| A lot of scholars in mathematics education have attached much importance to the research of problem-posing. Current studies in this regard focus on two aspects:Firstly, problem-posing is only regarded as an effective or better way to solve the problem; secondly, problem-posing is thought as a relatively independent mathematical activity. Under the empirical or experimental studies among high school students, these two studies endeavor to look into the status quo or the effectiveness of strategies. The relevant research on Meta-cognitive and mathematical problem-posing is inadequate at home and abroad, not to mention empirical research. As for the high teacher-student meta-cognitive ability in mathematics problem-posing and the overall impact of the factors underlying the relationship between the research the author has not yet been seen reading in the literature. This thesis tends to explore how high teacher-student and its two sub-factors of meta-cognition (meta- cognitive knowledge and meta-cognitive monitoring) affects the capabilities of mathematical problem-posing which is divided into four dimensions by SOLO classification, fluency, complexity, flexibility, and originality. Taking ability of mathematical problem-posing and its four dimensions as the dependent variable, the thesis employs the research methodology of combining theory with practice for empirical research under the application of SPSS statistical analysis.In theory studies, after reading and analyzing the literature, the author defines problem-posing and mathematical problem-posing respectively and furthermore, put forward that mathematical problem-posing contains fluency, complexity, flexibility, and originality. These four dimensions are treated as dependent variables, the two sub-factors of meta-cognition (meta-cognitive knowledge and meta-cognitive control) as independent variables. Meanwhile the variable grade is introduced to process data, such as correlation analysis, variance analysis and contingency table analysis.The empirical studies concentrate on the investigation of 300 students in freshman, sophomore and junior in two universities of Guangxi with 284 valid questionnaires. The thesis applies statistical software SPSS15.0 to test the relevance of meta-cognitive knowledge, meta-cognitive monitoring and mathematical problem-posing. The conclusions are drawn as follows:(1) The analysis of independent samples T of groups in high and low level shows that meta-cognitive groups in high and low level is discriminating to the meta-cognitive level of problem-posing. In other words, there are obvious differences.(2) problem-posing ability and meta-cognitive total scores have a very distinct return with a good return model y=7.663+0.107 x; the meta-cognitive total scores are closely related to the fluency, complexity, flexibility of mathematical problem-posing, while the total scores have inconspicuous collocation with the originality of mathematical problem-posing, so does the meta-cognitive knowledge. The correlation of meta-cognitive monitoring and mathematical problem-posing fluency and flexibility is remarkable, while the correlation of complexity, originality in mathematical problem-posing is not obvious.(3)The scores of meta-cognitive affect the mathematical problem-posing ability and flexibility of mathematical problem-posing. Students with high level of Meta-cognition are often more capable and flexible to pose mathematical problems. However, they have no obvious impact on fluency, complexity, and originality of mathematical problem-posing.(4) There are not many differences between the level of meta-cognition and meta-cognitive monitoring of the students in different grades, but differences of meta- cognitive knowledge of the students in different grades are remarkable. The discrepancies are showed as follows:the level of meta-cognitive knowledge of freshmen and sophomore is obviously different, while the level between freshmen and junior, sophomore and junior is not; the differences between the scores of students'mathematical problem-posing abilities and the fluency, complexity, and flexibility of mathematical problem-posing are not prominent, whereas the originality of mathematical problem-posing has distinct discrepancies among them; the originality of mathematical problem-posing in freshmen and junior grade is obviously different, and junior have higher level of originality than freshmen. The originality of mathematical problem-posing between freshman and sophomore, sophomore and junior is not conspicuous different.Finally, the author draw a conclusion that stimulates teachers'teaching and students' learning. Putting the conclusion which is made through the exploration of literature and investigation research into the practical teaching activities, the author suggests employing mathematics problem-posing teaching on the basis of meta-cognition. The meta-cognitive knowledge requires teachers to change their teaching concepts, transform the static view of teaching into dynamic teaching concepts, absorb more new knowledge, and adopt new teaching methodology; students should enrich their way of learning. From the perspective of meta-cognitive monitoring, teachers need to pay much attention to reflective teaching, and students should develop the habit of asking questions. |
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