Heuristic Mathematical Teaching And Research

Heuristic teaching as the very perfection of Chinese traditional teaching thought, has been gradually improved enriched in many successive studies. However, concrete studies related to mathematics heuristic teaching are lacking because of its own characteristics. Based on the achievements of heuristic teaching and the double principles of correspondence, between teaching and learning, between teaching and math teaching, this thesis aims to give theoretical build and practical probe according to the study of math classes.The author makes studies from the following perspectives by using theoretical and practical methods, qualitative and quantitative methods. First, the results are given a summarization about general heuristic teaching and mathematics heuristic teaching. And the theoretical and practical basis of mathematics heuristic teaching are thought over in advance according to theory ,questionnaires and class observation. Second, in view of the features of mathematics subject, some aspects of mathematics heuristic teaching are researched and built , goal , meaning , basic characteristics , conditional , strategies, heuristic factors. Then,qualitative and quantatitive analyses are given systenaticly of the features and functions of heuristic guide talking and the real teaching situation of using the talking in class.And it is tried to build metacognitive guide talking chain with grades in class.It is also explored exterimentally to use metcognitive guide talking to inspire students to produce cretive information. Finally,some suggestions are put forward to about the questioning and strategies of heuristic teaching.Some important results are gotten about mathematics heuristic teaching:1. The study of the features.The features includes the following aspects: stimulation of teaching scene,the building of math learning,the structurization of mathematics knowledge and the process of mathematics teaching2.The building of conditional systems.Many factors restricts the implementation of mathematics huristic teaching, so conditional systems are built to make it have an effect.The building of conditional about stimulation of teaching scene,the building of math learning,the structurization of mathematics knowledge and the process of mathematics teaching .3. The study of basic strategies about mathematics heuristic teaching. 4. The analysis of factors about heuristic .Many factors are analyzed systematically, the aim, what to learn,how to learn and how to inspire.5. The reasonable utilization of heuristic guide talking.The study of the features about heuristic guide talking.Metacognitive guide talking refers that teachers give some hints to students'cognitive activities, that is of great function,making clear cognitive activity,guiding thinking strategies,promoting transformation and stimulating students'self-consciousness.The author gives concrete analyses of the usage of metacognitive guide talking for 27 class cases and tries to build guide talking chain with grades.6. Many results of investigation and experimentation.