Case: Finding Approximate Solution of Equation by Dichotomy

When we talk about this lesson, we can create the following question situations: The column "Extraordinary 6+ 1" hosted by Li Yong, a famous host of CCTV, has a link called "price quiz". Do students know how to guess the price quickly? At this time, the students are talking in succession and their emotions are high. At this time, the teacher took out the watch prepared in advance and played a question-and-answer game with the students for them to experience. "The price of my watch is between 100 and 300, and it is an integer. Please guess its price. I will only give you a high, low or correct answer. Who can guess accurately and quickly? " Through this game, the students' enthusiasm is aroused and a preliminary concept of the main content of this lesson is established.

Comments: Use fun games to create problem situations. Stimulate students' interest in learning and let them actively enter the learning state.

Second, the use of mathematical experiments to create teaching situations

Case: Definition of Probability

Before class, please prepare 1 coins in pairs. After class, organize students to do coin toss experiments, which are divided into 10, 50 times, 100 times, etc. The number of times a student throws his head up is recorded in pairs, and the students are in high spirits. After finishing, the teacher asked in time, "If you throw it casually once, what is the probability of being faced up?" ? Please use your experimental records to explain. As all the students took part in the experiment, everyone will gain something.

Commentary: Under the new curriculum standard, we should attach importance to students' practical operation, cooperative communication and independent inquiry, and create teaching situations by using mathematics experiments, so that students can feel the fun of mathematics and cultivate their cooperative ability.

Third, the use of life, production practice to create teaching situations

Case: Arithmetic Average and Geometric Average

Ask the students practical questions first in class: "The teacher gives you a cup of sugar water, but you don't feel sweet. What should I do? " Students will answer "sugar" without thinking, and then ask "why does sugar become sweet? What is the reason? Please use mathematical relations to explain. " This question combines students' real life, inspires students to think deeply and abstracts inequalities. A, b, n are all real numbers, and A < B, then there will be a+n/b+n > a/b.

Comments: Through the creation of this teaching situation, we can arouse students' enthusiasm, guide students to actively explore knowledge, form students' awareness of applying mathematical knowledge, and improve students' mathematical application ability.

Fourth, use well-known proverbs to create teaching situations.

Case: the probability of independent events happening at the same time.

Ask a question in class first, "Is it true that three heads are better than one?" The students talked a lot, some said yes, some said no, and then the teacher came up with a question. Please verify it: there is a math problem, assuming that the probability of Zhuge Liang solving it is 0.8, the probability of the second is 0.5, the second is 0.45, and the third is 0.4. Everyone can solve it independently, so who is the more likely to solve at least one of the three two stooges? At this time, the students quickly got into thinking and calculation.

Comments: When students have interest in learning, they have the motivation to learn. They use well-known proverbs to create appropriate teaching situations, thus stimulating students' interest in learning and improving teaching efficiency.

Fifth, create a situation with interesting stories.

Case: Sum formula of equal proportion series

There are many interesting stories related to mathematics at all times and in all countries. When learning the summation formula of equal ratio series, the teacher can tell the students a short story about the origin of chess in class: in ancient India, there was a king who had supreme power and incomparable wealth, but he was tired of this life and longed for freshness and excitement. One day, an old man came to see the king with his invention-chess. The king saw this new gadget and liked it very much, so he played chess with the old man. For four days in a row, the king was very satisfied and said to the old man, "You have brought me endless fun. I will reward you. You can get anything you want from me. " The old man said slowly, "Although you are the richest man in the world, I'm afraid you can't meet my requirements." The king is unhappy. He said sternly, "Go ahead, even if you want half the kingdom." So the old man said his request: "Please put one wheat in the first grid, two wheat in the second grid, four wheat in the third grid, eight wheat in the fourth grid, and so on, and double it every time until it is placed in the sixty-four grid." The king burst out laughing. He immediately ordered someone to bring a bag of wheat and give it to him as the old man said. But a bag of wheat was quickly eaten up. The king felt very strange, so he ordered people to get another bag, followed by the third bag and the fourth bag ... the wheat piled up like a mountain, but it was far from the sixty-fourth party. The king's face gradually changed from surprise to gloom, and finally he flew into a rage. It turns out that the wheat in his vault has been removed, and he can't reach the fiftieth square on the chessboard. The king thought the old man was cheating him, so he ordered the old man to be killed.

After the story was finished, the teacher continued to sum up: "There is nothing wrong with what the old man said, and his demands are really difficult to meet. According to calculations, the total amount of wheat in 64 squares on the chessboard is about 258.7 billion tons, and now the annual output of wheat in the world cannot reach this figure. " In the students' surprise, if teachers introduce new lessons in time, they will achieve ideal results.

Commentary: Emotional stories can touch people's hearts and make students more excited, energetic and inspiring.

In a word, the new curriculum reform puts the reform of students' learning style in a prominent position, and inquiry learning is paid more and more attention. Only by creating problem situations in various forms to reveal the contradictions of things and stimulate students' cognitive conflicts can we stimulate learning motivation and actively explore, so that students can truly become the masters of learning.