An Inquiry Into The Concept Of Function And Its Teaching: The New Curriculum

Function is a core concept in school mathematics. However, its teaching is very difficult due to the modern definition based on a mapping of elements from one number set to another. For implementing the visions of new curriculum, we have to re-examine the concept of function in school mathematics and its teaching from the historical development of the concept of function and students' cognitive structure. In this thesis, we shall draw up a spiral picture for the concept of function in school mathematics and use it to analyze the experimental textbooks.The historical development of the concept of function has revealed that people have gone through two leaps to form the modern concept of function. This kind of historical analysis suggests us to set up two levels for the concept of function in school mathematics. Meanwhile we also obtain certain enlightenment about function concept teaching though the contrasting between curriculum and history.Research has showed that students have encountered significant difficulties in the learning of function due to their cognitive development levels. Based on this research, we have made some advices on how to help students remove the difficulties.As teachers often refer to textbooks for content selection and organization of lessons, we have systematically analyzed the content structure of function in the experimental textbooks of the new curriculum. Meanwhile we also come out with several steps of the teaching of the concept of function.Finally we propose a spiral teaching plan from the previous analysis and the APOS theory. We have also made several suggestions for the effective teaching and learning of the concept of function in schools at the end of the thesis.