REFERENCES
- Bar-David, E., Compton, E., Drennan, L., Finder, B., Grogan, K., & Leonard, J. (2009). Nonverbal number knowledge in preschool-age children. Mind Matters: The Wesleyan Journal of Psychology, 4, 51–64.
- Cantlon, J., Fink, R., Safford, K., & Brannon, E. M. (2007). Heterogeneity impairs numerical matching but not numerical ordering in preschool children. Developmental Science, 10, 431–440.
- Cantrell, L., Boyer, T. W., Cordes, S., & Smith, L. B. (2015). Signal clarity: An account of the variability in infant quantity discrimination tasks. Developmental Science.
- Cantrell, L., & Smith, L. B. (2013). Open questions and a proposal: A critical review of the evidence on infant numerical abilities. Cognition, 128, 331–352.
- Clearfield, M. W., & Mix, K. S. (1999). Number versus contour length in infants’ discrimination of small visual sets. Psychological Science, 10, 408–411.
- Clearfield, M., & Mix, K. S. (2001). Amount versus number: Infants' use of area and contour length to discriminate small sets. Journal of Cognition and Development, 2, 243–260.
- Cordes, S., & Brannon, E. M. (2008). The difficulties of representing continuous extent in infancy: Using number is just easier. Child Development, 79(2), 476–489.
- Cordes, S., & Brannon, E. M. (2009a). Crossing the divide: Infants discriminate small from large numerosities. Developmental Psychology, 45, 1583–1594.
- Cordes, S., & Brannon, E. M. (2009b). The relative salience of discrete and continuous quantity in young infants. Developmental Science, 12, 453–463.
- Cordes, S., Goldstein, A., & Heller, E. (2013). Sets within sets: The influence of set membership on numerical estimates. Journal of Experimental Psychology: Human Perception and Performance, 40(1), 94–105.
- Cordes, S., Williams, C. L., & Meck, W. H. (2007). Common representations of abstract quantities. Current Directions in Psychological Science, 16, 156–161.
- Davidson, K., Eng, K., & Barner, D. (2012). Does learning to count involve a semantic induction? Cognition, 123, 162–173.
- Defever, E., Sasanguie, D., Vandewaetere, M., & Reynvoet, B. (2012). What can the same–different task tell us about the development of magnitude representations? Acta Psychologica, 140, 35–42.
- Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., … Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428–1446.
- Feigenson, L. (2005). A double-dissociation in infants’ representations of object arrays. Cognition, 95, B-37–B-48.
- Frick, R. W. (1987). The homogeneity effect in counting. Perception and Psychophysics, 41, 8–16.
- Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 43–74.
- Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47, 1539–1552.
- Geary, D. C., & Brown, S. C. (1991). Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children. Developmental Psychology, 27, 398–406.
- Geary, D. C., Brown, S. C., & Samaranayake, V. A. (1991). Cognitive addition: A short longitudinal study of strategy choice and speed-of-processing differences in normal and mathematically disabled children. Developmental Psychology, 27, 787–797.
- Gelman, R., & Gallistel, C. R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.
- Gelman, R., & Tucker, M. F. (1975). Further investigations of the young child's conception of number. Child Development, 46, 167–175.
- Halberda, J., & Feigenson, L. (2008). Developmental changes in the acuity of the ‘number sense’: The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44, 1457–1465.
- Hannula, M., Rasanen, P., & Lehtinen, E. (2007). Development of counting skills: Role of spontaneous focusing on numerosity and subitizing-based enumeration. Mathematical Thinking and Learning, 9, 51–57.
- Huang, Y. T., Spelke, E., & Snedeker, J. (2010). When is four far more than three? Children's generalization of newly acquired number words. Psychological Science, 21, 600–606.
- Jordan, K. E., & Brannon, E. M. (2006). A common representational system governed by Weber's law: Nonverbal numerical similarity judgments in 6-year-olds and rhesus macaques. Journal of Experimental Child Psychology, 95, 215–229.
- Kaldy, Z., & Leslie, A. M. (2003). Identification of objects in 9-month-old infants: Integrating ‘what’ and ‘where’ information. Developmental Science, 6, 360–373.
