


1945:

  1. Polya, George (1945), How to Solve It: A New Aspect of the Mathematical Method (Princeton: Princeton University Press).


1950:

  1. Turing, A. M. (1950), "Computing Machinery and Intelligence", Mind 59(236): 433-460.


1956:

  1. Whorf, Benjamin Lee (1956), Language, Thought and Reality (Cambridge: MIT Press).


1958:

  1. McSwain, E.T. and Cooke, Ralph J. (1958), Understanding and Teaching Arithmetic in the Elementary School (New York: Holt, Rinehart and Winston).


1961:

  1. McCulloch, Warren (1961), "What is a Number, that a Man May Know It, and a Man, that He May Know a Number?", General Semantics Bulletin 26,27: 7-18.


1962:

  1. Simon, Herbert (1962), "An Information Processing Theory of Intellectual Development", Monographs of the Society for Research in Child Development 27(2, Serial No. 82).


1964:

  1. Banks, J. Houston (1964), Learning and Teaching Arithmetic, Second Edition (Boston: Allyn and Bacon).


1965:

  1. Benacerraf, Paul (1965), "What Numbers Could not Be", The Philosophical Review, 74(1): 47-73


  2. Piaget, Jean (1965), The Child's Conception of Number (New York: Norton).


1967:

  1. Putnam, Hilary (1967), "Mathematics without Foundations", The Journal of Philosophy, 64(1): 5-22.


1968:

  1. Bobrow, Daniel G. (1968), "Natural Language Input for a Computer Problem-Solving System", in Marvin Minsky (ed.), Semantic Information Processing (Cambridge: MIT Press): 146-226.


  2. Polya, George (1968), Induction and Analogy in Mathematics (Mathematics and Plausible Reasoning, Vol 1) (Princeton: Princeton University Press).


1969:

  1. Quine, Willard Van Orman (1969), "Ontological Relativity", Ontological Relativity and Other Essays (New York: Columbia University Press): 26-68.

1971:

  1. Baier, Annette (1971), "The Search for Basic Actions", American Philosophical Quarterly 8(2): 161-170.


  2. Linderholm, Carl E. (1971), Mathematics Made Difficult: A Handbook for the Perplexed (New York: World Publishing).


1972:

  1. Groen, G.J. and Parkman, J. M. (1972), "A Chronometric Analysis of Simple Addition", Psychological Review 79: 329-343.


1973:

  1. Benacerraf, Paul (1973), "Mathematical Truth", The Journal of Philosophy, 70(19): 661-679.


  2. Hayes, John R. (1973), "On the Function of Visual Imagery in Elementary Mathematics", in W. G. Chase (ed.), Visual Information Processing (New York: Academic Press): 177-214.


  3. Klahr, David (1973), "Quantification Processes", in W. G. Chase (ed.), Visual Information Processing (New York: Academic Press): 3-34.


  4. Klahr, David (1973), "A Production System for Counting, Subitizing and Adding", in W. G. Chase (ed.), Visual Information Processing (New York: Academic Press): 527-546.


  5. Klahr, David (1973), "The Role of Quantification Operators in the Development of Conservation of Quantity", Cognitive Psychology 4(3): 301-327.


  6. Newell, Allen (1973), "Production Systems: Models of Control Structures", in W. G. Chase (ed.), Visual Information Processing (New York: Academic Press): 463-526.


1975:

  1. Resnik, Michael (1975), "Mathematical Knowledge and Pattern Cognition", Canadian Journal of Philosophy 5(1): 25-40.

1976:

  1. Belnap, Nuel D. Jr. and Steel, Thomas B. Jr. (1976), The Logic of Questions and Answers (New Haven: Yale University Press).

1977:

  1. Groen, G. and Resnick, L. (1977), "Can preschool children invent addition algorithms?", Journal of Educational Psychology 69: 645-652.


  2. Shapiro, S.C. (1977), "Representing numbers in semantic networks: prolegomena", in Raj Reddy (ed.), Proceedings of the 5th International Joint Conference on Artificial Intelligence, (Los Altos: Morgan Kaufmann): 284.


1978:

  1. Brown, John Seely and Burton, Richard R. (1978), "Diagnostic Models for Procedural Bugs in Basic Mathematical Skills", Cognitive Science 2(2): 155-192.


