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  • 1.
    Abdulhamid, Lawan
    et al.
    University of the Witwatersrand, Johannesburg, South Africa.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. University of the Witwatersrand, Johannesburg, South Africa.
    Primary mathematics teachers’ responses to students’ offers: An ‘elaboration’ framework2018In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 51, p. 80-94Article in journal (Refereed)
    Abstract [en]

    Responding constructively ‘in-the moment’ to student offers is described as a critical, and yet difficult, aspect of skilful and responsive teaching. South African evidence points to limited evaluation of student offers in schools serving poor communities. In this paper, we present and discuss an ‘elaboration’ framework emerging from a grounded analysis of data drawn from video recordings of 18 mathematics lessons prepared and conducted by four in-service primary school teachers in South Africa. This analysis led to a categorization of the situations in which teacher responses to student offers occurred, and the nature and range of these responses. Three response situations are identified within the framework: breakdown, sophistication, and individuation/collectivization, with a range of response (and non-response) categories in each situation. Literature on responsive feedback is drawn in to explore hierarchies and relationships between the emergent categories within situations of elaboration. The elaboration framework provides a tool for lesson observation, and a model for thinking about developments in responsive teaching.

  • 2.
    Askew, Mike
    et al.
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Abdulhamid, Lawan
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Mathews, Corin
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Morrison, Samantha
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Ramdhany, Viren
    University of Johannesburg, South Africa.
    Tshesane, Herman
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Teaching for structure and generality: Assessing changes in teachers mediating primary mathematics2019In: Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education, Pretoria, South Africa, 7-12 July 2019: Volume 2, Research reports (A-K) / [ed] M. Graven, H. Venkat, A. A. Essien & P. Vale, Pretoria, South Africa: PME , 2019, p. 41-48Conference paper (Refereed)
    Abstract [en]

    From a sociocultural perspective that a teacher’s use of mediational means is central to student learning, this paper presents an analysis of six teachers and their mediating, across a two-three year time gap. Drawing on the Mediating Primary Mathematics framework – developed to examine the type and quality of mediational means – we propose two composite assessments of quality of mediation – extent and depth – that indicate the extent to which teaching addresses mathematical structure and generality. The findings reveal a range of differences in these two assessments for each of the six teachers, but that all six teachers were more coherent in their use of mediational means in the later lesson than in the earlier one. These findings have implications for other schooling systems and researchers seeking to improve the quality of mathematics instruction.

  • 3.
    Askew, Mike
    et al.
    School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Mathews, Corin
    School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Ramsingh, Valerie
    School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Takane, Thulelah
    School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Roberts, Nicky
    Centre for Education Practice Research, University of Johannesburg, Johannesburg, South Africa.
    Multiplicative reasoning: An intervention’s impact on foundation phase learners’ understanding2019In: South African Journal of Childhood Education, ISSN 2223-7674, E-ISSN 2223-7682, Vol. 9, no 1, article id a622Article in journal (Refereed)
    Abstract [en]

    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. 

  • 4.
    Ekdahl, Anna-Lena
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, South Africa.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, South Africa.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, South Africa.
    Askew, Mike
    Wits School of Education, University of the Witwatersrand, South Africa.
    Weaving in connections: Studying changes in early grades additive relations teaching2018In: South African Journal of Childhood Education, ISSN 2223-7674, E-ISSN 2223-7682, Vol. 8, no 1, article id a540Article in journal (Refereed)
    Abstract [en]

    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.

  • 5.
    Ramdhany, Viren
    et al.
    University of Johannesburg, South Africa.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Christiansen, Iben Maj
    Stockholm University, Sweden.
    Dissonance and continuity in the mathematical education and training experiences of pre-service secondary mathematics teachers2018In: African Journal of Research in Mathematics, Science and Technology Education, ISSN 1811-7295, Vol. 22, no 2, p. 186-195Article in journal (Refereed)
    Abstract [en]

    The education and professional development of pre-service mathematics teachers occur across different contexts. Key contexts of mathematics learning and learning to teach are school, university undergraduate mathematics and mathematics teaching-related learning in teacher education courses. International literature suggests that each of these contexts legitimises different views of mathematics teaching and learning. For pre-service teachers traversing these contexts, moves between sites can be experienced in more continuous or more dissonant ways. The disjunctures associated with dissonant experiences lead to openings for value judgments related to the distinctions that are drawn, opening possibilities for a wider range of pedagogic decisions. In this paper, we explore, through interviews with four pre-service teachers in one post-graduate certificate of education (PGCE) course, perceptions of continuity and dissonance across sites related to mathematics and mathematics education, and teaching and learning. Our findings point largely to experiences of continuity between the high school and undergraduate contexts, with the PGCE course recognised as different from these contexts. 

