| The influence of function concept on the development of mathematics is long-drawn-out. At present, the function has permeated almost every branch of mathematics. The famous German mathematician F. Klein regarded function as the spirit of mathematicians and the foundationstone of middle school mathematics. The concept of function as well as its method of thinking has become one of major points of mathematics teaching in middle school. To most students, the study of function concept is a leap from the understanding of concrete numeral relation in real world to the understanding of abstract numeral relation. However, because of the complexity of function concept, it is very difficult to teach it.Beginning with the concept of function, this paper conducts an empirical research on the understanding of functions among junior and senior middle school students by means of a questionnaire survey. Students' answers are analyzed, classified and compared to the historical evolution of the function concept. It is revealed that most of the definitions given by students have their analogues in history, and are close to those of many mathematicians during the period from Leibniz to Bourbaki, including those which haven't been mentioned in the classroom. Moreover, students have the same knowledge with ancient mathematicians in the domain of function, analytic expressions and graphs.If we can notice the parallelism between students' conception of the function and historical knowledge, there is no doubt that it will exert great significance on our teaching method. It can help us not only to predict the difficulties in teaching, but also choose reasonable teaching methods and optimize our process of teaching. From the strange ideas of students, we can get useful information for our teaching. Finally some implications and suggestions to teaching of the concept of function are given in terms of the historical parallelism.
|
PDF Full Text Request