Abstract
In this chapter, we start by defining what it means to be a counter and then explain what children need to be able to do to be successful at counting. Additionally, we define subitizing, explain its importance, and how it differs from counting. We complete the first section by discussing the importance of counting as a prerequisite to other aspects of arithmetic. In the following section, we discuss several challenges that counting poses for children experiencing mathematical difficulties, illustrated by examples from our research. One of these challenges includes the language of counting. In English, aspects of the language and sequencing of counting can be difficult for children, especially the teen number words, decade boundaries, counting above 100, and sequencing of numbers. Many of these characteristics are common to other languages too. Other aspects of counting that prove difficult for many children are maintaining one-to-one correspondence while counting unfamiliar sequences, understanding cardinality, finger gnosis, and using the formal symbolic notation for counting. In the final section of this chapter, we discuss and outline the activities that we have found to be useful to enhance the counting skills of children with mathematical difficulties.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alibali, M. W., & DiRusso, A. A. (1999). The function of gesture in learning to count: More than keeping track. Cognitive Development, 14, 37–56.
Andrews, P., & Sayers, J. (2015). Identifying opportunities for grade one children to acquire foundational number sense: Developing a framework for cross cultural classroom analyses. Early Childhood Education Journal, 43(4), 257–267.
Back, J., Sayers, J., & Andrews, P. (2013). The development of foundational number sense in England and Hungary: A case study comparison. In Eighth Congress of European Research in Mathematics Education (CERME 8), Antalya, Turkey, 6th to 10th February, 2013 (pp. 1835–1844).
Baroody, A. J., & Wilkins, J. L. (1999). The development of informal counting, number, and arithmetic skills and concepts. In J. V. Copley (Ed.), Mathematics in the early years (pp. 48–65). National Council of Teachers of Mathematics; National Association for the Education of Young Children.
Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of learning disabilities, 38(4), 333–339.
Berteletti, I., & Booth, J. R. (2015). Perceiving fingers in single-digit arithmetic problems. Frontiers in Psychology, 6, 226.
Callahan, L. G., & Clements, D. H. (1984). Sex differences in rote-counting ability on entry to first-grade: Some observations. Journal for Research in Mathematics Education, 15(5), 378–382.
Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15(3), 179–202.
Carr, M. (2001). Assessment in early childhood settings: Learning stories. Sage.
Carrazza, C., & Levine, S. C. (2019). How numbers are presented in counting books matters for children’s learning: A parent-delivered intervention. Conference talk: Society for Research in Child Development, Baltimore, MD.
Christelow, E. (1989). Five little monkeys jumping on the bed. Clarion Books.
Clements, D. H., & Sarama, J. (2017/2019). Learning and teaching with learning trajectories [LT]2. Retrieved from Marsico Institute, Morgridge College of Education, University of Denver.
Cowan, R. (1987). When do children trust counting as a basis for relative number judgments? Journal of Experimental Child Psychology, 43(3), 328–345.
Crollen, V., Seron, X., & Noël, M. P. (2012). Is finger-counting necessary for the development of arithmetic abilities? In F. Domahs, L. Kaufmann, & M. H. Fischer (Eds.), Handy numbers: Finger counting and numerical cognition. Frontiers E-books.
Dantzig, T. (2007). Number: The language of science (4th ed.). Penguin.
Dowker, A. (2005). Individual Differences in Arithmetic: Implications for Psychology, neuroscience and education. Psychology Press.
Dowker, A., & Roberts, M. (2015). Does the transparency of the counting system affect children’s numerical abilities? Frontiers in Psychology, 6, 945.
Ear8002. (2012, August 20)."Elmer Bernstein": "The Great Escape" from Athens (X 2) [Video]. Retrieved from https://www.youtube.com/watch?v=eeOoh2i7VCw
Frank, M. C., Everett, D. L., Fedorenko, E., & Gibson, E. (2008). Number as a cognitive technology: Evidence from Pirahã language and cognition. Cognition, 108(3), 819–824.
Franke, M. L. (2003). Fostering young children’s mathematical understanding. In C. Howes (Ed.), Teaching 4- to 8-year olds. Paul H. Brookes Publishing.
Franke, M. L., Kazemi, E., & Turrou, A. C. (2018). Choral counting & counting collections: Transforming the PreK-5 math classroom. Stenhouse Publishers.
Fuson, K. C. (1988). Children’s Counting and Concepts of Number. Springer.
Fuson, K. C., & Hall, J. (1983). The acquisition of early number word meanings: A conceptual analysis and review. In H. P. Ginsburg (Ed.), The development of mathematical thinking. Academic Press.
Fuson, K. C., & Kwon, Y. (1992). Korean children’s understanding of multidigit addition and subtraction. Child development, 63(2), 491–506.
Fuson, K. C., & Secada, W. G. (1986). Teaching children to add by counting-on with one-handed finger patterns. Cognition and Instruction, 3(3), 229–260.
Gathercole, S., & Alloway, T. P. (2008). Working memory and learning: A practical guide for teachers. Sage.
Geary, D. C., & Hoard, M. K. (2005). Learning disabilities in arithmetic and mathematics: Theoretical and empirical perspectives. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 253–267). Psychology Press.
