Comparative Study On Introduction Of Function And Mapping In High School

The knowledge of function is one of the most important contents in the mathematics teaching in high schools. As the rudimentary and knowledge of function, the introduction of function and mapping has a direct impact on the students'understanding and mastery of function. Therefore, it should be given sufficient attention. The thesis takes the teaching of the introduction of function and mapping as an example. By summarizing the learning situation and thinking mold of the contemporary high school students, comparing the difference of textbook in new version and old one, and doing some relevant comparative study of teaching practice, it's expected to draw some useful conclusions, achieve the goals of helping teachers understand new curriculum rationale thoroughly and utilize materials in an active way, so that students would have a better understanding and application of function.The main research contents and conclusions of this thesis are summarized as follows:Firstly, is the research of the current situation of function and mapping teaching in high schools. By means of questionnaires, discussion and communication, it is discovered in the research that there are certain difficulties existing in teachers and students, for instance, the difficult mastery of the new curriculum standards and the difficulty of teaching, the contradiction between cognitive habits of high school students and modes of teaching, students'confusion of the relationship between function and mapping, so on and so forth.Secondly, is the research on measurement of students'learning effects. By reading references, doing research, teaching experience of my own, five metrics of the learning effects of high school students are presented as follows: test scores, classroom responses, feelings of individual students, following-up impact of learning, and personal ability.Thirdly, function and mapping are compared in textbooks of new version and old one. By doing research on the new teaching rationale, curriculum standards and textbooks, it is discovered that the option of teaching methods should depend on the actual situation. New teaching rationale and new curriculum standards require teachers to utilize textbooks based on the actual situation, since textbook is only a reference tool for teaching, so rigid use of the textbook is not desirable. The same goes to the function teaching. Teaching effects would be different when using different methods of the introduction of function and mapping. What is suitable for students'learning and development is the best.Fourthly, is the comparative study on the effect introduction methods of function and mapping have on teaching effects. By teaching and researching, it is found that to different levels of students, the introduction of function and mapping impact on them in different ways. To better-than-average students, in the sequence of introducing function first, followed by mapping, it is conducive to develop students'innovative thinking. While to students who have relatively weak learning base, as they don't have deep impression on function learning in junior middle schools, there is little meaning of the introduction methods of function connected to the function learning in junior middle schools. In addition, majority of students experienced frustration on learning function in junior middle schools, thus developing the idea that function is difficult to learn, and having the fear of learning function. Therefore, it is not suitable for them to teach function in the sequence of introducing function first, followed by mapping, while the reverse way has some advantages, that is teach function in the sequence of introducing mapping first, followed by function, to transfer the understanding difficulty of function to the simple and vivid mapping, which is helpful to reunderstanding of function. So, that is the way suitable of this kind of students. By analyzing, when explaining function and mapping, flexible introduction methods should be considered to different levels of students in terms of level teaching.