  2. Gelman, R. and Gallistel, C.R. (1978), The Child's Understanding of Number (Cambridge: Harvard University Press).


1979:

  1. Robertson, Jane I. (1979), "How to Do Arithmetic", American Mathematical Monthly 86(6; June/July): 431-439.

1980:

  1. Bach, Kent (1980), "Actions Are Not Events", Mind 89(353): 114-120.


  2. Brown, John Seely and VanLehn, Kurt (1980), "Repair Theory: A Generative Theory of Bugs in Procedural Skills", Cognitive Science 4(4): 379-426.


  3. Frege, Gottlob (1980), The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, Trans. J. L. Austin. (Evanston: Northwestern University Press).


  4. VanLehn, Kurt and Brown, John Seely (1980), "Planning Nets: A Representation for Formalizing Analogies and Semantic Models of Procedural Skills", in Richard E. Snow, Pat-Anthony Federico, and William E. Montague (eds.), Aptitude, Learning, and Instruction: Vol. 2 Cognitive Process Analyses and Problem Solving (Hillsdale: Lawrence Erlbaum Associates): 95-137.


1981:

  1. Mac Lane, Saunders (1981), "Mathematical models: a sketch for the philosophy of mathematics", American Mathematical Monthly 88: 462-472.

1982:

  1. Brainerd, Charles J. (1982), Children's Logical and Mathematical Cognition: Progress in Cognitive Development Research (New York: Springer-Verlag).


  2. Brown, John Seely and VanLehn, Kurt (1982), "Towards a Generative Theory of 'Bugs'", in Thomas P. Carpenter, Thomas A. Romberg, and James M. Moser (eds.), Addition and Subtraction: A Cognitive Perspective (Hillsdale: Lawrence Erlbaum Associates): 117-135.


  3. Carpenter, Thomas P. and Moser, James M. (1982), "The Development of Addition and Subtraction Problem-Solving Skills", in Thomas P. Carpenter, Thomas A. Romberg, and James M. Moser (eds.), Addition and Subtraction: A Cognitive Perspective (Hillsdale: Lawrence Erlbaum Associates): 9-24.


  4. Davis, Randall and Lenat, Douglas B. (1982), "AM: Discovery in Mathematics as Heuristic Search", in Randall Davis (ed.), Knowledge-Based Systems in Artificial Intelligence, (New York: Springer-Verlag): 3-225.


  5. Romberg, Thomas A. (1982), "An Emerging Paradigm for Research on Addition and Subtraction Skills", in Thomas P. Carpenter, Thomas A. Romberg, and James M. Moser (eds.), Addition and Subtraction: A Cognitive Perspective (Hillsdale: Lawrence Erlbaum Associates): 1-7.


  6. Starkey, Prentice and Gelman, Rochel (1982), "The Development of Addition and Subtraction Abilities Prior to Formal Schooling in Arithmetic", in Thomas P. Carpenter, Thomas A. Romberg, and James M. Moser (eds.), Addition and Subtraction: A Cognitive Perspective (Hillsdale: Lawrence Erlbaum Associates): 99-116.


1983:

  1. Bundy, Alan (1983), The Computer Modelling of Mathematical Reasoning (New York: Academic Press).


  2. Davis, Robert B. (1983), "Complex Mathematical Cognition", in Herbert Ginsburg (ed.), The Development of Mathematical Thinking (New York: Academic Press): 253-290.


  3. Fodor, Jerry A. (1983), Representations: Philosophical Essays on the Foundations of Cognitive Science (Cambridge: MIT Press).


  4. Fuson, Karen C. and Hall, James W. (1983), "The Acquisition of Early Number Word Meanings: A Conceptual Analysis and Review", in Herbert Ginsburg (ed.), The Development of Mathematical Thinking (New York: Academic Press): 49-107.


  5. Ginsburg, Herbert P., et al. (1983), "Protocol Methods in Research on Mathematical Thinking", in Herbert Ginsburg (ed.), The Development of Mathematical Thinking (New York: Academic Press): 7-47.


  6. Resnick, Lauren B. (1983), "A Developmental Theory of Number Understanding", in Herbert Ginsburg (ed.), The Development of Mathematical Thinking (New York: Academic Press): 109-151.


  7. Riley, Mary S., et al. (1983), "Development of Children's Problem-Solving Ability in Arithmetic", in Herbert Ginsburg (ed.), The Development of Mathematical Thinking (New York: Academic Press): 153-196.


  8. Secada, Walter, et al. (1983), "The Transition from Counting-All to Counting-On in Addition", Journal for Research in Mathematics Education 14(1): 47-57.


