When preschoolers count to check their arithmetic predictions, their counts are better than when they simply count a set of items on count-only tasks. This is so even for 2 1/2- and 3-year-olds dealing with small values. Such results lend support to the view that learning about verbal counting benefits from a nonverbal count-arithmetic system and challenge theories that place understanding of verbal counting at 4 1/2 or 5 years. That preschoolers readily engage in predicting-and-checking number tasks has implications for educational programs.
ButterworthG. (1999). The mathematical brain. London: Macmillan.
2.
DehaeneS. (1997). The number sense: How the mind creates mathematics. New York: Oxford University Press.
3.
GelmanR.ButterworthB. (2005). Number and language: How are they related?Trends in Cognitive Sciences, 9, 6-10.
4.
McCrinkK.WynnK. (2004). Large-number addition and subtraction by 9-month-old infants. Psychological Science, 15, 776-782.
5.
BarthH.La MontK.LiptonJ.SpelkeE.S. (2005). Abstract number and arithmetic in preschool children. Proceedings of the National Academy of Sciences, U.S.A., 102, 14116–14121.
6.
BisanzJ.ShermanJ.L.RasmussenC.HoE. (2005). Development of arithmetic skills and knowledge in preschool children. InCampbellJ.(Ed.), The handbook of mathematical cognition (pp. 143–162). New York: Psychology Press.
7.
BryantP.ChristieC.RenduA. (1999). Children's understanding of the relation between addition and subtraction: Inversion, identity, and decomposition. Journal of Experimental Child Psychology, 74, 194–212.
8.
CareyS. (2004). On the origin of concepts. InMillerJ.(Ed.), Daedalus. Cambridge, MA: MIT Press.
9.
CordesS.GelmanR. (2005). The young numerical mind: What does it count?InCampbellJ.(Ed.), The handbook of mathematical cognition. New York: Psychology Press.
10.
FusonK. (1988). Children's counting and concepts of numbers. New York: Springer-Verlag.
11.
GelmanR.S. (1969). Conservation acquisition: A problem of learning to attend to relevant attributes. Journal of Experimental Child Psychology, 7, 167–187.
12.
GelmanR.GallistelC.R. (1986). The child's understanding of number. Cambridge, MA: Harvard University Press.
13.
GelmanR.LucarielloJ. (2002). Learning in cognitive development. InPashlerH.GallistelC.R.(Eds.), Stevens' Handbook of Experimental Psychology (3rd ed., Vol. 3). New York: Wiley.
14.
HartnettP.M.GelmanR. (1998). Early understandings of numbers: Paths or barriers to the construction of new understandings?Learning and Instruction: The Journal of the European Association for Research in Learning and Instruction, 8, 341–374.
15.
HodentC.BryantP.HoudéO. (2005). Language-specific effects on number computation in toddlers. Developmental Science, 8, 420–423.
16.
HurewitzF.PapafragouA.GleitmanL.GelmanR. (2006). Asymmetries in the acquisition of numbers and quantifiers. Language learning and development, 2, 77–96.
17.
MixK.S.HuttenlocherJ.LevineS.C. (2002). Quantitative development in infancy and early childhood. New York: Oxford University Press.
18.
PiagetJ. (1952). The child's concept of number. New York: Norton.
19.
SarneckaL.GelmanS. (2005). Six does not just mean a lot: Quantitative development in infancy and early childhood. Cognition, 92, 239–352.
20.
ZurO.GelmanR. (2004). Doing arithmetic in preschool by predicting and checking. Early Childhood Quarterly Review, 19, 121–137.
