High School Mathematics Difficulties Instructional Design

In the math teaching process in the high school ( senior middle school), it is found that some students have difficulty in grasping the difficult points. These students often grasp them only in the knowledge level. That is because they lack learning methods, can't understand the difficult points or have different thinking modes. Of course, teachers also feel puzzled about how to teach this part of knowledge. This essay try to do some research on the teaching design of the outstanding difficult points in the high school math based on the teaching theory, aiming to master better the students' thinking process in learning math, stimulate the development of their math thinking modes, push the reform of the class teaching methods, promote the Education for All-round Development and improve the teachers' teaching methods so as to raise the teaching level.This article is written based on the following related theories: the Cognitive Development Theory by Jeam Paul Piaget, the Cognitive Development Theory by Lev Semenovich Vygoskey, the meaningful learning theory by D. P. Ausubel, the educational and psychological methods of the cognitive characters of the high school students, the math definition teaching and testing teaching method and so on. In the article, the above theories are used to analyze 8 representative difficult points in the high school math, illustrate the reasons why they become difficult ones, designing some effective teaching methods, and therefore explain why they are designed in that way and how to break through these difficult points. These 8 representative cases are : the teaching of thefunction concept, the graph teaching of the triangle function y - A sin(ωx+(?)), theteaching of the basic plane vector principals, the teaching of the second definition of the oval, the teaching of the plane angle and the dihedral angle, the teaching of the volume of the sphere, the teaching of the Math Induction, the teaching of the deducing fomular:1~2+2~2+3~2+…+n~2= (n(n+1)(2n+1))/6.Finally, the article analyses, contracts and summarizes the designing of these cases, and induces the types of these difficult points: (1) the difficult points caused by the abstraction of math; (2) the difficult points caused by the hidden characters of the inner relation of the teaching contents; (3) the difficult points caused by the deepening of the teaching contents; (4) the difficult points caused by lack of basic knowledge and (5) the difficult points caused by the confusing contents. Then some general methods are offered to solute them.