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ERIC Number: ED501159
Record Type: Non-Journal
Publication Date: 2003-Jul
Pages: 8
Abstractor: Author
Empirical Generalisation as an Inadequate Cognitive Scaffold to Theoretical Generalisation of a More Complex Concept
Williams, Gaye
International Group for the Psychology of Mathematics Education, Paper presented at the 27th International Group for the Psychology of Mathematics Education Conference Held Jointly with the 25th PME-NA Conference (Honolulu, HI, Jul 13-18, 2003), v4 p419-426
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. (Contains 1 footnote, 1 figure, and 2 tables.) [Additional support was provided by the Mathematical Association of Victoria. For complete proceedings, see ED500860.]
International Group for the Psychology of Mathematics Education. 35 Aandwind Street, Kirstenhof, Cape Town, 7945, South Africa. Tel: +27-21-715-3559; Fax: +27-88-021-715-3559; e-mail:; Web site:
Publication Type: Reports - Research; Speeches/Meeting Papers
Education Level: N/A
Audience: N/A
Language: English
Sponsor: Melbourne Univ. (Australia).; Australian Research Council.; Spencer Foundation, Chicago, IL.
Authoring Institution: N/A