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References  

Anghileri, J. (2001). Principles and practices in arithmetic teaching.Buckingham: Open University Press.

Anghileri, J. (1989). An investigation of young children’s understanding of multiplication. Educational Studies in Mathematics. 20, 367-385.

Clark, F. B., & Kamii, C. (1996). Identification of multiplicative thinking in children in Grades 1-5. Journal for Research in Mathematics Education, 27(1), 41-51.

Mulligan, J. (1992). Children’s solutions to multiplication and division word problems:A longitudinal study. Mathematics Education Research Journal, 4(1), 24-41.

Mulligan, J. T., & Mitchelmore, M.C. (1997). Identification of multiplicative thinking in children in Grades 1-5. Journal for Research in Mathematics Education, 28(3), 309-331.

Mulligan, J. and Wright, R. (2000). Interview-based assessment of early multiplication and division. Proceedings of the 24th International Conference for the Psychology of Mathematics Education, 4, 17-24.

Steffe, L. P. (1992). Schemes of action and operation involving composite units.Learning and Individual Differences, 4, 259-309.

Steffe, L. P. (1994). Children’s multiplying schemes. In G. Harel & J. Confrey (Eds.),The development of multiplicative reasoning in the learning of mathematics. (pp. 3-39). Albany, NY: State University of New York Press.

Steffe, L. P., & Cobb, P. (1998). Multiplicative and divisional schemes. Focus on Learning Problems in Mathematics, 20(1), 45-61. 

Acknowledgements

Dr Joanne Mulligan created the initial description of the multiplication and division aspect of The Numeracy Continuum. It has been refined several times based on information from its use in hundreds of classrooms over more than 10 years. The contributions made by all of the students and teachers are gratefully acknowledged. 

NSW Department of Education © 2010

NumeracyContinuum introVid_tbn

The Numeracy Continuum Introduction Video