Homework is not only an important way for students to master and consolidate the knowledge, skills and methods they have learned, but also an effective way to train students to use the knowledge, skills and methods they have learned to solve new problems. Homework is an activity for students to deepen their understanding of what they have learned, expand their learning content and realize autonomous learning. Homework should be conducive to hierarchical guidance, cultivate students' awareness and ability of exploration and innovation, and pay attention to students' personality development. Based on the above reasons, I design my math homework from the following angles:

First, design homework related to mathematical culture (history of mathematics)

One of the values of mathematics education is to convey mathematics culture to students and feel the charm of mathematics. In teaching, I often design and collect "History of Mathematics" homework according to the content of teaching materials, and students can finish it through the internet and books. This kind of homework, any student, especially those with learning difficulties, can complete it smoothly through their own efforts, and even do it well. For example, when learning the content of Pythagorean theorem, let students consult the proof method of Pythagorean theorem and related mathematical history; When learning the content of plane Cartesian coordinate system, let students collect the stories of mathematician Descartes, improve students' interest and enhance their cultural literacy.

Therefore, in order to understand the intention of textbooks, teachers should not only attach importance to the teaching of mathematical knowledge, but also attach importance to mathematical culture, feel the influence of mathematical culture and improve students' cultural literacy.

Second, design practical work (hands-on operation)

The new curriculum standard points out that "according to the specific teaching content, mathematics teaching should pay attention to enabling students to gain direct experience as well as indirect experience, … to gain basic knowledge, basic skills, basic ideas and basic activity experience of mathematics, thus encouraging students to study actively and individually, and constantly improving their ability to find, ask, analyze and solve problems." Among them, the experience of basic activities, including hands-on practical activities, combines the teaching content, designs practical assignments, and mobilizes students to actively participate. For example, when teaching "Data Collection and Arrangement", according to the students' situation, I arranged the homework of designing questionnaires, making preview courseware and choosing suitable occasions and questions as a group for actual investigation. Through such homework, students' cooperative consciousness and practical ability have been improved.

Third, the design expansion work (expansion and improvement)

In mathematics learning, students' lively and personalized learning can fully mobilize their enthusiasm for participation and activate their thinking. Designing and compiling math problems is a good attempt. For example, I made good use of such a topic when I studied the square difference formula of algebraic operation.

The title is this: "Calculation". With the joint efforts of everyone, there are two common ways to solve this problem. In order to consolidate the method of solving problems, I did not repeat several similar questions for students to imitate the answers, but designed an assignment: "Make up several similar questions and answer them." Unexpectedly, the students' enthusiasm is very high, and many students can answer the questions themselves correctly. One difficult topic was consolidated, the students happily showed their own topics, and everyone's wisdom was displayed.

Fourth, design learning methods and refine homework (accumulation of mathematical thinking methods)

Mathematical thinking method is the essence of mathematics, and the understanding and application of mathematical thinking method is an important content for students to continue their study in the future. In teaching, in addition to teachers' infiltration in the classroom, students can be guided to sum up basic mathematical thinking methods, and more importantly, students' habit of induction can be cultivated and their ability of induction can be improved. You can design mathematical ideas and methods to accumulate such homework. For example, after learning the knowledge of function once, let the students illustrate what mathematical ideas and methods are used through examples. In geometry teaching, students are required to come up with several different methods to record and show a theme. This kind of homework can reflect students' personality, especially stimulate excellent students' enthusiasm for exploration and improve their mathematical ability.