A Comparative Study On Difficulty Of High School Geometry Curricula Between1^st&2^nd Curriculum Reform In Shanghai

Reform of geometry curriculums has often been the focus of curriculum reform of elementary education. In order to find out the differences between the two Shanghai curriculum reforms of mathematics (the first one in the1990s and the second one in the early20th century) in teaching requirements for senior middle schools in the grasp of geometry, we are dedicated to the research into the geometry curriculums in senior middle schools of the two reforms. The main issues of the research are:1. Based on the documents, in what way can the degree of difficulty in geometry curriculum in senior middle schools be reasonably evaluated?2. In terms of curriculum criterion and requirements on textbooks, what are the differences between the two curriculum reforms of mathematics in the degree of difficulty for senior middle schools in the grasp of geometry?3. By means of observing teachers’teaching practice and their assignments, we expect to determine how difficult it is to carry out the geometry curriculum during the second reform and what teachers should do to further develop the teaching materials so as to make the most of their advantages.The research adopts a model of degree of difficulty of course to compare the mathematics syllabus of Shanghai’s first reform and the mathematics curriculum criterion of Shanghai’s second reform in the degree of difficulty in the section of geometry. Also, a’"comprehensive difficulty model of senior middle school geometry" is built to analyze the degree of difficulty of examples, drills and exercises of geometry from first and second curriculum reforms, the supplementary exercises from two senior middle school teachers when they teach the chapter of line and plane in three-dimensional space and the geometry exercises from the recent five years’ college entrance examinations.According to the comparison, when getting a in an interval of (0,0.989), whenever mathematics is for liberal arts or for science, it shows that the geometry in the mathematics curriculum criterion of the second reform is more difficult than that in the mathematics syllabus of the first reform.Through comprehensive difficulty model of senior middle school geometry, we get similar findings when studying the examples of geometry from first and second curriculum reforms, drills, exercises and the geometry questions from the recent five years’college entrance examinations. There is a tendency that much emphasis is put on "illustration","exploration","operation","reasoning" and "knowledge capacity" instead of "background". In the teaching materials of the second reform, more emphasis is put on "illustration","operation","context" and "knowledge capacity" but less on "exploration" and "reasoning". On the other hand, when it comes to "exploration","operation","reasoning" and "knowledge capacity", exercises from college entrance examinations are more difficult than those from teaching materials of two reforms, which means that exercises in the teaching materials cannot meet the needs of the college entrance examinations.By observing two senior middle school teachers performing teaching practice on chapter14from the teaching materials of the second reform, line and plane in three-dimensional space, by encoding and calculating the comprehensive degree of difficulty of the supplementary exercises they give out in class and by interviewing the two teachers, we can see that the degree of difficulty of geometry taught in class is higher than what the second reform requires, and approaches but doesn’t reach that of corresponding exercises in the college entrance examinations.Ponders and suggestions on the findings of the researching and the relevant interviews are given at the end.