A importância do referencial de "metade" e o desenvolvimento do conceito de proporção
Palabras clave:
Proporção, Desenvolvimento, Referencial de metade, EstratégiaResumen
O presente artigo versa sobre a importância do referencial de "metade" na compreensão inicial da criança sobre proporções. O desempenho de crianças é analisado em diversas investigações documentadas na literatura, revelando que o referencial de "metade" tem sido estratégia frequente em julgamentos sobre proporção. Tal fato, entretanto, tem passado desapercebido pela maioria dos pesquisadores e só recentemente é que este tópico tem sido explorado (Spinillo, 1987, 1990;Spinillo & Bryant, 1989,1990,1991). O uso dos limites de "metade" como estratégia para determinar as similaridades e dissimilaridades estruturais entre razões é ainda relacionado ao uso de códigos relativos e aos resultados encontrados em estudos na área de categorias perceptuais. Implicações para pesquisas futuras são sugeridas para se testar a extensão e aplicabilidade desta estratégia em problemas de proporção.
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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.
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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Publicado
2012-08-29
Cómo citar
Spinillo, A. G. (2012). A importância do referencial de "metade" e o desenvolvimento do conceito de proporção. Psicologia: Teoria E Pesquisa, 8(3), 305–317. Recuperado a partir de https://periodicos.unb.br/index.php/revistaptp/article/view/17142
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