THE IMPORTANCE OF "HALF" IN THE DEVELOPMENT OF THE CONCEPT OF PROPORTION
Keywords:
Proportion, Development, , StrategyAbstract
This paper focuses on the importance of "halt" in
children's initial understanding of proportion. Children's performance was
analised in several well-documented studies and it revealed that "half" is
an important and frequent strategy in children's proportional judgements.
This issue, however, has been negleted in the literature about proportions,
and only recently it has been studied empirically (Spinillo, 1987, 1990;
Spinillo & Bryant, 1989, 1990, 1991). The "half" boundary is a strategy that children use to infer the structural similarities and dissimilarities
between ratios. This is related to the use of relative codes and also to the
results found in categorical perception. Future researches are suggested
in order to explore more about the "ha/f" boundary in proportional
judgements.
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References
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discrimination of speech sounds within and across phonemic boundaries. Journal
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Part I - Differentiation of stages. Educátional Studies in Mathematics, 11,
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Noelting, R. (1980b). The development of proportional reasoning and the ratio concept.
Part II - Problem-structure at sucessive stages: Problem-solving strategies and
the mechanism of adaptative restructuring. Educátional Studies in Mathematics,
11, 331-363.
Parrat-Dayan, S. (1982). De la fraction (moitie) sur Fobjet a la fraction (moite)
relationnelle. Revue Suisse de Psychologie Puré et Appliquee, 2, 139-153.
Piaget, J. & Inhelder, B. (1975). The origin of the idea of chance in children. New York:
W. Norton.
Siegler, R. S. & Vago, S. (1987). The development of proportionality concept: Judging
relative fullness. Journal of Experimental Child Psychology, 25, 371-395.
Spinillo. A. G. (1978). The development of proportional reasoning in young children.
15th Annual Conference of the British Psychological Society - Developmental
Section (Resumos), York, U. K.
Spinillo, A. G. (1990). The development of the concept of proportion in young children.
Tese de Doutoramento não publicada. University of Oxford, Oxford, U. K.
Spiniilo, A. G. (submetido). As relações de primeira ordem em tarefas de proporção:
Uma outra explicação quanto as dificuldades das crianças.
Spiniilo, A. G. & Bryant, P. E. (1988). The importance of "half" in children's proportional
judgements. 3rd European Conference on Developmental Psychology
(Resumos), Budapest.
Spiniilo, A. G. & Bryant, P. E. (1989). The initial understanding of ratio and proportion.
13th International Conference for The Psychology of Mathematics Education
Spiniilo, A. G. & Bryant, P. E. (1989). The initial understanding of ratio and proportion.
13th International Conference for The Psychology of Mathematics Education
(Resumos), Paris.
Spiniilo, A. G. & Bryant, P. E. (1990). Ratio and proportion: Judging discrete and
continuous quantities. 4th European Conference on Developmental Psychology
(Resumos), Stirling, U. K.
Spiniilo, A. G. & Bryant, P. E. (1991). Children's proportional judgements: The
importance of "half". Child Development, 62, 427-440.
Wohlwill, J. F. (1960). Absolute vs. relational discrimination on the dimension of
number. Journal of Genetic Psychology, 96, 353-363.
Wohlwill, J. F. (1963). The learning of absolute and relational number discriminations
by children. Journal of Genetic Psychology, 101, 217-228.
Woodruff, G. & Premack, D. (1981). Primitive mathematical concepts in the
chimpanzee: Proportionality and numerosity. Nature, 293, 568-570.
Olver and P. M. Greenfield (Orgs.), Studies in cognitive growth (pp 168-182).
New York: John Willey and Sons.
Bryant, P. E. (1974). Perception and understanding in young children: An experimental
approach. London: Methuen.
Eimas, P. D., Siqueland, E. R., Jusczyk, P. & Vigorito, J. (1971). Speech perception in
infants. Science, 171, 303-306.
Harnad, S. (1987). Categórica! perception. The groundwork of cognition. Cambridge:
Cambridge University Press.
Inhelder, B. & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence.
London: Routledge and Kegan Paul.
Lawrenson, W. & Bryant, P. E. (1972). Absolute and relative codes in children. Journal
of Child Psychiatry, 13, 25-25.
Liberman, A. M., Harris, K. S., Hoffman, H. S. & Griffith, B. C. (1957). The
discrimination of speech sounds within and across phonemic boundaries. Journal
of Experimental Psychology, 61, 379-388.
Noelting, R. (1980a). 1 ne development of proportional reasoning and the ratio concept.
Part I - Differentiation of stages. Educátional Studies in Mathematics, 11,
217-253.
Noelting, R. (1980b). The development of proportional reasoning and the ratio concept.
Part II - Problem-structure at sucessive stages: Problem-solving strategies and
the mechanism of adaptative restructuring. Educátional Studies in Mathematics,
11, 331-363.
Parrat-Dayan, S. (1982). De la fraction (moitie) sur Fobjet a la fraction (moite)
relationnelle. Revue Suisse de Psychologie Puré et Appliquee, 2, 139-153.
Piaget, J. & Inhelder, B. (1975). The origin of the idea of chance in children. New York:
W. Norton.
Siegler, R. S. & Vago, S. (1987). The development of proportionality concept: Judging
relative fullness. Journal of Experimental Child Psychology, 25, 371-395.
Spinillo. A. G. (1978). The development of proportional reasoning in young children.
15th Annual Conference of the British Psychological Society - Developmental
Section (Resumos), York, U. K.
Spinillo, A. G. (1990). The development of the concept of proportion in young children.
Tese de Doutoramento não publicada. University of Oxford, Oxford, U. K.
Spiniilo, A. G. (submetido). As relações de primeira ordem em tarefas de proporção:
Uma outra explicação quanto as dificuldades das crianças.
Spiniilo, A. G. & Bryant, P. E. (1988). The importance of "half" in children's proportional
judgements. 3rd European Conference on Developmental Psychology
(Resumos), Budapest.
Spiniilo, A. G. & Bryant, P. E. (1989). The initial understanding of ratio and proportion.
13th International Conference for The Psychology of Mathematics Education
Spiniilo, A. G. & Bryant, P. E. (1989). The initial understanding of ratio and proportion.
13th International Conference for The Psychology of Mathematics Education
(Resumos), Paris.
Spiniilo, A. G. & Bryant, P. E. (1990). Ratio and proportion: Judging discrete and
continuous quantities. 4th European Conference on Developmental Psychology
(Resumos), Stirling, U. K.
Spiniilo, A. G. & Bryant, P. E. (1991). Children's proportional judgements: The
importance of "half". Child Development, 62, 427-440.
Wohlwill, J. F. (1960). Absolute vs. relational discrimination on the dimension of
number. Journal of Genetic Psychology, 96, 353-363.
Wohlwill, J. F. (1963). The learning of absolute and relational number discriminations
by children. Journal of Genetic Psychology, 101, 217-228.
Woodruff, G. & Premack, D. (1981). Primitive mathematical concepts in the
chimpanzee: Proportionality and numerosity. Nature, 293, 568-570.
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Published
2012-08-29
How to Cite
Spinillo, A. G. (2012). THE IMPORTANCE OF "HALF" IN THE DEVELOPMENT OF THE CONCEPT OF PROPORTION. Psicologia: Teoria E Pesquisa, 8(3), 305–317. Retrieved from https://periodicos.unb.br/index.php/revistaptp/article/view/17142
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