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Empirical generalisation as an inadequate cognitive scaffold to theoretical generalisation of a more complex concept

Williams, Gaye 2003, Empirical generalisation as an inadequate cognitive scaffold to theoretical generalisation of a more complex concept, in Proceedings of the 2003 joint meeting of PME and PMENA : PME27/PME-NA25, University of Hawai'i, Honolulu, HI, pp. 419-426.

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Title Empirical generalisation as an inadequate cognitive scaffold to theoretical generalisation of a more complex concept
Author(s) Williams, GayeORCID iD for Williams, Gaye orcid.org/0000-0002-4739-3564
Conference name International Group for the Psychology of Mathematics Education. Joint meeting (27th : 2003 : Honolulu, HI)
Conference location Honolulu, Hawaii
Conference dates 2003
Title of proceedings Proceedings of the 2003 joint meeting of PME and PMENA : PME27/PME-NA25
Editor(s) Pateman, Neil A.
Dougherty, Barbara J.
Zilliox, Joseph T.
Publication date 2003
Conference series International Group for the Psychology of Mathematics Education Joint Meeting
Start page 419
End page 426
Total pages 8
Publisher University of Hawai'i
Place of publication Honolulu, HI
Summary The impact of prior learning on new learning is highlighted by the case of Dean, a Year 8 student who developed his own method to find the sum of the interior angles of a polygon without knowing why his method worked. Enriched transcripts and visual displays of the cognitive, social (Dreyfus, Hershkowitz, & Schwarz, 2001) and affective elements (Williams, 2002) of Dean's interrupted abstraction process informed the identification of factors that inhibited Dean's constructing process. It was found Dean possessed an empirical, not theoretical, generalization (Davydov, 1990) about sums of interior angles of triangles that was an inadequate cognitive artifact for constructing the new more complex theoretical generalization. The study suggests use of tasks designed with the opportunity develop assumed knowledge in conjunction with new concepts.
Notes Reproduced with the specific permission of the copyright owner.
Language eng
Field of Research 130208 Mathematics and Numeracy Curriculum and Pedagogy
Socio Economic Objective 970113 Expanding Knowledge in Education
HERDC Research category E1.1 Full written paper - refereed
Copyright notice ©International Group for the Psychology of Mathematics Education (PME).
Persistent URL http://hdl.handle.net/10536/DRO/DU:30006223

Document type: Conference Paper
Collections: School of Education
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Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO. If you believe that your rights have been infringed by this repository, please contact drosupport@deakin.edu.au.