High School Students Solve The Problem Of Function The Topic Link Analysis Of The Case

Though being extremely important as the first step to solve the problems, examining the topic is not given enough attention in the actual teaching among teachers and students. Therefore the process of examining the topic in the function problem solving may remain more problems, since knowledge of function is rich in content and abstract to understand. However, the results published in literatures available, lack of response to performance at different stages of students’analytic ability analysis, lack of knowledge of different sections for high school the issues involved in the analytic research, lack of case based analytic research.Using the method of literature Review, comparative study, interview, and the method of "Case+reflection", the paper analyses this issue from two aspects of the case based on Polya’s Theory of Examing the Topic, Bartlett’s "Schema Theory", Mathematics Multivariate characterization Theory as well as Discovery Method. On one hand, this paper compared the mathematical learning performances at three types of students on different stages from the perspectives of both answering process and the analytic train of thought for a certain question, analyzes the existing differences, and obtains the successful essential factors towards examining; on the other hand, it uses a case to list often error-prone points of high school students in solving function problems, and puts forward matters needing attention while examining.Conclusions based on the case analysis:1. Figure out examining differences of the three types of students in different phases from two respective perspectives:the knowledge skills and analytic ability.2. Summarize necessary conditions of a successful examining:(1) outstanding text comprehension;(2) the sharp image observation ability;(3) grasp basic knowledge solidly;(4) the complete knowledge schema;(5) relatively rich experience.3Items needs attention for the study of function:(1) note the implied conditions;(2) omit no conditions;(3) understand the question correctly.Suggestions:1. to concentrate on improving the students’ analytic ability:(1) to improve text comprehension;(2) to improve ability of image observation;(3) to strengthen basic knowledge;(4) to strengthen the links between different knowledge;(5) to cultivate good habits of examining.2. Teachers should pay attention to these problems during function teaching:(1) to figure out confusing concepts;(2) to be skillful at teaching of Multivariate characterization;(3) to summaries the conclusion related to the character of the function;(4) to be good at representations of Multivariate characterization in mathematics teaching.3A few proposal on "examining teaching ":(1) do not substitute for students to examine;(2) do not to be so impatient to correct them;(3) to present overall analytic process;(4) to guide the students to draw the knowledge structure map.