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Chandler, C. C., & Kamii, C. (2009). Giving change when payment is made with a dime: The difficulty of tens and ones. Journal for Research in Mathematics Education, 40(2), 97-118.

Klein, T., & Beishuizen, M. (1994). Assessment of flexibility in mental arithmetic. In J. E. H. LuitVan (Ed.), Research on learning and instruction in kindergarten and primary school (pp. 125-152). Doetinchem, the Netherlands: Graviatt Publishing Company.

Ross, S. H. (1989). Parts, wholes and place value: A developmental view. Arithmetic Teacher, 36(6), 47-51.

Rousham, L. (2003). The empty number line: A model in search of a learning trajectory? In I. Thompson (Ed.), Enhancing primary mathematics teaching (pp. 29-39). Philadelphia: Open University Press.


The description of multi-unit place value draws on research carried out around the world. In particular the work of Dr Noel Thomas, Dr Janet Bowers, and Professors Les Steffe, Paul Cobb, and Karen Fuson have contributed to the current description. The contributions made by research at Leiden University by Professor Beishuizen are also gratefully acknowledged.