An Empirical Study Of High School Students Using The Construction Method To Solve Problems

Mathematical problem-solving,has always been a tradition in China.However,research about mathematical problem-solving still remains in training solution method and directly displaying the problem solving skills.It is far from enough to reveal the thinking and thinking process of solving problems by using the theory of Mathematical Psychology,and there are many deficiencies in the research on the solution of the structured approach.Therefore,this study regards mathematical representation and structured approach as the research perspective and object.From the perspective of mathematical representation,it analyzes and studies the related problems of senior high school students using structured approach to solve problems.In this study,90 high-school students with Olympic Math training experience were selected as research objects.The goal was to analyze the different mathematical representation interventions and to study the double-factors,such as mathematical representation and gender,mathematical representation and training group,mathematical representation and item difficulty of influence for senior high school students applying structured approach to solve problems,by referring to relevant mathematical representations and structured approach research around the world.The two test questionnaires A and B on the construction method based on high school mathematics competition training courses and revised national high school mathematics competition problems over the years were compiled.The two test questionnaires had the same items but different interventions on the mathematical representation.The following conclusions were given following by research.(1)Under different degrees of mathematical representation intervention,there was significant differences in the influence of high school students using structural method to solve the problem.(2)Under different degrees of mathematical representation intervention,there was no significant difference between the male and female high school students using the structure method to solve the mathematical problems;The inter-subjective effect test shows that there was significant difference between the inter-subjective effects of mathematical representation,while gender did not show significant difference,and the interaction between gender and mathematical representation was also not significant.(3)Under different degrees of mathematical representation intervention,there was significant difference among senior high school students with different Mathematical Olympiad training years using the structure method to solve the mathematical problems;The inter-subjective effect test showed that there was significant difference between the inter-subjective effects of mathematical representation,while different Mathematical Olympiad training groups showed significant difference,meanwhile,the interaction between different Mathematical Olympiad training groups and mathematical representation was also significant.(4)Under different degrees of mathematical representation intervention,there was significant difference in different item difficulty by using structural methods in senior high school students.The intervention of mathematical representation increased the mean value of higher item difficulty.The inter-subjective effect test showed that there was significant difference between the inter-subjective effects of mathematical representation,while difference item difficulty showed significant difference,meanwhile,the interaction between different item difficulty and mathematical representation was also significant.Based on the above research,I put forward some specific suggestions for mathematical representation and applying structured approach to solving mathematical problem.So,in the daily mathematical problem-solving teaching and studying,teachers should not only pay attention to the accumulation of students' mathematical knowledge,but also pay more attention to the optimization of knowledge quality of students.It is reasonable and effective to carry out problem-solving teaching and studying under the premise of understanding and grasping the students' problem-solving psychology.