The cognitive processing of numerical bases: a review of empirical evidence

We review the empirical research on numerical bases in the context of spoken and written numerical expressions, visual number symbols and the mappings between these expressions and symbols. Most of this research has been carried out with speakers of Indo-European languages, which have decimal systems. Children typically acquire spoken numerical expressions before they learn associated visual number symbols, but numerical expressions are language-specific. The structure of the numerical expressions influences number word learning, with evidence that an explicit base-10 structure in the spoken numerical expressions (i.e. base transparency) is advantageous. Later, when visual base-10 number symbols are acquired, inconsistencies in the mapping between those and the numerical expressions affect numerical and mathematical learning. We also review research on base-20 numeration systems and on inversion in number words: when the order of constituents in the spoken number word is inversed in relation to their order in the visual number symbols, e.g. 'fourteen' versus '14'. In conclusion, we discuss evidence about how using number symbols with a non-decimal base affects the processing of numbers and make suggestions for future research.This article is part of the theme issue 'A solid base for scaling up: the structure of numeration systems'.