A Study On Pedagogical Content Knowledge Development Of Junior Mathematics Teacher

The development of teacher's knowledge has always been being one important part of teacher's professional development. A mathematics teacher can not be a good one only with enough knowledge on mathematics. He/she is also supposed to possess the knowledge on how to teach the mathematics, i.e. mathematics pedagogical content knowledge. It shows the specialization of mathematics teachers and it is the key characteristics of mathematics teachers, which make them different from mathematicians and the teachers of other projects. As the core of mathematics teachers' professional development, the development of mathematics pedagogical content knowledge affects teachers' mathematics teaching activities and the quality of mathematics classroom teaching. So it is significant to the teacher's professional development.The new mathematics curriculum reform demands a higher requirement to the teachers' mathematics pedagogical content knowledge. But in the process of implementing the new curriculum, the development status of teachers' mathematics pedagogical content knowledge is not so good as it was supposed to be, for it has been ignored in teachers' pre- and pro- service education. Nevertheless, because the concept of mathematics pedagogical content knowledge itself is quite abstract, its connotation is universe and its development mechanism is uncertain, so seldom researches which study teachers' mathematics pedagogical content knowledge provide feasible development methods. Considering that mathematics teachers in China pay attention to long-term learning the mathematics knowledge, Therefore the key research problem of this thesis is how to transform mathematics teachers' mathematical knowledge to their mathematics pedagogical content knowledge effectively so as to promote the development of mathematics pedagogical content knowledge.Basing on exploring the connotation of transforming the mathematics teachers' mathematical knowledge to their mathematics pedagogical content knowledge (shortened "The knowledge transformation" ), this dissertation adopts comparative research method of expert teacher and novice teacher, Combining case study and researches to explore the factors which influence the transformation. And it also try to proposes some strategies to promote the development of middle school mathematics teachers' mathematics pedagogical content knowledge, moreover it adopts the method of micro-experiment to test the effectiveness of these strategies. It gets the following conclusions:Firstly, About the connotation of the knowledge transformation. The transformation from the Teachers's mathematics knowledge, it contains three aspects: about noumenal mathematics knowledge, about the structure and orgnize of the mathematics, about the methodology in mathematics. As the aim of the transformation, Teachers' mathematics pedagogical content knowledge does not simply equal mathematical knowledge and teaching knowledge, and it is a kind of comprehensive knowledge. It mainly contains two categories and five aspects: the knowledge on combining certain mathematics content with teaching (including knowledge about organizing and expressing the mathematical knowledge); the knowledge about combining certain mathematical contents and students (including knowledge about students' cognition characteristics and their misinterpretation, their learning-difficulties, and also the knowledge about strategies of dealing with students' misinterpretation and difficulties). Apparently, there are three parts, i.e. understanding, representation, and adaptation in the process of transforming teachers' mathematical knowledge to their mathematics pedagogical content knowledge. Deeply, the knowledge transformation can be defined as following: on the basis of their mathematical knowledge and teaching experience, teachers assimilate and adapt to their knowledge about general teaching method, students, mathematics curriculum and teaching situation to construct cognition schema of mathematical knowledge teaching.Secondly, About the factors that influence middle school math teachers' knowledge transformation. This research consists of two stages: Stage one, observing 6 teachers' teaching of Translation and Rotation of Graphic, the Property of quadrilateral and Linear Function, videotaping their teaching process and interviewing bother teachers and students deeply, it obtains the main differences on knowledge transformation between new teachers and expert ones. It exhibits the following six facets: the degree of understand and interpret mathematical knowledge , the level of applying teaching tasks , the methods of demonstrating teaching contents , purposes of representation, adjusting the tasks of text book , adaptation of representation. And on the basis of the study on difference, it explores the reasons why there are differences on knowledge transformation between these two kinds of teachers, we can conclude that there are 3 factors leading three different representations between new teachers and expert teachers: the knowledge teachers possess, the ideas teachers hold, the experience teachers have. It is which lay a foundation for the research on influencing factors of the transformation.Stage two, it designs convey questions according to the conclusion of the case study. It finds out the factors that influence the knowledge transformation by interviewing and studying 150 mathematics teachers in 8 middles schools, and it also finds out the extent those factors influence the transformation: As a whole, The best influencing factor is teacher's experience system, teacher's conception system is in the next place, teacher's knowledge system as following. Concretely, there are 3 factors that directly influence the transformation by extent: teachers' mathematics teaching experience, their mathematics view with which they tend to handle mathematical problems, and the transfixion degree of their understanding about mathematical knowledge. Furthermore, there are more 5 direct factors: teachers' own teaching efficacy, teachers' general efficacy, and the width of teachers' understanding about mathematical knowledge, and teachers' mathematical view of instrumentalism orientation tendencyThirdly, About the strategies of developing middle-school mathematics teachers' mathematics pedagogical content knowledge. Researches on the connotation and the influencing factors of the knowledge transformation provides important evidence for construction of transformation strategy. Combining with existed strategies on developing teachers' specialization and applying the cognitiveload theory, this dissertation try to propose the strategy------"Action Learning based on Cmap" ,ituses the concept map, pays attention to adjusting of teachers' knowledge system, concept system and experience system generally, pays attention to "operation-schema" activity mode, realizes combination of externalization and internalization of mathematics teaching knowledge, realizes integration of self-reflection, partners' mutual aid, and specialization guidance. It also carries on micro-experimental study to verify that this strategy can improve the transformation and promote the development of mathematics pedagogical content knowledge.The creative points of this dissertation are in the following: It is the first one that suggests to study the development of teacher's mathematics pedagogical content knowledge through translation from their mathematical knowledge to it. This is a new research perspective; this study adopts Grounded Theory method to try to explore the factors that influence the knowledge transformation , applying the Cmap method to analysis and promate the transformation; and try to propose the strategy of developing middle-school teachers' mathematics pedagogical content knowledge—"Action Learning basing on Cmap".