Senior primere leerlinge se begrip van sekere algemene getaleienskappe, met besondere verwysing na die distributiewe eienskap

[摘要] ENGLISH ABSTRACT:Number properties, amongst others the commutative, associative and distributive propertiesand general rearrangement principles, form the building blocks of manipulative algebra.Research and observation have shown that sec~mdary school pupils do not sufficientlymaster manipulative algebra, i.e. they do not possess sufficient mastery towards the nature,meaning, functionality and logic of algebraic manipulations. They are hence not aware thatalgebraic manipulations are based on the number properties, on the one hand because theywere not given sufficient opportunity to experience algebra as generalised arithmetic whenthey were introduced to algebra, and on the other hand because the number properties,about which young children possess intuitive knowledge, were never explicated for them.This study investigates the level of awareness of several number properties present in seniorprimary (especially standard 3) pupils, and utilises a few activities to attempt to lead pupilstowards a higher level of awareness. In addition this study attempts to determine whetherpupils who follow the experimental primary mathematics curriculum (project pupils)possess a higher level of awareness than pupils who follow the traditional curriculum (nonprojectpupils). As part of the latter effort, two investigation methods are utilised withregards to specifically the distributive property, i.e. clinical interviews and questionnaires.This also serves as part of a wider effort to design a measuring instrument with whichpossible differences between the learning outcomes of project and non-project pupils can bemeasured ..From the results of this study, it seems to appear that the large majority of pupils areexplicitly aware of the commutative properties of addition and multiplication and thegeneral rearrangement principles, to a lesser extent with regards to a minus sign beforebrackets, and that there does not exist a significant difference about the level of awarenesstowards these properties between project and non-project pupils.With regards to the distributive property, there appears to exist a considerable amount ofdifference in the level of awareness between project and non-project pupils, the firstmentioned being the higher. However, the opinion is expressed that the level of awarenessamong project pupils is not high enough, and that project pupils must be given sufficientopportunity in (at least standards 4 and 5) to explicate this property for themselves.Finally, a model of the levels of awareness, based on results of this study, is proposed.

[发布机构] Stellenbosch University