Mathematical Inquiry Learning

The inquiry learning is widely concerned as one of the most popular learning-style at present. The study on the inquiry learning of mathematics with itself characteristic has still been weak. The inquiry learning of mathematics shouldn' t only been considered as "study of special problem" because the learning of mathematical problem solving, of whose course is exploratory, has more specific characteristic. Although the inquiry learning of mathematics with unselfconscious participant universally exists, it shouldn't been widely understood without any limits. The theoretical and practical study on the inquiry learning of mathematics which is based on these phenomena should be considered as the breakthrough of the paper.The paper applies both qualitative researclh and quantitative research. Firstly, it rethinks the theoretical base on the inquiry learning of mathematics; then, constructs a basic theory of inquiry learning with the characteristic of mathematical learning, including a process theory. At the same time, a more comprehensive experimental research has been made. Finally, the degree of the theory about the inquiry learning of mathematics has been enhanced by rethinking.Primary productions and characteristic in the thesis:(1) Research on the characteristic of mathematical inquiry learningThe characteristic of mathematical inquiry learning comprises the deep operation of thought, action of mathematical intuition, more comprehensive inquiry content and the primary form in solving problem, etc.(2) Constructing the process theory of mathematical inquiry learningThe process theory is the main characteristic of this paper. An effective mathematical inquiry learning should include several key factors: process knowledge; mathematical reasoning; self-controlling; process assessment and so on.(3) Primary discoveries in the survey and experimental researchThe primary discoveries in the survey and experimental research consist of: (1) Teachers and students are interested in the inquiry learning of mathematics;(2)There appears some seemly "proper" mistakes when teachers instruct students about action of inquiry learning;(3)Students take part in exploratory activities passively;(4)The learning style based on "collect-inquiry" has great achievements;(5)It is latent practicable to put mathematical inquiry learning into practice.Furthermore, the thesis supplies the methods of students' action and teachers' instruction by the rethinking of discoveries in the survey and experimental research.