Selected Works of Ding Ersheng on Mathematical Education

Author: Ding Ersheng / Country: Mainland China
Publisher:
Publish Date: 2005-12-28
Features: First, the content of the textbook is extremely poor and outdated, far behind the actual needs of socialist construction. The current mathematics curriculum in primary and secondary schools is basically based on the system formed before the 16th and 17th centuries. Plane geometry is largely based on Euclidean geometry from over two thousand years ago. These contents are products of historical conditions before the 17th century, adapted to the low level of social productivity at that time. However, by the 1960s, these contents have become extremely outdated and backward, far behind the actual needs of socialist construction.
Of course, some basic concepts of elementary mathematics are still widely used in people's daily activities and production, and they are also essential for learning higher mathematics. We still study them in primary and secondary schools. But the issue is not here. The serious problem lies in the unreasonable current mathematics teaching system. Under this system, a middle school student after 12 years of study still cannot learn mathematics widely used in modern production and cutting-edge technology, such as analytical geometry, calculus, differential equations, probability theory and mathematical statistics, and mathematical logic. Instead, they spend a lot of precious time studying almost all outdated content accumulated in the historical development of elementary mathematics.
Over the 12 years of primary and secondary education, seven years are spent on arithmetic and four years on geometry, accounting for three-quarters of the total class hours. In arithmetic, a lot of time is wasted solving complex arithmetic problems. Although the "chicken-and-rabbit problem" no longer exists, similar problems are still abundant. Algebra was introduced to replace and simplify arithmetic, making it easy to solve arithmetic problems using algebraic methods. However, in the current arithmetic curriculum, arithmetic methods are retained in large quantities while rejecting the advanced and simpler algebraic methods.
In middle school geometry, the Euclidean geometry system from over two thousand years ago is preserved intact. In the 1960s, it is still taught as an important part of general mathematics, requiring every middle school student to spend four years studying it, which is completely unnecessary. The material of Euclidean geometry is merely a reflection of the properties of simple geometric figures and geometric facts encountered in production and daily life. In its original form, it is simple and clear for anyone to understand and master useful geometric facts, such as similar triangles and the fact that the sum of the angles in a triangle is 180°. These can be mastered by students in a very short time. However, due to a one-sided pursuit of systematic completeness, pure methods, and rigorous reasoning, geometry has become a、、、.
Moreover, the method of Euclidean geometry is also outdated and backward, failing to meet the demands of modern production and modern mathematics. The ancient synthetic method is no longer sufficient in modern mathematics. With the powerful tools of modern mathematics, there is no need to emphasize the synthetic method, which is a regression. More seriously, the geometry curriculum still retains a large number of problems with no scientific value or practical significance, wasting the precious time and talent of countless young students and the energy of middle school teachers. Why is this still done? To a large extent, it is to cope with college entrance exams. In fact, if you think carefully, what is the difference between this and reading the Four Books and Five Classics and writing eight-legged essays in feudal China to take the imperial examinations? The Confucian shop has been overthrown, and the imperial examinations have been abolished. Why should the Euclidean geometry system, this foreign eight-legged essay and foreign dogma, be so sacred and inviolable? Germany and France have long broken free from the framework of Euclidean geometry, Japan is also in the process of breaking free, and the majority of people tend to break free. Most other countries have also significantly reduced Euclidean's synthetic geometry system. If these ancient things cannot meet the needs of capitalism and are being abolished, can they still meet the needs of our socialist construction?
Some people argue that plane geometry can cultivate logical thinking, and solid geometry can develop spatial imagination. Of course, cultivating logical thinking and spatial imagination is important, whether for college entrance exams or for participating in production labor. These are necessary for middle school students. But the question is not here. The question is whether spatial imagination must be cultivated through solid geometry. Is solid geometry the best tool for developing spatial imagination? Solid geometry studies the relationships between simple geometric elements and the properties of figures, which can be mastered in a short time. In reality, most of the time is spent on proofs, which have little effect on cultivating spatial imagination. Therefore, even after studying solid geometry, students do not have strong spatial concepts. In fact, the most effective way to cultivate spatial imagination is to let students engage in hands-on activities, such as assembling machine parts or making models. If the goal is to develop the ability to recognize three-dimensional figures, using drafting is much better than using solid geometry. Drafting is highly practical in production. Why can't drafting be used to replace solid geometry in cultivating spatial imagination?
As for cultivating logical thinking, why must plane geometry be used? Can't calculus and other subjects also cultivate logical thinking? The deductive reasoning format of plane geometry not only fails to effectively cultivate thinking ability but also hinders the development of dialectical thinking. Deductive methods are mainly for organizing mathematical knowledge. However, relying solely on deduction to develop mathematics is insufficient. Relying solely on a deductive system to educate students can easily lead to one-sided, subjective, and rigid thinking, making them believe that mathematical truth is the result of deductive reasoning rather than a summary of practice. Of course, the methods of formal logic are very useful for mathematics. However, it should also be noted that formal logic is far from sufficient for mathematics. Relying solely on formal logic to educate students can have the opposite effect.
The above situation fully demonstrates that the Euclidean geometry system, as a subject in secondary school mathematics, is merely a foreign eight-legged essay and foreign dogma, which must be. Of course, none of this negates the practical value of some basic properties of figures and certain geometric relationships. P32-P34