for the learning of mathematics

an international journal of mathematics education

Alf Coles ,  Nathalie Sinclair - Vol. 37 Num. 1 (2017)
 Re-thinking place value: from metaphor to metonym


In this article, we question what is an appropriate balance of ordinal and cardinal work in the early learning of number. We see an over-emphasis, in current research and practice, on the cardinal that leads, for example, to only using small numbers. We report on empirical work we have carried out in the UK and Canada that suggests the potential for re-balancing attention to the ordinal, alongside the cardinal. We point to the potential of two relatively novel technologies that allow access to ordinal and symbolic ways of working with number: a multi-touch applet (TouchCounts) and a 'tens chart' that is a structured representation of our numeral system that contrasts with the more typically used 100 chart.