The training of the students' abilities has been the basic direction and one of the main purposes of mathematics teaching. The traditional classification of basic mathematical abilities is calculating ability, space imaginative power and abstract thought. With the development of the society and the technology, more and more people have realized the value of the applying mathematics. By the end of 1980's, all the developed countries had done research on the development of education and paid more attention to the mathematics courses reforming, especially to the applying mathematics.Since 1990s, a more scientific and modern education of mathematics has been set up. The Education Department of People's Republic of China points in its curriculum standard of mathematics for full time middle school students that mathematics is a wide-used skill, which is helpful for people to collect, arrange and describe information. Forming a pattern to solve mathematical problems is the direct way to produce wealth for the society. So the research on students' capability of applying mathematics and educational pattern of mathematics applying orientation has been considered as the major research area in national mathematics courses reforming. However, the progress of that in China is not very rapid since the education system here has been influenced by the education for examination for a long time.This essay makes a systematic review on the achievements in scientific research and elucidates in detail the general concepts of mathematics capability structure and mathematics applying capability of middle school students. It discusses the important theoretical and practical problems about the mathematics applying orientation. Through investigating and analyzing the situation of the students' attitude, consciousness and capacity, the author elaborated the realistic value of implementation of mathematics application-oriented teaching. The essay makes a conclusion, which contains teaching experience, teachingprinciples and teaching process of mathematics applied orientation, and presents an operational description on characteristics and implementation of some typical teaching patterns. The essay is based on the curriculum standard and plenty of theoretical research. On the contrary of the traditional teaching methods, it presents the new teaching ideas and the new teaching pattern of applying mathematics. It is the author's best wish to give a little enlightenment for the other mathematics teachers in training the students' capability of applying mathematics. |