  9. Van Lehn, Kurt (1983), "On the Representation of Procedures in Repair Theory", in Herbert Ginsburg (ed.), The Development of Mathematical Thinking (New York: Academic Press): 197-252.


1984:

  1. Baroody, Arthur J. (1984), "The Case of Felicia: A Young Child's Strategies for Reducing Memory Demands During Mental Addition", Cognition and Instruction 1(1; Winter): 109-116.


  2. Carpenter, Thomas P. and Moser, James M. (1984), "The Acquisition of Addition and Subtraction Concepts in Grades One Through Three", Journal for Research in Mathematics Education 15(3): 179-202.


  3. Greeno, J.G., Riley, M.S, and Gelman, R. (1984), "Conceptual Competence and Children's Counting", Cognitive Psychology 16: 94-143.


  4. Kitcher, Philip (1984), The Nature of Mathematical Knowledge, (Oxford: Oxford University Press).


1985:

  1. Ashcraft, Mark (1985), "Is It Farfetched That Some of Us Remember Our Arithmetic Facts?", Journal for Research in Mathematics Education 16(2): 99-105.


  2. Baroody, Arthur (1985), "Mastery of Basic Number Combinations: Internalization of Relationships or Facts?", Journal for Research in Mathematics Education 16(2): 83-98.


  3. Dellarosa, Denise (1985), "Abstraction of Problem-Type Schemata Through Problem Comparison", University of Colorodo Technical Report 85-146.


  4. Dellarosa, Denise, et al. (1985), "Children's Recall of Arithmetic Word Problems", University of Colorodo Technical Report 85-147.


  5. Dellarosa, Denise (1985), "SOLUTION: A Computer Simulation of Children's Recall of Arithmetic Word Problem Solving", University of Colorodo Technical Report 85-148.


  6. Fletcher, Charles R. (1985), "Understanding and Solving Arithmetic Word Problems: A Computer Simulation", Behavioral Research Methods, Instruments and Computers 17: 365-371.


  7. Kintsch, Walter and Greeno, James G. (1985), "Understanding and Solving Word Arithmetic Problems", Psychological Review 92(1): 109-129.


  8. Minsky, Marvin (1985), The Society of Mind (esp. sections 18.6-18.8 "Magnitude From Multitude", "What Is A Number?", "Mathematics Made Hard"). (New York: Simon & Schuster Inc).

1986:

  1. Hiebert, James and Lefevre, Patricia (1986), "Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis", in James Hiebert (ed.), Conceptual and Procedural Knowledge: The Case of Mathematics (Hillsdale: Lawrence Erlbaum Associates): 1-27.


1987:

  1. Anzai, Yuichiro (1987), "Doing, Understanding, and Learning in Problem Solving", in David Klahr (ed.), Production System Models of Learning and Development (Cambridge: MIT Press): 55-97.


  2. Greeno, James G. (1987), "Instructional Representations Based on Research about Understanding", in Alan Schoenfeld (ed.), Cognitive Science and Mathematics Education (Hillsdale: Lawrence Erlbaum Associates): 61-88.


  3. Lakoff, George (1987), Women, Fire and Dangerous Things: What Categories Reveal about the Mind (Chicago: University of Chicago Press).


  4. Neches, Robert (1987), "Learning through Incremental Refinement of Procedures", in Herbert Ginsburg (ed.), Production System Models of Learning and Development (Cambridge: MIT Press): 163-219.


  5. Ohlsson, Stellan (1987), "Truth Versus Appropriateness: Relating Declarative to Procedural Knowledge", in Herbert Ginsburg (ed.), Production System Models of Learning and Development (Cambridge: MIT Press): 287-327.


  6. Rosenbloom, Paul and Newell, Allen (1987), "Learning by Chunking: A Production System Model of Practice", in Herbert Ginsburg (ed.), Production System Models of Learning and Development (Cambridge: MIT Press): 221-286.


  7. Schoenfeld, Alan H. (1987), "What's All the Fuss About Metacognition?", in Alan Schoenfeld (ed.), Cognitive Science and Mathematics Education (Hillsdale: Lawrence Erlbaum Associates): 189-215.


  8. VanLehn, Kurt (1987), "Learning one subprocedure per lesson", Artificial Intelligence 31(1): 1-40.


1988:

  1. Cummins, Denise Dellarosa, et al. (1988), "The Role of Understanding in Solving Word Problems", Cognitive Psychology 20: 405-438.


