The Mathematics Curriculum and Assessment Policy (CAPS) document defines ‘mathematics [as] . . . a human activity’ (DBE, 2011a, p.8). This adoption of a realistic approach to the learning and teaching of mathematics appears to be partial, however, in that at the entry point of the Intermediate Phase, the recommendations of the policy makers are read as prescriptions by practitioners. In particular, the recommendation that ‘as the number range for doing calculations increases up to Grade 6, learners should develop more efficient techniques for calculations, including using columns’ (DBE, 2011b, p.13) is taken as a prescription to push the standard methods as the way to solving (often de-contextualized) problems from the very start of Grade 4, in disregard to the admonition that ‘these techniques should only be introduced and encouraged once learners have an adequate sense of place value and understanding of the properties of numbers and operations’ (DBE, 2011b, p.13).
In the background of reports that place South African schools well below international standards with regard to mathematics, with only a third of the learners in grade 3 having attained the minimum standard required of learners at their level in 2011, this report focuses on an exploration into the purported catalytic role that the emergent model of an empty number line can play in shifting learners’ attention from counting (calculation by counting ) towards a focus on the structural properties of number (calculation by structuring). The use of emergent models is meant to support and improve upon learners’ informal solution strategies whilst seeking to reverse what Freudenthal referred to as the “anti-didactical” use of models in a ‘top-down instructional design strategy in which static models are derived from crystallized expert mathematical knowledge’ (Gravemeijer and Stephan, 2002, p.146).
With a particular focus on poor performance in numeracy, the Wits Maths Connect-Primary (WMC-P) project was established with the overarching aim of improving the learning and teaching of primary school mathematics. My investigation is located within one Grade 4 class in one of the WMC-P project schools, and in this project, I act as both the teacher of six intervention lessons focused on additive relation problems, as well as researcher of the models and strategies that learners use prior to the intervention lessons, within these lessons, and subsequently. This report presents evidence to illustrate, firstly, that at the entry point of grade 4 level, learners are highly dependent on concrete strategies for solving addition and subtraction problems, and secondly that with proper intervention, learners can make significant shifts towards more abstract calculation.
On the one hand, the key finding that the majority of the problems were tackled using tallies in the pre-test confirms what research has observed regarding the tendency for learners to remain highly dependent on concrete strategies at grade 2 (Venkat, 2011) and grade 3 (Ensor et al., 2009). Also, the results indicate a high proportion of incorrect answers resulting from the use of the column model across all questions in the pre-test and the post-test. On the other hand, the imposition of the use of the empty number line in the delayed-post-test points to the fact that improvements can be achieved in relatively short time frames, and importantly, that these improvements can be retained beyond their immediate coverage in class.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/14924 |
| Date | 18 July 2014 |
| Creators | Tshesane, Herman Makabeteng. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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