By Jinfa Cai
Read or Download A Cognitive Analysis of U.S. and Chinese Students' Mathematical Performance on Tasks Involving Computation, Simple Problem Solving, and Complex problem solving (Journal for Research in Mathematics Education, Monograph, N.º 7) PDF
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Extra info for A Cognitive Analysis of U.S. and Chinese Students' Mathematical Performance on Tasks Involving Computation, Simple Problem Solving, and Complex problem solving (Journal for Research in Mathematics Education, Monograph, N.º 7)
Findings from the SIMS showed that Japanese students thought the mathematics tested was more difficult than American students did, and they liked it less than students from the United States. Japanese students also thought that mathematics was more important than American students did. , 1992) reported that most students from China and Korea did not view mathematics as a subject to be memorized, whereas more than half of the American students believed that learning mathematics is mostly memorizing.
Bjorklund, 1990), children's strategies in solving problems are closely related to their cognitive development. Psychologists have also found that older children use more sophisticated strategies than younger children and that cognitive strategies are mediators of cognitive development. In mathematics, from simple counting tasks to complex mathematical problem solving, individuals use different strategies (Carpenter, Moser, & Romberg, 36 Theoretical Basis of the Study 1982; Schoenfeld, 1979, 1985; Siegler & Shrager, 1984).
332) These previous investigations demonstrated the value of error analysis in capturing students' understanding of mathematical knowledge. The examination of students' misconceptions provides an indication of their proficiencies in mathematical problem solving and reasoning. Mathematical justz$cation. 29), "make and evaluate mathematical conjectures and arguments," and "validate their own thinking" (p. 81). Studies by Senk (1985, 1989) showed not only that students have great difficulty in providing sound mathematical justifications when solving geometric proof problems but also that the degree of difficulty was related to students' levels of geometric thought.