Research On The Teaching Design Of High School Mathematics "Sequence" And The Cultivation Of Innovative Ability

It is of great importance for secondary school teachers who engage in mathematics teaching to know how to cultivate students' innovative ability,ideas,and interests at the high school level,which is also the foundation for national development and national rejuvenation.Serve as the foundation of advanced mathematics,sequence,as a discrete function,is very important in high school mathematics learning.It can not only train students' logical thinking,improve their analysis ability and induction ability,but also a good learning point to cultivate students' innovative thinking ability.This paper attempts to make some explorations in this area,in order to deliberately cultivate and guide potential students in the future teaching career and cultivate talents with mathematical innovation ability from an early stage,hoping that mathematical talents like Galois and Abel can appear in China.The contents mainly include:The first chapter mainly describes the research background,status,and implications of sequence.The second chapter describes the history of the development of the sequence and the relevant mathematicians who have made great contributions,introduces elements of ideology and politics into the teaching,and discusses the status of sequence in the study of mathematics in high school.The third chapter compares the differences among different versions of textbooks about the contents of sequence at first,then designs the teaching plan which fits the learning situation better.Meanwhile,it points out the problems that we should pay attention to in the teaching of sequence,studies the role of sequence in the college entrance examination and demonstrates it through examples.Through the research of the content of sequence involved in high school textbooks,chapter four describes the equivalence of the summation formula between the arithmetic progression and the geometric progression which is discussed from the perspective of the limit,it also expands the Fibonacci sequence general formula and its properties that appear in the chapter review questions of sequence of the human-taught textbook,and also lists a number of famous sequences that can arouse the interest of middle school students in mathematics,as well as the practice problems and related problems that appear in the middle school textbooks,use sequence to establish models to solve some practical mathematical problems,and train secondary school mathematics teachers to study textbooks,explore the innovative ability of teaching materials,and then cultivate students' innovative ability.