  2. Fuson, Karen C. (1988), Children's Counting and Concepts of Number (New York: Springer-Verlag)


  3. Nathan, Michael J., et al. (1988), "Tutoring Algebra Word Problems", University of Colorodo Technical Report 88-12.


  4. Weaver, Charles A. and Kintsch, Walter (1988), "The Conceputal Structure of Word Algebra Problems", University of Colorodo Technical Report 88-11.


1989:

  1. Diamond, Cora (ed) (1989), Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939 (Chicago: University of Chicago Press).


1990:

  1. Defays, Daniel (1990), "Numbo: A Study in Cognition and Recognition", The Journal for the Integrated Study of Artificial Intelligence, Cognitive Science, and Applied Epistemology 7(2):217-243.


  2. Harnad, Stevan (1990), "The Symbol Grounding Problem", Physica D 42: 335-346.


  3. Rapaport, William (1990), "Computer Processes and Virtual Persons: Comments on Cole's Artificial Intelligence and Personal Identity", Technical Report 90-13 (Buffalo: SUNY Buffalo Department of Computer Science).


  4. Wynn, Karen (1990), "Children's Understanding of Counting", Cognition 36: 155-193.
    5.

1991:

  1. Lewis, Anne B. and Nathan, Mitchell, Nathan J. (1991), "A Framework for Improving Students' Comprehension of Word Arithmetic and Word Algebra Problems", University of Colorodo Technical Report 91-05.


  2. Ohlsson, Stellan and Rees, Ernest (1991), "The Function of Conceptual Understanding in the Learning of Arithmetic Procedures", Cognition and Instruction 8(2): 103-179.


  3. Simon, Tony, et al. (1991), "A Computational Account of Children's Learning About Number Conservation", in Douglas H., Jr. Fisher, Michael J. Pazzani, and Pat Langley (eds.), Concept Formation: Knowledge and Experience in Unsupervised Learning (San Mateo: Morgan Kaufmann Publishers): 423-462.


  4. Sfard, Anna (1991), "On The Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of the Same Coin", Educational Studies in Mathematics 22: 1-36.


1992:

  1. Ashcraft, Mark H. (1992), "Cognitive arithmetic: A review of data and theory", Cognition 44(1-2): 75-106.


  2. Bromberger, Sylvain (1992), "Why Questions", in Sylvain Bromberger (ed) On What We Know We Don't Know (Chicago: University of Chicago Press): 75-100.


  3. Campbell, Jamie I. D. (ed) (1992), The Nature and Origins of Mathematical Skills (Amsterdam: Elsevier).


  4. Dehaene, Stanislas (1992), "Varieties of numerical abilities", Cognition 44(1-2): 1-42.


  5. Rickard, Timothy C., et al. (1992), "An Interactive Activation Model of Arithmetic Fact Retrieval", University of Colorodo Technical Report 92-15.


  6. VanLehn, Kurt, et al. (1992), "A Model of the Self-Explanation Effect", Journal of the Learning Sciences 2(1): 1-59.


  7. Wynn, Karen (1992), "Evidence Against Empiricist Accounts of the Origins Numerical Knowledge", Mind and Language 7(4; Winter): 315-332.


1993:

  1. Hauser, Larry (1993), "Why Isn't My Pocket Calculator a Thinking Thing", Minds and Machines 3(1): 3-10.


  2. Leblanc, Mark D. (1993), "From Natural Language to Mathematical Representations: A model of 'Mathematical Reading'", in Hyacinth S. Nwana (ed.), Mathematical Intelligent Learning Environments (Oxford: Intellect Books): 126-144.


  3. Nwana, Hyacinth S. (1993), "Mathematical Intelligent Learning Environments", in Hyacinth S. Nwana (ed.), Mathematical Intelligent Learning Environments (Oxford: Intellect Books): 3-13.


  4. Nwana, Hyacinth S. (1993), "The Anatomy of FITS: A Mathematical Tutor", in Hyacinth S. Nwana (ed.), Mathematical Intelligent Learning Environments (Oxford: Intellect Books): 79-109.


  5. Rapaport, William (1993), "Mere Calculating Isn't Thinking: Comments on Hauser's 'Why Isn't My Pocket Calculator a Thinking Thing?'", Minds and Machines 3(1):11-20.


1994:

  1. Crangle, Colleen and Suppes, Patrick (1994), Language and Learning for Robots (Stanford: CSLI Publications).


  2. George, Alexander (ed) (1994), Mathematics and Mind (Oxford: Oxford University Press).


  3. Johnson, Jeffrey; McKee, Sean; and Vella, Alfred eds. (1994), Artificial Intelligence in Mathematics (Oxford: Clarendon Press).


