First, comprehensively implement the so-called "all-round" problem of curriculum objectives, that is, comprehensively implement all kinds of primary school mathematics curriculum objectives. The basic starting point of mathematics curriculum in compulsory education stage is to promote students' all-round, sustained and harmonious development. Therefore, combined with the overall requirements of the national curriculum reform and the characteristics of its own disciplines, it has established four-dimensional goals of "knowledge and skills", "mathematical thinking", "problem solving" and "emotion and attitude". But this four-dimensional goal belongs to the overall goal of guiding curriculum design and teaching design, rather than the specific teaching goal of guiding each class design. In the specific teaching design process, we should further decompose and refine with reference to the above goals, so as to generate microscopic goals with stronger teaching guidance. Robert Gagne, a famous educational psychologist, put forward a universally recognized learning classification method after 40 years of research. That is, learning results can be divided into five categories: verbal information, intellectual skills (from low to high, it is divided into four categories: discrimination, concepts, rules and advanced rules), cognitive strategies, motor skills and attitudes. According to this classification standard, combined with the classification of objectives in China's mathematics curriculum standards, we can divide the specific teaching objectives in junior high school mathematics into the following categories: (1) knowledge, such as mathematical symbols. (2) intellectual skills, including discrimination, concepts, general rules and advanced rules; (3) Action skills, including various hands-on operation abilities; (4) Thinking methods, including both general learning methods and specific problem-solving methods; (5) Emotions and attitudes, including interests, curiosity, self-information, pride and other emotions, attitudes and values. With such a reference frame, teachers can use it as a reference to make clear how many teaching objectives need to be implemented and which ones they have neglected or even omitted. For example, referring to this framework, we can avoid the problem of motor skill training that is easily ignored in mathematics teaching. At the same time, in the process of fully implementing the curriculum objectives, we need to pay attention to the implicit nature of some types of objectives. For example, from the perspective of predictability, emotional and attitude goals can be divided into preset goals and non-preset goals. The so-called preset goals refer to the goals listed in advance when preparing lessons. For example, when teaching pi, teachers should consider introducing China's ancient mathematical civilization to stimulate students' patriotic feelings; It is necessary to introduce the use of pi and cultivate students' mathematical values. The so-called non-default goal refers to the goal that can't be set exactly in the preparation stage of teaching, but the goal that should be implemented whenever there is an opportunity in the teaching process. For example, in the teaching process, a student puts forward a novel question, which leads to the opportunity to arouse students' curiosity; A student answers well, and then the goal of cultivating students' self-confidence in learning appears. In mathematics teaching, every class does not necessarily have preset emotional and attitude goals, but it must have non-preset emotional and attitude goals. Because there is interaction between teachers and students in every class, every interaction between teachers and students is an opportunity to educate students about their emotions and attitudes. Non-preset emotional and attitude goals are usually implicit. You need to keep an eye on it. Similarly, the thinking method is usually not independent, and it needs to be trained with specific mathematical content as the carrier and combined with specific content learning. The method of fractional line needs to combine a certain number; The ingenious calculation of area depends on a specific area calculation problem. Teachers only need to grasp how many types of specific teaching goals there are as a whole, and realize some hidden goals, so that they will not miss the goal when designing their own teaching. Second, the so-called "deep" problem of ensuring students' learning in place is to consider the learning level of mathematics content. As mentioned earlier, there are different types of mathematics learning, including knowledge learning. There are concept learning, rule learning and problem solving, but each kind of learning has its ideal end point. According to the research results of psychology, the ideal end point of mathematics knowledge learning is to be able to recall when needed. The learning of mathematical skills such as concepts, rules and problem solving generally ends with solving practical mathematical problems in life, while the learning of thinking methods ends with being able to consciously and skillfully use or even create. Mathematics learning can't reach the ideal end. Explain that learning is not in place and the goals of the course or teaching have not been completed. For example, in the teaching of the concept of "rational numbers and irrational numbers", if students can only distinguish which numbers are rational and which numbers are irrational, it does not mean that the learning task has been completed. If we can illustrate the application of the concept of irrational numbers in real life and design the situation of applying these two concepts, it means that learning has reached a higher level. If teachers want to accurately judge whether their teaching and students' learning are in place and guide students' learning more effectively, they must