In the paper Using intuition from everyday life in ‘filling’ the gap in children’s extension of their concept to include negative numbers, the authors reports 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.
The authors 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 and conceptualize modelling as the transformation of outside-school knowledge into school mathematics, and discuss the opportunities and difficulties involved. Their instructional method build on Realistic Mathematics Education (RME) developed by Freudenthal’s followers at the Freudenthal Institute (Treffers, 1987; Gravemeijer, 1994).
The study involved a series of teaching sequences, each of about 5 one hour- long sessions, with groups (of three children at a time in the first experiment and four in the second experiment) of grade 6 pupils who had not yet received any instruction in negative numbers. The final sequence led the children to construct the integers and operations of addition and subtraction.
Authors: LIORA LINCHEVSKI and JULIAN WILLIAMS
Educational Studies in Mathematics 39: 131–147, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands.
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