A Case Study Of PCK Of High School Mathematics Teachers

Teachers’PCK is a unique kind of teaching experience, which is also the core of teachers’ personal knowledge. Moreover, PCK has a very complex structure. Based on literature research, this study develops a theoretical framework. PCK will be discussed from three angles:before class, on class and after class and it is further subdivided into13dimensions.The subjects of this study are three Grade One mathematics teachers from a key high school in Hubei province. One of them is a new teacher who is in the first teaching year; another one is an experienced teacher who has been teaching mathematics for21years; and the last one is a special-grade teacher who has been teaching for23years. In this study, text analysis, classroom observation, after-class interviews are adopted to collect materials. By way of observing and analyzing three teachers’classes of "vector subtraction computing and its geometric meaning", findings of the study can be summarized as follows:1. Differences in before-class PCKBoth the new teacher and the experienced one believe that the most important aspect of mathematics teaching is to teach students how to solve mathematical problems, while the special teacher thinks that it is significant to develop students’comprehensive abilities. By detailed analysis, we can find that teachers’different understandings of educational value directly affect their setting of teaching goals and the arrangement of teaching processes.Unlike experienced and special teachers who can accurately grasp the content of instruction and the difficult of teaching, novice teacher can not easily make this. In addition, three subjects all know how to apply previous knowledge into new ones. And the special teacher always considers the application of present lectures into later use.Novice and experienced teachers usually understand students’individual differences by means of checking their mastering of relevant knowledge. However, the special-grade teacher also pays attention to students’character, interests and hobbies, which are important to students’comprehensive developments. In order to help students of different levels master specific subjects, both novice teacher and experienced teacher are inclined to adequately lower the difficulty of teaching, while the special one always divides the teaching into several layers and adopts different kinds of teaching activities. 2. Differences in on-class PCKThe novice teacher doesn’t realize the importance of timely diagnosis of students’learning. He does not always support students’different solutions to a question and change his design of teaching. However, experienced and special teachers are concerned about students’understanding of relevant knowledge and keep frequent interaction with students. When students make mistakes, teachers can regulate and control classroom teaching flexibly.What’s more, novice teacher and experienced teacher are focused on the learning of mathematical knowledge and developing the ability of solving problems, while the special teacher pays attention to the development of comprehensive ability. In addition, the novice teacher and experienced teacher don’t have the awareness of creating a good classroom atmosphere conducive to teaching and learning activities.3. Differences in after-class PCKIt mainly deals with after-class activities. Firstly, the novice teacher usually checks the effects of learning by means of students’performance in assignments and exams, and makes only minor adjustments to teaching programs. However, teachers with enough teaching experience always make use of classroom interaction, after-class interviews to evaluate students’grasp of knowledge and accordingly change their teaching contents, teaching strategies and so on.New teachers are with an ability of self-reflection, they are humble to ask experienced teachers for advice. However, most of their reflections are on teaching fragments, not on overall situations of mathematical class.4. Ways of increasing teachers’PCKBoth the novice teacher and experienced teacher think that the most important way for improving teacher’s level of PCK lies in:systematic study of textbooks, after-class reflection, daily communicati on with colleagues and organized activities. For the special-grade teacher, besides the above mentione d factors, frequent readings of professional books as well as finishing college entrance examination tes ts are also necessary.5. Ways of increasing PCK of high school mathematics teachersAccording to the findings of this study, suggestions on promoting PCK level of high school mathematic teachers are as follows:(1) Make a systematic study of mathematics textbooks, including mathematical knowledge in elementary, middle and high schools.(2) Regularly organizing professional activities, and communicating with colleagues.(3) Developing good habits of self-reflection after class.(4) Extensively reading educational monograph to increase pedagogical knowledge.