From The "confusion" To "knowledge"

Though the issue of development of cognition is a hot topic ever after the establishment of the Piaget's principles of genetic epistemology, the relative researches in the field of mathematic teaching are rare. The starting point of my research is to construct the analysis framework and practical strategies about the grow of cognition during the mathematic teaching by taking an interdisciplinary view, based on the international research findings and reflections on the native educational theories and the practice of mathematical lesson study.The research mainly takes the qualitative analysis, and quantitative analysis as supplementary method. Firstly, the dissertation indicates the dual dimension to understand the principle of "from puzzle to taste" through combing the findings what other researchers have done about "puzzle" and "taste", and points out the theory basics and practical values of the principle. Secondly, the dissertation builds the process theory of "from puzzle to taste" from process dimension. In this part, the author especially explores the basis and mechanism of "improving of taste", explores the structure and functions of the capacity of taste, and investigates the actuality of the students' capacity of taste, and analyzes the core factors that effect student from puzzle to taste. At the basis of the former part, starting with the absence of taste in the real mathematical teaching life, the dissertation brings up the proposition that the rarest quality in mathematics education is seeking taste for students, and gives some concrete indirections to seek taste. In the last part of the dissertation, the author primarily discusses the incomplete question how the teachers' understanding in mathematical teaching would do "from puzzle to taste", and introduces several ideas of teaching realm.The innovations and main results of the research are as follows:1. Bringing up the genetic principle of "from puzzle to taste" in mathematical teaching, "from puzzle to taste" have two dimensions. The one is process dimension. It includes "puzzle, learning, knowing, taste", which is similar to the four noble truths of "suffering, accumulating, extinction, Way" in Buddhism. Another one is tacit dimension. It is the structure of "from-to" of tacit knowing, accordingly, "puzzle" is equal to the subsidiary awareness of tacit knowing, "taste" is equal to the focal awareness of tacit knowing. From nothing to having will form "puzzle", while from having to nothing need to improve "taste".2. Analyzing the logical starting point and end point of student cognition in the mathematical teaching...