Perceptions of proportionality in young children: Matching spatial ratios

Cognition

Volumn 75, Issue 2, 2000, Pages 145-170

  Sophian, Catherine ^a  

^a UNIVERSITY OF HAWAII   (United States)

Author keywords

Mathematical development; Ratios; Spatial proportionality

Indexed keywords

ADULT; ARTICLE; CHILD; COGNITION; CONTROLLED STUDY; DEPTH PERCEPTION; FEMALE; HUMAN; HUMAN EXPERIMENT; MALE; MATHEMATICS; MEMORY; NORMAL HUMAN; PERCEPTION; PRIORITY JOURNAL; REINFORCEMENT; STIMULUS;

ADULT; AGE FACTORS; CHILD, PRESCHOOL; CONCEPT FORMATION; FEMALE; HUMANS; MALE; MATHEMATICS; MIDDLE AGED; RANDOM ALLOCATION; SPACE PERCEPTION;

EID: 0034657337     PISSN: 00100277     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0010-0277(00)00062-7     Document Type: Article

References (38)

1. Baillargeon R., Needham A., DeVos J. The development of young infants' intuitions about support. Early Development and Parenting. 1:1992;69-78.
2. Barsalou L.W. Perceptual symbol systems. Behavioral and Brain Sciences. 22:1999;577-660.
3. Briars D.J., Larkin J.L. An integrated model of skill in solving elementary word problems. Cognition and Instruction. 1:1984;245-296.
4. Cummins D.D. Children's interpretations of arithmetic word problems. Cognition and Instruction. 8:1991;261-289.
5. DeCorte E., Verschaffel L. Beginning first graders' initial representation of arithmetic word problems. Journal of Mathematical Behavior. 4:1985;3-21.
6. Dehaene S. The number sense: how the mind creates mathematics. 1997;Oxford University Press, New York.
7. Dixon J.A., Moore C.F. The developmental role of intuitive principles in choosing mathematical strategies. Developmental Psychology. 32:1996;241-253.
8. Durkin K. The representation of number in infancy and early childhood. Pratt C., Garton A.F. Systems of representation in children. 1993;133-166 Wiley, New York.
9. Empson, S. B. (1995). Equal sharing and shared meaning: the development of fraction concepts in a first-grade classroom. Paper presented at the meeting of the American Educational Research Association, San Francisco.
10. Fischbein E. Intuition and information processing in mathematical activity. International Journal of Educational Research. 14:1990;31-50.
11. Gelman R., Meck B. Early principles aid initial but not later conceptions of number. Bideaud J., Meljac C., Fischer J.P. Pathways to number. 1992;171-189 Lawrence Erlbaum, Hillsdale, NJ.
12. Greer B. Multiplication and division as models of situations. Grouws D. Handbook of research on mathematics teaching and learning. 1992;276-295 Macmillan, New York.
13. Kieren T.E. Personal knowledge of rational numbers: its intuitive and formal development. Hiebert J., Behr M. Number concepts and operations in the middle grades. 1988;162-181 Lawrence Erlbaum, Hillsdale, NJ.
14. Mack N. Learning fractions with understanding: building on informal knowledge. Journal for Research in Mathematics Education. 21:1990;16-32.
15. Mack N.K. Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education. 26:1995;422-441.
16. Moore C.F., Dixon J.A., Haines B.A. Components of understanding in proportional reasoning: a fuzzy set representation of developmental progressions. Child Development. 62:1991;441-459.
17. Moyer R.S., Landauer T.K. Time required for judgements of numerical inequality. Nature. 215:1967;1519-1520.
18. The Third National Mathematics Assessment: results, trends, and issues. 1983;Educational Testing Service, Princeton, NJ.
19. Nunes T., Schliemann A.D., Carraher D.W. Street mathematics and school mathematics. 1993;Cambridge University Press, Cambridge.
20. Piaget J. The child's conception of number. 1952;Norton, New York.
21. Piaget J., Inhelder B. The child's conception of space. 1956;Norton, New York.
22. Piaget J., Inhelder B. The origin of the idea of chance in children. 1975;Norton, New York.
23. Pylyshyn Z. Is vision continuous with cognition? The case for cognitive impenetrability of visual perception. Behavioral and Brain Sciences. 22:1999;341-423.
24. Resnick L.B. Developing mathematical knowledge. American Psychologist. 44:1989;162-169.
25. Resnick L.B. Situated rationalism: biological and social preparation for learning. Hirschfeld L.A., Gelman S.A. Mapping the mind: domain specificity in cognition and culture. 1994;474-493 Cambridge University Press, New York.
26. Reyna V.F., Brainerd C.J. The origins of probability judgment: a review of data and theories. Wright G., Ayton P. Subjective probability. 1994;239-272 Wiley, New York.
27. Riley M.S., Greeno J.G. Developmental analysis of understanding language about quantities and of solving problems. Cognition and Instruction. 5:1988;49-101.
28. Singer J.A., Kohn A.S., Resnick L.B. Knowing about proportions in different contexts. Nunes T., Bryant P. Learning and teaching mathematics. 1997;115-132 Psychology Press, East Sussex, UK.
29. Sophian C., McCorgray P. Part-whole knowledge and early arithmetic problem-solving. Cognition and Instruction. 12:1994;3-33.
30. Sophian C., Wood A. Proportional reasoning in young children: the parts and the whole of it. Journal of Educational Psychology. 89:1997;309-317.
31. Spinillo A.G., Bryant P. Children's proportional judgments: the importance of "half" Child Development. 62:1991;427-440.
32. Starkey P., Spelke E.S., Gelman R. Numerical abstraction by human infants. Cognition. 36:1990;97-127.
33. Steffe L.P., Cobb P., von Glasersfeld E. Construction of arithmetical meanings and strategies. 1988;Springer, New York.
34. Stigler J.W., Fuson K.C., Ham M., Kim M.S. An analysis of addition and subtraction word problems in American and Soviet elementary mathematics textbooks. Cognition and Instruction. 3:1986;153-171.
35. Strauss M.S., Curtis L.E. Infant perception of numerosity. Child Development. 52:1981;1146-1152.
36. Streefland L. Fractions: a realistic approach. Carpenter T.P., Fennema E., Romberg T.A. Rational numbers: an integration of research. 1993;289-325 Lawrence Erlbaum, Hillsdale, NJ.
37. Streefland L. Charming fractions or fractions being charmed? Nunes T., Bryant P. Learning and teaching mathematics. 1997;347-371 Psychology Press, East Sussex, UK.
38. Vurpillot E. Visual world of the child. 1976;International Universities Press, New York.