Reflective Teaching Of Mathematics

Reflective teaching rose in the 1980's. Researchers, teachers and students have been experiencing development of ability and maturation of thought in reflection. At the same time, the teaching theories have been enriched and developed continuously. With the existent researches as basis and with the planar principles of "teaching corresponding with learning" and "teaching corresponding with mathematics" as base points, reflective teaching of mathematics is making theoretical construction and practicing exploration through mathematics lesson study activities and has formed characteristics of reflection and teaching pattern and enriched the theory concerned.This dissertation adopts the method of combining theoretic study with practicing study and qualitative study with quantitative study. First, the dissertation trims and analyzes the existent study results of common reflective teaching and reflective teaching of mathematics. Based on these results, the dissertation defines the purpose, methods and pivotal questions of reflective teaching study of mathematics. Second, the dissertation borrows the corresponding theories of philosophy, psychology, didactical theory, sociology, and so on and constructs theory foundation of reflective teaching study of mathematics. At the same time, the dissertation collects a great deal of cases of reflective teaching of mathematics from practicing activities of questionnaire inquiry and lesson study. Based on these productions, the dissertation explores the meanings of reflection and essences of reflective teaching and discusses the mechanism of reflective teaching from three aspects: functional elements, functional steps and functional pattern. The dissertation makes varied teaching projects about mathematics concepts teaching, mathematics question-resolved teaching and mathematics reasoning activities. Then, the dissertation does corresponding case study of reflective teaching of mathematics based on these projects. At last, based on the results above, the dissertation reflects reflective teaching study of mathematics and pointes out the deficiencies and developing trends. The main results are as follows:1. Defining the connotation of reflective teaching of mathematicsIn the mathematics classroom, teaching mathematics knowledge is the basic goal. The teacher leads students to make use of reflection to study mathematics and construct new knowledge and methods and also develop students' reflective abilities.2. Establishing the characteristics of reflective teaching of mathematicsThe characteristics are reflective, retrospective, introspective, investigating, countering, researching, and constructive and so on.3. Constructing the mechanism of reflective teaching of mathematicsReflective principle of "middle of the road", reflective course of "high-point" and reflective steps of "exploration in the labyrinth" are established with detailed illumination through lesson case into each step.4. Establishing three patterns of reflective teaching of mathematicsBased on the characteristics of mathematics teaching, three teaching patterns, such as "continual-questioning reflection", "productive reflection" and "interacting reflection", are established to improve the operation quality of reflective teaching of mathematics.5. Doing the case study of reflective teaching of mathematicsThe case studies are done of different teaching contents, different teachers and different students, which surrounded mathematics concept, mathematics question-resolved and mathematics reasoning to indicate that reflective teaching of mathematics can promote students' reflective learning of mathematics and to improve the students' reflective abilities with the deficiencies in teaching practices pointed out at the same time.