Why did Russia devolve calculus to middle school?

It seems to us that calculus is called "decentralization" in secondary school, but in the Russian context it is necessary, not "decentralized", to teach calculus at the secondary level. This is why.

Let's get things straight, and we can't just talk. According to the research of the School of Mathematics Science of Beijing Normal University, the course of "algebra and Mathematical Analysis preliminary" in 10-11 grade of Russian secondary school has a total of six chapters. The chapters are: Trigonometric functions, derivative and its application, original function and integral, exponential and logarithmic functions, review questions, and exercises with certain difficulty. The textbook can be completed in 139 hours (the basic course (A) with a Zhou Co time of 3) or 204 hours (a typical course (B) with a Zhou Co time of 5). The book is characterized by: first, trigonometric functions, according to the historical order of the calculus content, Gong and logarithmic function of learning arranged after the calculus. At the same time, the textbook introduces relevant historical knowledge in the last section of each chapter. The greatest feature of textbooks is to provide a rich exercise system suitable for mathematics teaching activities.

It is reasonable for the A.kolmogorov academician, the editor of the textbook, to arrange the teaching material in this way, and also the need of logic to carry out elementary mathematics. The advantage of this arrangement is that it restores the historical appearance of calculus, the book has a wealth of historical knowledge, similar to teaching physics lectures, so that students understand the history of the development of calculus and its origin, at the same time, according to the inherent logic of mathematical concepts to expand the knowledge system of mathematics, so that students have a solid knowledge structure, not "castles in the castle ”。 Why do you say that?

Compared with our domestic situation, the domestic high school mathematics textbooks used to focus on all elementary functions (trigonometric, Gong and logarithmic functions, etc.), in fact, the third grade all the time to meet the "college entrance Examination" to prepare, calculus knowledge (listed as "elective") in the form of a fictitious. We want to ask: under this kind of teaching content arrangement, Gong is how to explain to the student. Also ask: 2 of the √2 (irrational number) of how the second party is defined. If there is no real and limit concept in calculus, this is something that no one can tell the students clearly. This "knowledge flaw" (i.e. the elementary function "castles in the Castle"), which is not supported by the concept of infinitesimal calculus, always exists in the skull of our high school graduates. From this point of view, the Chinese children's mathematical knowledge structure than the Russian children "real", we are more "virtual", because the children have logical flaws in their minds. So, what are we going to do?

In the electronic version of basic calculus, chapter eighth, page No. 432 of the first section, J.keisler the following definitions:

DEFINITION

Let A and R are Real,a >0. We define A's R-side (sorry, R should hit the upper right corner of a, I won't play up) equals St (A's k/h), where K/h≈r.

Here, H and K are two infinitely large natural numbers, and their ratios are infinitely close to the real number R. We can only ensure that the following conditions are true:

K≤hr < K+1 (both sides divided by h,1/h to infinity)

It's OK. In fact, the k/h (Super rational number) of a is easily imagined by the students. Since then, the "logic defect" in the skull of middle school students in China has disappeared, and Beijing has surpassed Moscow.

Explanation: Pocket electronic book involves to the middle school mathematics teaching reform, this is I originally did not think of.