  4. Jones, Randolph M. and VanLehn Kurt (1994), "Acquisition of Children's Addition Strategies: A Model of Impasse-Free, Knowledge-Level Learning", Machine Learning 16: 11-36.


  5. Sfard, Anna and Linchevski, Liora (1994), "The Gains and Pitfalls of Reification - The Case of Algebra", Educational Studies in Mathematics 26: 191-228.


1995:

  1. Hutchins, Edwin (1995), Cognition in the Wild, (Cambridge: MIT Press).


  2. Hofstadter, Douglas, et al. (1995), Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought (New York: BasicBooks).


  3. Wynn, Karen (1995), "Origins of Numerical Knowledge", Mathematical Cognition 1(1): 35-60.


  4. Zhang, Jiajie and Norman, Donald A. (1995), "A Representational Analysis of Numeration Systems", Cognition 57: 271-295.

1996:

  1. LeBlanc, Mark D. and Weber-Russell, Sylvia (1996), "Text Integration and Mathematical Connections: A Computer Model of Arithmetic Word Problem Solving", Cognitive Science 20(3): 357-407.


  2. Noss, Richard, et al. (1996), "The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic", Educational Studies in Mathematics 33(2): 203-233.


  3. Regier, Terry (1996), The Human Semantic Potential: Spatial Language and Constrained Connectionism (Cambridge: MIT Press).


  4. Slavit, David (1996), "An Alternate Route to the Reification of Function", Educational Studies in Mathematics 33(3): 259-281.


  5. Wynn, Karen (1996), "Infants' Individuation and Enumeration of Actions", Psychological Science 7(3): 164-169.


1997:

  1. Brenner, William (1997), "Arithmetic as Grammar", Philosophical Investigations 20(4): 315-325


  2. Dehaene, Stanislas (1997), The Number Sense (Oxford: Oxford University Press).


  3. Furse, Edmund (1997), "Human and Machine Understanding of Mathematics", Univeristy of Glamorgan Technical Report CS-97-1.


  4. McGee, Vann (1997), "How We Learn Mathematical Language", Philosophical Review, 106(1): 35-68


  5. Zorzi, Marco (1997), "On the Representation of Number Concepts", Proceedings of the 19th Annual Conference of the Cognitive Science Society: 1098.


1998:

  1. Clark, Andy and Chalmers, David (1998), "The Extended Mind", Analysis 58(1): 7-19.


  2. Devlin, Keith (1998), The Language of Mathematics: Making the Invisible Visible (New York: Henry Holt and Company).


  3. English, Lyn D. (1998), "Reasoning by Analogy in Solving Problems", Mathematical Cognition 4(2): 125-146.


  4. Fuson, Karen C. (1998), "Pedagogical, Mathematical, and Real-World Conceptual Support Nets: A Model for Building Children's Multidigit Domain Knowledge", Mathematical Cognition 4(2): 147-186.


  5. Giroux, Jacinthe and Lemoyne, Gisèle (1998), "Coordination of Knowledge of Numeration and Arithmetic Operations on First Grade Students", Educational Studies in Mathematics 35(3): 283-301.


  6. Goodson-Espy, Tracy (1998), "The Roles of Reification and Reflective Abstraction in the Development of Abstract Thought: Transitions from Arithmetic to Algebra", Educational Studies in Mathematics 36(3): 219-245.


  7. Harel, Guershon (1998), "Two Dual Assertions: The First on Learning and the Second on Teaching (or Vice Versa)", American Mathematical Monthly 105(6): 497-507.


  8. Hauser, Marc and Carey, Susan (1998), "Building a Cognitive Creature from a Set of Primitives: Evolutionary and Developmental Insights", in Denise Dellarosa Cummins and Colin Allen (eds.), The Evolution of Mind (Oxford: Oxford University Press): 51-106.


  9. Lebiere, Christian (1998), "The Dynamics of Cognition: An ACT-R Model of Cognitive Arithmetic", PhD Dissertation. Computer Science Department, Carnegie Mellon University.


  10. Pirie, Susan E.B. (1998), "Crossing the Gulf between Thought and Symbol: Language as (Slippery) Stepping-Stones", in Heinz Steinbring, Maria G. Bartolini Bussi, and Anna Sierpinska (eds.), Language and Communication in the Mathematics Classroom (Reston: NTCM): 7-29.


