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Arithmetic problem solving and simultaneous-successive and planning processes in sixth grade Chinese children Fan, Aimei Amy

Abstract

This study explored the interrelationships among cognitive processes (planning and simultaneous and successive processing) based on Planning, Attention, Simultaneous, Successive (PASS) theory, the math problem-solving components (problem translation, problem integration, and planning) based on Mayer's (1982) model, and their underpinning math achievements. The effects of planning and simultaneous and successive processing on the comparison problem, a type of math problem specifically difficult to children and even college students, were also investigated. One hundred Chinese sixth graders participated in the present study. The student's PASS processes were measured individually by using subtests of Kaufman Assessment Battery for Children (K-ABC) (simultaneous processing: Picture Series, Triangles; sequential processing: Number Recall, Word Order). The student's planning process was measured by Matching Numbers, a planning subtest of Cognitive Assessment System (CAS). The student's cognitive components in math problem solving were measured by a group administered math test designed by Mayer. In addition, a set of comparison problems designed by the investigator was group administered. The results of multiple regression analyses suggested that sequential processing was significantly associated with translation problem-solving component. Both simultaneous processing and planning were significantly associated with the integration problem-solving component. Moreover, Matching Numbers and simultaneous processing were significantly associated with the problem-solving component of planning. Students' performances in mathematical comparison problems were analyzed by a series of 2 X 2 mixed factorial ANOVAs, with the level of each PASS cognitive processing (high vs. low) and the problem type (consistent language vs. inconsistent language) as independent variables, respectively. The results showed that there were main effects of problem type and level of cognitive processing, and of the interaction among simultaneous processing and problem type, Matching Numbers and problem type. As findings of previous studies, inconsistent language (IL) comparison problems were much more difficult than consistent language (CL) comparison problems for Chinese sixth graders in this study. However, students with high simultaneous scores performed well in solving both comparison problems, whereas students with lower simultaneous scores tended to perform similar with high simultaneous students in consistent language (CL) problems but much poorer than their peers with high simultaneous processing in inconsistent language (IL) problems. Similarly, students with high Matching Numbers performed similarly in both types of problems. But those with low Matching Numbers performed significantly poorer in IL problems than their peers with high simultaneous processing do. These results can help us explain students' special difficulty with inconsistent language (IL) comparison problems. Finally, the manifestations of PASS processes in the special groups of good and poor problem solvers in composite scores of math problem solving were compared. Students who were poor math problem solvers were poor at both subtests of simultaneous processing (Photo Series and Triangles), Matching Numbers, and Word Order, but performed similar with their peers who were good math problem solvers in Number Recall. The profile of PASS processes in good the poor problem solvers in inconsistent language (IL) comparison problems were also compared. Poor problem solvers in IL problems were poorer at all PASS processes compared to their peers who performed well in IL problems. It is concluded that all PASS processes (as measured by planning and simultaneous and sequential processing) involved in arithmetic word problem solving. In particular, simultaneous processing and planning are the essential cognitive processes to build up a correct problem representation, which in turn leads to successful problemsolving performance in arithmetic word problems.

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