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Doerr, Helen M.; English, Lyn D. – Journal for Research in Mathematics Education, 2003
Discusses the nature of tasks used to elicit the development of such systems by middle school students. Analyzes mathematical reasoning development of students across tasks and the diversity of thinking patterns identified on problem tasks. Discusses student reasoning about the relationships between and among quantities and their application in…
Descriptors: Cognitive Development, Concept Formation, Data Analysis, Mathematical Models
English, Lyn D. – 1993
The focus of this report 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 9-year-olds, one low and one high achieving in school…
Descriptors: Academic Achievement, Analogy, Case Studies, Cognitive Development