reform, every reform

… Is the norm in our country. I even composed a sequel (to a well-known melody), but I will not share it with readers. In the autumn of 2016, I participated in several meetings on education in Poland, and I also had several speeches, already strictly subject-based, at didactic conferences and meetings with teachers. It will be good if I write down my reflections.

The current reform of the organization of education is only a political idea, the implementation of a certain philosophy, invented in Prussia in the XNUMXth century and implemented not far from Poland at the beginning of the XNUMXth century: first we will destroy what we have, and then we will think. Yes, there are many weighty arguments for and against. For myself, I found that since the beginning of our independence in the XNUMXth century, each - without exception - the new government immediately began to reform education, always promising teachers that they would do better. I noted that the current government is the first to make no promises. Well, even then - at least here honestly.

Primary schools ("folk") - the invention of Frederick the Great. He did not do this out of love for the people - he concluded that an educated soldier shoots better.

Note that the system of such schools worked quite well. In general, whatever the Germans do, they do just that. A characteristic example is the discovery of the talent of one of the greatest scientists of all time: Charles Frederic Gauss (1777-1855). In a rural school near Hannover, an intelligent teacher (!) realized that an inconspicuous-looking boy might be a genius. So he passed the boy “higher”, it came to the prince, who was also able to assess who was in front of him, he poured a penny into further study ... and the world found someone truly extraordinary - and My thesis is that the most important for society are teachers, received another confirmation.

One hundred years of education

A brief overview of the school systems prevailing in Poland during the hundred years of our new independence will be of interest.

Very late, only in 1932. the so-called Jędrzewiczowska introduced order and united various systems - the remnants of sections. Prior to that, there were seven-year elementary schools. The middle schools had a system separate from the elementary schools. Education in junior high school lasted eight years: three years in junior high school and five years in high school. Theoretically, after the fourth grade of elementary school, a student could continue his education in the main secondary school, but the condition was the passing of an entrance examination, which often did not take into account the elementary school curriculum. That is why the so-called pre-exam preparation classes. There were three types of gymnasiums: humanitarian, mathematical and natural sciences, and classical, with Greek and Latin. The gymnasium ended with a matriculation exam, which was the basis for admission to higher educational institutions (without an entrance exam). Public education was paid.

Photo 1. Training kit for grade 1 of elementary school.

In 1932, the aforementioned educational reform was carried out, uniting the primary and secondary school system. Although there were still seven years in elementary school when the student wanted to continue his education, he entered junior high school after six years. Since then, the high school has been divided into a four-year high school and a two-year high school, followed by a matriculation exam.

After the war, the seven-year elementary school (in the changed name: elementary) was abandoned, the gymnasium disappeared, and the secondary school grew to four years. The author of these words passed the matriculation exams in the eleventh grade. So it was until the 70s, when it was proposed USSR-GDR model XNUMX-year comprehensive school. The press was choked with praise in honor of this idea and how it grows with us, a young, educated Pole. "Everyone will have a secondary education - this is proof of our concern for the younger generation!" It was like the situation of the African cascade, which, in order to govern an educated nation, granted a master's degree to all its subjects. So it was even better with him than in the Polish People's Republic - they all had higher education.

Photo 2a. (left) and 2b. Is it a snake or not a snake? Right: failed attempt to connect all buttons with a polyline

However, I must pay tribute to the educational authorities of that time. This reform was the only one that was properly prepared. There were approved programs (and meaningless "basic curricula"), trained teachers and administration. And maybe that's why the reform ... did not come into force. Someone sane realized that this still makes no sense, while other sane activists (then everyone was called “commies”) accepted rational arguments. The hostess, who claims that salt should be taken instead of sugar for baking a cake, cannot count on the fact that guests praise pastries - it is better to throw everything away before serving.

So the result is the longest-lived 8 + 4 system. The math program deserves a separate paragraph, but for now I'm talking only about the organization. In the late 90s, the idea was revived pre-war three-stage system, this time in the 6 + 3 + 3 option and - without discussing the realities - the reform was implemented. However, a dozen years have passed, at that time good junior schools were created, and most importantly, teachers learned to work in this system. In global education research, we have stepped over a dozen positions to be at the forefront of Europe.

I also note that in the field of higher education, we are now striving in Europe to adopt a unified system (the so-called. Bolognese system) and, despite the resistance and the associated nonsense, “somehow it works out”, in raising children, “everyone scratches the patella”. How many countries, so many systems. And very well. There is one principle in education, namely: there are no rules.

