Thesis (MEd)--University of Stellenbosch, 2002. / ENGLISH ABSTRACT: Algebra deals amongst others with the relationship between variables. It differs from
Arithmetic amongst others as there is not always a numerical solution to the problem.
An algebraic expression can even be the solution to the problem in Algebra. The
variables found in Algebra are often represented by letters such as X, y, etc.
Equations are an integral part of Algebra. To solve an equation, the value of an
unknown must be determined so that the left hand side of the equation is equal to the
right hand side.
There are various ways in which the solving of equations can be taught.
The purpose of this study is to determine the existence of a cognitive gap as
described by Herseovies & Linchevski (1994) in relation to solving linear equations.
When solving linear equations, an arithmetical approach is not always effective.
A new way of structural thinking is needed when solving linear equations in
their different forms.
In this study, learners' intuitive, informal ways of solving linear equations were
examined prior to any formal instruction and before the introduction of algebraic
symbols and notation. This information could help educators to identify the
difficulties learners have when moving from solving arithmetical equations to
algebraic equations. The learners' errors could help educators plan effective ways of
teaching strategies when solving linear equations.
The research strategy for this study was both quantitative and qualitative. Forty-two Grade 8 learners were chosen to individually do assignments involving different types
of linear equations. Their responses were recorded, coded and summarised.
Thereafter the learners' responses were interpreted, evaluated and analysed.
Then a representative sample of fourteen learners was chosen randomly from the
same class and semi-structured interviews were conducted with them From these
interviews the learners' ways of thinking when solving linear equations, were probed.
This study concludes that a cognitive gap does exist in the context of the
investigation. Moving from arithmetical thinking to algebraic
thinking requires a paradigm shift. To make adequate provision for this change
in thinking, careful curriculum planning is required. / AFRIKAANSE OPSOMMING: Algebra behels onder andere die verwantskap tussen veranderlikes. Algebra verskil
van Rekenkunde onder andere omdat daar in Algebra nie altyd 'n numeriese oplossing
vir die probleem is nie. InAlgebra kan 'n algebraïese uitdrukking somtyds die
oplossing van 'n probleem wees. Die veranderlikes in Algebra word dikwels deur
letters soos x, y, ens. voorgestel. Vergelykings is 'n integrale deel van Algebra. Om
vergelykings op te los, moet 'n onbekende se waarde bepaal word, om die linkerkant
van die vergelyking gelyk te maak aan die regterkant. Daar is verskillende maniere
om die oplossing van algebraïese vergelykings te onderrig.
Die doel van hierdie studie is om die bestaan van 'n sogenaamde "kognitiewe gaping"
soos beskryf deur Herseovies & Linchevski (1994), met die klem op lineêre
vergelykings, te ondersoek. Wanneer die oplossing van 'n linêere vergelyking bepaal
word, is 'n rekenkundige benadering nie altyd effektiefnie. 'n Heel nuwe, strukturele
manier van denke word benodig wanneer verskillende tipes linêere vergelykings
opgelos word.
In hierdie studie word leerders se intuitiewe, informele metodes ondersoek wanneer
hulle lineêre vergelykings oplos, voordat hulle enige formele metodes onderrig is en
voordat hulle kennis gemaak het met algebraïese simbole en notasie.
Hierdie inligting kan opvoeders help om leerders se kognitiewe probleme in verband
met die verskil tussen rekenkundige en algebraïese metodes te identifiseer.Die foute
wat leerders maak, kan opvoeders ook help om effektiewe onderrigmetodes te
beplan, wanneer hulle lineêre vergelykings onderrig. As leerders eers die skuif van rekenkundige metodes na algebrarese metodes gemaak het, kan hulle besef dat hul
primitiewe metodes nie altyd effektief is nie.
Die navorsingstrategie wat in hierdie studie aangewend is, is kwalitatief en
kwantitatief Twee-en-veertig Graad 8 leerders is gekies om verskillende tipes lineêre
vergelykings individueel op te los. Hul antwoorde is daarna geïnterpreteer, geëvalueer
en geanaliseer. Daarna is veertien leerders uit hierdie groep gekies en semigestruktureerde
onderhoude is met hulle gevoer. Vanuit die onderhoude kon 'n dieper
studie van die leerders se informele metodes van oplossing gemaak word.
Die gevolgtrekking wat in hierdie studie gemaak word, is dat daar wel 'n kognitiewe
gaping bestaan in die konteks van die studie. Leerders moet 'n paradigmaskuif maak
wanneer hulle van rekenkundige metodes na algebraïese metodes beweeg. Hierdie
klemverskuiwing vereis deeglike kurrikulumbeplanning.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/52915 |
| Date | 12 1900 |
| Creators | Jonklass, Raymond |
| Contributors | Murray, J. C., Olivier, A. I., Stellenbosch University. Faculty of Education. Dept. of Curriculum Studies. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 112 p. |
| Rights | Stellenbosch University |
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