Factor Analysis Of The Structure Of A Private School Students' Mathematical Ability

The research of mathematical ability is an important area in mathematical education. The research for its structure is the beginning of the mathematical ability. The structure of mathematical ability is a dynamic, multi-dimension, multi-level three-dimensional network structure which is composed of each ingredient of mathematical ability.The importance of this research lays the following aspects. First, ability structure's research is an important task in psychological research. Next, ability structures research has the guiding sense to educational practices. Third, ability structures research is the foundation and the premise to the ability test.At present much has been down on the related researches of mathematical ability, yet the methods of these researches are different. This paper made a test to examine students'operational ability, the reasoning ability, abstract and summary ability, concept understanding ability, spatial imagination ability, and problem solving ability, the thinking of transformation between algebra and geometry as well as the thinking of classification. The object of this research is the grade ten students of PEIJIA bilingual school in 2009. The method is factorial analysis combining with the factor score and the procedural analysis. This paper analyzed the structure of mathematical ability and the difference between males and females combining the cognitional psychology and mathematical study psychology. Compared with four-factor, five-factor and six-factor's results, we draw the following conclusion: five-factor model is more reasonable. The structure of mathematical ability consists of Problem representation ability, pattern recognition ability, signal comprehension ability, image reasoning ability and space thought ability, which is special for this school's students and is different from normal classification. Besides CPFS structure and the automatic operation of the students are also related to the above abilities. In the gender difference's aspect, both boys and girls have the same pattern recognition ability, but boys are inferior to girls in the signal comprehension, and superior to girls in problem representation, space thought and image reasoning. Finally, we made some suggestions and teaching strategies to improve the student's mathematical ability.