Algebraïese simbole : die historiese ontwikkeling, gebruik en onderrig daarvan

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.