  11. Sfard, Anna (1998), "Symbolizing Mathematical Reality into Being - or How Mathematical Discourse and Mathematical Objects Create Each Other", in Paul Cobb, Erna Yackel, Kay McClain (eds.), Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Mathematical Discourse, Tools, and Instructional Design (Mahwah: Erlbaum): 37-98.


  12. Sharon, Tanya and Wynn, Karen (1998), "Individuation of Actions from Continuous Motion", Psychological Science 9(5): 357-362.


  13. Slavit, David (1998), "The Role of Operation Sense in Transitions from Arithmetic to Algebraic Thought", Educational Studies in Mathematics 37(3): 251-274.


  14. White, C. Stephen, Alexander, Patricia A., Daugherty, Martha (1998), "The Relationship between Young Children's Analogical Reasoning and Mathematical Learning", Mathematical Cognition 4(2): 103-123.


  15. Wynn, Karen (1998), "An Evolved Capacity for Number", in Denise Dellarosa Cummins and Colin Allen (eds.), The Evolution of Mind (Oxford: Oxford University Press): 107-126.


1999:

  1. Bisanz, Jeff (1999), "The Development of Mathematical Cognition: Arithmetic", Journal of Experimental Child Psychology, 74(3): 153-156.


  2. Butterworth, Brian (1999), What Counts: How Every Brain is Hardwired for Math (New York: Free Press).


  3. Clements, Douglas H. (1999), "Subitizing: What is it? Why Teach it?", Teaching Children Mathematics 5(7): 400-405.


  4. Davis, Phillip J. and Hersh, Reuben (1999), The Mathematical Experience (New York: Mariner Books).


  5. Ernest, Paul (1999), "Forms of Knowledge in Mathematics and Mathematics Education: Philosophical and Rhetorical Perspectives", Educational Studies in Mathematics, 38(1-3): 67-83.


  6. Fischbein, Efraim (1999), "Intuitions and Schemata in Mathematical Reasoning", Educational Studies in Mathematics, 38(1-3): 11-50.


  7. Lucas, John Randolph (1999), The Conceptual Roots of Mathematics (Oxford: Routledge).


  8. Mason, John and Spence, Mary (1999), "Beyond Mere Knowledge of Mathematics: The Importance of Knowing-To Act in the Moment", Educational Studies in Mathematics, 38(1-3): 135-161.


  9. Michell, Joel (1999), Measurement in Psychology: Critical History of a Methodologial Concept (Cambridge: Cambridge University Press).


  10. Tirosh, Dina and Stavy, Ruth (1999), "Intuitive Rules: A Way to Explain and Predict Students' Reasoning", Educational Studies in Mathematics, 38(1-3): 51-66.


2000:

  1. Borasi, Raffaella and Siegel, Marjorie (2000), Reading Counts: Expanding the Role of Reading in Mathematics Classrooms (New York: Teachers College Press).


  2. Devlin, Keith (2000), The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip (New York: Basic Books).


  3. Dubinsky, Ed (2000), "Meaning and Formalism in Mathematics",International Journal of Computers for Mathematical Learning 5(3;September): 211 -240.


  4. Freund, Max (2000), "A Complete and Consistent Formal System for Sortals", Studia Logica 65: 367-381.


  5. Horrocks, Ian and Tobies, Stephan (2000), "Reasoning with Axioms: Theory and Practice", in A.G. Cohn, F. Giunchiglia, and B. Selman (eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the Seventh International Conference (KR2000): 285-296.


  6. Lakoff, George and Núñez, Rafael E. (2000), Where Mathematics Comes From: How The Embodied Mind Brings Mathematics Into Being (New York: Basic Books).


  7. Markman, Arthur B. and Dietrich, Eric (2000), "In Defense of Representation", Cognitive Psychology 40(2): 138-171.


  8. Peterson, Scott A. and Simon, Tony J. (2000), "Computational Evidence for the Subitizing Phenomenon as an Emergent Property of the Human Cognitive Architecture", Cognitive Science 24(1): 93-122.


  9. Sfard, Anna (2000), "Steering (Dis)Course Between Metaphor and Rigor: Using Focal Analysis to Investigate an Emergence of Mathematical Objects", Journal for Research in Mathematics Education 31(3): 296-327.


  10. Sherry, Lance (2000), "Using Rule-Based Models for Training Complex Skills", PCAI: Intelligent Web Applications & Object Oriented Development (March/April 2000): 24-27.


