Teaching Research On The New Textbook "Preliminary Elementary Number Theory"

Elementary number theory is a branch doing research into the rule of number and the nature of integer in mathematics, one of the ancient braches of number theory. The special subject of Preliminary Elementary Number Theory was first introduced into senior high school courses since the publishing of Course Standards of Senior High School Mathematics in 2003. Studying this subject are favorable for deepening students' understanding of the scientific, practical and cultural value of mathematics as well as broadening students' eyes into mathematics. However, a huge challenge is also existing when educational workers starting this new course in high schools. I find that many teachers in both high schools and professional high schools are facing a lot of difficulties in this new course, including not well adapting of the new knowledge, being lack of referential material, and being inadequate of teaching experiences etc. Therefore, studying on the new teaching material Preliminary Elementary Number Theory is of great value to teaching.This thesis first makes an exploration on the necessity and feasibility of teaching Preliminary Elementary Number Theory in high schools, and studies on both domestic and foreign teaching situations on basis of the document analysis method. Then, through two actual surveys of starting the selected course of Preliminary Elementary Number Theory in high schools in forms of questionnaire: it invesigates the professional knowledge structure, the understading and its teaching methods of Preliminary Elementary Number Theory of teachers;also investigates the understading and interest on this cousrse of students. On these basements, the thesis enters the practical problem of the teaching content and the teaching method of Preliminary Elementary Number Theory, namely the problem of "What to teach and how to teach".Combination the above preliminary investigation results and the practical problem in Preliminary Elementary Number Theory teaching, this thesis draws the conclusion that education workers should pay attention to course content selection, teaching goal determination, teaching difficulty assurance, and teaching method choice. Aiming to this, the thesis further designs the detailed teaching case under the theory of pedagogical psychology.In the end, this thesis brings forwards suggestions on how to implement the Preliminary Elementary Number Theory teaching, e.g. to reasonably select the teaching content and correctly grasp the teaching requirement; to enhance the connections of new and former knowledge when teaching the new ones and reduce the teaching difficulty; to make discovery study on cases according to their studying content, characteristics and the theoretical knowledge; to introduce proficient teaching in number theory area in order to inspire students' interest; and to adequately make use of technology and information etc.