Study On The Development Of Mathematics Instructive Beliefs Of Student Teachers

The research on teacher education is a hot problem which is an international focus, and also is a stubborn strategy problem normal university has to confront with. Some nations tried to search for some efficient ways to give their student teachers some foundational abilities and capacities. Naturally, teacher educators headed to train each student teacher to be an expert, but most research on novice and expert emphasized the general characters about class management or teaching theory, few on teacher's subject knowledge and beliefs of teaching and learning. Some research wanted to tackle with problem such as knowledge based on student teacher's professional development from cognition science, they found way in which student teachers constructed and developed knowledge of teaching and learning from social constructivist perspective, other studied subject conception, self identification of teachers, and their impact with instructive efficiency from feeling and attitude. The research showed people for beyond to get the answer in this field. Most of the research focused on describing current condition and compose assumption. Of course, there were some valuable works, but how to develop student teachers' professional knowledge and beliefs is still a problem.With this background, this paper posed this problem "could student teachers do efficiently develop their belief system of teaching and learning while they learning to teaching in the learning and practice?" This problem could be divided into two sub-problems: (1) What was character of belief system of what mathematics conception was, how to pupil learn mathematics, and how to teachers teach mathematics, and what function do the experiences of student teachers studying basic mathematical courses and mathematics educational course in normal university exert to their initial beliefs and teaching practices? (2) How did student teacher 'instructive beliefs exert (how to change and develop), what trait did the level of belief development present, which factors did affect development of belief levels?Based on investigating and surveying the instructive beliefs of 79 student teachers, and using instructive beliefs questionnaire of student teacher and learning experiences hint survey, Based on interview (instructive action rank table) and inquiry (a series of questionnaires of student teachers learning to teach), by tracing to look into teaching notes and instructive records of the 5 student teachers, we drew the following conclusions.(1) Instructive beliefs of student teacher were found on the foundation belief of how to learning, other beliefs of teaching and mathematics nature derivated from the belief their learning at some degree which lay in the central palace, other lay at the edge and found on the learning experiences of own feeling-based. The instructive beliefs of student teacher lay between mathematics was composed of many disorder regularities and operations which was asked coherent and understanding, both were not mutually repelled, understanding could acquire from mastering regularities and, concepts, methods, then gained some kinds of relations.(2) The instructive theories and styles of previous secondary school teachers and current university instructors seriously affected the learning and life experiences of student teachers, production and consolidation of instructive beliefs and mathematical cognitive constructions, and learning styles not being linked up between secondary school and college restricted the well-being development of the instructive beliefs about advanced mathematics, and reinforced the impact to learning to teach mathematics. Production and development of instructive beliefs of student teachers were close together with model and standard of teacher cultivation; student teachers were alive and learning under the impact of school culture and social settings.(3) Development levels of instructive beliefs of the 4 student teachers displayed an unstable, chaotic and weak following orders, student teachers hasn't received reflective relativism belief level, all almost oscillated between the isolationism and the naive idealism, in that the secondary school and the college have not given student teachers the more challenging, reflective learning resource, theories and chances. Instructive beliefs of student teacher on mathematics nature and how to teacher teach mathematics have not apparently changed and developed, but belief of how to pupil learn mathematics slightly has had some changes, student teacher showed learning belief from taught pupil how to learn mathematics rather than themselves.(4) Their instructive beliefs emerging at college showed no differences from their instructive action in the teaching practice, and both were teacher-centered and traditionalism. However, as soon as they got abundant and diverse experiences, student teachers could consider pupils' difference of learning styles and diversity of cognitive ways into their teaching plans and actions, but these actions and thoughts lied in an unstable state, when they could not control and understand easily concepts, paces, and difficulties of those taught contents and knowledge, beliefs of pupil investigating by oneself and constructing mathematics which should be needed and imposed by those course reform theories and practices didn't appear at large at lesson.Lastly, according to our conclusions, and conditions, objectives, mentoring ways, and models of student teacher training of current teacher education at college in China, we raised a three-dimension development model of instructive action and beliefs to practice progressively for teacher educators at each educated stage of student teachers learning mathematics and teaching.