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Switch to: References
Citations of:
Questions for future research
Trends in Cognitive Sciences 9 (1):6-10 (2005)
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One of the most important questions in the young field of numerical cognition studies is how humans bridge the gap between the quantity-related content produced by our evolutionarily ancient brains and the precise numerical content associated with numeration systems like Indo-Arabic numerals. This gap problem is the main focus of this paper. The aim here is to evaluate the extent to which cultural factors can help explain how we come to think about numbers beyond the subitizing range. To do this, (...) |
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Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by (...) |
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Number morphology (e.g., singular vs. plural) is a part of the grammar that captures numerical information. Some languages have morphological Number values, which express few (paucal), two (dual), three (trial) and sometimes (possibly) four (quadral). Interestingly, the limit of the attested morphological Number values matches the limit of non‐verbal numerical cognition. The latter is based on two systems, one estimating approximate numerosities and the other computing exact numerosities up to three or four. We compared the literature on non‐verbal number systems (...) No categories |
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Wales uses languages with both regular (Welsh) and irregular (English) counting systems. Three groups of 6- and 8-year-old Welsh children with varying degrees of exposure to the Welsh language—those who spoke Welsh at both home and school; those who spoke Welsh only at home; and those who spoke only English—were given standardized tests of arithmetic and a test of understanding representations of two-digit numbers. Groups did not differ on the arithmetic tests, but both groups of Welsh speakers read and compared (...) |
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In recent years, neologicists have demonstrated that Hume's principle, based on the one-to-one correspondence relation, suffices to construct the natural numbers. This formal work is shown to be relevant for empirical research on mathematical cognition. I give a hypothetical account of how nonnumerate societies may acquire arithmetical knowledge on the basis of the one-to-one correspondence relation only, whereby the acquisition of number concepts need not rely on enumeration (the stable-order principle). The existing empirical data on the role of the one-to-one (...) |
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