Miura, I.T. (1987). Mathematics achievement as a function of language. Journal of Educational Psychology, 79, 79–82.

Miura, I.T., Kim, C.C., Chang, C.M., & Okamoto, Y. (1988). Effects of language characteristics on children’s cognitive representation of number: Cross-national comparisons. Child Development, 59, 1445–1450.

Miura, I.T., & Okamoto, Y. (1989). Comparisons of U.S. and Japanese first graders’ cognitive representation of number and understanding of place value. Journal of Educational Psychology, 81, 109–114.

Miura, I.T., Okamoto, Y., Kim, C.C., Steere, M., & Fayol, M. (1993). First graders’ cognitive representation of number and understanding of place value: Cross-national comparisons: France, Japan, Korea, Sweden, and the United States. Journal of Educational Psychology, 85, 24–30.

National Center for Education Statistics. (2000). America’s kindergartners (NCES 2000– 070). Washington, DC: U.S. Government Printing Office. Available: http://nces.ed.gov/spider/webspider/2000070.shtml. [July 10, 2001].


Piaget, J. (1965). The child’s conception of number. New York: Norton. (Original work published 1941 )


Riley, M.S., Greeno, J.G., & Heller, J.I. (1983). Development of children’s problem-solving ability in arithmetic. In H.Ginsburg (Ed.), The development of mathematical thinking (pp. 153–196). New York: Academic Press.

Rittle-Johnson, B., & Siegler, R.S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: A review. In C.Donlan (Ed.), The development of mathematical skills (pp. 75–110). East Sussex, UK: Psychology Press.


Séron, X., Deloche, G., & Noël, M.P. (1992). Number transcribing by children: Writing Arabic numbers under dictation. In J.Bideaud, C.Meljac, & J.-P.Fischer (Eds.), Pathways to number: Children’s developing numerical abilities (pp. 245–264). Hillsdale, NJ: Erlbaum.

Shipley, E.F., & Shepperson, B. (1990). Countable entities: Developmental changes. Cognition, 34, 109–136.

Siegler, R.S. (1987). The perils of averaging data over strategies: An example from children’s addition. Journal of Experimental Psychology: General, 116, 250–264.

Siegler, R.S. (1991). In young children’s counting, procedures precede principles. Educational Psychology Review, 3(2), 127–135.

Siegler, R.S. (1994). Cognitive variability: A key to understanding cognitive development. Current Directions in Psychological Science, 3(1), 1–5.

Siegler, R.S. (1995). How does change occur: A microgenetic study of number conservation. Cognitive Psychology, 28, 255–273.

Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.

Siegler, R.S., & Jenkins, E.A. (1989). How children discover new strategies. Hillsdale, NJ: Erlbaum.

Siegler, R.S., & Robinson, M. (1982). The development of numerical understandings. In H.W.Reese & L.P.Lipsitt (Eds.), Advances in child development and behavior (vol. 16, pp. 242–312). New York: Academic Press.

Sophian, C. (1988). Early developments in children’s understanding of number: Inferences about numerosity and one-to-one correspondence. Child Development, 59, 1397–1414.



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement