Educational Studies in Mathematics

, Volume 39, Issue 1, pp 131-147

First online:

Using Intuition From Everyday Life in 'Filling' the gap in Children's Extension of Their Number Concept to Include the Negative Numbers

  • Liora LinchevskiAffiliated withLiora Linchevski, School of Education, Hebrew University of Jerusalem
  • , Julian WilliamsAffiliated withFaculty of Education, University of Manchester

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We report here an instructional method designed to address the cognitive gaps in children's mathematical development where operational conceptions give rise to structural conceptions (such as when the subtraction process leads to the negative number concept). The method involves the linking of process and object conceptions through semiotic activity with models which first record processes in situations outside mathematics and subsequently mediate activity with the signs of mathematics. We describe two experiments in teaching integers, an interesting case in which previous literature has focused on the dichotomy between the algebraic approach and the modelling approach to instruction. We conceptualise modelling as the transformation of outside-school knowledge into school mathematics, and discuss the opportunities and difficulties involved.