Research On Ancient Chinese Historical Data Related To High School

It is well known that learning sequence occupies the important part in the High school, which also plays the extremely important role to study the Calculus in university. In the traditional approach teaching the sequences, people pay more attention to the basic concept, enable the students to master the deduction of the formula, the proof of the theorem as well as the abilities to solve particular problems, while ignoring the penetration of the culture of Mathematics, which leads considerable students to view Mathematics as a boring subject so that lack the interests to learn Mathematics.In this thesis, the sequences learned in High school will be classified and some classical examples will be given. We try to integrate the history of mathematics into the teaching of the sequences in High school, in order to enrich the teaching content, improve the interests of the students and develop their mathematical thinking.The first Chapter is the introduction, where we present the question proposed and the research background recently, and analyze the meaning to integrate some idea in the research of the history of mathematics into the mathematical education.In the second Chapter, the development of the history of sequences is summed up. From <Zhou Bi Suan Jing>,<Jiu Zhang Suan Shu> to the Xi-Jin Dynasty and then the Wu-Dai Dynasty, the research of the sequences reached a peak. In the Tang and Song Dynasties, the research of the sequences focused mainly on the problems from the practical applications. Shijie Zhu in Yuan Dynasty and Dawei Cheng in Ming Dynasty went into more details of the sequences based on the known results. Later, the research for the sequences changed over to the problems of arithmetic progression sequences of higher order. For example, the method of "Duo Ji Shu" is the most important approach to solve such problems. Shiren Chen in<Shao Guang Bu Yi> made a depth study on this problem. By eighteenth Century, Youcheng Dong and Shanlan Li presented some new ideas to study the sequences.We classify some classical problems of sequences collected in the third Chapter, divided into the following four parts, the arithmetic progression, the geometric series, the summation problem of the arithmetic and geometric series and the comprehensive application of the sequences. We present and compare the ancient and modern method to study the problem of sequences. We attempt to let the students understand the origin of the sequences problems and the different method used by people in ancient Dynasties.Finally, in Chapter four, we present a case in the practice of teaching the sequences, that is, the problem of calculation of the general formulation of some sequences by means of equations. More important, we give the comparison of ancient and modern approach in detail. The students are required to master the method and understand how the ancient sages think and solve the related problems.