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Senior primere leerlinge se begrip van sekere algemene getaleienskappe, met besondere verwysing na die distributiewe eienskap
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 manipul...
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| Format: | Thesis |
| Language: | af_ZA |
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Stellenbosch : Stellenbosch University
2012
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| Summary: | 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. |
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