Research On Sequence Of Number Under The New Curriculum Of High School Mathematics

Sequence of number is attached with importance in both high school and university. It appears as anindependent chapter in the fifth compulsory textbook of PEP high school mathematic curriculum and“Sequence of number and Differences” is selected as an separate topic in the fourth compulsory textbook,hence, sequence of numbers plays an important role in the entire high school math curriculum. Sequence ofnumber is closely linked with practical issues in real life, such as savings, installment, organization ofitems, etc. Much attention has been paid to sequence of number by experts who advocate propositions forthe college entrance examination in China as well as those first-line math teachers and universitymathematics education experts. Besides these, sequence of number is also involved in many courses inuniversity mathematics, such as mathematic analysis, combinatorial mathematics, discrete mathematics,etc. This article aims to analyze the issues of sequence of number under the new curriculum of high schoolmathematics.Based on analysis of numerous literature works on sequence of number, this article verified thehistorical development of arithmetic progression and geometric progression. The status of sequence ofnumber in high school mathematics is also introduced in this article. A thorough and detailed inquiry,through analysis of demonstrations and survey data as well as other researching methods, is made oncommon problems of sequence of number one may encounter on papers of college entrance examination inChina and the close relationship of the two sequences is probed.On the basis of the exploration of a large number of college entrance examination test questions, thecommon types of test questions are investigated: questions on basic concepts, solving general term formula,summation of sequence of number, types based on classic sequences as background, types combined withmathematic modeling, examination of new definition, examination of the combination (of the sequence ofnumber) with functions, the confirmation of sequence inequality and so on. Detailed research is carried outon the skills of solving these problems, the knowledge involved as well as problems which should be paidattention to by teachers during teaching activity. This is the innovation of this article.Further survey is conducted on common test questions in college entrance examination on the basis of higher mathematic knowledge the author gained during undergraduate and postgraduate period. In-depthresearch is construed on the most common recurrence relations: first-order linear recurrence relations,second-order constant coefficient linear recurrence relations, fractional recurrence relation. Concerning theintroduction of the penetration of higher mathematic theory in the college entrance examination, thecontraction mapping was taken as an example in this article. The necessity of high school teachers learninghigher mathematics is justified through the research conducted on those sequences from high point of viewthrough the use of modern mathematical theory, viewpoint and methods.Hoping this research can serve as a reference or a revelation in the academic study of teachers and thestudy of students.