Multiplicative reasoning: teaching primary pupils in ways that focus on functional relations |
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| Authors: | Mike Askew |
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| Institution: | Division of Mathematics Education, School of Education, University of the Witwatersrand, Johannesburg, South Africa |
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| Abstract: | This paper examines a problem described as widespread and long-standing in mathematics education: supporting pupils into multiplicative reasoning, a form of reasoning that has been noted as central to large tracts of secondary mathematics and beyond. Also noted, however, is a persistent perception of multiplicative situations only in terms of repeated addition – a perception held not only primary pupils, but also among primary teachers and curriculum developers. The focus of this paper is to synthesize literature on multiplicative reasoning as a conceptual field together with a sociocultural discussion of the role of mediating artifacts in the development of this conceptual field. Bringing MR into the primary classroom can then be achieved, I propose, through a pedagogy oriented toward model-eliciting and teacher appropriation of pupils’ models as pedagogic tools with the subsequent re-appropriation of refined models by pupils. This pedagogy is illustrated through the analysis of two vignettes from a teaching experiment which demonstrate the beginnings of MR as an emergent conceptual field in the classroom. The paper concludes that it is possible to move primary teaching and learning toward understanding the functional aspects of multiplicative reasoning, but that any such moves requires attention to teachers’ pedagogic and content knowledge. |
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| Keywords: | Sociocultural theory elementary mathematics education multiplicative reasoning |
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