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

Vermeulen, Cornelis Franz (1991)

Thesis

ENGLISH ABSTRACT: Number properties, amongst others the commutative, associative and distributive properties and general rearrangement principles, form the building blocks of manipulative algebra. Research and observation have shown that sec~mdary school pupils do not sufficiently master 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 that algebraic manipulations are based on the number properties, on the one hand because they were not given sufficient opportunity to experience algebra as generalised arithmetic when they 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 senior primary (especially standard 3) pupils, and utilises a few activities to attempt to lead pupils towards a higher level of awareness. In addition this study attempts to determine whether pupils who follow the experimental primary mathematics curriculum (project pupils) possess a higher level of awareness than pupils who follow the traditional curriculum (nonproject pupils). As part of the latter effort, two investigation methods are utilised with regards 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 which possible differences between the learning outcomes of project and non-project pupils can be measured .. From the results of this study, it seems to appear that the large majority of pupils are explicitly aware of the commutative properties of addition and multiplication and the general rearrangement principles, to a lesser extent with regards to a minus sign before brackets, and that there does not exist a significant difference about the level of awareness towards these properties between project and non-project pupils. With regards to the distributive property, there appears to exist a considerable amount of difference in the level of awareness between project and non-project pupils, the first mentioned being the higher. However, the opinion is expressed that the level of awareness among project pupils is not high enough, and that project pupils must be given sufficient opportunity 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.

AFRIKAANSE OPSOMMING: Getaleienskappe, waaronder die kommutatiewe, assosiatiewe en distributiewe eienskappe en algemene herrangskikkingsbeginsels, vorm die boustene van manipulatiewe algebra. Navorsing en waarneming het aan die lig gebring dat hoerskoolleerlinge manipulatiewe algebra nie na behore beheers nie, dit wil se hulle beskik nie oor voldoende beheersing ten opsigte van die aard, betekenis, funksionalteit en logika van algebraise manipulasies nie. Hulle is dus nie daarvan bewus dat algebraiese manipulasies op die getaleienskappe berus nie, enersyds omdat hulle nie tydens die kennismaking met manipulatiewe algebra genoegsaam in die geleentheid gestel is om algebra as veralgemeende rekenkunde te ervaar nie, en andersyds omdat die getaleienskappe, waaroor jong kinders intuitiewe kennis besit, nooit vir hulle geeksplisiteer is nie. Hierdie studie stel ondersoek in na senior primere (hoofsaaklik standerd 3) leerlinge se vlak van bewustheid van enkele getaleienskappe, en benut enkele aktiwiteite om leerlinge na 'n hoer vlak van bewustheid daarvan te probeer lei. Hierbenewens word probeer om vas te stel of daar by leerlinge wat die eksperimentele primere wiskunde-kurrikulum volg (projekleerlinge) 'n hoer vlak van bewustheid aanwesig is as by leerlinge wat die tradisionele kurrikulum volg (nie-projekleerlinge). As· deel van laasgenoemde poging, word twee ondersoekmetod~s gevolg ten opsigte van spesifiek die distributiewe eienskap, naamlik kliniese onderhoude en vraelyste. Dit dien ook as deel van 'n breer poging om 'n meetinstrument te ontwerp waarmee moontlike verskille tussen die leeruitkomste van projek- en nie-projekleerlinge gemeet kan word. Dit wil uit die bevindinge van hierdie studie voorkom asof die oorgrote meerderheid leertinge eksplisiet bewus is van die kommutatiewe eienskappe ten opsigte van optelling en vermenigvuldiging en die algemene herrangskikkingsbeginsels, in 'n mindere mate ten opsigte van die minusteken voor hakies, en dat daar nie 'n noemenswaardige verskil in die vlak van bewustheid oor hierdie eienskappe by projek- en nie-projekleerlinge bestaan nie. Sover dit die distributiewe eienskap betref, lyk dit asof daar 'n redelike verskil in die vlak van bewustheid by projek- en nie-projekleerlinge is met eersgenoemde die hoogste. Tog word die mening uitgespreek dat die vlak van bewustheid by projekleerlinge nie hoog genoeg is nie, en dat hulle in minstens standerd 4 en 5 in die geleentheid gestel moet word om hierdie getaleienskap vir hulself te eksplisiteer.

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