Research On The Teaching Of Sequence In The View Of Function

The series is one of the important basic knowledge of high school mathematics,it is the carrier of many mathematical thinking methods.The series is also one of the functions in high school research,it is the bridge of students’ understanding of discrete functions.The series teaching research based on function’s view is still in the primary stage for now.The writer attempts to summarize the previous research results,regards the high school mathematics teaching materials as the bases,and chooses the practical experience of education as a reference,studies the applications in high school teaching that function thinking does in depth.After doing the survey to 174 students which are chosen from three different classes in three different levels’ high schools in Nanchang and interviewing four high school math teachers in different teaching ages in Nanchang,the writer gets to know the understanding of the relationship between function and sequence of students and teachers.Trough studying,the writer gets to know the following conclusions:(1)The teachers’ understanding of the relationship between the function and series is proportional to the teaching age of them.That is to say,the longer the teachers teach,the more depth the teachers’ understanding,vice versa.Teachers nearly use sequence to assist their teaching in function as they do not think too much about using series to study function.(2)Students understand the relationship between the function and sequence not in the deep way,they only know that the series is a special kind of function,but what they know about this quality can bring them what kind of benefits in problem-solving and how to master this relationship in different aspects is very little.(3)The ability of students to contact knowledge that they’ve learned before with knowledge they learn now is relatively poor,they rarely connect knowledge of function they’ve learned previously when they learning the series.(4)The students feel it’s necessary to use the knowledge of function to solve the problems of sequence,but there are very few students would actually think of this when they doing the math problems.The writer believes that this is related to the choice students and teachers make when handling the problems of sequence.(5)The fact that the students barely use series knowledge to solve the function problems is consistent with the conclusions which come from the interview with the teachers.(6)The facts that students do not take initiative to use the knowledge,qualities,and images of function to deal with the sequence problemswhich should have been easier if they solve them by using functional thinking and that students think teachers do not illustrate the relationship between function and series in detail in class,do not solve series problems in a functional thinking way in sequence teaching class are strongly related.