Einstein said: "When you forget all the knowledge you have learned, the rest is education." This sentence means that our mathematics teaching should change from knowledge-based to student-based. This is the case in classroom teaching, and so should the homework as one of the feedback classroom teaching effects. However, the repetitive and single-form homework on weekdays makes students become "mechanics", and students' curiosity, thirst for knowledge and creativity are restrained. Therefore, as a front-line teacher, while constantly reforming classroom teaching, we should also change the original concept of homework and realize that homework should also conform to the requirements of curriculum reform and present new forms.

This requires teachers to guide homework reform with the concept of new curriculum standards, and improve the design concept of math homework from the perspective of paying attention to people's future development, personality development and all-round development. Realize that homework is not just doing exercises, but also doing mathematical activities related to exercises, so that students can explore and create simulated knowledge through their own personal experience and feelings. Only by making homework a carrier for students to understand life, society and science, and a place for students to develop their potential, embody their personality and cultivate their abilities, can homework really play its best role. Therefore, the author believes that the new concept of homework that matches the new concept of classroom should be open, holistic and diverse. That is to show the open content in diversified forms and adopt effective strategies to promote the overall optimization of knowledge. So how to cut into diversified homework design?

First, operational homework-developing students' comprehensive ability

This kind of homework mainly comes from examples and exercises involving graphics and geometry. The content of geometry knowledge in primary school mathematics is mainly divided into two parts: plane figure and three-dimensional figure. When learning the position, characteristics and formula calculation of graphics, it is often necessary to make some teaching AIDS and learning tools to help students understand. What I got from the paper is superficial, but I don't know how to do it. Students can make their own works, build a bridge between materialization and internalization of knowledge structure through personal experience, and show their works in class. This is not only the application of knowledge, but also the all-round development of ability and emotion. This kind of homework can be subdivided into manual, art and puzzle homework.

1. Manual operation

When completing such topics, teachers should give students some enlightening hints, such as which convenient production materials can be selected and general production requirements. For example, before learning to "know the corner", let students make a model of the corner by hand. Materials can be toothpicks, sticks or hard paper strips, and experience the characteristics of the corner by hand.

2. Art homework

When completing such problems, teachers can ask students to prepare a blank sheet of paper of their own size. And remind you to pay attention to determining the proportion when drawing. On the basis of drawing correctly, you can also play freely according to your personal preferences. For example, after learning the direction and location, the homework is: design a guide map of the park and draw the route between the main attractions and attractions. As a result, the students not only completed the requirements specified by the teacher, but also drew humanized facilities such as convenience stores and toilets. So as to truly experience the application value of mathematical knowledge in the process of completion.

3. Puzzle homework

When completing this kind of topic, it is required to spell first, and then combine the spelling process, paste the spelled work on paper or describe it on paper with mathematical language or symbols, so as to leave traces of process knowledge. For example, after learning the spelling of graphics, the homework is: please cut and paste the spelling as required, paste the results on paper, and write the conclusions you find. By trying, the students clearly found the relationship between numbers.

Homework like this can help students understand things in operation, better understand physical knowledge and develop students' spatial concept.

Second, practical homework-cultivate students' sense of numbers

This kind of homework mainly comes from examples and exercises involving quantity and quantity. The main contents of quantity and measurement in primary school mathematics are: length unit, weight unit, time unit, area and unit of volume. The advancing speed of these measuring units is not exactly the same, some quantities are abstract, and students' perceptual knowledge in this respect is poor, so it is difficult for students to correctly establish the concept of quantity. Therefore, the teacher's oral preaching or a lot of practice can't make students really understand and experience. Therefore, we need to create practical conditions, provide practical ways, and strengthen our understanding of ideas through personal experience. When designing such problems, teachers are required to have a correct, clear and complete understanding of these concepts. When learning this kind of knowledge, students should practice for everyone, practice more, strengthen practice and increase their feelings. For example, after learning grams and kilograms, the homework is: "Weigh different objects, estimate them, weigh them, and feel the mass of 1 kg and 1 gram." After learning the knowledge of kilometers, let the students walk around the 400-meter playground for two and a half times. Students naturally experience knowledge and promote understanding through personal practice.

