Study On The Concept Teaching Of Function In Senior Mathematics

Function is a core concept in senior middle school mathematics or even, more generally, mathematics. In college entrance examination, test on function accounts for a high proportion. Teachers in practice tried all the way they could--from the particular to the general, precede step by step, increase the difficulty gradually--to help the students to understand this concept. However, the students struggled a lot in understanding it.What is the main reason for the difficulty in studying this function chapter and in which way does the difficulty show up? For teachers what kind of strategy should we choose to relieve these difficulties? We aim to answer these problems in this thesis.Our key method relies on a comparison on the function concept between junior middle school and senior middle school. We use examination, interview and investigation through class to justify a better method for teaching the function concept. We have thus a fundamental research.Our researches reveal that lots of students did not master the concept of function well in their junior middle school. They are not fully aware of the variables, the one-to-one rules, thus it is difficult for them to build up the relationship between the graph and the formula and in addition it is hard for them to understand the abstract quantitative relations without the actual background. Therefore they would feel helpless and no sense of achievement.We conclude that the main reasons for the difficulties are:(1) The function itself is a complicated knowledge system. Students are not fully capable of the set theory, thus they don’t understand the mapping problem fully.(2) Students are not fully mature in their thinking level. They are not capable of the assignment using dialectical thoughts and change with time viewpoints.(3) Students care only about the ability of solving the problems, they ignore the essence of this concept.In view of these problems, we try to give some strategies according to our practice and our discussions, which will help the students or in some sense teachers to strengthen their understanding.First, it is necessary to help the students to combine their knowledge with the new ones, and rebuild their cognition structure. We need always remind them their junior middle school knowledge with the new ones. Meanwhile we should be fully aware of our aims and tasks.While teaching, we should pay attention the state of the students. We should also focus our attention on all the students of different levels. In addition, we should pay attention to the typical examples and the teaching of the symbol language so as to make students feel the inner beauty of mathematics. The use of the blackboard is always needed.We also note that teachers should try hard on cultivating students’ good habits. We should insert some contents like history of mathematics and so on which will motivate the interest of the students. It is necessary for teachers to pay attention to their qualities and use the information technologies; these means will help students to increase their efficiency.