The first time was 65438+February, 20 17, in Xi' an. Compared with the excitement and excitement of the first contact with panoramic mathematics, I have more rational love this time. Maybe everything should start with love. With love, everything will come naturally.

Ok, slowly sort out the harvest of this day and share the "wonderful scenery" found in "Panoramic Mathematics" this day.

1) Turn on the camera from "4520"

At the beginning of the class, Teacher Zhang wrote the very common multiplication formula "4520" on the blackboard. Ask a question: which formulas can this formula be used to calculate?

Students began to write, and teachers toured, constantly encouraging students to write more.

The teacher counted the number of people who wrote four formulas, three formulas, two formulas and one formula.

Start writing the formulas written by the students on the blackboard. Guess before writing: multiply, divide and add. The teacher also instructed: subtraction can write.

The panoramic mode of the classroom is thus opened-the relationship between addition, subtraction, multiplication and division. Of course, the relationship between addition and multiplication is emphatically analyzed, and the relationship between the four operations is made clear. One: 1+4+2 is replaced by multiplication formula, and the teacher guides the students to think and finally draws a conclusion, which can be rewritten into countless multiplication formulas.

It also opened a wonderful scene in the classroom-"There are two kinds of relationships in the world, one is similar and the other is opposite." Philosophy and mathematics have always been twins.

Wonderful scenes in the classroom can also be presented by students' gains:

1: I know multiplication is a simple operation of addition.

Health 2: I know that some relationships are both close and antagonistic.

S3: Every formula has many expressions.

Health 4: The opposition between addition and division.

Health 5: I used to know that multiplication is a product and division is a quotient. Now I know that addition and multiplication are combinations, and subtraction and division are points. The teacher answers the questions and distinguishes between "harmony" and "combination". The name of the result has not changed.

Health 6: With the participation of decimals, any addition formula can be written as multiplication formula.

Health 7: One formula can calculate many formulas.

Health 8: I used to think that addition is simpler than multiplication, but today I know that multiplication is simpler than addition.

Health 9: A multiplication can help us solve many problems.

Student 10: It must be the addition of the same addend before it can be changed into a multiplication formula.

……

To tell you the truth, I'm a little intoxicated. Senior two students, through the teacher's guidance, have clarified the relationship between the four operations. For them, today's class should make them grow a lot.

Accustomed to the step-by-step classroom, this class, which twists and turns, climbs slowly and constantly appreciates the beautiful scenery of the road, will definitely give students a fresh and interesting feeling and a good experience, and the growth of students will increase a lot compared with usual.

2) Put "Decimal" in the spotlight

At the beginning of the class, the teacher asked the sixth grade students, "Have you learned the meaning of decimals?"

"I learned."

"Are there any questions?"

"No." It is almost a unified answer.

"No problem is the biggest problem."

Start with the English translation of "decimal" and return to Chinese from English: decimal+tiny.

Then guide the students to analyze: why should they be named decimal?

Admire teacher Zhang's knowledge in this deep well is too rich:

The generation of decimals, decimals and fractions, why are there false fractions? ...

Unit of measurement, RMB model and grid model, the quantity varies with the unit 1.

Four beauties of decimals: accuracy, conciseness, symmetry and unity.

Thank you, Teacher Zhang, for leading us into the world of decimals. If the last class is full of twists and turns, there will be a stirring beauty.

He said that the classroom should see the changes and growth of students, but also go beyond: open more windows for students.

He also said that what he wants to convey to students are three kinds of consciousness: on the road of learning (asking for help from fellow teachers, consulting reference books and surfing the Internet), and on the research methods (from the outside to the inside, combining pros and cons, from the whole to the part, and from where there is no problem), he has a global vision (mathematical history, mathematical culture and regional mathematics).

He did it in this class and landed.

These wonderful scenes will be remembered once you walk.

3) Can I learn Mobius circle in the second grade?

At first, I didn't understand what Mr. Zhang was going to say, so I went to Baidu specially: the meaning of topology, but it was also ambiguous.

I didn't know what Mr. Zhang wanted to do until he came on stage with some paper tape: Do you want to talk about Mobius circles? This content is arranged in the sixth grade in the Beijing Normal University edition, and the students on the stage are now in the second grade.

Yes, it is Mobius circle.

Teacher Zhang used the three-stage teaching method of question-guess-verify to stimulate students' interest in learning, guess and verify constantly, which opened a window for students and rebuilt their confidence in mathematics learning.

Perhaps the meaning of this course is to let students know that there is such a thing, and there is no need to delve into it now. "Sow a seed" is enough.

Such a wonderful scene makes students feel deja vu, and the future is wonderful, which is also very good.

4) Hong Jie's "philosophy" evaluation.

Because the teacher talks too much, Hong Jie's evaluation can only be compressed endlessly. However, I still want to say: what is concentrated is the essence.

Written on A4 paper, it is clear at a glance and concise. The words and pictures on each piece of paper are a good title for an article (excerpt):

What else is there in this class? What is missing?

Why would he do that?

Where do I agree or disagree, which is enlightening?

I eat, so I am.

So, I think I'm here.

Teaching should let students experience "re-creation"

Leave first, then approach.

Different coordinates, different perspectives.

Psychology, textbooks, teaching and learning

Math ≠ math book

……

We all admire Mr. Hong Jie's "brain hole", which is not as big as usual: poetry, dialectics and inspiration are all in it.

Every time he shows us an idea that makes us think, I have to stay for half a day and pause for a while before listening to his next idea.

Teacher Zhang's team is doing research. With such a commentator, the prospect of panoramic mathematics can only get better and better.

Teacher Hong Jie said that math is not a math book, and I don't think math is a math teacher. But can we escape? Just now, Teacher Luo said in the group, "How long does it take for an ordinary teacher to become a local' Zhang Hongwei'?" Perhaps, we can't be the "math madman" and the person who is passionate as soon as he steps onto the podium, but we can have his ideas, his practice, higher expectations and a sense of responsibility for education, and perhaps we can enjoy the wonderful scenery of "my own mathematics".

Finally, let's use teacher Zhang's words as inspiration: the paper will not test it, and the world will test him!