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, according to the overall requirements of the national curriculum reform and the characteristics of its own disciplines, four-dimensional goals of "knowledge and skills", "mathematical thinking", "problem solving" and "emotion and attitude" are established. 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 refer to the above objectives, further decompose and refine them, so as to generate microscopic objectives with stronger teaching guidance. After 40 years' research, Robert Gagne, a famous educational psychologist, put forward a universally recognized learning classification method, that is, learning achievements can be divided into five categories: verbal information, intellectual skills (divided into four categories from low to high: discrimination, concept, 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, stories and anecdotes about mathematics. (2) intellectual skills. Including discrimination, concepts, general rules, advanced rules and so on. (3) motor skills. Including all kinds of hands-on operation ability; (4) thinking method. It includes both general learning methods and specific problem-solving methods; (5) Emotion and attitude. Including interest, curiosity, self-information, pride and other emotions, attitudes and values. With such a frame of reference, 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 cannot be set accurately in the preparation stage of teaching, but should be implemented as long as 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 stimulate students' thirst for knowledge; 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 teacher-student interaction in every class, every teacher-student interaction is an opportunity to educate students' emotions and attitudes. Non-preset emotional and attitude goals are usually hidden and need to be paid attention to at any time. 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. Only when teachers grasp the specific teaching goals as a whole and realize some hidden goals can they not miss the goals when designing their own teaching. Second, the so-called "deep" problem of ensuring students' learning in place is to consider to what extent the learning of mathematics content is in place. As mentioned above, there are different types of mathematics learning, including knowledge learning, concept learning, rule learning and problem solving, but each learning type 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 not reach the ideal end point, that is, learning is not in place, and there is no goal of completing the course or teaching. For example, in the teaching of the concepts of rational number and irrational number, if students can only distinguish which numbers are rational and which numbers are irrational, it does not mean that the task of learning has been completed, but if they can give examples of the application of irrational number concepts in real life and design the situation of using these two concepts, it marks 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 classification of educational objectives (cognitive field), which divides the learning in cognitive field into six levels: memory, understanding, application, analysis, evaluation and creation, providing a good evaluation standard for mathematics teachers to judge the depth of teaching. Third, the scientific application of teaching methods requires that the teaching methods adopted must be based on scientific learning and teaching psychology, so as to at least "pay" to achieve the set goals. Mathematics teaching essentially 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 include both concrete concepts and definition 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 (lecture). If teachers are clear about this and design corresponding teaching methods and procedures, they can finish teaching well. 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. There are also some differences in the cognitive development level of primary school students of different ages. 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, rather than relying on 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 the teaching analysis link 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 use of new materials and methods. The so-called "new" problem is to apply some new educational ideas, teaching methods and teaching contents in teaching design, so as to make teaching innovate constantly. 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 role of calculators and computers in promoting the contents and methods of mathematics learning. Teachers are used to using the Internet, which can develop vigorously 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 "initiative" is a design that can better guide students' learning, but if teachers use it frequently, students will gradually lose interest in this beginning, thus affecting 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. V. Paying attention to real life problems In teaching design, we should try to select some real problems, situations and materials from the real world, and try to avoid using some abstract and virtual teaching contents and forms. Mathematics curriculum standard emphasizes that "everyone should learn 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 relationship between mathematics and real life problems is a basic principle that mathematics teaching design must follow. After all, mathematics comes from life, and it will eventually return to life and serve it. 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. By adopting these instructional design methods, students can not only feel that mathematics is closely related to their own lives and the value of mathematics learning, but also feel that their skills are being strengthened and enjoy the happiness brought by mathematics learning.