The main article is listed below (along with abstract). If any IQs Corner reader would like to read the issue and provide a guest blog post, email me and I'll provide a copy.
From numerical concepts to concepts of number
Lance J. Rips, Amber Bloomfield and Jennifer Asmuth
Behavioral and Brain Sciences , Volume 31, Issue 06, December 2008, pp 623-642
- Abstract: Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children’s understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a þ b ¼ b þ a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas.
- Here is a description of the journal as lifted from its official site. BBS is the internationally renowned journal with the innovative format known as Open Peer Commentary. Particularly significant and controversial pieces of work are published from researchers in any area of psychology, neuroscience, behavioural biology or cognitive science, together with 10-25 commentaries on each article from specialists within and across these disciplines, plus the author's response to them. The result is a fascinating and unique forum for the communication, criticism, stimulation, and particularly the unification of research in behavioural and brain sciences from molecular neurobiology to artificial intelligence and the philosophy of the mind. As Cambridge continues its philosophy of moving towards fully online submission, refereeing and commentary, see preprints of articles currently undergoing commentary at http://www.bbsonline.org