A Research On Exercise Teaching Of Geometric Figures And Transformations In Junior Mathematics

Geometric figures and transformations are new contents of The Standard for Mathematics of Full-time Compulsory Education (2001). As the main parts of space and graph, they are of great educational value to students: beneficial to the development of the space conception of students; beneficial to the development of geometry intuition of students, the understanding of mathematics and their creativity. Geometric transformation is an effective tool for the study of geometric problems and it can be a basis of argumentation.Geometric transformations repeatedly occur in test paper in High School Entrance Examinations. Students are not flexible enough to adapt to this kind of problems, and always do poorly. That is because teachers teach students in an inactive way and look at the problems in isolation and even introduce a lot of extracurricular exercises by exercises-stuffed teaching method to let them solve problems blindly and mechanically. To solve this problem, the following research on the exercises in Geometric Figures and Transformations has been done in the paper:1.How many typical problems in Geometric Figures and Transformations? How to understand them and teach them effectively?Some typical problems and the ways to solve them have been collected in this part of the essay to introduce the related knowledge. In order to make students flexible in dealing with exercises, some typical ways of teaching have been explored by case study method.2.How does the geometric transformation instruct people to add auxiliary line as a tool?The substantive characteristic of translation, rotation and turnover transformation is the change of position of figures before and after the transformation. But the figures themselves are congruent. Considering this characteristic, in order to make the essential features of figures more prominent, the scattered elements of geometry (line segments, angles, and triangles) have been collected through geometric transformation, and the implicit and unfirm relations have been made explicit and close. While dealing with the problems related to isosceles triangles, regular triangles and squares, geometric transformations are used frequently. Making the unobvious conditions obvious is often used.3.How to deeply understand geometric problems by the ideas of transformations?There are a lot of classical conclusions in geometry. If the ideas of geometric transformations are used to understand them, they will be taken for granted, and without proof. Thus, geometric figures and transformations are beneficial to the development of geometry intuition of students, the understanding of mathematics and their creativity.4.How many applications does the geometric transformation have in the daily life? How to teach effectively?This part mainly illustrates the understanding that geometric transformation can't be divided from the reality of maths through the teaching research on application problems in geometric transformation. In fact, the process of grasping knowledge is the process of re-creation to students.Based on the above research, this paper presents several measures to improve the effectiveness of exercise teaching of Geometric Figures and Transformations.