Research Outputs (Education)

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Browsing Research Outputs (Education) by Author "Askew, M."

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    Deconstructing South African Grade 1 learners' awareness of number in terms of cardinality, ordinality and relational understandings.
    (2020) Askew, M.; Venkat, H.
    The cardinal and ordinal aspects of number have been widely written about as key constructs that need to be brought together in children’s understanding in order for them to appreciate the idea of numerosity. In this paper, we discuss similarities and differences in the ways in which understandings not only of ordinality, cardinality but also additive and multiplicative relations have been theorized. We examine how the connections between these can be considered through a focus on number line representations and children positioning and comparing numbers. The responses of a cohort of South African Grade 1 learners’ (6- and 7-year-olds) to a numerical magnitude estimation task and to a numerical comparison task are analysed and the findings compared to those in the international literature, some of which argue that children’s early, informal, understandings of cardinality and ordinality are underpinned by an intuitive logarithmic model relating number order and size. A main finding presented here is that the responses from learners in this study exhibited a better fit with an exponential model of the relationship between cardinality and ordinality. These findings raise questions about whether some of the findings in previous research are as universal as sometimes claimed.
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    Multiplicative reasoning: An intervention's impact on Foundation Phase learners' understanding
    (2019) Askew, M.; Venkatakrishnan, H.; Mathews, C.; Ramsingh, T.T.; Roberts, N.
    BACKGROUND: Given the context of low attainment in primary mathematics in South Africa, improving learners' understanding of multiplicative reasoning is important as it underpins much of later mathematics. AIM: Within a broader research programme aiming to improve Foundation Phase (Grades 1-3, 7-9-year-olds) learners' mathematical performance, the aim of the particular research reported on here was to improve learners' understanding of and attainment in multiplicative reasoning when solving context-based problems. SETTING: The research was conducted in a suburban school serving a predominantly historically disadvantaged learner population, and involved teachers and learners from three classes in each of Grades 1-3. METHODS: A 4-week intervention piloted the use of context-based problems and array images to encourage learners to model (through pictures and diagrams) the problem situations, with the models produced used both to support problem solving and to support understanding of the multiplicative structures of the contexts. RESULTS: Cleaning the data to include those learners participating at all three data points - pre-, post- and delayed post-test - provided findings based on 233 matched learners. These findings show that, on average, Grade 1 learners had a mean score average increase of 22 percentage points between the pre-test and the delayed post-test, with Grades 2 and 3 having mean increases of 10 and 9 percentage points, respectively. CONCLUSION: The findings of this study demonstrate that young learners can be helped to better understand and improve their attainment in multiplicative reasoning, and suggest the usefulness of trialling the intervention model more broadly across schools.
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    Weaving in connections: Studying changes in early grades additive relations teaching
    (2018) Ekdahl, A,L.; Venkatakrishnan, H.; Runesson, U.; Askew, M.
    In this article, we present aspects of teaching that draw attention to connections - both within and between examples - in order to explore the potential objects of learning that are brought into being in the classroom space and thus what is made available to learn. Our focus is on exploring differences in teaching over time, in the context of learning study style development activity of additive relation problems in three Grade 3 classes in South Africa. In a context where highly-localised and fragmented instruction has been noted, this study reports on the nature and extent of changes in connections in instruction over time. The application of a coding framework focused on simultaneity and connections in teaching points to a richer range of structural relationships within examples, and more connecting work between examples in the second year in comparison to the first year.