2. Finding the growth point of knowledge is the condition to highlight key points and break through difficulties.
Primary school mathematics is a highly systematic subject. Mathematics teaching is to guide students from the old to the new, organize active migration, promote reasoning from the known to the unknown, understand the relationship between simple problems and complex problems, and constantly improve the cognitive structure. Therefore, the formation of new knowledge has its fixed growth point, and finding the growth point of knowledge can highlight the key points and break through the difficulties. We can identify the growing point of knowledge according to the following three points: (1) Some new knowledge belongs to the same kind or similar to some old knowledge, so we should highlight "* * * similarity" and then break through the difficulties; (2) Some new knowledge is composed of two or more old knowledge, so it is necessary to highlight the "connection point" and then break through the important and difficult points; (3) If some new knowledge is developed from some old knowledge, it is necessary to highlight the "evolution point" and then break through the key and difficult points. For example, in the teaching of "problem-solving strategies", although each strategy has its own applicable topic, in the process of forming new strategies, we should comprehensively use existing strategies, such as drawing and listing when learning replacement and hypothesis strategies, and we should run through the comprehensive method and analysis method. Therefore, the teaching of this unit is a process of reorganizing the cognitive structure of mathematics, and it is necessary to highlight the "evolution point" and then break through the important and difficult points.
3. Adopting appropriate teaching methods is the key to highlight key points and break through difficulties.
The Mathematics Curriculum Standard for Full-time Compulsory Education (Revised Edition) points out that teachers' teaching should be based on students' cognitive development level and existing experience, facing all students and paying attention to heuristic and personalized teaching. Teachers should play a leading role, properly handle the relationship between teaching and autonomous learning, and guide students to think independently, actively explore and cooperate through effective measures, so that students can understand and master basic mathematical knowledge and skills, mathematical ideas and methods, get necessary mathematical thinking training and gain basic mathematical activity experience. After reading this passage carefully, we can know that adopting appropriate teaching methods according to students' reality is the key to highlight key points and break through difficulties. For example, when teaching problem-solving strategies, the appropriate teaching methods are independent thinking, trying to solve problems, cooperation and exchange, comparison and induction, reflection and summary, and forming experience. This teaching method can make students understand and form problem-solving strategies in the process of solving problems, realize the value of strategies, consciously use strategies to solve problems, truly highlight key points and break through difficulties.
4. Accumulating basic mathematical experience is the basis of highlighting key points and breaking through difficulties.
The basic experience of mathematics refers to the understanding formed by the leap from sensibility to rationality through the actual operation, investigation and thinking of specific things under the guidance of mathematical objectives. Mathematics experience comes from daily life experience, which is higher than daily experience. Mathematical activities in primary schools can be divided into four categories: mathematical activities directly derived from life; Indirect sources do mathematical activities of life; Pure mathematics activities designed for mathematics learning; Mathematical activities with connected artistic conception. The teaching of "problem-solving strategy" is a mathematical activity indirectly derived from life. Therefore, teachers should design hierarchical mathematics learning activities, guide students to experience and reflect on the problem-solving process, sort out the problem-solving experience, reflect on the obtained mathematical experience, and re-recognize the students' cognitive process, so as to master the problem-solving strategy, feel the value of the strategy, accumulate mathematical experience, and effectively break through the difficulties in teaching. Take "Problem Solving Strategies-Enumeration", the first volume of the fifth grade, as an example. Teaching examples 1 Let students go through the process from disorder to order and learn to list them in an orderly way. Teaching example 2 should guide students to solve problems by enumerating strategies, or think repeatedly and feel the list, and type "?" List laws concisely and orderly; Teaching example 3 should inspire students to analyze problems from different angles and further feel the characteristics of enumeration strategies. In the teaching of each example, students should be guided to review and reflect, accumulate mathematical experience, and establish the consciousness of actively solving problems with strategies.
5. The rational application of information technology is the guarantee to highlight key points and break through difficulties;
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. Modern information technology has become a powerful tool for students to learn mathematics and solve problems. Therefore, in the process of highlighting teaching priorities and breaking through teaching difficulties, we should give full play to the advantages of modern information technology, turn actions into static, hidden into obvious, difficult into easy, abstract into intuitive, and effectively promote the breakthrough of teaching difficulties through the combination and complementarity with traditional technologies. For example, in the teaching of the first volume of "Problem-solving Strategies-Substitution and Hypothesis" in grade six, information technology is used to visually demonstrate the problem-solving process through drawing, so that students can use these two strategies to analyze the quantitative relationship and ensure the smooth breakthrough of important and difficult points.