  11. Star, Jon R. (2000), "On the Relationship Between Knowing and Doing in Procedural Learning", in B. Fishman and S. O'Connor-Divelbiss (eds.), Fourth International Conference of the Learning Sciences (Mahwah: Lawrence Erlbaum Associates): 80-86.


2001:

  1. Bassok, Miriam (2001), "Semantic Alignments in Mathematical Word Problems", in Dedre Gentner, Keith J. Holyoak and Boicho K. Kokinov (eds.), The Analogical Mind: Perspectives from Cognitive Science (Cambridge: MIT Press): 401-433.


  2. Bazzini, Luciana (2001), "From Grounding Metaphors to Technological Devices: A Call for Legitimacy in School Mathematics", Educational Studies in Mathematics 47(3): 259-271.


  3. Butterworth, Brian, et al. (2001), "Storage and Retrieval of Addition Facts: The Role of Number Comparison", The Quarterly Journal of Experimental Psychology 54A(4): 1005-1029.


  4. Campbell, Jamie I. D. and Xue, Qilin (2001), "Cognitive Arithmetic Across Cultures", Journal of Experimental Psychology: General 130(2): 299-315.


  5. Hofstadter, Douglas R. (2001), "Epilogue: Analogy as the Core of Cognition", in Dedre Gentner, Keith J. Holyoak and Boicho K. Kokinov (eds.), The Analogical Mind: Perspectives from Cognitive Science (Cambridge: MIT Press): 499-538.


  6. Marcus, Gary F. (2001), The Algebraic Mind: Integrating Connectionism and Cognitive Science (Cambridge: MIT Press).


  7. Polk, Thad, et al. (2001), "A Dissociation Between Symbolic Number Knowledge and Analogue Magnitude Information", Brain and Cognition 47: 545-563.


2002:

  1. Brannon, Elizabeth and Roitman, Jamie (2002), "Non-verbal Representations of Time and Number in Non-Human Animals and Human Infants", in Warren H. Meck (ed.), Functional and Neural Mechanisms of Interval Timing (Boca Raton: CRC Press): 143-182.


  2. Griffin, Sharon (2002), "The Development of Math Competence in the Preschool and Early School Years: Cognitive Foundations and Instructional Strategies", Mathematical Cognition (Greenwich: Information Age Publishing): 1-32.


  3. Heirdsfield, Ann (2002), "The Interview in Mathematics Education: The Case of Mental Computation", Australian Association for Research in Education 2002 Conference.


  4. Raman, Manya (2002), "Coordinating Informal and Formal Aspects of Mathematics: Student Behavior and Textbook Messages", Journal of Mathematical Behavior 21: 135-150.


  5. Speiser, Bob (2002), "How Does Building Arguments Relate to the Development of Understanding?", Journal of Mathematical Behavior 21: 491-497.


  6. Squire, Sarah and Bryant, Peter (2002), "The Influence of Sharing on Children's Initial Concept of Division", Journal of Experimental Child Psychology 81: 1-43.


2003:

  1. Brannon, Elizabeth (2003), "Number Knows No Bounds", Trends in Cognitive Sciences, 7(7): 279-281.


  2. Cooper, Barry and Harries, Tony (2003), "Children's Use of Realistic Considerations in Problem Solving: Some English Evidence", Journal of Mathematical Behavior 22: 451-465.


  3. Husserl, Edmund (2003), "Philosophy of Arithmetic: Psychological and Logical Investigations", in D. Willard (trans), Philosophy of Arithmetic: Psychological and Logical Investigations with Supplementary Texts from 1887-1901 (Boston: Kluwer Academic Publishers): 5-299


  4. Lemer, Cathy, et al. (2003), "Approximate Quantities and Exact Number Words: Dissociable Systems", Neuropsychologia 41: 1942-1958.


  5. Shapiro, Stuart C. and Ismail, Haythem O. (2003), "Anchoring in a grounded layered architecture with integrated reasoning", Robotics and Autonomous Systems 43: 97-108.


  6. Stoianov, I., Zorzi, M., Umiltà, C. (2003) "A connectionist model of simple mental arithmetic", in F. Schmalhofer, R.M. Young, and G. Katz (eds.), Proceedings of EuroCogSci03: 313-318.


