Educational Studies in Mathematics

, Volume 96, Issue 3, pp 275–287 | Cite as

Conceptualising the more knowledgeable other within a multi-directional ZPD

  • Yasmine Abtahi
  • Mellony Graven
  • Stephen Lerman


From a Marxian/Vygotskian perspective, learning is social in origin and it happens in the presence of others that are more knowledgeable. Extending this view to the learning of mathematics, such learning also becomes inseparable from the presence of others (people and artefacts). Researchers over decades have studied different interactions to see how such learning with others occurs, what is the role of the (more knowledgeable) other, and if at all this role alternates between the participants. In this paper, we looked at a 5-year-old’s (Lila) interaction with her mother (Mellony) and a television remote control as Lila attempted to count in threes using the three by three physical layout of the numbered buttons 1–9 on the remote control. We specifically looked at the emergence of the Zone of Proximal Development (ZPD) as Lila’s attention was caught by the properties of the remote control and by her mother’s questions. We also pay attention to how the role of the more knowledgeable other alternates among the participants. Our findings suggest that Lila, at times, used resources provided by the physical properties of the remote control and sometimes, used resources provided by Mellony to think about the task of counting in threes. In Lila’s interaction, we interpreted a multi-directional ZPD as the role of the more knowledgeable other alternated between Mellony, Lila and the remote control.


ZPD More knowledgeable others Tools Learning 


Compliance with ethical standards

Ethical statement

The manuscript has not been submitted elsewhere. The work has not been published elsewhere. There were no human participants in the research—the paper is based on an opportunistic (unplanned) video recording of the 5-year-old daughter of the second author. The research is not funded by anyone.

Conflict of Interest

The authors declare that they have no conflicts of interest.


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Yasmine Abtahi
    • 1
  • Mellony Graven
    • 2
  • Stephen Lerman
    • 3
  1. 1.Faculty of EducationUniversity of OttawaOttawaCanada
  2. 2.Education DepartmentRhodes UniversityGrahamstownSouth Africa
  3. 3.Department of EducationLondon South Bank UniversityLondonUK

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