Elsevier

Advances in Psychology

Volume 91, 1992, Pages 365-409
Advances in Psychology

Chapter 10 Mathnet: Preliminary Results From A Distributed Model Of Arithmetic Fact Retrieval

https://doi.org/10.1016/S0166-4115(08)60892-4Get rights and content

Summary

In this chapter we explore modeling of arithmetic fact retrieval within a connectionist or “neural net” framework. We first sketch briefly some of the major empirical phenomena emerging from research on arithmetic facts, and review previous attempts to develop distributed connectionist models of arithmetic fact retrieval. We then describe a new model, MATHNET, and present preliminary findings concerning the model's ability to simulate several phenomena of human fact retrieval. We conclude by discussing limitations of our initial modeling, and directions to be pursued in subsequent work.

References (60)

  • K.F. Miller et al.

    Starting to add worse: Effects of learning to multiply on children's addition

    Cognition

    (1990)
  • C. Peterson et al.

    Explorations of the mean field theory learning algorithm

    Neural Networks

    (1989)
  • J.A. Anderson

    Psychological computation with neural networks.

    IEEE Transactions on Systems, Man, and Cybernetics

    (1983)
  • J.A. Anderson et al.

    Distinctive features, categorical perception, and probability learning: Some applications of a neural model.

    Review

    (1977)
  • J.A. Anderson et al.

    Experiments with representation in neural networks: Object motion, speech, and arithmetic.

  • M.H. Ashcraft

    Children's knowledge of simple arithmetic: A developmental model and simulation.

  • M.H. Ashcraft et al.

    Cognitive arithmetic: Evidence for retrieval and decision processes in mental addition

    Journal of Experimental Psychology: Human Learning and Memory

    (1978)
  • J.I.D. Campbell et al.

    An encoding complex view of cognitive number processing: Comment on Mc Closkey, Sokol, and Goodman (1986)

    Journal of Experimental Psychology: General

    (1988)
  • J.I.D. Campbell et al.

    Mental multiplication skill: Structure, process, and acquisition

    Canadian Journal of Psychology

    (1985)
  • A. Caramazza et al.

    Dissociations of calculation processes.

  • G.W. Cottrell et al.

    Learning simple arithmetic procedures.

  • M.G. Dyer

    The promise and problems of connectionism

    Behavioral and Brain Sciences

    (1988)
  • R.M. French

    Using semi-distributed representations to overcome catastrophic forgetting in connectionist networks.

    CRCC Technical Report 51–1991

    (1991)
  • T. Geszti

    Physical models of neural networks.

    (1990)
  • E.G. Gonzalez et al.

    Mental manipulation of arithmetic symbols

    Journal of Experimental Psychology: Learning, Memory, & Cognition

    (1982)
  • E.G. Gonzalez et al.

    Notational constraints on mental operations.

  • D.J. Graham

    Connectionist networks of cognitive arithmetic: Explorations in back-propagation architectures and training sequencing.

    (1990)
  • D.J. Graham et al.

    Sequential learning in a connectionist model of mental arithmetic.

    Paper presented at the meeting of the Psychonomic Society, Chicago, Illinois.

    (1988)
  • G.J. Groen et al.

    A chronometric analysis of simple addition

    Psychological Review

    (1972)
  • S.J. Hanson et al.

    What connectionist models learn: Learning and representation in connectionist networks

    Behavioral and Brain Sciences

    (1990)
  • Cited by (0)

    View full text