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Educational Studies in Mathematics

, Volume 12, Issue 2, pp 151–169 | Cite as

Concept image and concept definition in mathematics with particular reference to limits and continuity

  • David Tall
  • Shlomo Vinner
Article

Abstract

The concept image consists of all the cognitive structure in the individual's mind that is associated with a given concept. This may not be globally coherent and may have aspects which are quite different from the formal concept definition.

The development of limits and continuity, as taught in secondary school and university, are considered. Various investigations are reported which demonstrate individual concept images differing from the formal theory and containing factors which cause cognitive conflict.

Keywords

Formal Theory Formal Concept Cognitive Structure Cognitive Conflict Concept Definition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. School Mathematics Project: 1967 (Revised 1970), Advanced Mathematics (Metric), Books 1–4, Cambridge University Press.Google Scholar
  2. SchwarzenbergerR. L. E. and TallD. O.: 1978, ‘Conflict in the learning of real numbers and limits’, Mathematics Teaching 82, 44–49.Google Scholar
  3. Tall, D. O.: 1977 (a), ‘Cognitive conflict and the learning of mathematics’, paper presented to the International Group for the Psychology of Mathematics Education, Utrecht, Holland.Google Scholar
  4. TallD. O.: 1977(b), ‘Conflicts and catastrophes in the learning of mathematics,’ Mathematical Education for Teaching, 2, 4, 2–18.Google Scholar

Copyright information

© D. Reidel Publishing Co. 1981

Authors and Affiliations

  • David Tall
    • 1
    • 2
  • Shlomo Vinner
    • 1
    • 2
  1. 1.Mathematics Education Research CentreUniversity of WarwickUK
  2. 2.Israel Science Teaching CenterHebrew UniversityIsrael

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