Skip to main content
Log in

The mathematical knowledge and understanding young children bring to school

  • Articles
  • Published:
Mathematics Education Research Journal Aims and scope Submit manuscript

Abstract

As part of the Victorian Early Numeracy Research Project, over 1400 Victorian children in the first (Preparatory) year of school were assessed in mathematics by their classroom teachers. Using a task-based, one-to-one interview, administered during the first and last month of the school year, a picture emerged of the mathematical knowledge and understanding that young children bring to school, and the changes in this knowledge and understanding during the first year of school. A major feature of this research was that high quality, robust information on young children’s mathematical understanding was collected for so many children. An important finding was that much of what has traditionally formed the mathematics curriculum for the first year of school was already understood clearly by many children on arrival at school. In this article, data on children’s understanding are shared, and some implications for classroom practice are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Anderson, A. (1997). Family and mathematics: A study of parent-child interactions.Journal for Research in Mathematics Education, 28(4), 484–511.

    Article  Google Scholar 

  • Aubrey, C. (1993). An investigation of the mathematical knowledge and competencies which young children bring into school.British Educational Research Journal, 19(1), 27–41.

    Article  Google Scholar 

  • Baroody, A. J. (1987).Children’s mathematical thinking. New York, NY: Teachers College Press.

    Google Scholar 

  • Baroody, A. J., & White, M. S. (1983). The development of counting skills and number conservation.Child Study Journal, 13, 95–105.

    Google Scholar 

  • Baroody, A. J., & Wilkins, J. L. M. (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). Reston VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Bertelli, R., Joanni, E., & Martlew, M. (1998). Relationship between children’s counting ability and their ability to reason about number.European Journal of Psychology of Education, 13, 371–383.

    Article  Google Scholar 

  • Board of Studies New South Wales. (2002).Mathematics K-6 syllabus 2002. Sydney: Author.

    Google Scholar 

  • Bobis, J. (1996). Visualisation and the development of number sense with kindergarten children. In J. Mulligan & M. Michelmore (Eds.),Children’s number learning: A research monograph of MERGA/AAMT (pp. 17–34). Adelaide: Australian Association of Mathematics Teachers.

    Google Scholar 

  • Bobis, J. (2002). Is school ready for my child?Australian Primary Mathematics Classroom, 7(4), 4–8.

    Google Scholar 

  • Bobis, J., Clarke, B. A., Clarke, D. M., Gould, P., Thomas, G., Wright, R., & Young-Loveridge, J. (2005). Supporting teachers in the development of young children’s mathematical thinking: Three large scale cases.Mathematics Education Research Journal, 16(3), 27–57.

    Google Scholar 

  • Brainerd, C. J. (1979).The origins of the number concept. New York: Praeger.

    Google Scholar 

  • Cheeseman, J., & Clarke, D. M. (2005). Early numeracy coordinators in Victorian primary schools: Components of the role, highlights and challenges. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, & A. Roche (Eds.),Building connections: Research, theory and practice (Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia, pp. 225–232). Melbourne: MERGA.

    Google Scholar 

  • Clarke, B. A., & Faragher, R. (2004). Possibilities not limitations: Developing mathematics thinking in children with special needs. In B. Clarke, D. M. Clarke, D. V. Lambdin, F. K. Lester, G. Emanuelson, B. Johansson, A. Wallby, & K. Wallby (Eds.),International perspectives on learning and teaching mathematics (pp. 379–395). Goteborg, Sweden: National Center for Mathematics Education, Goteborg University.

    Google Scholar 

  • Clarke, B. A., & Robbins, J. (2004). Numeracy enacted: Preschool families’ conception of their children’s engagement with numeracy. In I. Putt, R. Faragher, & M. McLean (Eds.),Mathematics education for the third millenium: Towards 2010 (Proceedings of the 27th annual conference of the Mathematics Education Research Group of Australasia, Vol. 1, pp. 175–182). Townsville, Queensland: MERGA.

    Google Scholar 

  • Clarke, D. M. (2001). Understanding, assessing and developing young children’s mathematical thinking: Research as a powerful tool for professional growth. In J. Bobis, B. Perry, & M. Mitchelmore (Eds.),Numeracy and beyond (Proceedings of the 24th Annual Conference of the Mathematics Education Research Group of Australasia, pp. 9–26). Sydney: MERGA.

