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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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.
- Barton, B.: 1996, 'Making sense of ethnomathematics: ethnomathematics is making sense', Educational Studies in Mathematics 31, 201–233. CrossRef
- Behr, M., Lesh, R., Post, T. and Silver, E.: 1983, 'Rational number concepts', in R. Lesh and M. Landau (eds.), Acquisition of Mathematical Concepts and Processes, Academic Press, New York.
- Brown, J. S., Collins, A. and Duguid, P.: 1989, 'Situated cognition and the culture of learning', Educational Researcher 18(1), 32–42. CrossRef
- Chaiklin, S. and Lave, J.: 1993, Understanding Practice, Cambridge University Press, Cambridge, U.K.
- Dirks, M. K.: 1984, 'The integer abacus', Arithmetic Teacher 31(7), 50–54.
- Engestrom, Y.: 1991, 'Non scolae sed vitae discimus: Toward overcoming the encapsulation of school learning', Learning and Instruction 1(3), 243–259. CrossRef
- Fischbein, E.: 1987, Intuition in Science and Mathematics, D. Reidel, Dordrecht.
- Freudenthal, H.: 1983, Didactical Phenomenology of Mathematical Structures, Kluwer Academic Publishers, Dordrecht.
- Glaeser, G.: 1981, 'Epistemologie des nombres relatifs', Recherches en Didactiques des Mathematiques 2(3), 303–346.
- Gravemeijer, K.: 1994, 'Educational development and developmental research in mathematics education', Journal for Research in Mathematics Education 25(5), 443–471. CrossRef
- Gray, E. M. and Tall, D. O.: 1994, 'Duality, ambiguity, and flexibility: a 'proceptual' view of simple arithmetic', Journal for Research in Mathematics Education 25(2), 116–140. CrossRef
- Heckman, P. E. and Weissglass, J.: 1994, 'Contextualised mathematics instruction: moving beyond recent proposals', For the Learning of Mathematics 14(1), 29–33.
- Hefendehl-Hebeker, L.: 1991, 'Negative numbers: Obstacles in their evolution from intuitive to intellectual constructs', For The Learning of Mathematics 11(1), 26–32.
- Lave, J.: 1988, Cognition in Practice: Mind, Mathematics and Culture in Everyday Life, Cambridge University Press, New York.
- Lave, J.: 1996, 'Teaching, as learning, in practice', Mind, Culture, and Activity 3(3), 149–164. CrossRef
- Lave, J. and Wenger, E.: 1991, Situated Learning: Legitimate Peripheral Participation, Cambridge University Press, Cambridge, UK.
- Leont'ev, A. N.: 1981, 'The problem of activity in soviet psychology', in J. V. Wertsch (trans. and ed.) The Concept of Activity in Soviet Psychology, M. E. Sharpe, Armonk, N.Y., pp. 37–71.
- Liebeck, P.: 1990, 'Scores and forfeits — an intuitive model for integer arithmetic', Educational Studies in Mathematics 21(3), 221–239. CrossRef
- Linchevski, L. and Williams, J. S.: 1996, 'Situated intuition, concrete manipulations and mathematical concepts: the case of integers', Proceedings of the Twentieth International Group for the Psychology of Mathematics Education Vol. 3, University of Valencia, Valencia, pp. 265–272.
- Lytle, P. A.: 1994, 'Investigation of a model based on neutralization of opposites to teach integers', Proceedings of the Nineteenth International Group for the Psychology of Mathematics Education, Universidade Federal de Pernambuco, Recife, Brazil, pp. 192–199.
- Semadeni, Z.: 1984, 'A principle of concretization permanence for the formation of arithmetical concepts', Educational Studies in Mathematics 15(4), 379–395. CrossRef
- Sfard, A.: 1991, 'The dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin', Educational Studies in Mathematics 22, 1–36. CrossRef
- Sfard, A. and Linchevski, L.: 1994, 'The gains and pitfalls of reification: the case of algebra', Educational Studies in Mathematics 26, 87–124. CrossRef
- Treffers, A.: 1987, Three Dimensions: A model of Goal and Theory Description in Mathematics Instruction — the Wiskobas Project, Kluwer Academic Publishers, Dordrecht.
- Walkerdine, V.: 1988, The Mastery of Reason: Cognitive Development and the Production of Rationality, Routledge, London.
- Wertsch, J. V.: 1991, Voices of the Mind: a Sociocultural Approach to Mediated Action, Harvester, London.
- Wertsch, J. V.: 1996, 'The primacy of mediated action in sociocultural theory', Mind, Culture, and Activity 1(4), 202–208.
- Williams, J. S. and Linchevski, L.: 1997, Situated Intuitions, Concrete Manipulations and the Construction of the Integers: Comparing two Experiments, paper presented to the annual conference of the American Educational Research Association, Chicago, March 1997.
- Using Intuition From Everyday Life in 'Filling' the gap in Children's Extension of Their Number Concept to Include the Negative Numbers
Educational Studies in Mathematics
Volume 39, Issue 1-3 , pp 131-147
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