First of all, teaching should start with contradictions.
Teaching begins with contradictions and begins with problems. Thinking begins with questions and surprises. In teaching, students can design a suspense or interesting story that is difficult to answer, stimulate students' strong desire for knowledge, and play the role of enlightenment and induction. For example, when teaching the sum formula of arithmetic sequence, a teacher first told a math story: German "math prince" Gauss, when he was studying in primary school, the teacher gave an arithmetic problem: 1+2+3+...+ 100 =? As soon as the teacher finished reading the topic, Gauss wrote the answer on his blackboard: 5050, and the other students were still adding one by one. So, how did Gauss do it so fast? At this time, the students were shocked and had a strong inquiry reaction. This is arithmetic progression's summation method-reverse addition.
Second, doubt the key and difficult points.
Some contents in the textbook are very boring and difficult to understand. For example, concepts such as limit of sequence, infinite geometric progression sum are abstract and difficult to understand. For example, some students are still skeptical about the equation = 1 after learning the limit of sequence. To this end, a teacher inserted a story of "Analysis of the Legend of Divided Cattle" in her teaching: It is said that there was an old man in ancient India who left a will and shared 19 cows with his three sons. The oldest score is 1/2, the youngest score is 1/4 and the oldest score is 1/5. According to Indian canon, cows are regarded as gods and cannot be slaughtered. Only the whole head can be divided, and the will of the ancestors must be unconditionally obeyed. After the death of the old man, the three brothers racked their brains to divide the cows, but they couldn't figure anything out. Finally, they decided to turn to the government for help. The government was at a loss, so it pushed it off on the grounds that "it is difficult for honest officials to break housework." When Zhicuo, a neighboring village, knew it, he said, "This is easy to handle! I have a cow to lend you. So, there are 20 cows in all. If the boss scores 1/2, you can get 10 heads; The second child scored 1/4 and got 5 heads; Old three points 1/5 can get four heads. You wait for three people to divide 19 cows, and then give me back the rest! " It's wonderful! However, in addition to admiration, there will always be a trace of doubt. It seems that the boss should only get 9.5 heads. How did he finally get the head of 10? The students are very interested ... after analysis, the teacher turned the problem into the application of the summation formula of infinite equal ratio series that the students learned. Solve doubts in fun.
Third, doubt the mistakes in the textbook.
British psychologist Bernbridge said, "Everyone makes mistakes, and it is unforgivable for a teacher not to use them." The most common mistake students make in the process of learning mathematics is to ignore the change of conditions or research scope, or not to check and think after solving a problem. Therefore, where students are prone to make mistakes, let them try to "hit a wall" and "fall down", let them fully "expose the problem", and then carefully analyze and guide them with their mistakes, so that students can suddenly realize and leave a deep impression.
For example, if the function images are all above the X-axis, please find out the range of the value of the number A. Students often misinterpret a0 and get 0 1 due to the influence of the mindset, but ignore the situation that a=0.
Fourth, doubts are at the end.
Good lessons should also end in contradictions, so that there is no end. At the end of a class, new questions are put forward according to the knowledge system, so that on the one hand, old and new knowledge can be organically linked, and at the same time, students' new desire for knowledge can be stimulated, so as to make full psychological preparation for the teaching of the next class. This fascinating psychological design is often used in China and Zhang Hui's novels. Whenever the story reaches its climax, the contradictions and conflicts of things intensify to its climax, and readers eagerly look forward to the ending of the story, the author ends with "I want to know what will happen next", forcing readers to continue reading! Isn't it the same in the classroom? A good class is not finished when it is finished, but the words are poor.
For example, when solving inequalities, a teacher first uses the students' existing knowledge to solve this problem, that is, by solving two groups of inequalities. Then, use the following solution: the original inequality can be changed to: that is, so the solution set of the original inequality is:, and students will be surprised, alas! How is this solved? The solution is great! The teacher said, "Do you want to know the answer? We will discuss it in detail in the next class. " This aroused the students' thirst for knowledge and made full psychological preparation for the next class.
Of course, the questions raised by teachers must be transformed into contradictions in students' own thinking. Only by transforming objective contradictions into students' own thinking contradictions can we have the effect of solving doubts.