Research On The Teaching Design Of High School Sequence Limit Based On The New Curriculum Standard

In the new edition of senior high school mathematics curriculum standard(2017edition,revised in 2020),the learning requirements of sequence limit in the curriculum standard include: establish and understand the ?-N definition of sequence limit through the limit process of typical convergence sequence,master the four operation rules of sequence limit,etc.The content of sequence limit plays a very important role in mathematics.At the same time,limit is the preparatory knowledge of calculus,which plays a vital role in the development of calculus.Under the above background,this paper tries to solve the following problems through research.(1)How do high school students understand and master sequence limit before and after classroom teaching?(2)In the teaching process,what teaching methods and strategies can promote students' understanding of sequence limit?(3)Can students have a deeper understanding of the concept of limit if the?-N definition of sequence limit is introduced in the teaching process of sequence limit?This research selects the students of an experimental demonstration high school in Shanghai as the research object.Based on the requirements of the new curriculum standard,the author carries out the teaching activities of sequence limit,carries out the questionnaire survey and pen and paper test for senior high school students,and carries out the questionnaire survey on 11 senior high school mathematics teachers.After data analysis and statistics,the author draws the following conclusions.Firstly,before classroom teaching,the students' main misunderstanding of "limit" includes "last term","maximum value","supremum and infimum" and "asymptote".After the classroom teaching,the students have a good understanding and mastery to solve simple sequence limit problems,the answer completion rate and accuracy rate have been greatly improved.But some students are still confused about sequence limit after class.Even if they have been carried out teaching activities,many students still can not understand the ?-N definition of sequence limit and the actual meaning of its expression.Secondly,in view of students' cognitive impairment,teachers should pay attention to the following points in classroom teaching: 1.Try to separate the classroom concept teaching from the daily life language of high school students,so as to reduce mutual interference;2.Try to help students understand and master the content of sequence limit in various methods;3.Give examples of various types of sequences in classroom teaching and give research on their sequence limits;4.Use APOS theory to design activities,and carry out the definition teaching of sequence limit for students,so as to promote students' understanding of sequence limit.Thirdly,it is helpful for senior high school students to understand sequence limit if they are taught the descriptive definition of sequence limit at first,and then the?-N definition of sequence limit as an expanded content.Finally,the author reflects on the whole research process,summarizes the limitations of this study in sample selection and textbook applicability,and looks forward to whether the teaching strategies of this study can be widely promoted in practice.