Cognitive Science and Mathematics Education

By Alan H. Schoenfeld | Go to book overview

ers. If we look both at our own thinking and that of our students from that point of view, there is the potential for significant progress.


Acknowledgments

I would like to thank Andy diSessa, Bat-Sheva Eylon, Jim Greeno, Lisa Quinn, and Fred Reif for their comments on an earlier draft of this chapter.


REFERENCES

Brown J. S., & Burton R. R. ( 1978). "Diagnostic models for procedural bugs in basic mathematical skills". Cognitive Science, 2, 155-192.

Bundy Alan. ( 1975). Analysing mathematical proofs (or reading between the lines). (Res. Rep. No. 2). Edinburgh: University of Edinburgh, Department of Artificial Intelligence.

Caramazza A. McCloskey M., & Green B. ( 1981). "Naive beliefs in sophisticated subjects: Misconceptions and trajectories of objects". Cognition, 9, 117-123.

Carey S. ( 1985). Conceptual change in childhood. Cambridge, MA: MIT Press.

Carpenter T. P., Lindquist M. M., Matthews W., & Silver E. A. ( 1983). "Results of the Third NAEP Mathematics Assessment: Secondary school". Mathematics Teacher, 76( a), 652-659.

diSessa A. A. ( 1983). "Phenomenology and the evolution of intuition". In D. Gentner & A. Stevens (Eds.), Mental models (pp. 15-33). Hillsdale, NJ: Lawrence Erlbaum Associates.

diSessa A. ( 1985, June). Knowledge in pieces. Paper presented at 5th annual symposium of the Jean Piaget Society, "Constructivism in the computer age," Philadelphia. Manuscript available from author, School of Education, University of California, Berkeley, CA 94720.

Gagné R. M., & Briggs L. J. ( 1979). Principles of Instructional design ( 2nd ed.). New York: Holt, Reinhart, & Winston.

Ginsburg H., and Opper S. ( 1969). Piaget's theory of intellectual development. Englewood Cliffs, NJ: Prentice-Hall.

Gardner Howard. ( 1985). The mind's new science. New York: Basic Books.

Kahneman D., & Tversky A. ( 1982). "On the study of statistical intuitions". In D. Kahnemann , A. Tversky, & P. Slovic (Eds.), Judgment under uncertainty: Heuristics and biases (pp. 493-508). Cambridge, England: Cambridge University Press.

Kilpatrick J. ( 1978). "Variables and methodologies in research on problem solving". In L. Hatfield (Ed.), Mathematical problem solving. Columbus, Ohio: ERIC.

Krulik S. (Ed.). ( 1980). Problem solving in school mathematics (1980 Yearbook of the National Council of Teachers of Mathematics.). Reston, VA: National Council of Teachers of Mathematics.

McCloskey M. ( 1983). "Naive theories of motion". In D. Gentner & A. Stevens (Eds.), Mental models (pp. 299-324). Hillsdale, NJ: Lawrence Erlbaum Associates.

McCloskey M., A. Caramazza, & B. Green. ( 1980). "Curvilinear motion in the absence of external forces: Naive beliefs about the motions of objects". Science, 210, 1139-1141.

McCorduck P. ( 1979). Machines who think. San Franciso. W. H. Freeman Co.

Meyer. R. A. ( 1980) "Mathematical problem-solving performance and intellectual abilities of"

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