2. The combination of numbers and shapes. The idea of the combination of number and shape is to make full use of "shape" to express a certain quantitative relationship vividly. That is, by making some graphs such as line segment, tree diagram, rectangular area diagram or set diagram, students can correctly understand the quantitative relationship and make the problem concise and intuitive. If there are many travel problems, students can clearly perceive the relationship between the total distance, the distance traveled and the remaining distance by using the line graph. Another example is the solution of fractional application problems, in which the relationship between the whole and the part is represented by a circle diagram or a line segment diagram, so that students can answer questions at a glance and understand clearly, which greatly improves their thinking and imagination.
3. Classified thinking method. The idea of classification is also an important way to train primary school students. The general classification requires the principles of mutual exclusion, no omission and simplicity. For example, if it is divisible by 2, integers can be divided into odd and even numbers; If we classify natural numbers by divisors, they can be divided into prime numbers, composite numbers and 1. Classification in geometry is more common. For example, when learning "angle classification", many concepts are involved, and the relationship between these concepts cultivates the law of quantitative change to qualitative change. Several angles are classified according to the degree, from quantitative change to qualitative change, and it is inferred that the largest angle in the triangle is greater than, equal to and less than 90, which can be divided into obtuse triangle, right triangle and acute triangle. Triangle can be divided into equilateral triangle and equilateral triangle, and equilateral triangle can be divided into equilateral triangle and isosceles triangle. Through classification and knowledge network construction, different classification standards will have different classification results, thus generating new mathematical concepts and the structure of mathematical knowledge.
4. Set the way of thinking. Modern classroom teaching should not only impart knowledge to students, but more importantly, consciously cultivate students' collective ideas contained in textbooks, which is conducive to cultivating students' abstract generalization ability and improving students' ability to analyze and solve problems. For example, in the teaching classification, some animals, plants and geometric figures with the same attributes are circled into a whole with a "circle" (closed curve), and this whole is a collection. When seeking the greatest common divisor of 8 and 12 in teaching, courseware or slides can be made to let students know clearly and intuitively that the common divisor of 8 and 12 is 1, 2 and 4, and the greatest common divisor is 4, thus breeding the idea of intersection.