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Can Adults Teach Number Concepts to Young Children?

by Constance Kamii
January/February 2016
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Article Link: http://exchangepress.com/article/can-adults-teach--number-concepts-to-young-children/5022759/

When kindergarten teachers teach children how to count objects, many of them believe that they are teaching number concepts. However, children often count some objects more than once and overlook the others. Teachers usually correct these children, but on the next day the children go back to their incorrect ways. 

To explain why it is so hard to teach kindergartners how to count objects, it is necessary to clarify the three kinds of knowledge Piaget (1945/1951; 1967/1971) distinguished according to their ultimate sources — physical knowledge, social-conventional knowledge, and logico-mathematical knowledge. 

Physical knowledge is knowledge of objects in the external world. Knowing that marbles roll but chips do not is an example of physical knowledge. The fact that paper can easily be torn but cloth cannot is another example. The ultimate source of physical knowledge is objects in the external world.

An example of social-conventional knowledge is knowledge of languages like English and Spanish. Under­standing the meaning of holidays like Thanksgiving is another example. Using rules of etiquette is also an example of social-conventional knowledge, which is found in the conventions people make over time. 

Physical and social-conventional knowledge have sources outside the individual, but logico-mathematical knowledge is made, or constructed, by each individual. If ...

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