1. Conditions, contents, strategies and methods of active learning through mathematics. Research related issues, and extract effective and operable strategies and methods of active learning. 2. Through the study of mathematics learning before class, stimulate students' interest in learning mathematics, stimulate students' enthusiasm for autonomous learning, and improve classroom teaching efficiency. 3. Through the research of active learning in mathematics, cultivate students' habit of active learning and ability of autonomous learning, and lay a good foundation for students' follow-up learning. 4. Study the relationship between active learning and mathematics classroom teaching to improve the efficiency of classroom teaching. 5. Through the research of active learning, guide teachers to establish a big teaching concept, make the classroom contact with life and society, and build a diversified and three-dimensional teaching network. Thirdly, the theoretical basis of the study is 1. In the teaching of Vygotsky's "zone of proximal development", it must be noted that children have two levels of development: one is the current level of development of children; The other is the level of development to be achieved. The difference between these two levels is called "zone of proximal development". 2. Modern Constructivism Theory According to modern constructivism theory, a learner's learning of mathematics is not taught by teachers or others, but an active construction process based on his existing mathematical experience and cognitive structure. Before learning, any learner does not walk into the classroom with a blank head, but starts a new study with his "unique mathematical reality". Pre-learning is the subject's active activity, and its value lies in first enabling students to gain "meaningful experience" in individual active thinking activities, and then transforming vague, difficult and contradictory situations into clear, definite and harmonious situations through classroom learning. 3. The Basic Concept of Mathematics Curriculum Standards "Mathematics Curriculum Standards" points out that mathematics teaching activities must be based on students' cognitive development level (the nearest development area) and existing knowledge and experience foundation (knowledge base). The content of students' mathematics learning should be realistic, meaningful and challenging, which is conducive to students' active observation, experiment, guess, reasoning and communication. The research of mathematics proposition strategy is to meet the diverse learning needs through various activities closely related to students' life, such as observation and discovery before class, life exploration, hands-on operation, investigation and interview, which shows that mathematics learning activity is an active, vivid, positive and personalized process. Four, how to write the basic requirements of pre-research-simple, fundamental, open and simple. Research questions should be simple, design should be easy to learn, and at least 70% of the content can be completed by students. Not at all. Grasp the root of knowledge and set up the learning process around the growing point and key content of knowledge. Open. Research questions should be open, so that all students can get different development in the learning process. Compilation method: first of all, we must grasp the roots. From teaching materials (textbooks), study teaching materials and clarify knowledge clues. Then solve simple problems. Find the thread of knowledge clues, study students' "zone of proximal development", and see the foundation that students already have to learn this knowledge, so as to solve the problem of making students "eager to learn". Five, the characteristics of pre-research and study plan are different, the creation situation is different, the premise evaluation is different, and the self-study outline is different.