Mediating primary mathematics: theory, concepts, and a framework for studying practice

Abstract

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.

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Notes

  1. 1.

    In previous writing developing this work, we have used the term “Mathematical Discourse in Instruction—Primary,” (MDI-P). The history of this work is a co-development of MDI frameworks between Hamsa Venkat and Jill Adler, which shared roots in sociocultural theory but differed in specific formulations across work in secondary and primary mathematics. In order to avoid confusions between the secondary and primary level models, we have changed our titling of the framework to MPM. Writing with Adler and her team is underway, detailing the histories and trajectories of development of both MPM and MDI.

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Correspondence to Hamsa Venkat.

Appendices

Appendix 1

Table 6 The MPM framework

Appendix 2

Table 7 MPM maps—Ms. M

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Venkat, H., Askew, M. Mediating primary mathematics: theory, concepts, and a framework for studying practice. Educ Stud Math 97, 71–92 (2018). https://doi.org/10.1007/s10649-017-9776-1

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Keywords

  • Primary mathematics teaching
  • Sociocultural theory
  • Mediation
  • South Africa
  • Artifacts
  • Inscriptions
  • Instructional quality