The first class is my math. In those 45 minutes, I didn't talk about the new knowledge in the book, but chatted with my classmates. I am free tonight.

When the bell rings, teachers and students say hello to each other.

Teacher: Students, my last name is # (blackboard writing: #). Let's talk about it together # How many strokes are there in this word?

Health: 12 strokes.

Teacher: (roll call for students to stand up and answer) 12 How did the word "#" come from?

Health: I counted them one by one.

Teacher: That means you get it by counting, right? When did you learn to count, before or after school?

Student: It should be before school. Anyway, I knew it when the kindergarten teacher taught us to count.

Teacher: So it wasn't the school teacher who taught you to count first. It must be your family, probably your parents.

Health: (Nodding) It should be Mom and Dad.

Teacher: Do you know why mom and dad taught you to count when you were so young?

The student was at a loss and the teacher motioned him to sit down. )

Teacher: Students, I believe most of you learned to count before you went to school (students nodded), so why did your parents teach you to count so early? I think the main reason is that adults know that mathematics is too important. Mathematics is everywhere in life, and people can't live without it. (blackboard writing: life is inseparable from mathematics). For example, if you come to me to buy sugar, I know you can't count. I may point to ten sweets and tell you that this is twenty sweets, which cost * * * money. Think about it. What's wrong with you?

Health: What a loss!

Teacher: Yes, you are so frustrated, so parents who love you don't have to teach you anything first. Counting the first song is the first thing you have to learn.

(Students laugh. )

Teacher: For another example, just before class, I saw you in the classroom, which was a little crowded.

Health: Yes, it's too crowded. There is nothing interesting in the classroom.

Teacher: Actually, not only your class is crowded, but also the classes in Grade Three and Grade Two. All classes are crowded. Can you see which class is more crowded from my description?

Health: No!

Teacher: Then how can we compare which class is more crowded?

Student 1: You can count the number of classes and compare them to see which class has the largest number of students and which class is the most crowded.

Student 2: When I checked in, I found that the classroom in Grade One is bigger than that in Grade Two and Grade Three, so I don't think it is very accurate to count the number of students separately.

Teacher: What should I do?

Student 2: You can count the number of students in each class, measure the length and width of the classroom in each class, and then divide the number of students by the area of the classroom to compare which class is more crowded.

Teacher: Great, class. Look, through mathematical measurement and calculation, we can clearly understand some phenomena in life. Life is inseparable from mathematics. In order to live a better life, we should learn math well! But I have seen your placement exam, and some students' math scores are still not ideal! Students who think they are not good at math boldly raise their hands.

Several students raised their hands shyly, and the teacher motioned for one of them to stand up and answer. )

Teacher: What do you think of math?

Student: It's too difficult to learn. In elementary school, it was always calculated. That's it

Teacher: Which one is it? Is it boring?

The students nodded, and many other students echoed. )

Teacher: Actually, mathematics is fascinating, and mathematics has infinite charm. (blackboard writing: mathematics has infinite charm.

(Many students disagree. )

Teacher: If you prefer music, please raise your hand. (The teacher asked one of the students who raised their hands to stand up and answer) Tell me who your singer is.

Health: Jay Chou.

Teacher: Do you think people all over the world know about Jay Chou?

Health: (hesitates) It's hard to say.

Teacher: Do you think people will still know about Jay Chou in 200 years?

Health: That's even harder to say.

Teacher: Do you know Beethoven?

Health: Of course. (Another classmate is whispering at the bottom, who doesn't know Beethoven! )

Teacher: Yes, who doesn't know Beethoven? Beethoven was born in 1770 and died in 1828, but now people all over the world will still remember him. Why? Because his symphony is so wonderful, it has become a classic of world music, and one of the reasons why it can become a classic is that the music is full of the perfect harmony of the golden section that we need to learn in junior high school mathematics. In addition to Beethoven, world heavyweight musicians Mozart and Schubert also created classics in music with the harmonious beauty of the golden section. Not only music but also painting needs mathematics. Who do the students say is the master of painting?

Health: Da Vinci, of course.

Teacher: Yes, we all know that Leonardo da Vinci's Mona Lisa is immortal in the history of painting, and the Vitruvian Man is also very famous. I suggest you search "Da Vinci and Mathematics" on the Internet after class, and you will find that he is not only a painter, but also a mathematician. He integrated mathematics into art, which is immortal. In addition, you can also search the mathematical problems in the pyramids of Egypt and Notre Dame de Paris. You will find that mathematics has shown infinite charm in various fields, and you will change your view of mathematics for some reasons. (Multimedia demonstration of Vitruvian people, Notre Dame de Paris, pyramids and other related introductions while explaining)

(The student nods. )

Teacher: Students, since life is inseparable from mathematics, and mathematics itself has infinite charm, what is the key to learning to "do mathematics"? (Note: The so-called "doing mathematics" is to shift attention from the traditional focus on mathematical content to the mathematical process. In other words, it emphasizes the teaching of the formation and development of mathematical knowledge in the human brain. "Doing" refers to engaging in some kind of work or activity. —— Excerpted from the online paper "Let students learn to do mathematics" (the teacher wrote on the blackboard: the key method of "doing mathematics")

Teacher: Students, let's give a simple example. Just now, many of you have been watching me and listening to me so much. Have you ever thought about my age when you look at me? Please guess how old I am.

Health 1: I guess you are 35 years old.

Teacher: How did you guess?

Health 1: (embarrassed to answer), I think you should be around 35 years old.

Teacher: Have you thought of any other methods?

Health 1: No.

Teacher: Students, he told me my age through observation, which is the first key I mentioned-observation, and we should observe it carefully. (blackboard writing: observe carefully)

Teacher: Raise your hand if you think of other ways!

Health 2: I compared you with my family, and I feel that you should be 37 years old.

Teacher: This classmate used a good method, too, because it was the first time we met, and everyone was strange to me. If you want to know my age, you can find it in your familiar family, and then compare it, and you can name an age. But if you want to compare, you can only find something similar, and you can't compare me with an old lady in her seventies and eighties. (The students laugh, and the teacher writes on the blackboard: Reasonable comparison. )

Teacher: Through observation and comparison, the students told me my age. Is this my exact age?

Health: Not necessarily. We guess.

Teacher: Yes, you guessed it right. Although it may not be accurate, I allow you to guess boldly, and mathematics also allows you to guess boldly again and again. (blackboard writing: take a bold guess. ), but what we guess is speculation after all, which is not convincing enough. What should we do next? Who will answer?

Health 3: (Loud and hearty) Teacher, because you look a little pale and have a little black spot on your face, and you just smiled and there are some lines on your face when you smiled, you are definitely not a girl in your twenties. You must be between 35 and 40 years old.

Teacher: Listen, everyone, how bright and confident she is. Using the words "absolute" and "sure", my age is really between 35 and 40. Why didn't the first two students use these words? Because the third student used "because of what, so what, so what", this is a causal relationship. What do you call this method?

Health: Reasoning.

Teacher: Yes, it is reasoning. We can infer a new knowledge and law with relevant knowledge, and our reasoning must be rigorous. (blackboard writing: strict reasoning. )

Teacher: Through the explanation of this specific problem, I put forward such requirements for everyone to learn "doing mathematics" in the future: careful observation, reasonable comparison, bold speculation and strict reasoning. Let's read together.

(Students read aloud in chorus. )

Teacher: Students, life is inseparable from mathematics, which has infinite charm. Let's join hands and do math thinking gymnastics every day!

This is a teacher's online, you can learn from it.