Exact number representations in first and second language

One of the major questions in the field of cognitive psychology is the extent to which our thought is dependent on, or formed by, the language we speak. In the mid-1900s, proponents of the linguistic relativity principle claimed that different languages with distinct grammatical properties and lexicons would have a major impact on the way the native speakers of that language perceived reality. This idea was based on the work of the anthropologists Sapir (1949), and Whorf (1956), and named the “Sapir-Whorf-Hypothesis” by Hoijer (1971). The opposite view is expressed by the theory of cultural universality (Au, 1983), meaning that basic concepts innate to human beings can be found in every culture irrespective of linguistic differences. The concept of number seems to be a good example for a theory of cultural universality at first sight, as all known cultures have developed at least some number words, and even pre-verbal infants and animals are able to single out the larger of two sets based on the respective number of items. The term “numerosity” was used by Dehaene (1997) for the awareness of quantity. Yet, it is still not clear whether nature has provided us with the concept of exact number or if this is a cultural acquirement based on the acquisition of verbal counting procedures. This chapter will review evidence supporting the language relativity hypothesis for the instance of exact number representations in a small number range (up to 10); other chapters in this book focus on the linguistic specificities of multi-digit number word systems and other aspects of mathematics Bahnmüller, this volume; Dowker, this volume). Presenting studies from different fields, this chapter will propose that the concept of exact numerosity is based on natural language, and furthermore that linguistic specificities even put constraints on the form of exact numerosity representations. The first focus is on the finding that grammatical properties shape the development of the concepts for one versus two, three, and more. Second, studies that describe a representational change in adults who learn a new number word system (including symbols for numerosities higher than four or five) will be presented. Third, differences in arithmetic fact retrieval in both first and second language will be reviewed. These findings will be discussed in the light of the “access-deficit-hypothesis” regarding developmental dyscalculia, suggesting that children with mathematical difficulties may have a problem in accessing number magnitude from symbols (e.g., presenting with longer response times