Mathematics teaching activities must be based on students' cognitive development level and existing knowledge and experience. As Ausubel, an American educational psychologist, pointed out in the title page of the book Educational Psychology: "If educational psychology must be reduced to a principle, I would say that the most important factor affecting learning is what students already know, and we should teach according to their original knowledge." Then, in teaching practice, how should teachers grasp the starting point of students' learning? First, improve the fuzziness of the starting point 1 and pay attention to the logical starting point: make a systematic and detailed analysis of the teaching materials. The so-called logical starting point refers to the knowledge base that students should have according to the learning progress of textbooks. The logical starting point of students is the most basic premise for teachers to find the starting point of teaching accurately. Teachers must grasp the textbooks as a whole, make clear the arrangement characteristics and arrangement system of existing textbooks in primary schools, and carefully study the internal relations and distribution of knowledge points and knowledge structures in various fields involved in each textbook. Only by knowing these clearly can we grasp the logical starting point of students, determine the key and difficult points of teaching and find the breakthrough point of teaching. For example, when teaching the derivation of parallelogram area formula, students should have the knowledge base of rectangle and square area formula, and this knowledge point has been studied for a long time, so before teaching, teachers need to know whether students have memorized rectangle and square area formulas and can skillfully use formulas to solve practical problems, so as to decide whether it is necessary to design a link to review old knowledge in teaching. To explore the triangle area formula, teachers should know that the parallelogram area formula that students have just learned is the logical starting point of this course. Generally speaking, there is no need to design a special review link, and the focus of teaching should be how to let students use the idea of "conversion" to explore the derivation of area formula. 2. Pay attention to the realistic starting point: effectively and deeply grasp the reserves. The so-called realistic starting point refers to the knowledge base that students have under the joint action of various learning resources. For example, before knowing cuboids, cubes, cylinders and spheres, students have a preliminary perception of their basic characteristics and can quickly distinguish different shapes; Before learning "possibility", students have had the experience of taking things from their pockets or schoolbags; Before learning "year, month and day", it is known that there are 12 months in a year ... These simple understandings of mathematics acquired by students directly affect and restrict students' mathematics learning. Therefore, teachers need to know students' life experience and related knowledge reserves in depth, and then guide students to improve and upgrade their existing knowledge from the perspective of mathematics, so as to realize the transition from shallow life experience to deep mathematical understanding. 3. Grasping the starting point of the masses: It is possible for all students to participate in the whole process. Under the class teaching system, what we need to pay most attention to is the starting point of the masses, that is, the starting point of most students' learning. For a specific lesson, teachers need to know: what are the contents of the teaching objectives that most students have mastered or partially mastered? What is the degree of mastery? What other knowledge can't most students learn? What can students master through self-study among the knowledge taught? What can be achieved through cooperation and discussion? What needs teacher's guidance and teaching ... Knowing the starting point of the public and the relevant learning situation, the teacher can determine which content can be slightly talked about or even not talked about, which content should be mainly guided, and where it is better to recruit people. Only in this way can the teaching design be targeted, and students' full devotion and full participation in mathematics learning can be realized as much as possible. 4. Grasp the individual starting point: make teaching smooth and wonderful possible. The realistic starting point of most students' mathematics learning is higher than the logical starting point, especially a few excellent students. The latter third of students are slow to accept new knowledge, and their realistic starting point is often lower than the logical starting point. For example, when teaching "volume and volume", I use the situation of "crow drinking water" to let students understand why crows can drink water. Students say that stones occupy a certain space, so they ask, "Who knows how much space stones occupy?" ? What else do you know about this problem? "In this way, excellent students get room for development, and their wonderful explanations are no less than teachers, while individual underachievers let them imitate and talk about the volume of books and pencil boxes. In gestures and repeated imitation, they also successfully understood the meaning of volume. Second, strive to grasp the starting point of impartiality 1. (1) Carry out the preliminary investigation seriously. Before the teaching design of the new curriculum, we use interviews or questionnaires to conduct preliminary research, and through the analysis of the research data, we can understand the existing knowledge base of students and find the starting point of teaching. For example, before teaching "quantity and quantity", I require each student to complete a pre-test form. Objective: To understand students' understanding of volume and volume. Please draw the size of 1 cubic centimeter. According to the students' cognitive situation, I abandoned the idea of integrating meaning and unit into a class, and focused on the understanding of meaning and the connection and difference between them. This kind of preliminary investigation can accurately grasp the realistic starting point of students and specifically understand the degree of differentiation between the mass starting point and the personal starting point. (2) Rational analysis of frontier operations. 2. Learn randomly in class. (1) Clever introduction of detection at the beginning of class. For the teaching of concepts, space and other knowledge, some teachers will come straight to the point and adjust the teaching design according to the students' answers; For some contents such as calculation and problem solving, clever teachers often use "try teaching method" to test students' learning starting point. (2) Keenly capture information in class. For example, when I was teaching "two-digit plus two-digit carry addition", I first tested the starting point of my first study through two review questions: "8+7" and "12+34" (to test the students' mastery of one-digit carry addition and two-digit carry addition), and the results showed that all the students calculated correctly. According to the students' logical starting point, I directly showed the example of "37+48" to test the second learning starting point (to understand the realistic starting point of students' binary addition). According to students' realistic starting point, I guide students to focus on the problem of how to do when a number is full in vertical calculation.