sort out the hierarchical problems of each kind of learning from the simple to the deep and learn the hierarchical analysis of mathematics learning. Recently, American scholars have completed the revision of Bloom's educational goal classification (cognitive field). Learning in the cognitive field is divided into six levels from low to high: memory, understanding, application, analysis, evaluation and creation, which provides a good evaluation standard for mathematics teachers to judge the depth of teaching. Mathematics teaching includes students' learning and teachers' teaching. Among them, "learning" is the foundation and "teaching" is the means. The fundamental purpose of mathematics teaching is to promote students' mathematics learning and physical and mental development, so it must be based on students' learning. In this sense, a good teaching design must grasp the psychological law of students' mathematics learning. For example, the concepts in primary school mathematics have both concrete concepts. There are also well-defined concepts. The research of modern learning psychology shows that the former concept is suitable for the learning mode of concept formation (discovery) and the latter concept is suitable for the learning mode of concept assimilation (teaching). If teachers are clear about this and design corresponding teaching methods and procedures, they can finish teaching better. Otherwise, you may get twice the result with half the effort. Mathematics teaching design must also respect students' cognitive development level and existing knowledge and experience. Pupils of different ages also have certain differences in cognitive development level. The cognition of seventh-grade students has concrete and vivid characteristics, so we must pay attention to the use of intuitive teaching AIDS in mathematics teaching, not just abstract mathematical symbols, description and reasoning of quantitative relations. In ninth grade mathematics teaching, adopting simple and interesting teaching situations suitable for junior students may make them feel "funny". At present, the international mathematics education community generally emphasizes doing a good job in teaching analysis in mathematics teaching. The teaching analysis here includes student analysis, learning task analysis and learning situation analysis. The purpose of analyzing students is to clarify students' learning needs, cognitive characteristics, knowledge level and learning starting point, and to provide basis for the selection of teaching content and strategies. The purpose of analyzing learning tasks is to clarify the levels and conditions of learning and lay the foundation for the formulation and promotion of teaching steps; The purpose of analyzing learning situation is to clarify the situational factors that affect learning and provide reference for the layout of teaching environment and the creation of teaching situation. These practices are worth learning and learning from primary school mathematics teachers in order to improve the scientific nature of their own teaching design. Fourth, strengthen the application of new materials and methods. The so-called "new" problem means that some new educational ideas, teaching methods and teaching contents should be considered in the teaching design. Make teaching constantly innovative. Using novel materials can better attract students' attention and improve the effect of mathematics learning. The development of modern information technology has a great influence on the value, goal, content and the way of learning and teaching of mathematics education. In the design of mathematics teaching, teachers should fully consider the positive role of calculators and computers in promoting the contents and methods of mathematics learning. Teachers are used to using the Internet, so they can make great efforts to develop and provide students with richer learning resources. Using multimedia courseware in teaching presentation can not only save the time of blackboard writing performance in class, but also make full use of audio, light, electricity, animation and other intuitive technologies to attract students' attention and make them devote more energy to learning content. The innovation of teaching design also means the constant change of teaching methods. For example, starting with "activity" is a design that can better guide students to learn, but if teachers use it frequently, it will also lead students to lose interest in this beginning and affect the learning effect. If teachers use direct introduction, interesting introduction, question introduction and game introduction in turn, classroom teaching will become colorful and students' interest in learning will become stronger. Fifth, pay attention to real life problems. In teaching design, we should try to select some real problems, situations and materials from the real world. Try to avoid using some abstract and virtual teaching contents and forms. Mathematics curriculum standard emphasizes "everyone learns valuable mathematics". "Valuable" here not only means "useful for students' further study", but more importantly, it emphasizes "useful for students to do anything". Highlighting the connection between mathematics and real life problems is a basic principle that mathematics teaching design must follow. After all, mathematics comes from life. Serve life. Moreover, mathematics related to real life problems can best stimulate students' interest in learning and cultivate their practical skills. In the process of teaching design, teachers can pay attention to the problems in real life in two ways. Using these instructional design methods, students can not only feel that mathematics is closely related to their own lives, but also feel the value of mathematics learning, and also feel that their skills are strengthening and enjoy the happiness brought by mathematics learning.