-Talking about how to cultivate the flexibility and creativity of calculation.

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What is written calculation? Written calculation is a written form that records the calculation process and results. There are various forms of pen calculation, which can be generally divided into horizontal pen calculation and vertical pen calculation; The same written calculation is also different in form and eclectic. As far as vertical pen calculation is concerned, there are standard vertical pen calculation and non-standard vertical pen calculation.

Looking at the current primary school mathematics textbooks, although there are differences in the concept and intensity of calculation teaching reform, one thing is very consistent, that is, the standard vertical pen calculation is the only destination of calculation teaching in middle and lower grades. For example, in the second phase, when learning four decimal operations, the standard vertical pen calculation becomes a wooden bridge for students to reach the other side of the calculation, and there is no other way.

Division is a difficult point in primary school calculation teaching, and the difficulty lies in vertical division. An excellent young teacher once told me that there was a "poor student" in her class who couldn't understand the process and method of "3 12÷3" and cried. Later, the child asked her, 300÷3= 100, 12 ÷ 3 = 4, 100+4 = 104, so it is easy to get the result. Why do we have to use vertical calculation? Are children who don't know the standard vertical pen calculation poor students? This child is not bad at all! He has a strong desire to learn. When he encounters difficulties, he can actively seek effective calculation strategies from the relationship between mathematical models and numbers, which not only solves the problem, but also dares to question it. Isn't this the "sense of number" (abbreviated as "sense of number") and mathematical spirit that mathematics education should cultivate? Indeed, adults must seriously reflect and actively respond to the question of the third-grade primary school student in front.

Friedenthal said that the standard form of long division "is almost impossible to become a' necessity' in the calculator era". Times have changed, and the standard form of program calculation-vertical pen calculation is no longer the application skill that students need to adapt to future social life and further development. International mathematics education research also shows that this standard program calculation is far from children's experience, and it is an algorithm that is difficult for children to master and easy to make mistakes. Children often know what it is but don't know why. Why does our primary school mathematics education still emphasize vertical algorithm, and primary school mathematics examination still needs to take vertical written calculation? Have you ever thought about the bad consequences caused by the compulsion and strengthening of vertical pen calculation?

Mastering vertical division must break through two difficulties: one is to understand how the format and steps of vertical division are abstracted from specific situational operations, and the other is to master the method of "trial and error". In order to solve the above difficulties, textbook editors have carefully designed and paved the way, and front-line teachers have tried their best to keep improving, but the teaching effect is still not satisfactory; Some people even exclaim that the reform of mathematics curriculum has led to a general decline in students' computing ability, and they must return to the old road of strengthening vertical written arithmetic training.

In fact, if the calculation ability of primary school students has indeed declined, we can't blame the curriculum reform. The specific objectives of integer calculation in mathematics curriculum standard (experimental draft) are divided into four categories: ① proficient in oral calculation; 2 can do oral calculations; 3 can calculate; 4 can write calculations. "Oral computing ability" and "written computing ability" should be the proper meanings of "computing ability"; "Being able to write" should include horizontal writing and vertical writing. If this interpretation is correct, then at present, any version of primary school mathematics textbooks has not fully achieved these goals.