ISSN : 1229-0718
The present study was designed to describe the two dissociable systems(formal and informal systems) of proportional reasoning and their development. For these ends, 4, 6, 8 and 10-year-olds were asked to judge the equivalence of proportions involving continuous or discrete quantities. In discrete condition where formal system may have been activated, only 10-year-olds succeeded; children aged 4, 6 and 8 performed chance level. Most importantly, 4- and 6-year-olds’ tendency to be misled by the absolute number was significantly related to their counting proficiency and 10 year olds’ successful performance was significantly related to their fluency in fraction use, indicating that their performance in discrete condition was influenced by their acquisition of mathematical convention.; In stark contrast, even 4-year-olds succeeded at matching proportions and children's performance gradually increases with age in continuous condition where informal system may have been activated.; children’s errors did not predominantly consist of erroneously choosing the absolute amount match.
석정서 (2008). 저학력 노인의 개념화를 평가하는 신경심리도구로서의 비율 추론 과제. 서울 대학교 석사학위 논문.
정윤경 (2005). 비율 추론 능력의 발달: 수행에 영향을 미치는 과제 변인을 중심으로. 한국심리학회지 발달, 18(4), 109-118.
Acredolo, C., O’Connor, J., Banks, L., & Horobin, K. (1989). Children’s ability to make probability estimates: Skills revealed through application of Anderson’s functional measurement methodology, Child Development, 60, 933-945.
Ahl, V., Moore, C. F., & Dixon, J. A. (1992). Development of intuitive and numerical proportional reasoning. Cognitive Development, 7, 81-108.
Antell, S. R., & Keating, D. (1983). Perception of numerical invariance in neonates. Child Development, 54, 695-701.
Baillargeon, R., Needham, A., & DeVos, J. (1992). The development of young infants’ intuition about support. Early development and parenting (1), 69-78.
Broaders, S. Wagner, S. C., Mitchell, Z., & Goldin-Meadow, S. (2007). Making Children Gesture Brings Out Implicit Knowledge and Leads to Learning. Journal of Experimental Psychology: General, Volume 136(4), 539-550.
Bryant P. (1974). Perception and understanding in young children. London Methuen.
Chapman, R. H. (1975). The development of children's understanding of proportions. Child Development, 46, 141-148.
Cooper, R. G. Jr. (1984). Early number development: Discovering number space with addition and subtraction. In C. Sophian (Ed.), Origins of cognitive skills (pp. 157-192). Hillsdale, NJ: Erlbaum.
Davies, C. (1965). Development of the probability concept in children. Child Development, 36, 779-788.
Dehaene, S., & Changeux, J. (1993). Development of elementary numerical abilities: a neuronal model. Journal of Cognitive Neuroscience 5, 390–407.
Dehaene, S., & Cohen, L. (1997). Cerebral pathways for calculation: Double dissociation between rote verbal and quantitative knowledge of arithmetic, Cortex 33, 219–250.
Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology. Vol 20(3-6), 487-506.
Dixon, J. A., & Moore, C. F. (1996). The developmental role of intuitive principles in choosing mathematical strategies. Developmental Psychology, 32, 241-253.
Duffy, S., Huttenlocher, J., & Levine, S. (2005). It's all relative: How young children encode extent, Journal of Cognition and Development, 6(1), 51-64.
Falk, R., & Wilkening, F. (1998). Children's construction of fair chance: Adjusting probabilities. Developmental Psychology, 34(6), 1340-1357.
Fischbein, E. (1990). Intuition and information processing in mathematical activity. International journal of Educational Research, 14, 31-50.
Gelman, R. (1991). Epigenetic foundations of knowledge structures: Initial and transcendent construction. In S. Carey & R. Gelman.(Eds), Epigenesis of mind: essays on biology and cognition (pp. 293-322). Hillsdale, NJ: Erlbaum.
Greeno, J. G., Riley, M. S., & Gelman, R. (1984). Conceptual competence for children’'s counting. Cognitive Psychology, 16, 94-143.