- Kamawar, D., LeFevre, J., Bisanz, J., Skwarchuk, S., Smith-Chant, B., Fast, L., … Watchorn, R. (2010). Conceptual knowledge of counting: How relevant is order irrelevance? Journal of Experimental Child Psychology, 105, 135–145.
- Kobayashi, T., Hiraki, K., & Hasegawa, T. (2005). Auditory-visual intermodal matching of small numerosities in 6-month-old infants. Developmental Science, 8, 409–419.
- Le Corre, M., & Carey, S. (2007). One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles. Cognition, 105, 395–438.
- Le Corre, M., Van de Walle, G., Brannon, E. M., & Carey, S. (2006). Re-visiting the competence/performance debate in the acquisition of the counting principles. Cognitive Psychology, 52, 130–169.
- McNeil, N. M., Uttal, D. H., Jarvin, L., & Sternberg, R. J. (2009). Should you show me the money? Concrete objects both hurt and help performance on mathematics problems. Learning and Instruction, 19, 171–184.
- Miller, A. L., & Baker, R. A. (1968). The effects of shape, size, heterogeneity, and instructional set on the judgment of visual number. American Journal of Psychology, 81, 83–91.
- Mix, K. S. (1999). Similarity and numerical equivalence: Appearances count. Cognitive Development, 14, 269–297.
- Mix, K. S. (2008a). Children's equivalence judgments: Cross-mapping effects. Cognitive Development, 23, 191–203.
- Mix, K. S. (2008b). Surface similarity and label knowledge impact early numerical comparisons. British Journal of Developmental Psychology, 26, 13–32.
- Mix, K. S., Sandhofer, C. M., Moore, J. A., & Russell, C. (2012). Acquisition of the cardinal word principle: The role of input. Early Childhood Research Quarterly, 27, 274–283.
- Petersen, L. A., & McNeil, N. M. (2013). Effects of perceptually rich manipulatives on preschoolers’ counting performance: Established knowledge counts. Child Development, 84, 1020–1033.
- Posid, T., & Cordes, S. (2015). How high can you count? Probing the limits of children's counting. Manuscript submitted for publication.
- Posid, T., & Cordes, S. (2014). The small–large divide: A case of incompatible numerical representations in infancy. In D. Geary D. Berch & K. Mann-Koepke (Eds.), Evolutionary origins and early development of basic number processing (pp. 253–276). San Diego, CA: Elsevier Academic Press.
- Redden, J. P., & Hoch, S. J. (2009). The presence of variety reduces perceived quantity. Journal of Consumer Research, 36, 406–417.
- Sarnecka, B. W., & Lee, M. D. (2009). Levels of number knowledge during early childhood. Journal of Experimental Child Psychology, 103(3), 325–337.
- Schaeffer, B., Eggleston, V. H., & Scott, J. L. (1974). Number development in young children. Cognitive Psychology, 6, 357–379.
- Siegel, L. S. (1973). The role of spatial arrangement and heterogeneity judgments on numerical equivalence. Canadian Journal of Psychology, 27, 351–355.
- Siegel, L. S. (1974). Heterogeneity and spatial factors as determinants of numerical ability. Child Development, 45, 532–534.
- Starkey, P., Spelke, E. S., & Gelman, R. (1990). Numerical abstraction by human infants. Cognition, 36, 97–128.
- Stock, P., Desoete, A., & Roeyers, H. (2009). Master of the counting principles in toddlers: A crucial step in the development of budding arithmetic abilities? Learning and Individual Differences, 19, 419–422.
- Strauss, M. S., & Curtis, L. E. (1981). Infant perception to numerosity. Child Development, 52, 1146–1152.
- Towse, J. N., & Hitch, G. J. (1997). Integrating information in object counting: A role for a central coordination process? Cognitive Development, 12, 393–422.
- Trick, L. M. (2008). More than superstition: Differential effects of featural heterogeneity and change on subitizing and counting. Perception and Psychophysics, 70, 743–760.
- Wynn, K. (1990). Children's understanding of counting. Cognition, 36, 155–193.
- Wynn, K. (1992). Children's acquisition of number words and the counting system. Cognitive Psychology, 24, 220–251.
- Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74, B1–B11.