  7. Walsh, Vincent (2003), "Cognitive Neuroscience: Numerate Neurons", Current Biology 13: R447-R448.


  8. Wiese, Heike (2003), Numbers, Language, and the Human Mind (Cambridge: Cambridge University Press).


  9. Wiest, Lynda (2003), "Comprehension of Mathematical Text", Philosophy of Mathematics Education Journal 17(May)


2004:

  1. Campbell, Jamie I. D. (ed) (2004), Handbook of Mathematical Cognition (London: Psychology Press).


  2. Casey, Beth, et al. (2004), "Storytelling Sagas: An Effective Medium for Teaching Early Childhood Mathematics", Early Childhood Research Quarterly 19: 167-172.


  3. Feigenson, Lisa; Dehaene Stanislas; Spelke, Elizabeth (2004), "Core Systems of Number", Trends in Cognitive Science 8(7; July)


  4. Goldfain, Albert (2004),"Using SNePS for Mathematical Cognition: A SNeRE Based Natural Language Algorithm for Computing GCD", CSE740 Progress Report (Buffalo: SUNY Buffalo Department of Computer Science).


  5. Geary, David C., et al. (2004), "Strategy Choices in Simple and Complex Addition: Contributions of Working Memory and Counting Knowledge for Children with Mathematical Disability", Journal of Experimental Child Psychology 88: 121-151.


  6. Koedinger, Kenneth R. and Nathan, Mitchell J. (2004), "The Real Story Behind Story Problems: Effects of Representations on Quantitative Reasoning", The Journal of the Learning Sciences 13(2): 129-164.


  7. Lerch, Carol M. (2004), "Control Decisions and Personal Beliefs: Their Effect on Solving Mathematical Problems", Journal of Mathematical Behavior 23: 21-36.


  8. Núñez R. (2004), "Embodied Cognition and the Nature of Mathematics: Language, Gesture, and Abstraction", in K. D. Forbus, D. Gentner, and T. Regier (eds.), Proceedings of the 26th Annual Conference of the Cognitive Science Society (Mahwah: Lawrence Erlbaum Associates): 36-37.


  9. Sriraman, Bharath (2004), "Reflective Abstraction, Uniframes and the Formulation of Generalizations", Journal of Mathematical Behavior 23: 205-222.


  10. Stoianov, I., Zorzi, M., Umiltà, C. (2004) "The role of semantic and symbolic representations in arithmetic processing: Insights from simulated discalculia in a connectionist model", Cortex 40: 194-196.


  11. Wang, Pei (2004), "Cognitive Logic versus Mathematical Logic", Working Notes of the Third International Seminar on Logic and Cognition, Guangzhou, May 2004.


  12. Zur, Osnat and Gelman, Rochel (2004), "Young Children Can Add and Subtract by Predicting and Checking", Early Childhood Research Quarterly 19: 121-137.


2005:

  1. Barwell, Richard (2005), "Ambiguity in the Mathematics Classroom", Language and Education 19(2): 118-126.


  2. Galistel, C. R. and Gelman, Rochel (2005), "Mathematical Cognition", in Keith J. Holyoak and Robert G. Morrison (eds.), The Cambridge Handbook of Thinking and Reasoning (Cambridge: Cambridge University Press): 559-588.


  3. Gelman, Rochel and Butterworth, Brian (2005), "Number and Language: How Are They Related?", Trends in Cognitive Science 9(1; January): 6-10.


  4. Kilpatrick, Jeremy; Holyes, Celia; Skovsmose, Ole; Eds. (2005), Meaning in Mathematics Education (New York: Springer).


  5. Morgan, Candia (2005), "Words, Definitions and Concepts in Discourses of Mathematics, Teaching and Learning", Language and Education 19(2): 103-117.


  6. Roy, Deb (2005), "Semiotic schemas: a framework for grounding language in action and perception", Artificial Intelligence 167(1-2): 170-205.


  7. Taddeo, Mariarosaria and Floridi, Luciano (2005), "The Symbol Grounding Problem: a Critical Review of Fifteen Years of Research", Journal of Experimental and Theoretical Artificial Intelligence 17(4): 419-445.


  8. Vitay, Julien (2005), "Towards Teaching a Robot to Count Objects", in L. Berthouze, F. Kaplan, H. Kozima, H. Yano, J. Konczak, G. Metta, J. Nadel, G. Sandini, G. Stojanov, and C. Balkenius (eds.)Proceedings of the Fifth International Workshop on Epigenetic Robotics: 125-128.


  9. Zhang, Qi (2005), "An Artificial Intelligent Counter", Cognitive Systems Research 6: 320-332.