In our view, teaching calculus in middle schools is the so-called "decentralization", but in Russia's view, teaching calculus in middle schools is necessary, not "decentralization". Why is this? Let's make things clear first, and don't talk blindly with your eyes closed. According to the research of the School of Mathematical Sciences of Beijing Normal University, the elementary algebra and mathematical analysis course in Russian middle schools10-1has six chapters. Each chapter is: trigonometric function; Derivative and its application; Primitive function and integral; Exponential and logarithmic functions; Review questions; There are some difficult exercises. Textbooks can be completed by 139 class hours (3 class hours per week for basic course (a)) or 204 class hours (5 class hours per week for typical course (b)). The characteristics of this book are: first talk about trigonometric function, arrange the contents of calculus in historical order, and arrange the study of exponential function and logarithmic function after calculus. At the same time, the textbook introduces the relevant historical knowledge in the last section of each chapter. The biggest feature of the textbook is that it provides a rich exercise system suitable for mathematics teaching activities. Academician A.Kolmogorov, the editor-in-chief of the textbook, arranged the contents of the textbook in this way, which is reasonable and also the need of developing elementary mathematics logically. The advantages of this arrangement are: the original history of calculus is restored, and the book is rich in historical knowledge, similar to the teaching of physics, so that students can understand the historical development and origin of calculus. At the same time, the knowledge system of mathematics is developed according to the inherent logic of mathematical concepts, which makes students' knowledge structure more solid, rather than "castles in the air". Why do you say that? Compared with our domestic situation, domestic high school mathematics textbooks focus on all elementary functions (trigonometric function, exponential function, logarithmic function, etc.). ). In fact, senior three is preparing for the "College Entrance Examination" all the time, and the knowledge of calculus (listed as an "elective course") is useless. We have to ask: under the arrangement of this teaching content, how is the exponential function explained to students? It is also necessary to ask: How is the power of 2 √2 (irrational number) defined? Without the concepts of real numbers and limits in calculus, no one can explain them clearly to students. This kind of "knowledge defect" (that is, the elementary function "castle in the air" without the support of the concept of calculus limit) always exists in the brains of middle school graduates in China. From this point of view, China children's mathematical knowledge structure is not so "real" as Russian children, but we are more "virtual" because there are logical defects in children's minds. So, what should we do? On page 432 of the first section of Chapter 8 of Basic Calculus, J.Keisler gave the following definition: Let A and R be real numbers, and a > 0. We define the power from A to R (sorry that R should be in the upper right corner of A, so I won't type it) equal to ST (the power of K/H of A), where k/h ≈ R, where H and K are two infinite natural numbers, and their ratio is infinitely close to the real number R as long as we can guarantee the following conditions: k ≤ HR