1, the ideological mathematics of "equation" is to study the spatial form and quantitative relationship of things. The most important quantitative relationship in junior high school is equality, followed by inequality. The most common equality relationship is "equality". For example, in constant-speed motion, there is an equal relationship among distance, speed and time, and a related equation can be established: speed * time = distance. In this equation, it is generally an equation with unknown quantity like this that is the "equation", and the process of finding the unknown quantity through the known quantity in the equation is to solve the equation. We were exposed to simple equations in elementary school, but in the first year of high school, we systematically studied the solution of one-dimensional linear equations and summarized five steps to solve one-dimensional linear equations. If we learn and master these five steps, any one-dimensional linear equation can be solved smoothly. Senior two and senior three will also learn to solve quadratic equations with one variable. In high school, we will also learn exponential equation, logarithmic equation, linear equation, parametric equation, polar coordinate equation and so on. The solution ideas of these equations are almost the same, and they are all transformed into the form of one-dimensional linear equation or binary quadratic equation in a certain way, and then the one-dimensional quadratic equation is solved by the familiar five-step solution or root formula. Energy conservation in physics, chemical equilibrium formula in chemistry, and a large number of practical applications in reality all need to establish equations, and the results can be obtained by solving the equations. Therefore, students must learn how to solve one-dimensional linear equations and one-dimensional quadratic equations before they can learn other forms of equations well. The so-called "equation" thought means that they are good at constructing related equations of mathematical problems with the viewpoint of "equation", especially the complex relationship between unknown quantities and known quantities encountered in reality. Then solve it by solving the equation. 2. The idea of "the combination of numbers and shapes" exists all over the world. Everything, except its qualitative aspect, is left to mathematics to study. Two branches of junior high school mathematics? -Algebra and geometry. Algebra studies numbers and geometry studies shapes. However, it is a trend to study algebra and geometry with shapes. The more you learn, the more inseparable number and shape are. In high school, there is a special algebraic method to learn geometry. The study of functions is inseparable from images. Images can often explain the problem clearly, and it is easier to find the key points of the problem, thus solving the problem. In the future mathematics study, we should pay attention to the thinking training of "combination of numbers and shapes" As long as any problem has a little edge with "shape", we should draw a sketch to analyze it according to the meaning of the problem. This is not only intuitive, but also comprehensive and holistic. It is of great benefit to solve the problem. Those who taste the sweetness will gradually develop the good habit of combining numbers and shapes. 3. The concept of "correspondence" has a long history. For example, we correspond a pencil, a book and a house to an abstract number "1", and two eyes, a pair of earrings and a pair of twins to an abstract number "2"; With the deepening of learning, we also extend "correspondence" to correspond to a form, a relationship, and so on. For example, when calculating or simplifying, we will correspond the left side of the formula, corresponding to A and Y corresponding to B, and then directly get the result of the original formula with the right side of the formula, that is, we will use the idea and method of "correspondence" to solve the problem. In the second and third grades, we will also see the one-to-one correspondence between points on the number axis and real numbers. One-to-one correspondence between a point on a rectangular coordinate plane and a pair of ordered real numbers, and the correspondence between a function and its image. The idea of "correspondence" will play an increasingly important role in future research. If you don't know, please help me You should have the freedom to teach!