Cognitive Style, Self-monitoring Of Effects And Characterization Of High School Mathematics Problem Solving

The study selected the second grade high school students form No.1 Middle School of Zhongshan in Guangdong province be the objects, and aimed at investigating the cognitive style and self-monitoring' effccts on the students' mathematical problem-solving effectiveness and representation.The study can be divided into two parts. The first part consists of the relevant research on cognitive style, self-monitoring and mathematical problem-solving effectiveness,with the way of Embedded Figures Test (EFT) and Cognitive Style Analysis test (CSA) in order to differentiate the cognitive style of students, The middle school students mathematics self-monitoring ability questionnaire to test the students'self-monitoring ability, and mathematics final examination scores as the indicator of mathematical problem-solving effectiveness. The second part is the experiment research on cognitive style mathematical problem-solving effectiveness and representation, used the high school students matematical test which worked by the researchor to test the students'mathematical problem-solving effectiveness and representation of different cognitive style studens. The correct rate as the the indicator of mathematical problem-solving effectiveness, and representations contain pictorial representations-schematic representations,direct translation strategy-problem model strategy and verbal representations-pictorial representations. We could make conclusions as follows:1. There is significant difference between different subject studesnts on cognitive style. Science students tend to be field-independence and image type, liberal arts students tend to be field-dependence and verbal type. Cognitive styles of boys and girls there was no significant difference.2. In the self-monitoring ability, the liberal arts students'management dimensions of self-monitoring were significantly higher than the science students, science boys' self-monitoring score, regulation and management dimensions were significantly lower than male students of liberal arts.3. The mathematics final examination scores was significantly higher of students in science of the field-independent cognitive style or image type, but The mathematics final examination scores was higher of students in liberal arts students of the field-independent cognitive style or verbal type.4.Self-monitoring ability score can significantly positively predict the mathematics achievement of students, especially the image type in science students and evaluative dimension of self-monitoring in liberal arts students.5. In test 1, there is no significant main effect of cognitive style in the mathematical problem-solving correct rate, but significant interaction between subject and gender. Among male students, field-dependence students'correct rate was significantly higher than field-independent students, but among female students, field-independence students'correct rate was significantly higher than field-dependent students. In test 2, there is significant main effcet of subject, the mathematical problem solving significant main effect on the subject, showing the science students'mathematical problem solving correct rate was significantly higher than liberal arts students.6.In the respects of representation in mathematical problem-solving, students selected pictorial representations more than schematic representations,direct translation strategy more than problem model strategy and verbal representations more than pictorial representations; field-independence studetns tended to select schematic representations,problem model strategy,verbal representations and pictorial representations; image type students tended to select schematic representations,verbal representations and pictorial representations.