Educational Studies in Mathematics

, Volume 39, Issue 1, pp 131–147

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

  • Liora Linchevski
  • Julian Williams

DOI: 10.1023/A:1003726317920

Cite this article as:
Linchevski, L. & Williams, J. Educational Studies in Mathematics (1999) 39: 131. doi:10.1023/A:1003726317920


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.

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Liora Linchevski
    • 1
  • Julian Williams
    • 2
  1. 1.Liora Linchevski, School of EducationHebrew University of JerusalemMount ScopusIsrael
  2. 2.Faculty of EducationUniversity of ManchesterU.K.