Young Children’s Number Sense Development: Age Related Complexity across Cases of Three Children


Zuhal YILMAZ


Abstract

Children start to develop number sense even well before they start the school. Developing number sense serves as an intermediate tool for learning conventional mathematics taught in schools. This number sense has three key areas: number knowledge, counting and arithmetic operations. As a result, the aim of this study was to examine aged related complexity of number sense development of young children’s aged four, six and seven under two key areas: number knowledge and counting. Semi structured task based clinical interviews were employed to examine number sense development. Five different assessment tasks were employed with three children. Children’s responses were analysed to identify their level of number sense understanding and difficulties with developing number sense. Findings were reported under two categories: first children’s ability to understand number concept and their ability to accomplish number word sequences and second counting. Findings of the study indicated a significant age related complexity and improvement in both two aspects of number sense. Older children with more experience developed better number sense than the younger children.


Keywords

Number sense, Counting, Young children

Paper Details

Paper Details
Topic Early Childhood Education
Pages 891 - 902
Issue IEJEE, Volume 9, Issue 4
Date of acceptance 30 May 2017
Read (times) 98
Downloaded (times) 50

Author(s) Details

Zuhal YILMAZ

Yeditepe University, Turkey


References

Alajmi, A., & Reys, R. (2007). Reasonable and reasonable- ness of answers: Kuwaiti middle school teachers’ perspectives. Educational Studies in Mathematics, 65(5), 77-94.

Anghileri, J. (2000). Teaching number sense. London: Continuum.

Aunio, P., Hautamäki, J., Heiskari, P. & Van Luit, J. E. H. (2006). The early numeracy test in Finnish: Children’s norms. Scandinavian Journal of Psychology, 47, 369–378.

Baroody, A. J., Lai, M. L., & Mix, K. S. (2006). The development of young children’s early number and operation sense and its implications for early childhood education. Handbook of Research on the Education of Young Children, 2, 187-221.

Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333–339.

Beswick, K., Muir, T., & McIntosh, A. (2004). Developing an instrument to assess the number sense of young children. International Education Research Conference (pp. 1324-9339). Melbourne, Australia: AARE.

Burton, G. M. (1993). Number sense and operations: Addenda series, grades K-6. Reston, VA: National Council of Teachers of Mathematics.

Case, R. (1998, April). A psychological model of number sense and its development. Paper presented at the annual meeting of the American Educational Research Association, San Diego, CA.

Chao, S. J., Stigler, J. W., & Woodward, J. A. (2000). The effects of physical materials on kindergartners' learning of number concepts. Cognition and Instruction, 18(3), 285-316.

Dehaene, S. (2001). Précis of “The number sense”. Mind and Language, 16, 16–32.

Dougherty, C. (2003). Numeracy, literacy and earnings: Evidence from the National Longitudinal Survey of Youth. Economics of Education Review, 22, 511-521.

Erdogan, S., & Baran, G. (2008). A study on the effect of mathematics teaching provided through drama on the mathematics ability of six-year- old children. Eurasia Journal of Mathematics, Science & Technology Education, 5(1), 79-85.

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

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

Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38, 293–304.

Golafshani, N. (2003). Understanding reliability and validity in qualitative research. The qualitative report, 8(4), 597-606.

Howden, H. (1989). Teaching Number Sense. Arithmetic Teacher 36(6), 6-11.

Jordan, N. C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and individual differences20(2), 82-88.

Jordan, N. C., Kaplan, D., Locuniak, N. M., & Ramineni, C. (2007). Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research & Practice, 22(1), 36–46

Jordan, N. C., Kaplan, D., Olah, L., & Locuniak, M. N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153– 175.

Jordan, N. C., & Levine, S. C. (2009). Socioeconomic variation, number competence, and mathematics learning difficulties in young children. Developmental Disabilities Research Reviews15(1), 60-68.

Kim, K. M. & Noh, S. (2010). Alternative mathematics assessment: A case study of the development of descriptive problems for elementary school in Korea. Eurasia Journal of Mathematics, Science & Technology Education, 6(3), 173-186

Klibanoff, R. S., Levine, S. C., Huttenlocher, J., Vasilyeva, M., & Hedges, L. V. (2006). Preschool children’s mathematical knowledge: The effect of teacher “Math Talk”. Developmental Psychology, 42(1), 59–69.

Mathison, S. (1988). Why triangulate? Educational Researcher, 17(2), 13-17.

McIntosh, A. J., Reys, B. J., & Reys, R. E. (1993). A proposed framework for examining number sense. For The Learning of Mathematics, 12(3), 2-8.

McIntosh, A., Reys, B., Reys, R., Bana, J., & Farrell, B. (1997). Number sense in school mathematics: Student performance in four countries. Perth: MASTEC, Edith Cowan University.

Murnane, R. J., Willett, J. B., & Levy, F. (1995). The growing importance of cognitive skills in wage determination. The Review of Economics and Statistics, 77, 251-266.

National Council of Teachers of Mathematics (1989). New directions for elementary School Mathematics. Reston, Va.

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

Opper, S. (1977). Piaget's clinical method. Journal of Children's Mathematical Behavior, 5, 90-107.

Reys, B. J. (1991). Developing number sense: Addenda series, grades 5-8. Reston, VA: National Council of Teachers of Mathematics.

Schneider, B., & Thompson, S. (2000). Incredible equations develop incredible number sense. Teaching Children Mathematics, 7(3), 146-148.

Siegler, R. S., & Shrager, J. (1984). Strategy choices in addition and subtraction: How do children know what to do? In C. Sophian (Ed.), The origins of cognitive skills (pp. 229-293). Hillsdale, NJ: Erlbaum.

Singh, P. (2009). An Assessment of Number Sense among Secondary School Students. International Journal for Mathematics Teaching and Learning. 1-27.

Stein, M. K. & Smith, M. S. (1998). Mathematical task as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School, 3(4), 268-275.

Van de Walle, J. (2004). Elementary and middle school mathematics: Teaching developmentally (5e). Boston: Pearson Education.

Wright, R. J., Stanger, G., Stafford, A.K., & Martland, J. (2006). Teaching number in the classroom with 4-8 years-olds. Sage Publications Ltd, p. 30-52.