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

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.

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References

  1. School Mathematics Project: 1967 (Revised 1970), Advanced Mathematics (Metric), Books 1–4, Cambridge University Press.

  2. SchwarzenbergerR. L. E. and TallD. O.: 1978, ‘Conflict in the learning of real numbers and limits’, Mathematics Teaching 82, 44–49.

  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.

  4. TallD. O.: 1977(b), ‘Conflicts and catastrophes in the learning of mathematics,’ Mathematical Education for Teaching, 2, 4, 2–18.

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Tall, D., Vinner, S. Concept image and concept definition in mathematics with particular reference to limits and continuity. Educ Stud Math 12, 151–169 (1981). https://doi.org/10.1007/BF00305619

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Keywords

  • Formal Theory
  • Formal Concept
  • Cognitive Structure
  • Cognitive Conflict
  • Concept Definition