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A Tentative Analysis Of Cognitive,Metacognitive Strategies And Correspondent Trainings In Mathematical Problem Solving Of Primary School Students

Posted on:2005-03-26Degree:DoctorType:Dissertation
Country:ChinaCandidate:H D LuFull Text:PDF
GTID:1117360125960024Subject:Principles of Education
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Nowadays problem-solving has been a heated topic of cognitive psychology. However, it is also a category with so many problems unsolved or unclear. Hence, the main purpose of this study was to investigate cognitive and metacognitive strategies, as well as correspondent trainings, in mathematical problem solving, confronting primary students when solving arithmetic word problems. The specific aims are, firstly, to observe cognitive and metacognitive strategies in general and representation strategies, secondly, to observe different effects resulting from applying different types of cognitive and metacognitive training, and thirdly, self-designed method was employed to evaluate metacognitive behaviors of primary students, which was hoped to provide insight into metacognitive aspects of mathematical problem solving. The subjects are middle and high-level graders in primary schools. Six experiments were conducted by taking arithmetic word problems as its material. The results of this study were as follows:( 1 ) Cognitive and metacognitive strategies employed by students coping with mathematic problems. At the very beginning, it revealed that cognitive and metacognitive aspects were closely related to their achievements in arithmetic word problems. They were related to text comprehension, problem representation, problem categorization, result estimate, solution plan, procedure self-evaluation. If we went further, we could know that text comprehension would, in a way, influenceproblem representation, problem categorization, solution plan and procedure self-evaluation. Those strategies would, in turn, have a direct effect on the achievements of students. Self-evaluation of all those strategies mentioned above, which constituted metacognitive strategies for solving word problem as a whole, were a series of ones employed by students at different stages. In addition, we found that, the choice of using direct translation strategy or problem model strategy had every reason to distinguish successful and unsuccessful students. (2) Strategic training during problem solving. First of all, three different types of strategic training were found, namely text comprehension training, representation strategy training and whole model strategy training, which had been proved to enhance students' abilities of problem solving, and as a result to help improve their achievements. Secondly, these three different types of strategic training went, respectively, with metacognitive training, that is, text comprehension training combined with metacognitive training, representation strategy training combined with metacognitive training, and finally whole model strategy problem training combined with metacognitive training. By so doing, students made great progress in their achievements concerning problem solving. However, we should draw our attention to the fact that, those trainings combined with metacognitive training did not show greater progress comparing with the above three types which were conducted independently. Thirdly, the effects of strategic trainings were consistent with students' original achievements. That is to say, strategic trainings and their original achievements were correlated by having an interaction with each other. To put it more explicit, those who had had lower scores made more progress than those withhigher scores in representation strategy training, whole model training and metacognitive training mixed with the above two. Fourthly, we also found that the effects of strategic training were in line with different types of word problem, i. e, either side had an obvious interaction with the other. Representation strategy training enhanced students' abilities of representation strategy when solving distance problem, but made no greater progress when solving fraction and project problem. On the other hand, whole model strategy training could greatly enhance students' abilities of whole model strategy when solving multiplication and project problem. At the same time, whole model strategy training, if combined with met...
Keywords/Search Tags:mathematical word problem solving, cognitive strategies, metacognitive strategies, training
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