  • 6.
    Venkat, Hamsa
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Askew, Mike
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Mediating primary mathematics: theory, concepts, and a framework for studying practice2018In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 97, no 1, p. 71-92Article in journal (Refereed)
    Abstract [en]

    In this paper, we present and discuss a framework for considering the quality of primary teachers’ mediating of primary mathematics within instruction. The “mediating primary mathematics” framework is located in a sociocultural view of instruction as mediational, with mathematical goals focused on structure and generality. It focuses on tasks and example spaces, artifacts, inscriptions, and talk as the key mediators of instruction. Across these mediating strands, we note trajectories from error and a lack of coherence, via coherence localized in particular examples or example spaces, towards building a more generalized coherence beyond the specific example space being worked with. Considering primary mathematics teaching in this way foregrounds the nature of the mathematics that is made available to learn, and we explore the affordances of attending to both coherence and structure/generality. Differences in ways of using the framework when either considering the quality of instruction or working to develop the quality of instruction are taken up in our discussion. 

  • 7.
    Venkat, Hamsa
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Askew, Mike
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Morrison, Samantha
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Abdulhamid, Lawan
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Shifts in early number learning in South Africa2019In: Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education, Pretoria, South Africa, 7-12 July 2019: Volume 3, Research reports (L-Z) / [ed] M. Graven, H. Venkat, A. A. Essien & P. Vale, Pretoria, South Africa: PME , 2019, p. 422-429Conference paper (Refereed)
    Abstract [en]

    In this paper, we report on outcomes from the Structuring Number Starters intervention project focused on early grades’ number learning in South Africa. Using tests drawn from the Maths Recovery programme, a cross-attainment sample of Grade 2 students in six schools took part in oral interview assessments early in 2011, 2014 and 2018, with professional development activities for their teachers occurring across this period. Student outcomes point to increasing proportions, over time, of students able to use more sophisticated counting strategies, and to work with number structure for more efficient calculation.

  • 8.
    Venkat, Hamsa
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwalersrand, Johannesburg, South Africa.
    Askew, Mike
    Wits School of Education, University of the Witwalersrand, Johannesburg, South Africa.
    Watson, Anne
    Department of Education, University of Oxford, Oxford, United Kingdom.
    Mason, John
    Architecture of mathematical structure2019In: For the Learning of Mathematics, ISSN 0228-0671, Vol. 39, no 1, p. 13-17Article in journal (Refereed)
    Abstract [en]

    In this paper, we provide an elaboration of the notion of mathematical structure – a term agreed upon as valuable but difficult to define. We pull apart the terminology surrounding the notion of structure in mathematics: relationship, generalising/generalisation and properties, and offer an architecture of structure that distinguishes and connects these terms. The terminology is then applied to teaching and learning phenomena related to multiplicative reasoning, illustrating how the demarcation of terms can offer a more precise language of description of learning about structure. We present ‘formatting activity’ as a key pedagogic action for accomplishing a focus on structure in teaching.

  • 9.
    Venkat, Hamsa
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Mathews, Corin
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Improving multiplicative reasoning in a context of low performance2019In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 51, no 1, p. 95-108Article in journal (Refereed)
    Abstract [en]

    In this paper we analyze the outcomes of a design experiment that sought to improve the multiplicative reasoning of 12–13 year-old learners across two schools in a South African context of low performance. Using a hybrid theoretical base in Realistic Mathematics Education, variation theory and analogical reasoning, a short-term intervention consisting of four lessons, designed with attunement to classroom culture and levels of learning, was implemented. Outcomes based on pre- and post-testing pointed to substantial gains in both schools, leading to interest in understanding the nature and extent of changes in models and calculation approaches in high performance and high gain item clusters. Increases in appropriate setting up of symbolic models of multiplicative situations and in more efficient calculation are discussed. 

1 - 9 of 9
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