First, the design of mathematical knowledge homework

The basic starting point of mathematics curriculum in compulsory education stage is to promote students' all-round, sustained and harmonious development. Students are the main body of learning. Only through students' own' re-creation' activities can all mathematical knowledge be incorporated into the cognitive structure and become effective and useful knowledge. Under this concept, the design of inquiry homework of mathematics knowledge should be based on mathematics textbooks, with further mastering the content of the text as the learning goal and paying attention to the "re-creation" of students' knowledge. Students discover and "create" what they want to learn. The knowledge acquired by students in this way can be deeply rooted in their minds.

The design of this kind of homework is often carried out after the end of the new class through wall newspapers, class meetings, knowledge contests and so on. Feedback what you have learned through homework, so that students can sum up something from it, such as problem-solving format, proof idea, knowledge structure block diagram, or some knowledge of mathematical history. The basic process of this kind of homework design is: asking questions → exploring teaching materials → finding information → reporting results → summarizing and evaluating. In the teaching process, we work with students to stimulate students' interest in learning mathematics for an example or an after-class reading problem in the textbook. For example, after attending Pythagorean Theorem, let the students consult the historical materials about Pythagorean Theorem from books and online in groups, and then exchange and report in the form of theme class meetings at class meetings, and so on. This knowledge-based inquiry homework not only overcomes the shortcomings of previous homework, but also improves students' ability to analyze problems.

Second, the design of math skills homework

Students' mathematics learning activities should be a lively, proactive and personalized process. Mathematics teaching should be closely linked with students' real life, and students can acquire knowledge and cultivate their abilities through autonomy, cooperation and inquiry. In the process of hands-on operation, students are focused, devoted and interested, which enhances their sense of independence and spirit of cooperation. Through observation, investigation, hypothesis, experiment and other forms of inquiry activities, they put forward their own explanations. Students' interest in learning mathematics has been cultivated, and students have changed from passive "asking me to learn" to active "I want to learn".

Skilled homework includes folding, design and hands-on operation. This kind of homework is designed by extracurricular group activities, so that students can put forward their own explanations or design and make their own works through observation, investigation, hypothesis, experiment and other forms of inquiry activities; Its basic process is: asking questions → analyzing teaching materials → looking for information → designing schemes → hands-on operation → reporting results → summarizing and evaluating. Let students design exercises with different difficulty levels and form a question bank, so that students at all levels can get proper exercise training, reflect individual differences and let all students get fresh development. In the teaching process of "cutting a geometry", the author first puts forward questions, so that students can take the initiative to "cut" taro, prepare in advance, cooperate in class and operate it by hand. In the process of operation, a student actually thought of doing the same research on polygons, and as a result, he groped for a conclusion that teachers couldn't think of! This kind of homework design cultivates students' hands-on production ability and creativity.

Starting from practical problems, writing inquiry homework for inquiry learning can cultivate students' innovative spirit and practical ability. After giving the "symmetrical figure", the author puts forward a question: "Planting four different flowers and plants in a rectangular open space, now divide this open space into four pieces according to the following requirements: (1) The whole figure after division is an axisymmetric figure. (2) The shapes of the four figures are the same; (3) The areas of the four figures are equal. Please draw more than four segmentation methods according to the above requirements. " There are no prescribed requirements for these topics. The author asks students to have rich imagination and do it by themselves. Many students make use of the geometric figures around them, putting them first and then demonstrating them, and their achievements are not small. This not only cultivates students' practical ability, but also cultivates students' innovative spirit of breaking away from convention.

Third, the design of practical work in life

"Mathematics comes from life" embodies the basic viewpoint of dialectical materialism, and "serving life" embodies the practical value of mathematics. Modern mathematics stresses that "mathematics comes from life and serves life". The design of new textbooks fully embodies this principle. Teachers should help students design many practical inquiry assignments in life, let students choose their own homework topics, really enter the big classroom of social life, visit and explore the problems existing in real life, and make their inquiry results serve the society.

The design of life practice homework is based on students' existing knowledge, combined with the needs of teaching materials, with practical problems as the background, to create problem scenarios, stimulate students' interest in learning, guide students to gradually form mathematical concepts through the exploration of problems, and cultivate students' ability to solve problems. The basic process of life practice homework design is: asking questions → life investigation → observing records → explaining and discussing → drawing conclusions → expressing statements. The design of this inquiry homework can truly reflect the characteristics of students as the main body.