Second, understand junior high school mathematics thinking method.

There are many kinds of mathematical thinking methods in junior high school mathematics, but the most basic mathematical thinking method is the combination of numbers and shapes. It is equivalent to grasping the essence of middle school mathematics knowledge to classify and discuss ideas, transformed ideas and function ideas and highlight these basic thinking methods.

1. The combination of numbers and shapes is an important mathematical thinking method, which is widely used, flexible and ingenious. It is a famous saying of Professor Hua Luogeng, a famous mathematician in China, that "the number is less intuitive when it is missing, and it is difficult to be nuanced when it is countless", which highly summarizes the role of the combination of number and shape [1]. In mathematics teaching, many laws, theorems and formulas can often be described by graphics. Using the intuition of graphics, we can change from abstract to concrete, fuzzy to clear, and make the difficulty of mathematical problems decrease, so that we can find creative ideas for solving problems from graphics. For example, algebraic equations often "support" the abstract thinking process with the help of geometric figures and graphic perception, so as to seek the dependence between quantities. For example, Xiao Bin and Xiao Ming insist on running every morning. Xiao Bin runs 4 meters per second and Xiao Ming runs 6 meters per second. If Xiao Ming stands at the starting point of the 1-meter track and Xiao Bin stands 1 meters in front of him, they both start in the same direction at the same time. How many seconds later does Xiao Ming catch up with Xiao Bin? At this point, we can draw the following circuit diagram:

According to the circuit diagram, we can find out the equivalent relationship

S Xiaoming =S Xiaobin +1, and then set the unknown sequence equation.

2. The idea of classified discussion is to divide mathematical objects into different kinds of mathematical ideas according to the similarities and differences of their essential attributes. Classifying mathematics content can reduce the difficulty of learning and enhance the pertinence of learning. Therefore, in teaching, students should be inspired to classify the same object according to different situations, and help them master the methods and principles of classification and form the idea of classification. For example, when taking any real number, the classification of the value of: when,; When < 3,.

3. The process of solving mathematical problems by transforming ideas is a series of transformation processes. Middle school mathematics embodies transformation ideas everywhere, such as simplifying the complex, making the difficult easy, turning the unknown into the known, and turning the higher order into the lower order, which is the most basic idea for solving problems. Therefore, in teaching, students should first realize that many commonly used mathematical methods are essentially transformation methods, so as to be convinced that transformation is possible and necessary; Secondly, combined with the specific teaching content, students are consciously trained to master this valuable thinking method. For example, when, find the value of. The problem can be directly substituted, but the simpler method should be to simplify and then evaluate, and then the original formula.

4. Dialectical materialism holds that everything in the world is in the process of movement, change and development, which requires us to attach importance to the teaching of functional thinking methods in teaching. The textbook of East China Normal University has infiltrated the function thought into all the contents of the textbooks of Grade One and Grade Two. Therefore, we should cultivate the thinking method of function consciously, planned and purposefully in teaching. For example, in the teaching of finding the value of algebraic expression, by emphasizing the basis of "when ………" as the first step of solving problems, the thinking method of infiltrating function-each value of letters, algebraic expression has a unique and definite value. As in the algebraic expression x2-4, when x=1, X2-4 =-3; When x=2, then x2-4 = ... By guiding students to discuss the above issues, the static knowledge mode will be transformed into dynamic discussion, which will actually give the form of function, and it will be understood from a moving point of view in students' minds, which is an important way to develop the thought of function.

These are the four most commonly used

Others are: induction, deduction and so on.