Investigation Of The Innovative Mathematics Questions Solving Based On Problems Representations For High School Students

As China is in the development of important strategic, cultivating talents is particularly urgent and important for building an innovative country. From the mid-1980 s, China’s basic education curriculum has been reformed greatly when cultivating innovative talents began to be advocated. In order to meet the requirements of the new mathematics curriculum, mathematics curriculums in high school focus on developing students’ sense of application and innovation. The entrance mathematics questions and the usual training test exercises must have the innovative characteristics including background, new structure and rich content.Students in high school must be able to analyze and process the information and knowledge through a new mode of thinking. Therefore, it is meaningful to research on innovative mathematic curriculum problem for cultivating innovative talents.From a psychological point of view, first, the problems have been proposed through the literature analytical method, as well as the basic theories and the related concepts. The influence of problems representations on the solving the innovative questions was studied in high school mathematics using examples analytical method; Second, the habits of problems representations in solving the innovative questions in middle school mathematics have been researched by questionnaire survey research approach; and finally, the ability to represent and resulting differences in solving the innovative problem for mathematics were studied and analyzed by questionnaire survey testing method for high school students. The results show that:(1) high school students in the first grade are not good at representing in solving mathematics innovative problems, while the students in experimental class have a better habit of representation.(2) On the whole, middle school students in the experimental class in the third grade have a better representations in mathematical innovation problems than the students in the first grade,with a higher proportion of students who have good representation.(3)Abilities of representation of third year experimental class students are better than the first year experimental class students’, such as understanding the nature of the concept, the conversion of three languages, representations of the problem background, methods selection and so on.Finally, combining the teaching practice, some thought on improving the ability of students to solving the innovative mathematics problems have been proposed.