    Google Scholar 

  • Clarke, D. M., & Clarke, B. A. (2004). Mathematics teaching in Grades K-2: Painting a picture of challenging, supportive, and effective classrooms. In R. N. Rubenstein & G. W. Bright (Eds.),Perspectives on the teaching of mathematics (66th Yearbook of the National Council of Teachers of Mathematics, pp. 67–81). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Clarke, D. M., Cheeseman, J., McDonough, A., & Clarke, B. A. (2003). Assessing and developing measurement with young children. In D. H. Clements (Ed.),Teaching and learning measurement (2003 Yearbook of the National Council of Teachers of Mathematics, pp. 68–80). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Clay, M. (1993).Reading recovery: A guidebook for teachers in training. Auckland, New Zealand: Heinemann.

    Google Scholar 

  • Clements, D. H. (1983). Training effects on the development and generalization of Piagetian logical operations and knowledge of number.Journal of Educational Psychology, 76, 766–776.

    Article  Google Scholar 

  • Clements, D. H. (2004). Major themes and recommendations. In D. H. Clements & J. Sarama (Eds.),Engaging young children in mathematics: Standards for early childhood education (pp. 7–72). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Clements, D. H., Sarama, J., & Gerber, S. (2005, April).Mathematics knowledge of entering preschoolers. Paper presented at the Annual Meeting of the American Educational Research Association, Montreal, Canada.

  • Clements, D. H., & Sarama, J. (2004).Engaging young children in mathematics: Standards for early childhood education. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Clements, M. A., & Ellerton, N. (1995). Assessing the effectiveness of pencil-andpaper tests for school mathematics. In B. Atweh & S. Flavel (Eds.),Galtha (Proceedings of the 18th Annual Conference of the Mathematics Education Research Group of Australasia, pp. 184–188). Darwin: MERGA.

    Google Scholar 

  • Coates, G. D., & Thompson, V. (1999). Involving parents of four-and five-year-olds in their children’s mathematics education. In J. V. Copley (Ed.),Mathematics in the early years (pp. 205–214). Reston VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Copley, J. V. (1999). Assessing the mathematical understanding of the young child. In J. V. Copley (Ed.),Mathematics in the early years (pp. 182–188). Reston VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Donaldson, M. (1978).Children’s minds. London: Fontana.

    Google Scholar 

  • Doverborg, E., & Samuelsson, I. P. (2000). To develop young children’s conception of numbers.Early Child Development and Care, 162, 81–107.

    Article  Google Scholar 

  • Economopoulos, K. (1998). What comes next? The mathematics of pattern in kindergarten.Teaching Children Mathematics, 5(4), 230–234.

    Google Scholar 

  • Education Department of Victoria. (1975).Curriculum guide: Applied number course sections A, B, C. Melbourne: Author.

    Google Scholar 

  • Fischer, F. (1990). A part-part-whole curriculum for teaching number in the kindergarten.Journal for Research in Mathematics Education, 21, 207–215.

    Article  Google Scholar 

  • Fuson, K. (1988).Children’s counting and concepts of number. New York: Springer-Verlag.

    Google Scholar 

  • Gelman, R., & Gallistel, C.R. (1978).The child’s understanding of number. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Gilmore, A. (1998).School entry assessment: The first national picture. Wellington, New Zealand: Ministry of Education.

    Google Scholar 

  • Ginsburg, H. P. (2002). Little children, big mathematics: Learning and teaching in the preschool. In A. Cockburn & E. Nardi (Eds.),Proceedings of the 26th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 181–185). Norwich, UK: PME.

    Google Scholar 

  • Ginsburg, H. P., Inoue, N., & Seo, K. (1999). Young children doing mathematics: Observations of everyday activities. In J. V. Copley (Ed.),Mathematics in the early years (pp. 88–99). Reston VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Greenes, C. (1999). Ready to learn. In J. V. Copley (Ed.),Mathematics in the early years (pp. 39–47). Reston VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Henderson, A. T., & Berla, N. (Eds.). (1994).The family is critical to student achievement: A new generation of evidence. Washington, DC: National Committee for Citizens in Education, Center for Law and Education.

    Google Scholar 

  • Hill, P. W., & Crévola, C. A. (1999). The role of standards in educational reform for the 21st century. In D. D. Marsh (Ed.),Preparing our schools for the 21st century (Association of Supervision and Curriculum Development Yearbook, pp. 117–142). Alexandria, VA: ASCD.

    Google Scholar 

  • Hughes, M. (1986).Children and number. Oxford: Basil Blackwell.

    Google Scholar 

  • Kilpatrick. J. Swafford, J., & Findell, B. (Eds.). (2001).Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.

    Google Scholar 

  • Klein, A., Starkey, P., & Wakeley, A. (1999, April).Enhancing pre-kindergarten children’s readiness for school mathematics. Paper presented at the annual meeting of the American Educational Research Association, Montreal, Canada.

  • Liedtke, W. (2000). Fostering numeracy: Parents of pre-school children can play an important role.Canadian Children, 25(1), 10–12.

