Solving The Dynamic Mathematical Problems For High School Entrance Examination By Using Geometry Sketchpad

Dynamic analysis of the questions is the key to help solve the questions, especially the dynamic questions in the entrance exam to the senior high school. By demonstrating and dynamic analyzing, students can be guided to probe the problems in a visual experimental way rather than be led by the sole words clues. The dynamic process can help the students have a visual sense and understand the question more clearly, and therefore solve the questions much easily. As a result, the students’ geometrical mode of thinking can also be developed.This thesis is to give an analysis about the dynamic process geometry problems. The questions used in the analysis are taken from the exam papers the students have when having the entrance exam for senior high school. The present study is undertaken to explore the following questions:(1) How to make Powerpoint of Geometry Sketchpad for teaching?(2) How to demonstrate the Geometry Sketchpad and help the students have a visual sense of the dynamic process when analyzing the question?(3) To help the students observe the different changes during the whole process and find out the solutions.Through the study, not only the students are guided to develop their dynamic thinking, they also sum up the approaches on how to solve the dynamic questions, which should also be emphasized here.(1) To solve the problem in a “static” way. No matter what kind of problems they are, the problems about the dot movement，line movement or the dimension movement, they belong to the same category. The way to solve these problems is to treat them in a static way. One way to solve this is to pay attention to the equivalents of the question in a special position in the movement and the variables. Besides, they should be also aware of the invariables, the restrictions and the special relations, etc.Sometimes the special position ought to be regarded as being static in a short period of time.(2) Concerning the problems with function, the final way to solve them comes down to the coordinate. The dots can be represented by letters which can be linked together to measure the length of the line with an aim to list out the equation accordingly.(3) When dealing with the graphic problems, it can be easier to work out the different movements by means of rough sketching. And the problems can be solved one by one with the drafts.(4) When listing the equivalents of the questions, relevant knowledge are often used, such as the knowledge of acute triangle, similarity, segment addition and subtraction， parallelogram, axisymmetric and centrosymmetric.Others, for example, if two segments are paralleled, they are equal, are required.