From numerical concepts to concepts of number

Behavioral and Brain Sciences 31 (6):623-642 (2008)
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+b=b+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
Keywords acquisition of natural numbers   mathematical concepts   representations of mathematics   theories of mathematical cognition
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 12,101
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

View all 47 references

Citations of this work BETA
David Peterson (2012). Where the Sidewalk Ends: The Limits of Social Constructionism. Journal for the Theory of Social Behaviour 42 (4):465-484.

View all 16 citations

Similar books and articles
Analytics

Monthly downloads

Added to index

2009-01-28

Total downloads

24 ( #76,922 of 1,102,113 )

Recent downloads (6 months)

6 ( #52,509 of 1,102,113 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.