Linguistic Influences on Mathematics

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Background

The topic of linguistic influences on mathematics, and in particular how the nature of the counting system and mathematical vocabulary of a particular language may influence numerical development and performance, has received an increasing amount of interest and attention in recent years. It is an important topic from several points of view: for example, improving our understanding of cross-cultural differences in mathematics; distinguishing between universal and non-universal aspects of arithmetic; and refining our understanding of the extent to which language and numerical understanding are related.
For example, a number of researchers, including Irene Miura, Yukari Okamoto and others have investigated the possibly facilitating effects of the relative transparency of the base-10 structure in East Asian counting systems. There is considerable evidence that speakers of Asian languages perform better than speakers of languages with less regular counting systems, both in learning the counting sequence and in learning to represent tens and units. It is, however, difficult to draw firm conclusions on how such results should be interpreted because there are so many other cultural and educational differences between Asian and Western children. This has led some research on children using different counting systems within the same educational system: e.g. Dowker, Bala & Lloyd’s (2008) study of Welsh children attending English-medium schools (irregular counting system) versus Welsh-medium schools (regular counting system). Such studies suggest that the counting system may affect some, but not all, components of arithmetic.
Recently there has been an increased amount of research on some languages with particular sources of irregularity: e.g. studies by Nuerk on the effects of inversion in the German counting system. Comparisons with other Europaean languages again suggest that the counting system affects some, but not all, aspects of number representation and arithmetic.
There have also been some recent studies of languages with very limited counting systems indeed: where the counting sequence ends at approximately 3. These include Pica et al’ s (2004) studies of the Mundoruku language of the Amazon, and Butterworth et al’s (2008) study of the Warlpiri and Piraha languages spoken by some Aboriginal Australians. These studies indicate that some numerical abilities do develop for numbers beyond those represented in these counting systems; but there is some disagreement between different research groups about the exact nature of the preserved numerical abilities.
While much of the work on linguistic effects on numerical development has focused on counting systems, there is also interesting work on effects of other aspects of language: e.g . David Barner’s work on count syntax and the mass-count distinction in different languages.
A Research Topic would draw together current research on the influence of a variety of language characteristics on a variety of aspects of arithmetic. It would thus make it possible to draw some tentative conclusions about how language affects arithmetic, and to create hypotheses for further research.

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