Even Zhilin took me as the answer, okay? 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 equivalence relation is "equation". For example, uniform motion, distance, speed and time are equivalent, and a related equation can be established: speed * time = distance. In this equation, there are generally known quantities and unknown quantities. An equation containing unknown quantities like this is an "equation", and the process of finding the unknown quantities through the known quantities in the equation is to solve the equation. We were exposed to simple equations in primary school, but in the first year of junior high school, we systematically studied the solution of one-dimensional linear equations and summarized five steps of solving one-dimensional linear equations. If you learn and master these five steps, any one-dimensional linear equation can be solved smoothly. In the second and third day of junior high school, you will also learn to solve one-dimensional quadratic equations, binary quadratic equations and simple triangular equations. 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 linear equations or quadratic equations in one variable by certain methods, and then solved by the familiar five steps to solve linear equations in one variable or the root formula to solve quadratic equations in one variable. Energy conservation in physics, chemical equilibrium formula in chemistry, and a large number of practical applications in reality all need to establish equations and get results by solving them. Therefore, students must learn how to solve one-dimensional linear equations and two-dimensional linear equations, and then learn other forms of equations. The so-called "equation" idea means that for mathematical problems, especially the complex relationship between unknown quantities and known quantities encountered in reality, we are good at constructing relevant equations from the viewpoint of "equation" and then solving them. 2. The idea of "combination of numbers and shapes" is universal, and "numbers" and "shapes" are everywhere. Everything, except its qualitative aspect, has only two attributes: shape and size, which are left for mathematics to study. Two branches of junior high school mathematics? -Algebra and geometry. Algebra studies numbers and geometry studies shapes. It is a trend to learn algebra by means of "shape" and geometry by means of "number". The more you learn, the more inseparable you are from "number" and "shape". In senior high school, a course called "Analytic Geometry" appeared, which used algebra to study geometric problems. In the third grade, after the establishment of the plane rectangular coordinate system, the learning of functions can not be separated from images. Often with the help of images, the problem can be clearly explained, and it is easier to find the key to 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" Any problem, as long as it is a little close to the "shape", should draw a sketch to analyze according to the meaning of the problem. This is not only intuitive, but also comprehensive, easy to find the breakthrough point, which is of great benefit to solving problems. Those who taste the sweetness will gradually develop the good habit of "combining numbers with 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 a form, a relationship, and so on. For example, when calculating or simplifying, we will correspond the left side of the formula, A, Y and B, and then directly get the result of the original formula with the right side of the formula. This is to use the idea and method of "correspondence" to solve problems. The second and third grades will also see the one-to-one correspondence between points on the number axis and real numbers, the one-to-one correspondence between points on the rectangular coordinate plane and a pair of ordered real numbers, and the correspondence between functions and their images. The thought of "correspondence" will play an increasingly important role in future research. 4, the idea of "transformation"-the best way is to contact Dora more! If you don't know, please help me You should have the freedom to teach! ! !