Algebraïese simbole : die historiese ontwikkeling, gebruik en onderrig daarvan
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Authors
Stols, Gert Hendrikus.
Issue Date
1996-06
Type
Language
af
Keywords
Mathematical symbols , Mathematics education , Symbolism , Notation , Teaching of algebra , Power of symbols , Concept formation , Algebraic language
Alternative Title
Abstract
Die gebruik van simbole maak wiskunde eenvoudiger en kragtiger, maar ook
moeiliker verstaanbaar. Laasgenoemde kan voorkom word as slegs eenvoudige en
noodsaaklike simbole gebruik word, met die verduidelikings en motiverings in
woorde.
Die krag van simbole le veral in die feit dat simbole as substitute vir konsepte kan
dien. Omdat die krag van simbole hierin le, skuil daar 'n groot gevaar in die gebruik
van simbole. Wanneer simbole los is van sinvolle verstandsvoorstellings, is daar geen
krag in simbole nie. Dit is die geval met die huidige benadering in skoolalgebra.
Voordat voldoende verstandsvoorstellings opgebou is, word daar op die manipulasie
van simbole gekonsentreer.
Die algebraiese historiese-kenteoretiese perspektief maak algebra meer betekenisvol
vir leerders. Hiervolgens moet die leerlinge die geleentheid gegun word om
oplossings in prosavorm te skryf en self hul eie wiskundige simbole vir idees spontaan in te voer. Hulle moet self die voordeel van algebraiese simbole beleef.
The use of symbols in algebra both simplifies and strengthens the subject, but it also increases its level of complexity.This problem can be prevented if only simple and essential symbols are used and if the explanations are fully verbalised. The power of symbols stems from their potential to be used as substitutes for concepts. As this constitutes the crux of mathematical symbolic representation, it also presents a danger in that the symbols may not be comprehended. If symbols are not related to mental representations, the symbols are meaningless. This is the case in the present approach to algebra. Before sufficient mental representations are built, there is a concentration on the manipulation of symbols. The algebraic historical epistemological perspective makes algebra more meaningful for learners. Learners should be granted the opportunities to write their solutions in prose and to develop their own symbols for concepts.
The use of symbols in algebra both simplifies and strengthens the subject, but it also increases its level of complexity.This problem can be prevented if only simple and essential symbols are used and if the explanations are fully verbalised. The power of symbols stems from their potential to be used as substitutes for concepts. As this constitutes the crux of mathematical symbolic representation, it also presents a danger in that the symbols may not be comprehended. If symbols are not related to mental representations, the symbols are meaningless. This is the case in the present approach to algebra. Before sufficient mental representations are built, there is a concentration on the manipulation of symbols. The algebraic historical epistemological perspective makes algebra more meaningful for learners. Learners should be granted the opportunities to write their solutions in prose and to develop their own symbols for concepts.
Description
Text in Afrikaans, abstract in Afrikaans and English
Citation
Stols, Gert Hendrikus. (1996) Algebraïese simbole : die historiese ontwikkeling, gebruik en onderrig daarvan, University of South Africa, Pretoria, <http://hdl.handle.net/10500/16122>