First, grasp the details and refine the main points of knowledge.
Knowledge is trivial, and the meticulous deepening of various types of knowledge points is conducive to cultivating students' keen and rigorous thinking, and they can deal with more subtle problems both in life and in exams. In the teaching process, teachers should deliberately explain and practice the knowledge points in detail, analyze the problems that are easily overlooked, and remind students of the habit of not doing problems seriously 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 in solving problems, we should pay more attention to the concept of rotation 180 degrees. Many students did not refine this knowledge point in solving problems, which led to confusion in the concept of answering questions. Let's use a middle school exam to explain:
For example, in the following figure, the one whose center is symmetrical but not axisymmetric is ().
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, good at applying knowledge points
The practical application of knowledge points is the ultimate goal of our teaching, but ordinary teachers will think that mathematics, a highly theoretical subject, is more suitable for imparting knowledge points in class, which will inevitably cause pressure and burden on students' learning. Linking the knowledge point of mathematics with daily life can make students feel the practical value of mathematics, and applying the knowledge point to practice can enhance students' impression of this knowledge point.
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 turn mathematics knowledge into practical problems through the application of knowledge points, so that students can realize the importance of what they have learned, and they can turn mathematics into reality whether they are enthusiastic about learning mathematics or in their later life and work.