How to break through the key points and difficulties in junior high school mathematics teaching
Although junior high school mathematics knowledge is not too profound, but the knowledge points are trivial, it is the goal of junior high school mathematics teachers to be able to flexibly apply trivial knowledge points to the answers to questions. Let's briefly talk about the skills of grasping knowledge points in junior high school mathematics teaching based on our own teaching experience and the questions in the senior high school entrance examination. First, it is a trivial matter to grasp the details and refine the main points of knowledge. The meticulous deepening of knowledge points of various problems is conducive to cultivating students' keen and rigorous thinking and being able to deal with more subtle problems in life and exams. In the teaching process, teachers should deliberately explain and practice the knowledge points in detail, analyze the problems that are easily overlooked in detail, and remind students of their careless habit of doing problems in order to deal with the "trap" in the exam. The details of mathematical knowledge are mainly the characteristics of graphics, such as the properties of triangles, the application conditions of the theorem of angular bisector, the knowledge of central symmetry and axial symmetry; The application conditions of the formula, such as the determination of two roots of binary linear equation; The concrete application of tangent theorem is the detail that students need to master, and it is also the main point of knowledge points. For example, the knowledge point of central symmetry, students know that the definition of central symmetry is: rotate a figure around a certain point 180 degrees. If it can coincide with another graph, the two graphs are said to be centrosymmetric at this point. But pay more attention to the concept of rotation 180 degrees when doing the problem. Many students didn't refine this knowledge point when doing the questions, which led to confusion in the concept when answering the questions. Let's explain it with a middle school exam: For example, in the figure below, the center is symmetrical but not axisymmetric (). In this question, the questioner deliberately chooses innovative graphics to examine the knowledge points of students' daily study, especially confusing graphics to examine students' understanding of 180 degree rotation, and reminds students to truly master every aspect of knowledge through the transformation of details, so as to handle every detail problem well. According to the topic, both options B and C are axisymmetric figures, so two options are excluded. According to the definition of centrosymmetric, among A and D, only A can overlap with the original figure after winding around 180 degrees, so the answer is A. Usually people misunderstand D and think it is also a centrosymmetric figure, that is to say, they don't notice that the rotation period of the fourth figure is 120 degrees, and not all the figures that can rotate are centrosymmetric figures. The alternate setting of this topic fully embodies the refinement of knowledge points and goes deep into every link of knowledge, so that students can fully understand the framework of knowledge. Second, flexible teaching methods and being good at applying knowledge points to practical applications are the ultimate goal of our teaching, but ordinary teachers will think that mathematics, a theoretical discipline, is more suitable for teaching knowledge points in class, which will inevitably cause pressure and burden on students' learning. Linking mathematics knowledge points with daily life can make students feel the practical value of mathematics, and applying knowledge points to practice can enhance students' impression of knowledge points. For example, when learning triangle similarity, students can measure the length of some distances in life through the characteristics of triangle similarity. Through practice, students can master the judgment conditions of triangle similarity and calculate details. When learning probability, you can throw a coin by yourself, and predict the pros and cons of the coin by counting the times of the pros and cons, thus verifying the correctness of the probability theory. As shown in the figure, in order to estimate the width of a river, a target point A is selected on the other side of the river, and points B, C and D are selected near the shore, so that points AB┴BC, CD┴BC and E are on BC, and points A, E and D are on the same straight line. If BE=20cm, EC= 10m, and CD=20m, the width AB of the river is equal to (). This topic is to use some knowledge points of triangle to solve practical problems in life. According to the similarity of triangles, we can know that △ABE and △DCE are similar triangles, so BE:CE=AB:CD, so we can conclude that the distance of AB is 40m, that is, the river width is 40m. This kind of practical problem is intended to guide students to apply the knowledge points they have learned in mathematics to real life and make boring numbers and figures practical. Teachers should adapt to this trend in the teaching process, and make mathematics knowledge solve practical problems by applying knowledge points. Students can realize the importance of the knowledge they have learned, and whether they are enthusiastic about learning mathematics or in their later life and work, they can make mathematics come alive. Third, improve efficiency and summarize knowledge points. Summarizing and sorting out mathematical knowledge points is the key link in learning mathematics. Students must consolidate basic knowledge in order to change various learning methods on this basis. What teachers should do is to improve teaching efficiency, pay attention to the induction and summary of knowledge points, and let students master knowledge points in an all-round way and use them flexibly in doing problems. For example, there are many trivial knowledge points about the relationship between edges and angles in the proof and operation of geometric figures; Steps to solve the parallelogram problem: add auxiliary lines; Application of triangle center; The application of midline theorem, etc. These knowledge points can be easily forgotten or confused if you don't pay attention. Teachers should help students sort out the knowledge points of various problems according to specific topics. Four. Conclusion Under the background of the new curriculum reform, junior high school mathematics teaching has become more creative and can attract students to study hard. The focus of mathematics knowledge needs the unremitting study and sharing of all front-line teachers. This paper simply expounds the grasp of knowledge points in junior high school mathematics teaching, and the deeper knowledge needs the efforts of colleagues.