Homework like this aims at helping to understand knowledge, feel the connection between mathematics and life, and appreciate the application value of mathematics with various forms of activities as the carrier.

Third, the investigation homework-to cultivate students' statistical awareness

This kind of homework mainly comes from statistics and probability in examples and exercises and some small surveys in other contents. The core goal of primary school mathematical statistics course is to cultivate students' statistical concept and random consciousness of analyzing problems through data. In the process of statistics, students can understand the formation of knowledge and feel the value of mathematical knowledge.

When designing such problems, teachers should have a correct understanding of relevant statistical professional knowledge and pay attention to the scientific nature of knowledge. Moreover, we should consider some interference factors that may appear in the process of students' statistics in advance, give necessary hints, and eliminate irrelevant factors that affect the acquisition of correct knowledge. For example, after learning to express the quantitative relationship with letters, the homework is to ask students to investigate the height and weight of their parents and express the standard weight of adult men and women with formulas containing letters. And calculate the weight of mom and dad, compare with the standard weight, and finally draw a conclusion.

This kind of practice exercises students' ability to find information, analyze problems, associate and solve problems, and promotes the formation of students' independent consciousness and subjective spirit. At the same time, in the process of participation, students' innovative ability and practical ability are also improved, so that knowledge can better serve life.

Fourthly, consulting homework-expanding students' mathematical vision.

This kind of homework mainly comes from the "Do you know" after the examples, and many examples in People's Education Edition have a paragraph about this. These materials include the introduction of mathematics knowledge, social knowledge, life knowledge and knowledge of nature, the history of mathematics, or the development process of a certain field or aspect; There is an interdisciplinary introduction of the latest research results ... but the introduction in textbooks is generally relatively simple.

So you can grasp this piece of content for further study. By searching or browsing related books on the Internet, students can learn and supplement their knowledge in detail, so as to realize a comprehensive understanding and accurate grasp of the contents of the teaching materials. At the same time, this kind of knowledge is often the hard work of mathematicians after a long period of research, which contains thousands of years of human wisdom, embodies mathematicians' indomitable spirit of studying and the cultural value of mathematics, increases their understanding of the history of mathematics, and achieves the goal of mutual infiltration between teaching and patriotic education and improving the comprehensive quality of primary school students.

When designing this kind of homework, teachers should search in advance, have a comprehensive and correct understanding of knowledge, make their professional knowledge extensive and profound, and pay attention to the problems that students may encounter in the search process to ensure that students can successfully complete their tasks.

Fifth, organize homework-cultivate students' inductive ability.

This kind of homework mainly comes from "review" after each unit. Each unit can be used after new teaching, especially for junior and senior high school students. This section focuses on the reorganization of this unit's knowledge, aiming at forming a clear context and thus building a complete knowledge system for students. So students can review what they have learned first, and then sort it out in their favorite way. When designing this kind of questions, teachers are required to have a good understanding of the horizontal and vertical connections of knowledge and the important and difficult knowledge. At the beginning of training, you just need to sort out your knowledge clearly, accurately and comprehensively. After several exercises, if students have a good foundation, they can also give corresponding examples for each knowledge point sorted out, and write tips, complete problem-solving process and matters needing attention. And write a few questions of the same type by yourself. In this way, the student actually becomes a little book editor.

In short, it is a long-term task to design diverse and effective exercises according to different learning contents and types. It is necessary for our front-line teachers to seriously study the spirit of curriculum standards, seriously explore the contents of teaching materials, and design and develop "doing" homework resources that are most conducive to students' long-term development. Enlarge the "length" and "width" of homework, so that our students can not only master the basic knowledge and skills necessary for study and life, but also learn to create, cultivate students' ability to learn to study and live with a long-term vision, and let students develop themselves while enjoying multiple homework!