Children's construction of mathematical knowledge in solving novel isomorphic problems in concrete and written form

Abstract

The focus of this article is children's construction and analogical transfer of mathematical knowledge during novel problem solving, as reflected in their strategies for dealing with isomorphic combinatorial problems presented in “hands-on” and written form. Case studies of low- and high-achieving 9-year-olds in school mathematics serve to illustrate a general progression through three identified stages of strategy construction. The important role of domain-general strategies in this development is highlighted. Included in the study's findings is the fact that achievement level in school mathematics does not predict children's attainment of the third stage, as is evidenced by the low-achieving student's construction of sophisticated combinatorial knowledge and the high-achieving student's failure to do so. Children's ability to recognize structural correspondence between the two isomorphic problem sets and the extent to which this facilitates problem solution are also reported.