## References

Carpenter, T. P., Corbitt, M. K., Kepner, H. S., Lindquist, M. M., & Reys, R. E. (1981). Results from the Second Mathematics Assessment of the National Assessment of Educational progress. Washington, D.C.: National Council of Teachers of Mathematics.

Gould, P. (2008). Children’s quantitative sense of fractions. Unpublished PhD Thesis, Macquarie University, Sydney.

Hackenberg, A. (2007). Units coordination and the construction of improper fractions: A revision of the splitting hypothesis. Journal of Mathematical Behavior, 26(1), 27-47.

Kamii, C., & Kysh, J. (2006). The difficulty of “length x width”: Is a square the unit of measurement? Journal of Mathematical Behavior, 25, 105-115.

Lamon, S. J. (1999). Teaching fractions and ratios for understanding. Mahwah, N. J. : Lawrence Erlbaum Associates.

Nunes, T., & Bryant, P. (2009). Paper 3: Understanding rational numbers and intensive quantities. London: Nuffield Foundation.

## Acknowledgements

This aspect of the numeracy continuum was developed for the NSW Department of Education and Training by Peter Gould and is based on his doctoral dissertation and related research. © 2010