ERIC Number: ED367540
Record Type: RIE
Publication Date: 1993
Reference Count: N/A
Children's Construction of Mathematical Knowledge in Solving Novel Isomorphic Problems in Concrete and Written Form.
English, Lyn D.
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 mathematics, serve to illustrate a general progression through three identified stages of strategy construction (non-planning stage, transitional stage, and odometer stage). The important role of domain-general strategies in this development is highlighted. It was found that achievement level in school mathematics does not predict children's attainment of the third stage, as 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 two isomorphic problem sets and the extent to which this facilitates problem solution are also reported. The study concludes that: (1) Children can construct important mathematical ideas through solving novel problems; (2) Level of achievement in school mathematics is not a reliable predictor of ability to solve novel problems; (3) Bright students' ability to generate ideas for themselves can be inhibited by formal mathematical rules; and (4) Assessment of students' mathematical competence must include a range of novel problems. (Contains 72 references.) (MDH)
Descriptors: Academic Achievement, Analogy, Case Studies, Cognitive Development, Cognitive Style, Constructivism (Learning), Elementary Education, Foreign Countries, Grade 4, Knowledge Level, Learning Processes, Learning Strategies, Mathematical Models, Mathematics Achievement, Mathematics Education, Problem Solving, Word Problems (Mathematics)
Publication Type: Reports - Research
Education Level: N/A
Authoring Institution: N/A
Identifiers: Australia (Brisbane); Combinatorics; Hands On Experience; Representations (Mathematics)