Thesis (DEd)--Stellenbosch University, 1995. / ENGLISH ABSTRACT: The rationale for this study essentially is the perceived and reported misconceptions in
algebra that exist within pupils in the Junior Secondary phase. These misconceptions are the
direct result of the incomplete mastery of algebra.
The purpose of this research is to attempt to contribute towards pupils' complete mastery of
algebra and the ensuing elimination of certain pupil misconceptions, by trying to increase
primary school pupils' level of awareness of the general number properties.
Primary school pupils who learn arithmetic in a problem based environment intuitively use
the general number properties to execute arithmetical calculations, while pupils in the
traditional teaching approach are taught standard algorithms which they must apply, often
without comprehension.
In the latter, the existence of the number properties is concealed. When these pupils officially
encounter the general number properties for the first time in standard 4 or 5, they are
probably not capable of integrating these new concepts into their existing knowledge
structure. This may lead to incomplete mastery and ensuing misconceptions, which can
become worse when pupils must apply exactly the same number properties in algebra to
execute algebraic manipulations.
The fact that primary school pupils in the problem based approach intuitively apply the
number properties, earlier led to the hypothesis that these pupils possess a higher level of
awareness of the number properties. However, research has indicated that these pupils
possess only a moderately higher level of awareness. This has led to this study during which
a 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 extent
that they become explicitly aware of the existence and nature of these fundamental concepts
in mathematics.
The technique how to link up with pupils' intuitive knowledge and to increase their level of
awareness 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 strategy
was formulated. This strategy is essentially based on the following parameters: Group
discussion, the use of calculators, and creating a cognitive disequilibrium. During the third
year of this study this strategy was implemented at a number of schools. During this phase
research concentrated on the distributive property only. Judging by the results, it appears as
if 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. This
model was used as a guide in the attempt to increase pupils' level of awareness of the
number properties. / AFRIKAANSE OPSOMMING: Die rasionaal vir hierdie studie is hoofsaaklik gelee in die waargenome en gerapporteerde
wanbegrippe in algebra wat by leerlinge in die Junior Sekondere fase bestaan. Hierdie
wanbegrippe is die direkte gevolg van die onvolledige beheersing van algebra.
Die doel van hierdie navorsing is om 'n hydrae te probeer lewer tot leerlinge se volledige
beheersing van algebra, en die gepaardgaande uitskakeling van bepaalde leerlingwanbegrippe,
deurdat gepoog word om laerskoolleerlinge se vlak van bewustheid van die algemene
bewerkingseienskappe te verhoog.
Laerskoolleerlinge wat probleemgebaseerde rekenkunde-onderrig ontvang, benut intu'itief die
algemene bewerkingseienskappe ten einde rekenkundige berekeninge uit te voer, terwyl aan
laerskoolleerlinge in die tradisionele onderrigbenadering standaardalgoritmes onderrig word
wat hulle dikwels sonder begrip moet toepas.
In laasgenoemde geval word die bestaan van die bewerkingseienskappe erg versluier.
Wanneer hierdie leerlinge in standerd 4 of 5 vir die eerste keer amptelik met die algemene
bewerkingseienskappe in aanraking kom, is hulle waarskynlik nie in staat om hierdie nuwe
begrippe met hul bestaande kennisstruktuur te integreer nie. Dit kan tot onvolledige
beheersing en gevolglike wanbegrippe lei, wat kan vererger wanneer leerlinge presies
dieselfde eienskappe in algebra moet benut ten einde algebra!ese manipulasies uit te voer.
Die feit dat laerskoolleerlinge in die probleemgebaseerde benadering intu'itief die
bewerkingseienskappe toepas, het tevore reeds tot die hipotese dat hierdie leerlinge oor 'n
hoer vlak van bewustheid van die bewerkingseienskappe beskik, aanleiding gegee. Navorsing
het egter aangetoon dat daar slegs 'n matige hoer vlak van bewustheid by hulle bestaan. Dit
het tot hierdie studie aanleiding gegee waartydens spesifiek gepoog word om leerlinge se
intuitiewe kennis van die bewerkingseienskappe wat hulle spontaan aanwend ten einde
rekenkundige bewerkings uit te voer, as vertrekpunt te neem, en te ontwikkel sodat hulle
eksplisiet bewus sal raak van die bestaan en wese van hierdie grondliggende waarhede in
wiskunde.
Die tegniek hoe om by laerskoolleerlinge se intui'tiewe kennis aan te sluit en hul vlak van
bewustheid van die bewerkingseienskappe binne 'n probleemgebaseerde omgewing te
verhoog, is gedurende die eerste twee jaar van hierdie studie ontwikkel. Aan die einde van
hierdie periode is 'n toepaslike onderrigstrategie geformuleer. Hierdie strategie steun sterk
op die volgende parameters: Groepsbespreking , die benutting van sakrekenaars, en die skep
van 'n kognitiewe disekwilibrium. Gedurende die derde jaar van hierdie studie is hierdie
onderrigstrategie in verskeie skole toegepas. Daar is gedurende hierdie fase slegs op die
distributiewe eienskap gekonsentreer. Volgens die resultate wil dit voorkom asof daar 'n
aansienlike verhoging in die betrokke leerlinge se vlak van bewustheid van die distributiewe
eienskap plaasgevind het.
Gedurende hierdie studie is ook 'n hierargiese model van vlakke van bewustheid geformuleer
aan die hand waarvan die poging aangewend is om leerlinge se vlak van bewustheid van
bewerkingseienskappe te verhoog.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/54936 |
| Date | January 1995 |
| Creators | Vermeulen, Cornelis Franz |
| Contributors | Human, P. G., Stellenbosch University. Faculty of Education. Dept. of Curriculum Studies. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | af_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 435 p. |
| Rights | Stellenbosch University |
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