Teaching Research Of High School Analytic Geometry Based On The Analysis Of Course Difficulty

Geometry and algebra were two independent branches of mathematics before analytic geometry was originated. Analytic geometry is a true combination of geometry method and algebra method. Quantities and spatial forms were combined together, with which geometry question was proved and calculated by using algebra, and it was a major breakthrough in the history of math. As an important part of high school math, analytic geometry was throughout the entire junior high school math learning. The difficulty of analytic geometry increased gradually and many students felt it after entering high school. What is the root of this phenomenon? This research attempts to start from the syllabus and curriculum standards to analyze the teaching problems in high school analytic geometry. It could not only help the teachers, but also provide a scientific basis for curriculum reform.In this study, course difficulty mode, teacher interviews, questionnaires and characteristics of analytic geometry questions were used in the analyzing process. The main contents are as follows:(1) Difficulty analyzing of high school analytic geometryHigh school analytic geometry is difficult, but lack of quantitative indicators, so that the difficulty can not be described accurately. Both vertical and horizontal angles were selected for quantitative analyzing the difficulty of high school analytic geometry. Course difficulty model was used for quantitative analysis from both depth and breadth of the perspectives, so that the subjective feelings could be explained by the objective quantitative calculations.(2) Survey of High School Analytic Geometry TeachingSchools of three different levels were chosen as the survey. Analytic geometry teaching in high school was analyzed based on curriculum breadth and width from the subjective and objective aspects, respectively. Interviews with teachers and students questionnaire were chosen for the subjective aspect, and characteristic of questions was chosen for the objective aspect.(3) Reflections on analytic geometry teaching in high schoolThis study was based on the results of the questionnaire survey and calculation of course difficulty model from the relationship between curriculum and course difficulty and the application of course difficulty model, respectively. Current problems that exist in analytic geometry teaching were pondered and relevant conclusions were drawn.Results indicated that: The difficulty of analytic geometry changed little in <syllabus> from 1996 to 2002, and the biggest change was 4.55%. <Curriculum standards>(2003) greatly enhanced the difficulty of analytic geometry, which increased the difficulty of 57.18% compared with 2002. According to the <curriculum standards>(2003), difficulty of analytic geometry was not big in high school math curriculum, and ranked 9th in the 14 modules. If the controllable subjective factor duration removed, which assumed that all learning modules equal, analytic geometry has increased the difficulty with ranking to 5th, but still not belong to the most difficult courses. Although substantial increased in new "Curriculum Standards", comparing with other high school math modules, the difficulty of analytic geometry was still only in the middle. However, the results of teacher interviews and the student questionnaires displayed inconsistent. Both teachers and students thought that analytic geometry was hard and students didn’t play well in the process of problem solving. This study suggested that the reason for this difference was man-made causes. If the trends of college entrance examination do not change, this kind of difficulty won’t change, too. The students’ poor ability of dealing with analytic geometry question is mainly because of their mechanical learning method, so that teachers should strengthen the training of students’ logical reasoning ability. This paper resorts the knowledge of high school analytic geometry math and common problem-solving approach to help students more comprehensive and systematic understand it.In summary, objective course difficulty model, subjective teacher interviews and questionnaires were used to discuss the current problem which exist in analytic geometry teaching. It provides a reference for the similar teaching environment, but also made a useful attempt for our math curriculum reform.