Geary, D. C., Hoard, M. K., Byrd-Craven, J., Nugent, L., & Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child development, 78(4), 1343–1359.
Gelman, R., & Butterworth, B. (2005). Number and language: How are they related? Trends in Cognitive Sciences, 9(1), 6–10.
Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Harvard University Press.
Gelman, R., & Meck, E. (1983). Preschoolers’ counting: Principles before skill. Cognition, 13, 343–359.
Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. The Journal of Special Education, 33(1), 18–28.
Ginsburg, H. (2020). Anna counts. DREME TE. https://prek-math-te.stanford.edu/counting/anna-counts
Gracia-Bafalluy, M., & Noël, M. P. (2008). Does finger training increase young children’s numerical performance? Cortex, 44(4), 368–375.
Graham, T. A. (1999). The role of gesture in children’s learning to count. Journal of Experimental Child Psychology, 74, 333–355.
Hilton, C. (2019). Fingers matter: the development of strategies for solving arithmetic problems in children with Apert syndrome. Frontiers in Education, 4, 131.
Hollister, A. (2009). Focused instruction on Quick Images: A guided math group video featuring Michael Flynn. In J. Storeygard (Ed.), My kids can: Making math accessible to all learners, k-5 (pp. 38–42). Heinemann.
Hughes, M. (1986). Children and number: Difficulties in learning mathematics. Wiley-Blackwell.
Johnson, N. C., Turrou, A., McMillan, B., Raygoza, M., & Franke, M. (2019). “Can you help me count these pennies?”: Surfacing preschoolers’ understandings of counting. Mathematical Thinking and Learning, 21(4), 237–264. https://doi.org/10.1080/10986065.2019.1588206
Jordan, N. C., Glutting, J., & Ramineni, C. (2008). A number sense assessment tool for identifying children at risk for mathematical difficulties. In A. Dowker (Ed.), Mathematical difficulties (pp. 45–58). Academic Press.
Jordan, N. C., Huttenlocher, J., & Levine, S. C. (1992). Differential calculation abilities in young children from middle-and low-income families. Developmental Psychology, 28(4), 644.
Noël, M. P. (2005). Finger gnosia: A predictor of numerical abilities in children? Child Neuropsychology, 11(5), 413–430.
Nunes, T., & Bryant, P. (1996). Children doing mathematics. Blackwell Publishers Ltd..
Parrish, S. (2010). Number Talks: Helping children build mental math and computation strategies. Math Solutions.
Pulley Sayre, A., & Sayr, J. (2004). One is a snail, ten is a crab: A counting by feet book. Walker Books Ltd..
Ramani, G. B., & Siegler, R. S. (2008). Promoting broad and stable improvements in low-income children’s numerical knowledge through playing number board games. Child Development, 79(2), 375–394.
Reeve, R., Reynolds, F., Humberstone, J., & Butterworth, B. (2012). Stability and change in markers of core numerical competencies. Journal of Experimental Psychology: General, 141(4), 649–666.
Sayers, J. (2015). Building Bridges—Making connections between counting and arithmetic: Subitising. Primary Mathematics, 13, 22–25.
Sayers, J., Andrews, P., & Boistrup, L. B. (2016). The role of conceptual subitising in the development of foundational number sense. In T. Meaney, O. Helenius, M. L. Johansson, T. Lange, & A. Wernberg (Eds.), Mathematics education in the early years (pp. 371–394). Springer.
Schaeffer, B., Eggleston, V. H., & Scott, J. L. (1974). Number development in young children. Cognitive Psychology, 6, 357–379.
Scherer, P., Beswick, K., DeBlois, L., Healy, L., & Opitz, E. (2016). Assistance of students with mathematical learning difficulties: How can research support practice? ZDM, 48, 633–649.
Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428–444.
Skinner, C. (1997). Board games for the nursery (Set A). BEAM.
Starkey, P., & Cooper, R. G. (1980). Perception of numbers by human infants. Science, 210, 1033–1035.
Steffe, L., & Cobb, P. (1988). Construction of arithmetical meanings and strategies. Springer.
Steffe, L., von Glasersfeld, E., Richards, J., & Cobb, P. (1983). Children’s counting types: Philosophy, theory, and application. Praeger.
Strauss, E., Sherman, E. M., & Spreen, O. (2006). A compendium of neuropsychological tests: Administration, norms, and commentary. Oxford University Press.
Thouless, H. (2014). Counting difficulties for students with dyslexia. In S. Pope (Ed.), Proceedings of the 8th British Congress of Mathematics Education (pp. 319–326). University of Nottingham.
Wager, A. A., & Parks, A. N. (2016). Assessing early number learning in play. ZDM, 48(7), 991–1002.
Wynn, K. (1990). Children’s understanding of counting. Cognition, 36(2), 155–193.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Thouless, H., Hilton, C., Webb, T. (2022). Counting. In: Xin, Y.P., Tzur, R., Thouless, H. (eds) Enabling Mathematics Learning of Struggling Students. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-95216-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-95216-7_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-95215-0
Online ISBN: 978-3-030-95216-7
eBook Packages: EducationEducation (R0)