Skip to main content

Assessing Young Children’s Mathematical Understanding: Opportunities and Expectations at the Transition to School

  • Chapter
  • First Online:
Mathematics and Transition to School

Part of the book series: Early Mathematics Learning and Development ((EMLD))

Abstract

One-to-one interviews have been used extensively in Australia by both researchers and teachers to assess young children’s mathematical understanding. This chapter discusses the use of a one-to-one task based interview developed as part of the Early Numeracy Research Project. The First Year of School Mathematics Interview component has been used in a range of research contexts, both prior to school and in the early years. A recent study, using the interview with children with Down syndrome where the interview was presented in a more flexible manner, raises important questions regarding its use both in research and practice. The opportunities and expectations during the transition to school and how these may be enhanced by the use of one-to-one assessment interviews is also discussed.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Abdelhameed, H., & Porter, J. (2006). Counting in Egyptian children with down syndrome. International Journal of Special Education, 21(3), 176–187.

    Google Scholar 

  • Bobis, J., & Gould, P. (1999). The mathematical achievement of children in the Count Me in Too program. In J. M. Truran & K. M. Truran (Eds.), Making the difference (Proceedings of the 22nd annual conference of the Mathematics Education Research Group of Australasia, pp. 84–90). Adelaide: MERGA.

    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.

    Article  Google Scholar 

  • Brown, R. I., & Semple, L. (1970). Effects of unfamiliarity on the overt verbalisation and perceptual motor behaviour of nursery school children. British Journal of Educational Psychology, 40(3), 291–298.

    Article  Google Scholar 

  • 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, 179–202.

    Article  Google Scholar 

  • Carpenter, T., & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In E. Fennema, & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 19–32). Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Clarke, D. J. (1989). Assessment alternatives in mathematics. Canberra: Curriculum Development Centre.

    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: 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: MERGA.

    Google Scholar 

  • Clarke, D., Cheeseman, J., Gervasoni, A., Gronn, D., Horne, M., McDonough, A., Montgomery, P., Roche, A., Sullivan, P., Clarke, B., & Rowley, G. (2002). Early Numeracy Research Project final report. Melbourne: Mathematics Teaching and Learning Centre, Australian Catholic University.

    Google Scholar 

  • Clarke, B. A., Clarke, D. M., & Cheeseman, J. (2006). The mathematical knowledge and understanding young children bring to school. Mathematics Education Research Journal, 18(1), 78–102.

    Article  Google Scholar 

  • Clarke, D., Clarke, B., & Roche, A. (2011). Building teachers’ expertise in understanding, assessing and developing children’s mathematical thinking: The power of task-based, one-to-one interviews. ZDM Mathematics Education, 43(6), 901–913.

    Article  Google Scholar 

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

    Google Scholar 

  • Downs, A., & Strands, P. S. (2006) Using assessment to improve the effectiveness of early childhood education. Journal of Childhood Family Studies, 15, 671–680.

    Article  Google Scholar 

  • Faragher, R., & Clarke, B. A. (2014). Educating learners with Down syndrome: Research, theory and practice with children and adolescents. London: Routledge.

    Google Scholar 

  • Faragher, R., Brady, J., Clarke, B. A., Clarke, D. M., & Gervasoni, A. (2008). Narrowing the gap: Empowering teachers and parents through understanding how children with Down syndrome develop mathematically. In L. Graham (Ed.), Proceedings of the ‘Narrowing the Gap: Addressing Educational Disadvantage’ conference (pp. 56–62). Armidale: SiMERR.

    Google Scholar 

  • Fleer, M., & Quinones, G. (2013). An assessment perezhivanie: building an assessment pedagogy for, with and of early childhood science learning. In D. Corrigan, R. Gunstrone, & A. Jones (Eds.), Valuing assessment in science education: Pedagogy, curriculum, policy (pp. 231–247). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Fuson, K. (1992). Research on whole number addition and subtraction. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 243–275). New York: Macmillan.

    Google Scholar 

  • Gervasoni, A. (2004). Exploring an intervention strategy for six and seven year old children who are vulnerable in learning school mathematics. Unpublished PhD thesis, Latrobe University, Bundoora, Australia.

    Google Scholar 

  • Ginsburg, H. (2009). The challenge of formative assessment in mathematics education: Children’s minds, teachers’ minds. Human Development, 52, 109–128.

    Article  Google Scholar 

  • Ginsburg, H., Klein, A., & Starkey, P. (1998).The development of children’s mathematical thinking: Connecting research with practice. In I. E. Siegel & K. A. Renninger (Eds.), Handbook of child psychology (5th ed., Vol. 4): Child psychology in practice (pp. 23–26). New York: Wiley.

    Google Scholar 

  • Higgins, J., Parsons, R., & Hyland, M. (2003). The numeracy development project: Policy to practice. In J. Livingstone (Ed.), New Zealand annual review of education (pp. 157–174). Wellington: Victoria University of Wellington.

    Google Scholar 

  • McDonough, A., Clarke, B. A., & Clarke, D. M. (2002). Understanding assessing and developing young children’s mathematical thinking: the power of the one-to-one interview for preservice teachers in providing insights into appropriate pedagogical practices. International Journal of Education Research, 37, 211–226.

    Article  Google Scholar 

  • Mulligan, J., & Mitchelmore, M. (1996). Children’s representations of multiplication and division word problems. In J. Mulligan & M. Mitchelmore (Eds.), Children’s number learning: A research monograph of MERGA/AAMT (pp. 163–184). Adelaide: AAMT.

    Google Scholar 

  • Schorr, R. Y. (2001). A study of the use of clinical interviewing techniques with prospective teachers. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 153–160). Utrecht: PME.

    Google Scholar 

  • Wishart, J. G. (1996). Avoidant learning styles and cognitive development in young children. In B. Stratford & P. Gunn (Eds.), New approaches to Down syndrome (pp. 173–205). London: Cassell.

    Google Scholar 

  • Wright, R. (1998). An overview of a research-based framework for assessing and teaching early number learning. 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. 701–708). Brisbane: MERGA.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Barbara Clarke .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media Singapore

About this chapter

Cite this chapter

Clarke, B. (2015). Assessing Young Children’s Mathematical Understanding: Opportunities and Expectations at the Transition to School. In: Perry, B., MacDonald, A., Gervasoni, A. (eds) Mathematics and Transition to School. Early Mathematics Learning and Development. Springer, Singapore. https://doi.org/10.1007/978-981-287-215-9_3

Download citation

Publish with us

Policies and ethics