Junior high school mathematics learning is an important part of human culture, and mathematics literacy is the basic literacy that every citizen should have in modern society. As an important part of promoting students' all-round development education, mathematics education should not only enable students to master the mathematics knowledge and skills needed by modern life and study, but also play an irreplaceable role in cultivating people's thinking ability and innovation ability. My parents taught me how to count when I was a toddler. Now I'm studying basic mathematics. In the future, we need to learn advanced mathematics and use mathematical knowledge to solve practical problems in life. For a simple example, the graphs that can calculate the area now are all ideal graphs. Can I find the area of a closed figure surrounded by a curve? Can you deduce the volume formula of a sphere? Can you calculate the volume of an oval water storage tank? Wait, you probably don't know all this. When you go to college, you can solve it with the knowledge of limit and calculus. Students, learning math well requires courage and wisdom, as well as efforts and methods. As long as you are willing to pay, as long as you are willing to use the "law", you will certainly gain something. How to Develop Good Math Learning Habits "Habits are slaves of all great men and accomplices of all losers. The greatness of great men benefits from the help of habit. Losers fail because the guilt of habit is also inevitable. " Therefore, good math study habits are the magic weapon to improve math scores. What are the good math study habits? Junior high school mathematics should develop good study habits from classroom study, homework and exams. First, the habit of classroom learning is the main position of learning activities. Classroom study habits are mainly manifested as: taking notes, comparing, asking questions, analyzing and cooperating. 1. Taking notes in class is not simply copying the teacher's blackboard. It is to sort out the knowledge points we have learned, the general rules and skills to solve certain types of problems, and common mistakes. Taking notes is actually the condensation and refinement of mathematical content. We should often browse our notes to strengthen our understanding and consolidate our memory. In addition, taking notes can make you concentrate and study more efficiently. 2. When we study basic knowledge (such as concepts, definitions, laws, theorems, etc.), we should use comparison, analogy and theorems. ) Understand their connotations and extensions, and distinguish similar and confusing basic knowledge, such as finding out the concepts of "similar term" and "similar square root", "proportional function" and "linear function", "axisymmetric figure" and "centrally symmetric figure", "square root" and "cube root", "radius" and "diameter". Be good at discovering and discovering your own misunderstandings and asking questions from teachers or classmates. Actively asking questions is an important way to acquire knowledge in classroom learning. At the same time, we should dare to question the views and practices of teachers and classmates and exercise our critical thinking. Even if you have some minor problems in your study, you should ask questions boldly, and you can't leave knowledge "dead ends", otherwise the problems will accumulate. Set obstacles for follow-up research. 4. Analysis: First, carefully examine the questions: first, clarify the conditions given by the questions and the questions to be answered, fill in some known conditions on the map, and mark some keywords to reveal the known conditions and dig out the hidden conditions. For example, when doing geometry, mark the known equiangle, line segment, area, known angle, line segment and position relationship in the graph to avoid forgetting. Words such as "no more than" and "insufficient" imply the existence of unequal relations. Only when the known conditions and the problems to be solved are clear can the problems be solved purposefully and directionally. Second, we should think carefully: according to the problems and conclusions in the topic, we should find their internal relations and draw conclusions from the problems, that is, "seeking results from the causes", or starting from the conclusions, we should find a solution to the problem according to the conditions of the problem, that is, "seeking results from the results", or combining the two methods, we should find a solution to the problem. Pay attention to "multiple solutions to one problem", "multiple solutions to one problem" and "multiple uses in one picture". You give me an idea, I give you an idea, and each of us has two ideas. "This is enough to show the importance of cooperation and exchange learning methods. Our main way of learning is autonomous learning. On the basis of independent thinking, exchange views with your deskmate in time. When studying in a group, we should actively express our views, listen to others' speeches and make reasonable judgments. Second, the habit of extracurricular homework is an integral part of mathematics learning activities, which includes: review, homework, etc. 1. Review the math knowledge learned that day in time, and find out the new content, key content and content that is difficult to understand and master. First, I can't remember to read textbooks and notes by my brain. Review in the shortest time. The effect of understanding and applying knowledge can be the best, but it will not be obvious when reviewing for a long time. This is the truth of "learning while learning". At the same time, we should insist on daily, weekly, unit and semester review, so as to review step by step and closely contact with each other, and skillfully use knowledge on the basis of correct understanding of knowledge. 2. Students who can learn homework will review first and then review when they finish on the same day. Never rely on others. Writing must be neat and logical. Check the homework and correct the existing mistakes in time. Iii. survey habits 1. Before testing and checking, we can systematize and deepen the knowledge at a certain stage with the help of notes, make up for the defects of knowledge and further master the knowledge we have learned. 