A Research Into Mathematics Teacher's Instructional Decision-making

The effectiveness of classroom teaching determines the degree to which the curriculum is implemented as well as the quality of talents cultivating. The key of the mathematics curriculum reform lies in the implementation of the curriculum; teacher's teaching behavior affects directly the effectiveness of the implementation of the curriculum, while the decision-making is a determinant factor affecting the teaching behavior. Therefore, the quality of the mathematics teachers' decision-making determines the level of curriculum implementation and the quality of talents cultivating. Since 1970s, studies on teachers' teaching decision has become a central content in the field of teacher and teaching study abroad, and is thought of as the direction of future study. However, the study on teachers' decision-making, especially that of the mathematics teachers just starts at home, the insufficiency of relevant study will inevitably affect the effective teaching in mathematics classroom and the implementation of the curriculum in either a direct or indirect way. Thereby, it is necessary and urgent to study the mathematics teachers' decision-making.Decision-making is the teacher's implicit cognitive thinking process, researchers can not fully probe this specific decision-making process without "entering" the teacher's mind through "internal understanding". The basic hypothesis of the qualitative study is that this internal understanding enables a deeper understanding on teachers' teaching behavior than the surface behavior study, the regular quiz with paper and pen and the standard interview. So to speak, the hypothesis of the qualitative study is in correspondence with the major presupposition of teachers' decision-making, therefore the former becomes the necessary choice. On the other hand, the case study is one of mathods of qualitative study. By probing case system whole, digging representative case's intrinsic characteristic(intrinsic case study) or inducing common conclusion from instrumental case(instrumental case study). Based on the study pathway of theory grounded, instrumental case study is adopted in this study. Namely, through the analysis of case data, a general conclusion is reached, hoping to be generalized or have implications to other cases.This research adopts specific methods as: literature analytical method, oral report method, classroom observed mathod, interview method, induced analytical method, comparatively analytical method, and so on.This research firstly makes a trace study on the specific process of the decision-making of case teaching plan from three aspects, namely, the analysis of the oral report of the case study, the after-class interview and the researchers' observed material. The following preliminary conclusion is reached: firstly, teaching beliefs, ways of thinking, and teacher's knowledge are the main influential factors of teachers' planning decision-making. Secondly, the subject's thinking mode on planning decision-making has the feature of "scrambles" and "linearity". it is proposed that mathematics teachers' thinking in the decision-making of teaching plan should switch from scrambling thinking to apprehensive thinking, and from linear thinking to creative thinking.Meanwhile, the present research also makes a follow-up study on the specific process of the interactive decision-making of the case study from different perspectives, such as the classroom record, after-class interview, students' interview, oral report, researcher's observed material and the production material. The following preliminary conclusion is reached: firstly, teaching beliefs, ways of thinking, teacher's knowledge and classroom context are the main influential factors of teachers' interactive decision-making. Secondly, the subject's thinking mode on interactive decision-making has the feature of the "forced landing" and "random". it is proposed that their thinking of interactive decision-making should switch from forced landing thinking to ascending thinking, from free thinking to random thinking.Based on the two questions and in combination with literature review, the subject's "domestic conception" and "the focus of the teaching factors" are further discussed. The subject's belief system is reflected from the perspective of decision-making while such material as the oral report of the case, after-class interview, and comprehensive interview is analyzed into categories. meanwhile, the main factor of instructional decision-making are described, namely the relationship among teaching beliefs, instructional thinking mode, teacher's knowledge, and real context. It is put forward that the subject's instructional thinking mode has the characteristics of dominance, independence, and ignorance of students' thinking process, which are reflected by the system of teaching beliefs.From the studies mentioned above, this dissertation made further theoretical investigation on relevant issues, and came to the following conclusions:First, Mathematic teachers' instructional thinking mode is an important factor in decision-making. It is the channel for input and output of teaching beliefs, the framework of teachers' knowledge. It interacts with the real context, bridging teachers' implicit teaching belief and their knowledge, and thereby, it influences teachers' decision-making and the formation of teachers' specific teaching behaviors.Second, Mathematic teachers' beliefs is supposed to transform from being knowledge transmission-based to the integration of knowledge transmission and the development of mathematics thinking-orientation, the knowledge transmission orientation firmly holds the basic teacher-standard, conservative, static and restrictive point of view, while the latter with a free, open, dynamic, child-based, and development-directed point of view. While teachers who believe the integration of the knowledge transmission and the development of mathematical thinking should bear in mind the two basic beliefs that they should help children learn mathematics and teach mathematics for improving their matjematics thinking mode. They can set up rich teaching plans and present them by means of appropriate situation to arouse teachers' suspicion and way of critical thinking.Thirdly, Mathematic teachers' instructional thinking mode should transform from "the thinking mode of knowledge-giving" to "the thinking mode of pedagogy". The former has the characteristics of subject-centeredness, emphasizing mastery of knowledge, considering knowledge as absolute truth, implementing academic elitism, considering teachers as professionals, adopting one-way transmission of teaching, having answers before raising questions, and teachers having the power of decision-making. The latter has the characteristics of learning-centeredness, students' self-construction, emphasis on students' development of intelligence, pursuit of broad and balanced development, considering teachers as helper and facilitator, encouraging critical thinking and experiential learning as well as the share of decision-making between students and teachers. Mathematic teachers with educational thinking mode should, based on the characteristics of mathematic instructional thinking mode, try to find the balancing point between mathematic thinking and thinking of mathematic teaching realizing the transformation of mathematic thinking from process mode to generation mode. This transformation can be realized by setting up training course on the basis of mechanism of generation thinking mode as well as by achieving balance and transformation between mathematical thinking and mathematical teaching thinking.To sum up, the significance and innovation of the present dissertation are as follows: firstly, as far as the choice of the topic is concerned, there are few relevant literatures about mathematics teachers' decision-making as well as teachers' decision-making in China. So to speak, this is the first doctoral dissertation on the study of mathematics teachers' decision-making. Secondly, with respect to the research methodology, the present dissertation adopts a qualitative case study, this is very rare in the field of subject teaching, particularly that of mathematics teaching. Thirdly, as for the content and conclusion of the dissertation, the present study proposes that instructional thinking mode is an important factor of mathematic teachers' decision-making, makes a further discussion about the relationship among the four major factors of mathematic teachers' decision-making, namely, teaching beliefs, instructional thinking mode, teachers' knowledge, and real context. A theoretical framework is proposed to evaluate planning and interactive decision-making. Besides, detailed content and means of the transformation of mathematic teachers' teaching beliefs and instructional thinking mode are put forward. Those researches enrich the mathematic theories in China.The following subjects will be our foci in the further study: influential factors of mathematic teachers' decision-making, the evaluation of mathematic teachers' decision-making and the theoretical framework of mathematic teachers' decision-making; as to the pre-service, in-service, and post-service training of mathematic teachers, emphasis shall be placed on the operable strategies of the transformation of teaching beliefs and instructional thinking mode as well as the comparison of decision-making between teachers under different background.