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Study On Problem-solving Of Symbolic-Graphic Combination: Perspective From Representation

Posted on:2006-12-15Degree:DoctorType:Dissertation
Country:ChinaCandidate:X B LuoFull Text:PDF
GTID:1117360152493088Subject:Curriculum and pedagogy
Abstract/Summary:PDF Full Text Request
The study of mathematical problem-solving is a characteristic of the mathematics education research in China. It can't localize to lay out the technique and stick to present the method. It should pay attention to mathematical ideas and mathematical methods and probe into the psychology of mathematics teaching and mathematics learning. The study of mathematical problem-solving is done little to analyze and investigate the mind of problem-solving by using the view of cognitive psychology. And the studies of symbolic-graphic combination had a lot of shortages. Based on these thoughts, this article selects the mathematical representation as a visual angle and the combination of symbolic-graphic as an object. The article is intended to investigate the problem-solving process of symbolic-graphic combination by using the mathematical representation.The subjects can construct and use the graphic representation in solving the problem that presented in algebraic representation. The graphic representation played different roles in different stages of the problem-solving process. The subjects can construct and use the algebraic representation in solving the problem that presented in graphic representation. The times of using the graphic representation to solve the algebraic problem are more than the times of using the algebraic representation to solve the graphic problem. Using the different representations had two forms. One case is using new representation in thinking and using original representation in writing the solution. Another case is using new representation in both thinking and writing the solution. The subjects are active and passive in using new representation.The graphic representation had four present modes, which called no-graph, passive-graph, active-graph, and example-graph. Firstly, we investigated the effects of different present modes of graphic representation on the problem-solving performance. There weren't distinct difference among three schools. And there wasn't distinct difference between the males and females. There were distinct difference among the excellent students, the common students and the learning-difficult students. The excellent students and the learning-difficult students were done best under the passive-graph condition. The common students were done best under the example-graph condition. They were done worst under the no-graph condition. We investigated the distinct differences between different groups. Secondly, we investigated the effects of different present modes of graphic representation on frequencies of using the graph. We counted the different students' frequencies of using the graph under the different conditions. And we investigated the distinct differences among the different groups in using the graph. Further, we investigated the distinct differences among the different students in using the graph.The graphic representation had three present types, which called graph-one, graph-two, and graph-three. There weren't distinct difference among three classes. The males' scores were higher than the females' scores. There wasn't distinct difference between the males and females. And firstly, we counted the different students' scores under the different present types. Secondly, we investigated the distinct differences among the different groups' scores. Thirdly, we investigated the distinct differences among the different students' scores.Based on the qualitative study, we concluded that the problem-solving activity of symbolic-graphic combination can divided into four segments, that is, inferring additional consequences from graph, elaborating mathematically and re-inquiring the new information, setting a new goal in using the intuitive representation, and monitoring the problem-solving process. The intuitive induction and the logical analysis were the main thinking modes in the problem-solving process of symbolic-graphic combination. They sustained and promoted each other in understanding the problem and solving the problem. Based on the quantitative study, we investigated the times th...
Keywords/Search Tags:mathematical problem-solving, mathematical representation, symbolic-graphic combination, symbolic representation, graphic representation
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