2. Seriously reflect on exams and inspections, and then review. Only by finding out the knowledge defects and weak links, finding out the reasons for the mistakes, improving the learning methods and making clear the direction of efforts can we succeed in the future examinations and inspections. Good study habits are the decisive factor to improve our academic performance, but we must persevere. There is little difference in intelligence between people who preview math textbooks. Mastering good learning methods is the premise of improving their mathematical ability. Preview math class is a good learning method. Preview the textbooks before class and enter the classroom with questions or interests, which will produce good psychological and thinking habits of wanting to learn, ask and practice, and help to concentrate on the key points and difficult points of the new lesson. You can preview it in the following ways. (1) After reading the textbook from coarse to fine, first browse the preview content, understand what to learn in this section, determine the preview focus, and then read intensively according to the focus. Understand concepts, definitions, theorems, formulas, etc. Are the most important, they are the key to solving the problem. So when previewing this part, the focus is not on their memory, but on their understanding and deduction. We should not only describe their connotations in our own language, but also further express their essence in symbolic language and graphic language, and even prove them with existing knowledge, so as to realize the appropriate deformation of the formula. It will also judge whether the inverse proposition of the theorem is true. (2) Write-keep records. In the process of preview, students often have a lot of things they don't understand. They can record some of their opinions and questions in the book, so as to fully explore the connotation of knowledge through the teacher's explanation and the cooperation of peers in class, thus deepening their understanding of knowledge. Form a knowledge structure that conforms to your own cognitive characteristics. Third, practice-initially applying what you have learned to solve problems is the purpose of mathematics learning. In the preview process, you are required to preview the examples and do simple exercises in the textbook after previewing the knowledge points. When previewing the examples, you should do the following thinking: What kind of questions do you belong to and what knowledge points are involved? What problem-solving methods are used? What is the basis of each step? Is there any other way to solve the problem? And so on. The selection of textbook examples is a very representative topic, which is usually not too difficult. It is mainly a simple application of the new knowledge learned. On the basis of understanding concepts, definitions, theorems and formulas, I am fully capable of solving them by myself. In order to consolidate the preview effect, it is necessary to do appropriate exercises. Simple topics similar to the examples in textbooks are the best exercises for our self-study. Fourth, thinking-summing-up-promotion will occur in the preview process. I will make all kinds of mistakes and deepen my memory of existing problems through reflection, so that I can solve them with the help of teachers and classmates in class. Mathematical thoughts and common problem-solving methods (1) There are four common mathematical thoughts: function and equation, conversion and conversion, classified discussion, and combination of numbers and shapes. 1. The function and equation function idea refers to analyzing and transforming problems with the concept and properties of functions. The idea of equation is to start with the quantitative relationship of the problem, transform the conditions in the problem into a mathematical model with mathematical language, and then solve the equation (group) to get the solution of the problem. Functions are closely related to equations, such as unary linear function baxy, which can be regarded as binary equation 0 about x and y? Ybax binary equation 0? Ybax can be regarded as a linear function with y as x, and it can be said that the study of function can not be separated from equation. The characteristics of sequence equation, solving equation and studying equation all embody the idea of applying equation. 2. The elimination method, method of substitution, the combination of numbers and shapes, and the scope of evaluation all reflect the idea of reduction. For example, many quadrilateral problems can be transformed into triangular problems to study; Studying the positional relationship between two straight lines can be transformed into studying the quantitative relationship of angles; For example, after learning the arithmetic rules of rational numbers in senior one, we should understand them in combination with several arithmetic rules: subtraction and multiplication are converted into addition, and division and multiplication are converted into multiplication. For example, if we require the area of irregular graphics, we can divide or supplement them and convert them into regular graphics, and so on. 3. Classification Discussion When solving some mathematical problems, we sometimes encounter many situations that need to be classified and solved one by one. Then we get a comprehensive solution, which is the idea of classified discussion. The main reasons for the classification discussion are as follows: (1) The mathematical concepts involved in the problem are defined by classification. For example, the definition of |a| is divided into a>0, a = 0, a0 and a0, △ > 0，△& lt； 0, △=0.(4) When solving some conditional open problems, we need to classify them according to several possible situations. For example, "there are several ways to make a straight line through a point on one side of a triangle and divide the original triangle into two, so that the cut triangle is similar to the original triangle", which requires classifying the position of the straight line, and there are four ways. Prove that the center of the circle is on the inside, outside and side of the fillet. When discussing classification, the principles to be followed are: determination of classification objects, unification of standards, no omission and no repetition. 4. The basic knowledge of junior high school mathematics combined with numbers and shapes can be divided into three categories: one is the knowledge of pure numbers, that is, real numbers, algebra, equations (groups), inequalities (groups) and inequalities (groups). One is the knowledge about pure shapes, such as simple geometric figures, triangles, quadrangles, similar shapes, right triangles, circles and so on. One kind is about the combination of numbers and shapes, such as the corresponding relationship between points and numbers on the number axis, the definition of acute trigonometric function is defined by right triangle and so on. The combination of numbers and shapes includes two aspects: "helping numbers with shapes" and "helping shapes with numbers", and its application can be roughly divided into two situations: or clarifying the relationship between numbers with the help of the vividness and intuition of shapes, that is, using shapes as a means and aiming at numbers. For example, the image of a function is used to intuitively explain the properties of the function. For example, "If the line segment AB=2cm, there is a point C on the straight line AB, and BC=6cm, then the length of the line segment AC is", and two different positions of the point C can be found by drawing; Or we can clarify some properties of shapes with the help of the accuracy and rigor of numbers, that is, numbers are the means and shapes are the purpose. For example, we can accurately clarify the geometric properties of function images by using resolution functions, and judge the positional relationship between straight lines and circles according to the distance from the center of a circle to a straight line, or judge the positional relationship between two circles according to the quantitative relationship between the radius and the center of a circle.