Hoemann, H., & Ross, B. (1971). Children's understanding of probability concepts, Child Development, 42, 221-236.
Huttenlocher, J, Duffy, S., & Levine, S. (2002). Infants and toddlers discriminate amount: Are they measuring? Psychological Science, 13(3), 244-249.
Huttenlocher, J., Jordan, N., & Levine, S.C. (1994). A mental model for early arithmetic. Journal of Experimental Psychology: General, 123, 284-296.
Huttenlocher, J., Newcombe, N., & Vasilyeva, M. (1999). Spatial scaling in young children. Psychological Science, 10(5), 393-398.
Jeong, Y. (2003). The Development of Proportional Reasoning: Equivalence matching with continuous vs. Discrete quantities. Dissertation submitted for Ph.D. at University of Chicago.
Jeong, Y. (2004). Children's judgments about proportional Equivalence with Discrete quantities, Korean Science Journal, XXXI(2), 57-80.
Jeong, Y., Levine, S., & Huttenlocher, J. (2007). The Development of Proportional Reasoning: Effect of Continuous vs. Discrete Quantities. Journal of Cognition and Development Vol8(2). 237-256.
Karplus, R., Pulos, S., & Stage, E. K. (1983). Early adolescence proportional reasoning on "rate" problems. Educational studies in Mathematics. 14, 219-233.
Kieren, T. E. (1988). Personal Knowledge of rational numbers: its intuitive an formal development. In J. Hiebert, & M.
Lemer, C., Dehaene, S., Spelke, E., & Cohen, L. (2003). Approximate quantities and exact number words: Dissociable systems, Neuropsychologia. 41, 1942-1958.
Noelting, G. (1980). The development of proportional reasoning and the ratio concept, part I Differentiation of stages. Educational studies in Mathematics, 11, 217-254.
Piaget, J., & Inhelder, B. (1975). The origins of the idea of chance in children. New York: Norton.
Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306, 499–503.
Resnick, L. B. (1995). Inventing arithmetic: Making children' intuition work in school. In C. Nelson(Eds), The Minnesota Symposium on Child Psychology, Vol. 28: Basic and applied perspectives on learning, cognition, and development (pp. 75-101). Mahwah, NJ: Erlbaum.
Reyna, V. F., & Brainerd, C. J. (1993). Fuzzy memory and mathematics in the classroom. In R.H. Logie & G. Davis (Eds.), Memory in Everyday Life (pp.91-136). Amsterdam: North-Holland.
Scholottmann, A. (2001). Children's Probability Intuitions: Understanding the Expected Value of Complex Gambles. Child Development, 71(1), 103-122.
Siegler, R. S., & Stern, E. (1998) Conscious and unconscious strategy discoveries: A microgenetic analysis. Journal of Experimental Psychology: General 127, 377-397.
Siegler, R. S., & Vago, S. (1978). The development of proportionality concept: judging relative fullness. Journal of Experimental Child Psychology, 25, 311-395.
Singer, J. A., Kohn, A. S., & Resnick, L. B. (1997). Knowing about proportions in different contexts. In T. Nunes, & P. Bryant, Learning and teaching mathematics (pp. 115-132). East Sussex, UK: Psychology Press.
Singer-Freeman, K. E., & Goswami, U. (2001). Does a half pizza equal half a box of chocolate? Proportional matching in an analogy task. Cognitive Development, 16, 811-829.
Sophian, C. (2000) Perceptions of proportionality in young children: Matching spatial ratios. Cognition. 75(2), 145-170.
Spinillo, A. G., & Bryant, P. (1991). Children's proportional judgments: The importance of "half". Child Development, 62, 427-440.
Starkey, P., & Cooper, R. (1980). Perception of numbers by human infants. Science 210(28), 1033–1034.
Starkey, P., Spelke, E. S., & Gelman, R. (1990). Numerical abstraction by human infants. Cognition 36, 97–128.
van Loosbroek., & Smitsman, A. W. (1990). Visual perception of numerosity in infancy. Developmental Psychology 26, pp. 916–922.
Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month old infants. Cognition, 74, B1-B11.