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Concept image and concept definition in mathematics with particular reference to limits and continuity
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Tall, David and Vinner, Shlomo. (1981) Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, Vol.12 (No.7). pp. 151-169. ISSN 0013-1954
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Official URL: http://dx.doi.org/10.1007/BF00305619
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.
| Item Type: | Journal Article |
|---|---|
| Subjects: | L Education > LB Theory and practice of education Q Science > QA Mathematics |
| Divisions: | Faculty of Social Sciences > Institute of Education |
| Library of Congress Subject Headings (LCSH): | Knowledge, theory of, Concepts, Mathematics -- Study and teaching, Mathematical ability |
| Journal or Publication Title: | Educational Studies in Mathematics |
| Publisher: | Springer Netherlands |
| ISSN: | 0013-1954 |
| Date: | 1981 |
| Volume: | Vol.12 |
| Number: | No.7 |
| Page Range: | pp. 151-169 |
| Identification Number: | 10.1007/BF00305619 |
| Status: | Peer Reviewed |
| Access rights to Published version: | Restricted or Subscription Access |
| References: | School Mathematics Project: 1967 (revised 1970). Advanced Mathematics (Metric), Books 1–4, Cambridge University Press. Schwarzenberger, R. L. E. and Tall, D. O.: 1978. Conflict in the learning of real numbers and limits, Mathematics Teaching 82, 44–9. Tall, D. O.: l977a. Cognitive conflict and the learning of mathematics, paper presented to the International Group for the Psychology of Mathematics Education, Utrecht, Holland. Tall, D. O.: 1977b. Conflicts and catastrophes in the learning of mathematics, Mathematical Education for Teaching, 2 4, 2–18. |
| URI: | http://wrap.warwick.ac.uk/id/eprint/507 |
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