Pre-service Secondry Teachers’ Development In Basic Knowledge And Skills For Teaching Mathematics

Professional standards of mathematics teachers have become more demanding all over the world in the new century since mathematics teachers play an important role in providing learning opportunities for students" learning. Consequently, mathematics knowledge for teaching became a matter of increasingly wide concern among mathematics teacher educators. At the same time, the traditional concept of classroom teaching skills was gradually replaced by procedural knowledge or practical knowledge.The term of Basic Gong for Teaching Mathematics (BGTM) was used in this study to describe the explicit and tacit characteristics of teachers’knowledge simultaneously and to reflect the interaction between theory and practice in the professional development of mathematics teachers. Moreover, the term with the word "basic" focused on the most important knowledge and skills for teaching mathematics, which should be emphasized at the beginning of teacher education and be progressing throughout the professional career of mathematics teachers.In this study, four pre-service secondary mathematics teachers’teaching behavior in three phases of teaching practice was analyzed to explore the content and stages of the development of BGTM. The research question was:What was the performance in BGTM in the mathematics lesson beginnings by pre-service mathematics teachers during three phases of teaching practice: regular micro-teaching, micro-teaching guided by expert mathematics teachers from high school, and student teaching? What changes occurred in those pre-service mathematics teachers" BGTM in the mathematics lesson beginnings?A pilot study on the common features of the lesson beginnings by the expert secondary mathematics teachers was firstly done to establish the analysis framework in this study. And then qualitative methods were used to analyze the videos of the lesson beginnings by the pre-service mathematics teachers.From the study, it could be found that there were possibly three levels in the development of pre-service secondary mathematics teachers" BGTM and two steps of changes had taken place during the process. The first change was from "unconscious’" to "conscious", the second change was from "unclear" to "relatively clear". The former provided the explicit orientation of the pre-service mathematics teachers" reflection and thinking, and the latter seemed difficult due to the lack of mathematics knowledge for teaching. The main findings of the study were as follows:For the BGTM of making connections between prior knowledge and new knowledge, at first, the teacher did not present the connections between prior knowledge and new knowledge, so that the teaching process was obscure, disorderly or disconnected; next, the teacher paid attention to the connections between knowledge and tried to make the teaching process more orderly; and then the teacher tried to use appropriate organization and explicit discourse to show the connections; the long-term objective was to clearly understand the connections and present them coherently.For the BGTM of explaining the essential reason for learning, at first, the teacher did not attend to the reason for learning a specific topic; next, the teacher paid attention to the reason for learning and tried to create problem context to show it; and then the teacher tried to create more appropriate problem context to present the reason for learning from the perspective of the essence of mathematics; the long-term objective was to deeply realize the essence of mathematics and appropriately present the essential reason for learning.For the BGTM of inspiring thinking through appropriate problems, at first, the teacher did not consider the formation process of knowledge; next, the teacher paid attention to the formation process of knowledge and accordingly design the learning tasks; and then the teacher tried to pose appropriate problems to inspire the students’ thinking; the long-term objective was to use progressive problems to inspire the students’ deep thinking of the key ideas in the lesson.For the BGTM of attending to precision in mathematics communication, at first, the teacher did not address the errors which the students tended to make; next, the teacher paid attention to the errors which the students tended to make and tried to help them attend to precision; and then, the teacher tried to keep precision all along the teaching process and help the students attend to precision as well; the long-term objective was to keep precision and attend to precision all along the teaching process.In addition, the findings about the development of the pre-service secondary mathematics teachers’BGTM convinced the effect of the courses and practice regarding to mathematics pedagogy in mathematics teacher preparation programs. The individual differences in the pre-service secondary mathematics teachers’BGTM implied that learning mathematics, observing exemplary lessons and practicing with guidance were likely to be crucial for pre-service mathematics teacher education. The findings are also beneficial to clarify the objectives, the key points and the difficult points of the development of pre-service secondary mathematics teachers’BGTM.