Research On The Relationship Between Functional Knowledge Structure And Teaching Of Senior One Students ——A Case Study Of Shanghai C High School

Function always plays an important role in mathematics learning in junior and senior high schools.Teachers also use various strategies in function teaching,but students' function level is not satisfactory.Individual function level is closely related to its functional knowledge structure,so it is particularly necessary to explore the specific situation of students' functional knowledge structure and the relationship between teachers' classroom teaching and the development of students' functional knowledge structure.In this study,two classes of students in grade one of C Middle School in Shanghai were selected as the research objects.Based on the CPFS structural testing method of Professor Yu Ping,the functional knowledge structure of the students before and after learning part of the functional content of grade one was tested by the testing method.During this period,the classroom teaching received by the students was recorded by classroom observation method.Finally,six representative students were selected to conduct relevant interviews so as to have a more comprehensive understanding of the current situation of functional knowledge structure of senior one students and its relationship with teaching.This paper mainly studies the following two sub-problems:(1)What is the current status of functional knowledge structure of students after they finish learning in junior high school(i.e.before learning function in senior one)?What is the status quo of function knowledge structure after finishing the part of function in senior one(power refers to the function,the concept of function and the properties of function)? What has changed in the meantime?(2)In the process of functional teaching,which teaching behavior means are related to the change of students' knowledge structure?The results show that :(1)the students show the best performance of "discernible reasoning" and the weakest performance of "node connection" in the functional knowledge structure after learning only in junior middle school;(2)In the knowledge structure of high school students,the performance of "equivalent reasoning" is the best,and the performance of "proposition application" is the weakest;(3)After functional learning in senior high school,there are still obvious deficiencies in the development of the dimension of "propositional application" in students' knowledge structure,and the difference in knowledge structure between the two classes becomes significant;(4)Teachers' neglect of "conceptual structure",emphasis on "proposition application",lack of students' autonomy in class and failure to group and stratified teaching are consistent with the changes in knowledge structure of students in junior and senior high schools.