Monday, January 7, 2008

Core Knowledge Theories

Core Knowledge Theory suggests that children are born with sets of rules for experiencing the world. However, the mechanisms by which they govern their lives are altered by experience. Two researchers who are proponents of this theory, Gopnik and Meltzoff, argue that irrespective of culture, children are both with the same initial theories and that they possess the mechanisms needed to revise those theories when faced with conflicting evidence. To qualify as a core knowledge system, the system must be domain specific, task specific, and encapsulated. This applies both to the physical world as well as the social world. Recently, some research in core knowledge theory has focused on children’s understanding of numbers.

In a series of experiments involving dot arrays, Xu and Spelke demonstrated that six-month-old infants were able to discriminate between eight and sixteen, and between sixteen and thirty two. However, the infants did not discriminate eight dots from twelve or sixteen from twenty four. Starkey and Cooper demonstrated that infants were unable to discriminate four from six dots, in a similar experiment. The findings suggest that infants are sensitive to 2:1 ratios such as 16:8 and 32:16, but not 3:2 ratios such as 12:8 or 6:4.

A second set of experiments by Lipton and Spelke sought to determine whether this finding was limited to the visual field, or also applied to auditory input. Infants heard sequences of sounds from a right-side and left-side speaker. The infants were again sensitive to 2:1 ratios (16 and 8 sounds) but not 3:2 ratios (12 and 8 sounds). These findings suggest that representations of approximate numerosities may be independent of sensory modality or stimulus format.

A third set of experiments indicated that the core knowledge of numbers is limited. When four cookies are placed into one box, and eight cookies are placed into a second box, Spelke found no response to the numerosity, even though it was a 2:1 ratio. Further, Xu and Spelke repeated their dot-array experiments with smaller numbers of dots: arrays of either one versus two dots, or two versus three dots. The findings of these studies indicated that although infants treat large numbers of visible items as a set, they appear to treat small numbers of visible items as individual objects, but not as a set of objects with a cardinal value.

Combining all the relevant data, it becomes clear that two different systems of core knowledge are at work. The first system is for representing objects and their constancy over time. The second system is for representing sets and their approximate numerical values. The systems are domain specific (one is for objects, one for sets), task specific (one for counting, one for comparison), and encapsulated (the situations evoking each system are different). The system for representing the relative size of sets seems to have a 2:1 limit, while the system for representing individual objects seems to have a 3:2 limit. A series of further studies by Spelke and others confirms an upper limit of three on core knowledge systems of numerosity. For example, Wynn showed that around age 3, children can differentiate “one” from “many.” Less than one year later, after the acquisition of “three”, children appeared to be able to differentiate just about any number from any other, with no real upper limit.

Reference: Spelke, E.S. (2000, November). Core knowledge. American Psychologist, 1233-1243.

No comments: