Research On Course Difficulty Of High School Mathematics Elective Courses Online

Elective course reform is the priority of deepening the ordinary high school curriculum reform and is also the core task of promoting the diversified development in ordinary high school, to carry out the national medium and long term program for education reform.In the process of the elective courses reforming, we are lack of the evaluation standards on whether the elective courses are developed, what aspects have been expanded and how to control the comprehensive difficulty of the courses. In terms of the development level and comprehensive difficulty of elective course about mathematical knowledge development, the main researches are as follows:First, the thesis sets up a reasonable analysis frame of curriculum breadth and depth. Mathematical development can be divided into horizontal development and vertical development. Horizontal development mainly refers to the development on the breadth of curriculum, measured by the increasing of the knowledge.Vertical development mainly refers to the development on the depth of curriculum, using mathematical abstraction degree analysis, abstract degree deg to express mathematics comprehensive depth value of the elective course content. To study the course breadth and depth, the thesis uses the method of abstraction degree to make mathematical abstraction degree analysis diagram. Mathematical abstraction degree analysis diagram use knowledge to represent elements with directional arrows to indicate a logical relationship between knowledge and level of abstraction. The abstract degree analysis method can reflect the numbers of course knowledge and show the comprehensive depth value of the curriculum, reflecting the depth of the curriculum.Secondly, the difficulty of the course is divided into three dimensions, namely "knowledge","computing and reasoning" and "thinking method". Meanwhile, each dimension can be subdivided into four levels, with different level corresponding different value, thus to identify the comprehensive difficulty of course through the calculation of weighted values of each dimension.Then, according to the established course breadth and depth analysis framework and curriculum comprehensive difficulty model, the thesis analizes the ordinary high school elective courses online "the development and exploration of compulsory content in high school mathematics"in Zhejiang province. The findings are as follows: in terms of curriculum development degree, each chapter has been developed on the breadth and depth of the course. However, curriculum development mainly confined to the subject itself, including the expansion between module and module, module and project and development outside the module, but lack the interdisciplinary development. Relating to the knowledge of the trigonometric function, there is the development on method level. In terms of curriculum integrated difficulty, each math problem involves at least two knowledge, two steps in arithmetic reasoning and at least contains one mathematical thinking method. The comprehensive difficulty degree of exercises is higher than examples. On "knowledge" and "computing and reasoning", the exercises are more difficult than examples; while on the "thinking method", the difficulty of examples is a little higher than that of exercises.Finally, the thesis offers some suggestions to the development and difficulty of curriculum in ordinary high school mathematics elective courses.(1) different mathematical knowledge is interrelated and mathematics is associated with other subjects. What’s more, mathematics is widely applied in daily life, so we need to strengthen the development between different math modules, between the module and the topic, the outside module. Meanwhile, it’s necessary to strengthen the interdisciplinary expansion.(2)To control reasonably the difficulty of elective courses, stimulating students’ interests and enhancing students’ confidence in learning mathematics.