Here are a couple of new publications of which I am very proud and which may be of interest to you. I’ve included them both lest the publishers involved think I’m playing favourites!
Chrisomalis, Stephen. 2008. The cognitive and cultural foundations of numbers. In The Oxford Handbook of the History of Mathematics, Eleanor Robson and Jacqueline Stedall, eds., pp. 495-517. Oxford: Oxford University Press.
Numbers are represented and manipulated through three distinct but interrelated techniques: numeral words, computational technologies, and numerical notation systems. Each of these has potential consequences for its users’ numerical cognition, but these consequences must be understood in terms of the functions and uses of each technique, not merely their formal structure. Most societies use numerical notation only to represent numbers, and have a variety of other techniques for performing arithmetic. The current Western practice of pen-and-paper arithmetic is anomalous historically. The transmission, adoption, and extinction of numerical systems thus depends primarily the social and economic context in which cultural contacts occur, and only minimally on their perceived efficiency for arithmetic.
Chrisomalis, Stephen. 2009. The origins and co-evolution of literacy and numeracy. IN The Cambridge Handbook of Literacy, David R. Olson and Nancy Torrance, eds, pp. 59-74. Cambridge: Cambridge University Press.
While number concepts are panhuman, numerical notation emerged independently only in state societies with significant social inequality and social needs beyond those of face-to-face interaction, and in particular with the development of written texts. This survey of seven ancient civilizations demonstrates that, although written numerals tend to develop alongside the first writing, the specific functions for which writing and numerals co-evolve are cross-culturally variable. A narrowly functionalistic approach that generalizes the Mesopotamian case to all early civilizations and proposes that numerals always emerge for accounting and bookkeeping is empirically inadequate. An alternate theory is proposed that regards the emergence of writing and numerical notation as an outgrowth of elite interests relating to social control, but leaving unspecified the particular domains of social life over which those elites use to control non-elites. Numerical notation is a special-purpose representational system that, in its simplest form, unstructured tallying, is a precursor to written communication, and which persists and expands as a parallel notation in literate contexts.