First, starting from textbooks, create problem situations.
One of the characteristics of the new high school mathematics textbook is to create various problem scenarios, reduce the difficulty of teaching, and make mathematics problems closely linked with reality. In every chapter of mathematics teaching material, every knowledge point is introduced, a situational question should be set first, and then new knowledge should be introduced. Some of these situational problems are displayed through the problems in students' life, some through exquisite patterns, some through vivid stories, some through students' hands-on operations, and some through students' games. Although knowledge points are displayed in different ways, editors are set according to students' cognitive needs. The given problem scenarios are all proved and verified by experts, and generally can achieve the ideal teaching effect. If we don't have a better problem scenario, we might as well choose directly, and "takenism" is also a good choice.
For example, the derivation of the sum formula of arithmetic sequence, except the story of Gauss (find "1+2+3+…+ 100 =?") )) As a good question situation, the question situation in the textbook is also very good: a pile of steel pipes, 4 above and 9 below, each floor is more than the previous floor from the second floor, and the total number of copper pipes can be obtained (except for direct addition, what other method can be used to get the total number? )。
Second, create problem situations with the help of real life.
A lot of mathematical knowledge comes from real life, so the introduction of mathematical problems can be linked with production and real life. If we adapt mathematics problems into practical application problems and let students think positively, we can guide students to explore new knowledge actively, thus forming and developing their mathematics application consciousness and improving their practical ability.
For example, there is an example in the teaching of inequality:
It is known that a, b and m are all positive numbers, a.
If you go directly to the certificate, students will feel boring, and this conclusion is easy to remember. It may be adapted into the following simple and interesting practical problem: put one gram of sugar into water to get b grams of sugar water. What is the concentration (mass fraction)? Add 50 grams of sugar to the sugar water. What is the concentration at this time? Is the sugar water sweet or weak? Students can easily make judgments and get conclusions to prove it.
Third, use interesting stories and math stories to create problem situations.
Combining interesting stories with historical stories in mathematics teaching can effectively stimulate students' interest and make them think positively. For example, in the first picture and introduction of the third chapter "Series" of "Full-time Ordinary High School Textbook (Compulsory)" published by People's Education Edition, the textbook quoted a chessboard diagram, and there are 8 rows and 8 columns on the chessboard, which constitutes 64 grids. Chess originated in ancient India, and there is such a legend about chess. The king wanted to reward the inventor of chess and asked him what he wanted. The inventor said, "Please put one grain in the first box, two grains in the second box, four grains in the third box, eight grains in the fourth box, and so on.". The number of grains in each cell is twice that in the previous cell until the 64th cell is full. The king thought it was not difficult, so he readily agreed to his request. Do you think the king has the ability to meet the above requirements of the inventor? Explaining the function of series summation can immediately attract students who are interested in this problem to study it in depth.
For example, when explaining "the probability of mutually independent events happening at the same time", we can create the following situations: It is often said that three heads are better than one Zhuge Liang? If it is known that Zhuge Liang's probability of solving the problem is 0.8, and the probability of solving the problem by the three stooges is 0.5, 0.45 and 0.4 respectively, and everyone must solve the problem independently, then at least one of the three stooges has a greater probability of solving the problem than Zhuge Liang.
Creating situations in this way greatly improves students' interest in learning mathematics, urges students to actively think about problems, keeps their thinking active and exerts their creative potential.
Fourth, create problem situations through operational experiments.
By using modern educational technology and guiding students to operate experiments or demonstrations, we can use some mathematical knowledge to understand the formation process of mathematical concepts, which not only develops students' thinking ability, understanding ability and creativity, but also improves students' learning enthusiasm.
For example, when explaining "mathematical induction", we can first demonstrate the domino effect with multimedia. Through the creation of this problem situation, students can quickly understand and master the definition and essence of mathematical induction.
Fifth, create problem situations from related disciplines.
Mathematics is the basis of learning physics, chemistry and other disciplines, and a lot of its knowledge is closely related to these disciplines, such as the application of probability theory in biogenetics, trigonometric functions and vectors in physics. Therefore, when explaining these knowledge points, we can appropriately create situations related to related disciplines, strengthen the instrumentality and foundation of mathematics, and stimulate students' enthusiasm for learning.
Sixth, starting from the knowledge points that students have mastered, create problem situations.
Use students' existing knowledge and experience to introduce concepts. Mathematical concept map is often "abstraction above abstraction", and the former concept is often the basis of the latter concept. In teaching, make full use of students' existing knowledge and related experience to introduce concepts. For example, in plane geometry, two straight lines intersect if they are not parallel, while in solid geometry, they may not necessarily intersect, but they may be different planes. In fact, many conclusions are valid in plane geometry, but not necessarily in solid geometry. If we can dig deeper step by step, not only can students consolidate their junior high school knowledge, but more importantly, they can gradually accept and understand new knowledge.
Seven, the misunderstanding in the situation creation:
(1), focusing only on fun and less on goals;
(2) Fictitious beauty, deceiving students;
(3), out of the circle of life, mechanically;
(4), more life breath, less scientific;
(5) Every class should have a situation.
In short, in mathematics teaching, as long as we closely focus on the teaching objectives and start from students' life experience and basic knowledge, we should create vivid, interesting and enlightening teaching situations, make learning become students' active and constructive activities, stimulate students' interest in learning, mobilize students' enthusiasm for learning, and finally maximize the benefits of classroom teaching.