Journal
JOURNAL FOR RESEARCH IN MATHEMATICS EDUCATION
Volume 31, Issue 2, Pages 168-190Publisher
NATL COUNCIL TEACHERS MATHEMATICS-NCTM
DOI: 10.2307/749750
Keywords
algebra; children's strategies; cognitive theory; high school, 9-12; prealgebra; problem solving; secondary mathematics; teacher beliefs
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Mathematics teachers and educational researchers ordered arithmetic and algebra problems according to their predicted problem-solving difficulty for students. Predictions deviated systematically from algebra students' performances but closely matched a view implicit in textbooks. Analysis of students' problem-solving strategies indicates specific ways that students' algebraic reasoning differs from that predicted by most teachers and researchers in the sample and portrayed in common textbooks. The Symbol Precedence Model of development of algebraic reasoning, in which symbolic problem solving precedes verbal problem solving and arithmetic skills strictly precede algebraic skills, was contrasted with the Verbal Precedence Model of development, which provided a better quantitative fit of students' performance data. Implications of the findings for student and reacher cognition and for algebra instruction are discussed.
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