Geometry Reforms Of Compulsory Education Enlighted By The History Of Mathematics

Since the end of last century, the grand mathematics reforms begun in primary and middle schools have entered a calm and thinking stage, and geometry reforms of compulsory education has become the focus. On one hand, it is mainly thought that traditional geometry courses must be reformed according to Elements by Euclid and Geometry Basis by Hilbert. On the other hand, although geometry courses reforms instructed by the Compulsory Educational Standard of full-time school (Trial draft) have brought in many new concepts and opened up the vision of most of the educators devoted to mathematics, it hasn't reached its original intention. The reforms that have a fracture in traditional geometry including plane geometry and elementary trigonometric as well as the completely essential to the traditional teaching methods have led to the big decline in geometry teaching levels in many areas.Mr. Zhang Dianzhou believes that two bases (basic knowledge and basic ability) are the traditional advantage of our Chinese mathematics education, and that we should not only inherit it but also give it a new meaning. However, Doctor Bao Lianshen believes that the essence of mathematics unity lies in its methods. Only on the premise that we should consider the internal relations of geometry courses can we fully develop its values of the external relations. Mr. Gu Lengyuan brought forward the educational reform thought searching for the intermediate zone between the eastern and western mathematics education, which shows the direction of further reforming geometry courses of the compulsory educational stages.When teachers carry out Mr. Gu's educational thoughts in adapting particular textbooks and making teaching designs, the history of mathematics may play an important and enlightening role."The historic order is an excellent guide to teaching."(Mr. Ke Laiyin) If we use the clue to the history of the mathematics for teaching designs and teaching guides, the biggest advantage lies in the following: it can help students feel the process of bringing forth new ideas of knowledge from the situation taken as a whole as well as from one aspect; it can strengthen the basis of our teachers team and it can help them form a complete knowledge system; it can combine developing qualities with acquiring knowledge. A series of measures should be taken to promote the further reforms in geometry courses of the compulsory educational stages. The main points are as follows:â‘ The characteristics of its internal and external relations are different as to different parts of geometry courses. As far as traditional geometry courses are concerned, the key is to reveal the internal relations of knowledge.â‘¡Comprehensively utilize logical and illogical relations of knowledge, and try to build up a precise and complete knowledge system.â‘¢It's an important form to carry out the exploratory teaching method, which can compensate the traditional course system that emphasizes grasping knowledge and forming skills. Here we should see exploratory teaching as follows: it can help students experience and understand the teaching and learning activities where knowledge takes place and develops directly and indirectly.As it known, teachers can select particular methods of exploratory teaching according to the teaching contents, the backgrounds of students and the students'strong points. So there's possibility that some difficult but important teaching contents can be brought back to classes in various forms during the compulsory educational stages. For example, the discovery of sine and cosine principles, and the concept of obtuse angle trigonometric function van be chosen as valuable subjects.During geometry reforms, the history of mathematics can give free vein to its function in 2 main ways:â‘ Reform the historic order of knowledge development and make the knowledge appear in order during the teaching process.â‘¡What if mathematicians in ancient times had had the knowledge that students in modern times possess? It means that we should imagine how knowledge may happen and apply it to teaching. The latter requires that teachers should have further understanding of the evolution of mathematics thoughts.The history of mathematics has influence on many aspects of geometry teaching, such as demonstrating the occasion and way of formulism penetration and disclosing the process of forming concepts. We may have further understanding of it thought the cases.It can be brought to light through educational reforms: Even if students have been using the present textbooks, students'enthusiasm, achievement, and their ability to solve problems may be improved if the educational reform measures referred to above are available, and we can develop the function of the history of mathematics in mathematics teaching. In a word, on the premise in search of the eastern and western mathematics education, the history order is an excellent teaching guide.