Using Intuition From Everyday Life in 'Filling' the gap in Children's Extension of Their Number Concept to Include the Negative Numbers |
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Authors: | Liora Linchevski Julian Williams |
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Institution: | (1) Liora Linchevski, School of Education, Hebrew University of Jerusalem, Mount Scopus, Israel, 91903, E-mail;(2) Faculty of Education, University of Manchester, M13 9PL, U.K. |
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Abstract: | 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.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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