Verhoging van laerskoolleerlinge se vlak van bewustheid van die distributiewe eienskap in rekenkunde

[摘要] ENGLISH ABSTRACT:The rationale for this study essentially is the perceived and reported misconceptions inalgebra that exist within pupils in the Junior Secondary phase. These misconceptions are thedirect result of the incomplete mastery of algebra.The purpose of this research is to attempt to contribute towards pupils' complete mastery ofalgebra and the ensuing elimination of certain pupil misconceptions, by trying to increaseprimary school pupils' level of awareness of the general number properties.Primary school pupils who learn arithmetic in a problem based environment intuitively usethe general number properties to execute arithmetical calculations, while pupils in thetraditional teaching approach are taught standard algorithms which they must apply, oftenwithout comprehension.In the latter, the existence of the number properties is concealed. When these pupils officiallyencounter the general number properties for the first time in standard 4 or 5, they areprobably not capable of integrating these new concepts into their existing knowledgestructure. This may lead to incomplete mastery and ensuing misconceptions, which canbecome worse when pupils must apply exactly the same number properties in algebra toexecute algebraic manipulations.The fact that primary school pupils in the problem based approach intuitively apply thenumber properties, earlier led to the hypothesis that these pupils possess a higher level ofawareness of the number properties. However, research has indicated that these pupilspossess only a moderately higher level of awareness. This has led to this study during whicha specific attempt is made to take pupils' intuitive knowledge of the number properties,which they spontaneously apply, as a point of departure, and to develop it to such an extentthat they become explicitly aware of the existence and nature of these fundamental conceptsin mathematics.The technique how to link up with pupils' intuitive knowledge and to increase their level ofawareness of the number properties inside a problem based environment, was developed during the first two years of this study. At the end of this period, a suitable teaching strategywas formulated. This strategy is essentially based on the following parameters: Groupdiscussion, the use of calculators, and creating a cognitive disequilibrium. During the thirdyear of this study this strategy was implemented at a number of schools. During this phaseresearch concentrated on the distributive property only. Judging by the results, it appears asif a considerable increase in level of awareness has taken place within these pupils.During this study a hierarchical model of levels of awareness was also formulated. Thismodel was used as a guide in the attempt to increase pupils' level of awareness of thenumber properties.

[发布机构] Stellenbosch University