    Google Scholar 

  • Lin, C., & Ness, D. (2000, April).Taiwanese and American preschool children’s everyday mathematics. Paper presented at the annual conference of the American Educational Research Association, New Orleans, Louisiana.

  • McClain, K., & Cobb, P. (1999). Supporting students’ ways of reasoning about patterns and partitions. In J. V. Copley (Ed.),Mathematics in the early years (pp. 112–118). Reston VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000).Principles and standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • Nelson, G. D. (1999). Within easy reach: Using a shelf-based curriculum to increase the range of mathematical concepts accessible to young children. In J. V. Copley (Ed.),Mathematics in the early years (pp. 135–145). Reston VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Paley, V. G. (1986). On listening to what children say.Harvard Educational Review, 56(2), 122–131.

    Google Scholar 

  • Pennington, B. F., Wallach, L., & Wallach, M. A. (1980). Nonconservers’ use and understanding of number and arithmetic.Genetic Psychology Monographs, 101, 231–243.

    Google Scholar 

  • Pepper, K. L., & Hunting, R. P. (1998). Preschoolers’ counting and sharing.Journal for Research in Mathematics Education, 20(2), 164–183.

    Article  Google Scholar 

  • Perry, B., & Dockett, S. (2002). Young children’s access to powerful mathematical ideas. In L. English (Ed.),Handbook of international research in mathematics education (pp. 81–111). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Perry, B., & Dockett, S. (2004). Early childhood numeracy.Journal of Australian Research in Early Childhood Education, 9(1), 62–73.

    Google Scholar 

  • Piaget, J. (1953). How children form mathematical concepts.Scientific American, 189(5), 74–79.

    Article  Google Scholar 

  • Resnick, L. (1983). A developmental theory of number understanding. In H. P. Ginsburg (Ed.),The development of mathematical thinking (pp. 109–151). Orlando, FL: Academic Press.

    Google Scholar 

  • Shane, R. (1999). Making connections: A “number curriculum” for preschoolers. In J. V. Copley (Ed.),Mathematics in the early years (pp. 129–134). Reston VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Sharpe, P. J. (1998). Thinking about thinking: A study of the adult’s role in providing for the development of number awareness in young children.Early Child Development and Care, 144, 78–89.

    Google Scholar 

  • Siegler, R. S. (2003). Implications of cognitive science research for mathematics education. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.),A research companion to principles and standards for school mathematics (pp. 289–303). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Stewart, R., Wright, B., & Gould, P. (1998). Kindergarten students’ progress in the Count Me in Too project. In C. Kanes, M. Goos, & E. Warren (Eds.),Teaching mathematics in new times (Proceedings of the 21st Annual Conference of the Mathematics Education Research Group of Australasia, pp. 556–563). Brisbane: MERGA.

    Google Scholar 

  • Sullivan, P., Cheeseman, J., Clarke, B. A., Clarke, D. M., Gervasoni, A., Gronn, D., Horne, M., McDonough, A., & Montgomery, P. (2000). Using learning growth points to help structure numeracy teaching.Australian Primary Classroom, 5(1), 4–8.

    Google Scholar 

  • Thompson, I. (1997). The early years number curriculum tomorrow. In I. Thompson (Ed.),Teaching and learning early number (pp. 155–160). Buckingham, UK: Open University Press.

    Google Scholar 

  • Tymms, P., Merrell, C., & Jones, P. (2004). Using baseline assessment data to make international comparisons.British Educational Research Journal, 30(5), 673–689.

    Article  Google Scholar 

  • Urbanska, A. (1993). On the numerical competence of six-year-old children.Educational Studies in Mathematics, 24, 265–275.

    Article  Google Scholar 

  • Victorian Department of Education and Training. (2001).Early numeracy interview booklet. Melbourne: Author.

    Google Scholar 

  • Young-Loveridge, J. (1988). The acquisition of numeracy.Set, 12(1), 1–8.

    Google Scholar 

  • Young-Loveridge, J. (1989). The development of children’s number concepts: The first year of school.New Zealand Journal of Educational Studies, 24(1), 47–64.

    Google Scholar 

  • Williams, E., & Shuard, H. (1982).Primary mathematics today. Essex: Longman.

    Google Scholar 

  • Wright, R. J. (1994). A study of the numerical development of 5-year-olds and 6-yearolds.Educational Studies in Mathematics, 26, 25–44.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Clarke, B., Cheeseman, J. & Clarke, D. The mathematical knowledge and understanding young children bring to school. Math Ed Res J 18, 78–102 (2006). https://doi.org/10.1007/BF03217430

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03217430

Keywords

Navigation