McLoyd, V.C. (1990). The impact of economic hardship on Black families and children: Psychological distress, parenting, and socioemotional development. Child Development, 61, 311-346.

Menninger, K. (1958/1969). Number Words and Number Symbols: A Cultural History of Numbers. (P. Broneer, Trans.). Cambridge, MA: MIT Press. (Original work published 1958.)

Miller, K.F. (1992). What a number is: Mathematical foundations and developing number concepts. In J.I.D. Campbell (Ed.), The Nature and Origin of Mathematical Skills (pp. 3-38). New York: Elsevier Science.

Miller, K.F., and Stigler, J.W. (1987). Counting in Chinese: Cultural variation in a basic cognitive skill. Cognitive Development, 2, 279-305.

Miller, K.F., Smith, C.M., Zhu, J., and Zhang, H. (1995). Preschool origins of cross-national differences in mathematical competence: The role of number-naming systems. Psychological Science, 6(1), 56-60.

Miura, I.T. (1987). Mathematics achievement as a function of language. Journal of Educational Psychology, 79(1), 79-82.

Miura, I.T., and 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(1), 109-114.

Miura, I.T., and Okamoto, Y. (2003). Language supports for mathematics understanding and performance. In A.J. Baroody and A. Dowker (Eds.), The Development of Arithmetic Concepts and Skills—Constructing Adaptive Expertise: Studies in Mathematical Thinking and Learning (pp. 229-242). Hillsdale, NJ: Erlbaum.

Miura, I.T., Kim, C.C., Chang, C., and 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., Kim, C.C., Steere, M., and 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(1), 24-30.

National Center for Education Statistics. (2007). The Nation’s Report Card, Mathematics 2007: National Assessment of Educational Progress at Grades 4 and 8. Washington, DC: Institute of Education Sciences, U.S. Department of Education.

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

Ostad, S.A. (1998). Developmental differences in solving simple arithmetic word problems and simple number-fact problems: A comparison of mathematically normal and mathematically disabled children. Mathematical Cognition, 4(1), 1-19.

Pica, P., Lemer, C., Izard, V., and Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian Indigene group. Science, 499-503.

Ramani, G.B., and Siegler, R.S. (2008). Promoting broad and stable improvements in lowincome children’s numerical knowledge through playing number board games. Child Development, 79, 375-394. Available: [accessed October 2008].

Rosser, R.A., Ensing, S.S., Glider, P.J., and Lane, S. (1984). An information processing analysis of children’s accuracy in predicting the appearance of rotated stimuli. Child Development, 55, 2204-2211.

Russell, R.L., and Ginsburg, H.P. (1984). Cognitive analysis of children’s mathematic difficulties. Cognition and Instruction, 1(2), 217-244.

Sarama, J., Clements, D.H., Starkey, P., Klein, A., and Wakeley, A. (2008). Scaling up the implementation of a pre-kindergarten mathematics curriculum: Teaching for understanding with trajectories and technologies. Journal of Research on Educational Effectiveness, 1, 89-119.

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