The development of proportional reasoning: Effect of continous versus discrete quantities

Journal of Cognition and Development

Volumn 8, Issue 2, 2007, Pages 237-256

  Jeong, Yoonkyung ^a   Levine, Susan C ^b   Huttenlocher, Janellen ^b  

^a The Catholic University of Korea   (South Korea)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CHILD; CHILD DEVELOPMENT; COGNITIVE DEVELOPMENT; CONCEPT ANALYSIS; CONCEPT FORMATION; CONTROLLED STUDY; CRITICAL THINKING; DECISION MAKING; FEMALE; HUMAN; HUMAN EXPERIMENT; INTUITION; LEARNING; MALE; MATHEMATICAL ANALYSIS; NORMAL HUMAN; PERCEPTION; PROBABILITY; PROBLEM SOLVING;

EID: 34447275224     PISSN: 15248372     EISSN: None     Source Type: Journal    
DOI: 10.1080/15248370701202471     Document Type: Article

References (37)

1. 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.
2. Brainerd, C. J., & Reyna, V F. (1990). Inclusion illusion: Fuzzy-trace theory and perceptual salience effects in cognitive development. Developmental Review, 10, 365-403.
3. Bryant, P. (1974). Perception and understanding in young children: An experimental approach. London: Methuen.
4. Chapman, R. H. (1975). The development of children's understanding of proportions. Child Development, 46, 141-148.
5. Davies C. (1965). Development of the probability concept in children. Child Development, 36, 779-788.
6. Duffy, S., Huttenlocher, J., & Levine, S. (2005). It's all relative: How young children encode extent. Journal of Cognition and Development, 6, 51-64.
7. Gao, F., Levine, S., & Huttenlocher, J. (2000). What do infants know about continuous quantity? Journal of Experimental Child Psychology, 77, 20-29.
8. Gentner, D., Rattermann, M. J., Markman, A., & Kotovsky, L. (1995). Two forces in the development of relational similarity. In T. J. Simon & G. S. Halford (Eds.), Developing cognitive competence: New approaches to process modeling. (pp. 263-313). Hillsdale, NJ: Lawrence Erlbaurn Associates, Inc.
9. Goswami, U. (1989). Relational complexity and the development of analogical reasoning. Cognitive development, 4, 251-268.
10. Hoemann, H., & Ross, B. (197 1). Children's understanding of probability concepts. Child Development, 42, 221 236.
11. Huttenlocher, J., Duffy, S., & Levine, S. (2002). Infants and toddlers discriminate amount: Are they measuring? Psychological Science, 13, 244-249.
12. Huttenlocher, J., Newcombe, N., & Vasilyeva, M. (1999). Spatial scaling in young children. Psychological Science, 10, 393-398.
13. Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence. New York: Basic Books.
14. Karplus, R., Pulos, S., & Stage, E. K. (1983). Early adolescence proportional reasoning on "rate" problems. Educational studies in Mathematics, 14, 219-233.
15. Lovett, S., & Singer, J. (1991, April). The development of children's understanding of probability: Perceptual and quantitative conception. Poster presented at the biennial meeting of the Society for Research in Child Development, Seattle, WA.
16. Miller, K. F. (1984). Children as a measurer of all things: Measurement procedures and the development of quantitative concepts. In C. Sophian (Eds.), Origins of cognitive skills (pp. 193-228). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
17. Miura, I. T., Okamoto, Y, Vlahovic-Stetic, V., Kim, C. C., & Han, J. H. (1999). Language Supports for children's understanding of numerical fraction: Cross-national Comparisons. Journal of Experimental Child Psychology, 74, 356-365.
18. Mix, K.S., Huttenlocher, J. & Levine, S. C. (2002). Quantitative development in infancy and early childhood. New York: Oxford.
19. Mix, K. S., Levine, S. C., & Huttenlocher, J. (1999). Early fraction calculation ability. Developmental Psychology, 35, 164-174.
20. Noelting, G. (1980). The development of proportional reasoning and the ratio concept, part I. Differentiation of stages. Educational studies in Mathematics, 11, 217 254.
21. Paik, J. H., & Mix, K. (2003). U.S. and Korean children's comprehension of fraction names: A reexamination of cross-nationat differences. Child Development, 74, 144-154.
22. Piaget, J., & Inhelder, B. (1967). The child's conception of space. New York: Norton.
23. Piaget, J., & Inhelder, B. (1975). The origins of the idea of chance in children. New York: Norton.
24. Resnick, L.B., & Singer, J. A. (1993). Protoquantitative origins of ratio reasoning. In T. P. Carpenter, E. Fenema, & T.A. Romberg (Eds.), Rational numbers: An integration of research (pp. 107-130). Hillsdale, NJ: Laurence Erlbaum Associates, Inc.
25. Resnick, L. B. (1995). Inventing arithmetic: Making children' intuition work in school. In C. Nelson (Ed.), The Minnesota symposium on child psychology, Vol. 28: Basic and applied perspectives on learning, cognition, and development (pp. 75-101). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
26. 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.
27. Schlottmann, A. (2001). Children's Probability intuitions: Understanding the expected value of complex gambles. Child Development, 71, 103-122.
28. Siegler, R. S., & Vago, S. (1978). The development of proportionality concept: Judging relative fullness. Journal of Experimental Child Psychology, 25, 311-395.
29. 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.
30. Song, M. J., & Ginsburg, H. P. (1987). The development of informal and formal mathematical thinking of Korean and American children. Child Development, 58, 1286-1296.
31. Song, M. J., & Ginsburg, H. P. (1988). The effect of Korean number system on young children's counting: A natural experiment in numerical bilingualism. International Journal of Psychology, 23, 319-332.
32. Sophian, C. (2000). Perceptions of proportionality in young children: Matching spatial ratios. Cognition, 75, 145-170.
33. Sophian, C., & Crosby, M. E. (April, 1999). Young children's match spatial proportions. Poster presented at the biennial meetings of the Society for Research in Child Development, Albuquerque, NM.
34. Sophian, C., & Wood, A. (1997). Proportional reasoning in young children: The parts and the whole of it. Journal of Educational Psychology, 89, 309-317.
35. Spinillo, A. G., & Bryant, P. (1991). Children's proportional judgments: The importance of "half." Child Development, 62, 427-440.
36. Vasilyeva, M., & Huttenlocher, J. (2004). Early development of scaling ability. Developmental Psychology, 40, 682-690.
37. Yost, P., Siegel, E., & McMichael, J. (1962). Nonverbal probability judgments by young children. Child Development, 33, 769-780.