Laboratory of Continuous Mathematical Education

Recently, we have seen quite a few topics about the educational system painted with a neutral negative. Yes, you can complain, you can go against the system, and you can offer reasonable additions. It will be about one St. Petersburg school, where they teach a lot, but among other things, the most important thing - they learn to learn. And here, it would seem, everything is simple, but there are enough features so that you can tell about it.



In the process of studying, we acquire some specific knowledge, they may be useful to us in the form we received, but most likely they will not be useful. You can take it as an axiom, you can prove it empirically, anyway - the school does not train specialists, and it should not. The school broadens the horizons, forms constructive thinking, and provides skills for processing and assimilating information .



It would seem that there is difficult; a textbook in hand, a little discipline, a motivation not to get a bad mark - that’s all that is needed, information has been learned. The theme is notched, answered perfectly, forgotten. But after five years, except for the vague "but somewhere I have already seen it," nothing remains. So the information did not come out, but it doesn’t matter, because diligence remains, the ability to take the right book, read it and mentally put yourself “excellent” for being such a wonderful specialist. Unless, of course, will be the right book. And time. And in school times, the memory was better, but now something is not remembered ... "And it is not my fault that it did not work out correctly, it was written in the book ... some kind."



I will allow myself to translate further speculations towards mathematics. After all, the school has a mathematical profile, and this is closer to me. And it is more difficult to deceive in exact sciences.

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Ask the student what he knows about the Viet theorem. Attempts to write out some spells from letters p and q can be safely considered helpless ... well, it turns out he writes part of her proof, well, well done, you can put "good"? But this is clearly not enough for its application, you need to know the wording, the condition of applicability. Information has a certain structure , mathematics is not a set of meaningless icons, and should not look like that to a student. This means that “cramming” is not limited, and the course must have a certain logical structure visible to the student. In the future, he himself will learn to distinguish the structure, but for now we will teach him to "good style."



But it’s not so easy for a teacher to build a good informative course with an understandable (self-evident) structure, so they usually prefer not to bother with telling students 50 interesting facts about triangles as if it was a program about wildlife on the BBC channel.



In LNMO, each course has a clear structure.



Ask the student what he is doing. Writes evidence. Why do we need this step? “It was so” is not the answer at all. Do colleagues often upset you with meaningless answers to the question of what they are doing: “I am writing a module,” “I work”? Such answers are often evidence of a complete lack of understanding of what is happening. And the meticulous teacher will ask what the letter m means in the proof, and the answer to the question will show possible misunderstanding, but in any case will not show understanding. After all, you can remember all the objects of evidence as a set of words. But mathematical reasoning is not a collection of meaningless words, and should not appear as such to a student.



Each action must withstand the critical question "why?". In a number of proofs, “tricks” are used (things that look as wonderful as they are meaningless), and they are so loved in olympiad tasks, but other actions should give a direct answer to the question. Reasoning should be logical , and the student must get used to it, require logicality from himself and from others.



In LNMO require rationale reasoning.







The presence of structure and consistency in information greatly simplifies its understanding. Now the student is able to "reject" the "handbook on higher mathematics for vocational schools" because he has no structure, and a number of things are not logical. One could learn from it, but it is hard. It is much more pleasant to take up the course of G. M. Fikhtenholz’s differential and integral calculus, although it will seem overwhelming to most school graduates. This is the first step to the acquisition of mathematical culture .



The ability to independently determine the quality of materials gives greater freedom in self-study, reducing the likelihood of “going in the wrong direction”, which is especially important for career growth. Yes, there is a big delay regarding the time of graduation, but who is sure that the university will somehow change the situation in a positive way? I now often had to prepare for exams in independently selected literature, observing fellow students who continue “to eat a cactus”. At work, so generally, a mess, let's not talk about sad things, and I’m not used to being sad because of other people's problems.



In general, to know a lot is good, but even better is to be able to do a lot. To do this, you should not be afraid to experiment , while having an idea of ​​the possible outcomes of the experiment, understand each step well. The classical school approach involves the use of specific techniques for specific tasks, “and now we have a solution of quadratic equations according to the Viete theorem,” and if you suddenly forget to say which method to solve the problem, then most likely the teacher will not get solutions. And now we will deal with the implementation of getting command line parameters via GetCommandLine (). Terribly boring and not vital.



In LNMO pose interesting problems.



And besides everyday interesting multi-task home tasks, various partly entertainment events take place. Four days ago, the “March Regatta” competition was held, which gathered more than 30 teams from different schools of St. Petersburg and the region. Schoolchildren competed in solving speed puzzles, something similar to the classic Olympiad, but the process is much more interesting from the outside - teamwork and oral defense of decisions makes up some element of the action. LNMO students won, which is not surprising for me, although they shared the first place with students of Lyceum No. 261. This shows that the level of LNMO students is not something supernatural, but it is still consistently high.







But if the “quick” tasks show a greater degree of intelligence and the presence of knowledge “on the surface”, then a really serious gap can be observed in long-term research work . From the statement of the problem to its solution, months and even years can pass, and here it is very opportune to systematize knowledge and the ability to think logically, and the ability to be creative.



In LNMO are engaged in research work.



The most important thing here, perhaps, is that it is interesting for students. They have a hobby related to solving the problem, they are actively developing in areas related to the problem. A good task is rarely associated with only one area, so this kind of work expands the mind quite well.







Therefore, research activities for schoolchildren are encouraged in the form of various activities related to job protection on a competitive basis. Participation in conferences such as ICYS (International Young Scientists Conference) or Intel ISEF (Science & Engineering Fair) is a truly exciting activity, and the prizes and gifts are very pleasing (who gives up on a modern laptop, for example). And yet, behind this show is the work, at least in part resembling a serious science, and in some cases, the results of such works have influenced the development of modern mathematics, physics, and programming. Students LNMO annually won awards at these competitions, and sometimes even the main ones. Still, the global scale of the event.







And now a similar competition is being held in St. Petersburg, I already wrote about this .



It may seem that such a deepening in science from school age impedes the socialization of students. In fact, the work takes place under the auspices of the supervisor and the teaching staff, so quite a lot of communication is assumed. The teaching staff, by the way, for the most part consists of doctors and candidates of science - it’s nice to listen to such people. And in order to protect a job, you need to be very good at presenting your ideas, so it turns out, this is a rare skill, but LNMO spends a lot of time on its development.



In general, students are not deprived of the attention. And the interest of teachers in the success of students can be surprised - this level in a rare private school is observed, despite the fact that LNME is a public educational institution, and more recently it has received the status of a lyceum. You can read about the merits of the school on its page, and from myself I will simply say that they teach very well, and this process is a pleasure. It would be very good if it continued in the university, but that's another story.







And so as not to be like last time , I warn you that the day is open doors very soon - March 21, so who are interested - do not miss the opportunity.