* * *

The world around us is changing at breakneck speed. The greatest invention of our time may turn out to be the Internet, prophetically predicted by Stanislaw Lem (in his stunning 1959 book Return from the Stars, Lem himself was surprised by the impact this not-so-successful book had on an entire generation). The school cannot remain indifferent to changes. We must think not only about how to teach, but - in the 20th century in the first place - what to teach. After all, we must prepare our children for professions that do not yet exist! Maybe these jobs don't even have names. Recall that we, teachers (of all levels), have the largest share in the so-called GDP. We are truly the best!!! Education is the axis of the world!!! It depends on us what our Commonwealth will be… well, not immediately, but in 30-XNUMX years. We do not work for ourselves or for our children. For grandchildren. Is this too far away for you? Let's do our job!

Rice. 1 Snake "calculated" by blocks or steps

Not much good can be said about the system of teacher education. The nonsense began with the fact that all teachers (that is, already active, working by profession) were driven into higher educational institutions - and this, moreover, "without interrupting work." Universities haven't changed their curricula because "one diploma!" Effect: The teacher went to lectures and exercises after exhausting work at school. I was a good student, but I could study for several hours a day. I couldn't imagine how a person who works "normally" would be able to handle this. It's a pity to keep writing...

Then it was different. However, the lack of properly educated teachers is the cause of the collapse of Polish education. The devil is in the details. What does "well educated" mean? Ah, that's a topic for another study. It is definitely only loosely related to academic degrees and titles.

We will constantly look for new methods and content of training. However, “we will look for” is not the same as “immediately implement - we will throw out the old, we will accept the new.” No. Let's implement only what is best. Often, new means only tinsel, a facade, or reheating old chops. Indeed, it may not make sense to teach children how to make a fire without matches, but orienting the cardinal points to the sun makes sense, even if everyone has a GPS. Let's keep common sense even in the XNUMXth century.

Math blocks

One of the most interesting didactic ideas is the popularization of Lego bricks, which we mentioned a month ago. This time, I'm going to talk about the teacher simulation classes that LEGO Education runs from my own scenarios. In this example, I will express what I expect from primary school teachers.

Photo 3. Another version of the snake

Definitely not something I've seen several times. The teacher states that the parallelogram task is too difficult for her. Another is afraid of the word "cubic". Some people don't even open my popular book "because it's the math itself." One lady “hates geometry”, someone divides by zero, someone does not see anything characteristic in the sequence of numbers 1, 3, 5, 7, 9, 11, 13, ... and so on. I am surprised that my students do not see the connection between the sequence of Fibonacci numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,…. and the sequence 5, 9, 14, 22, 35, 56, 90, 145, 234, ….. Now I know where this numerical immunity comes from. And that's what I teach computer science students in the first place.

The educational set of Lego bricks for the first grade of elementary school consists of a gray rug and bricks, as shown in the picture below. PHOT. one. One of the 1x1 bricks with a drawn eye. This will be the snake eye in the suggested exercises.

I looked at this set from the point of view of a "professional mathematician". I liked it, I started playing with it myself. It turned out that I can "conjure" a large piece of the "real" out of it. My colleagues will blame me for inventing the date. real math. For if this is true, then it is probably not true. Possibly, but I won't go into that discussion.

Photo 4. This puzzle is axisymmetric.

I'll say it. I liked the number of buttons in separate blocks in this set - but I will postpone this question until the next article. From the point of view of "university" mathematics, a very interesting problem is a part of algebraic geometry, the so-called divisional theory, algebraic tensor and faculties of mathematics unknown to students with a polytechnical education (and no other section, except for a narrow and complex section - namely, tensor algebra). I don't know if those who created this problem knew about it (it's number 5). Probably no.

In class with teachers, I said something like this: I'm the only one in the class who sees the depth of this - not because I'm "so smart", but because I've only been doing this professionally for twenty years. It would be absurd to expect teachers to have the same knowledge. But I encourage you to discuss other topics that I discuss below: symmetry, classification, number curiosities - I would like teachers to be able to convey this to their students, for example in the form of encouraging them to go there (please also read below about where to go with the Gzhes peak in the Western Tatras). If there is something beautiful in the profession of a teacher, it is the ability to direct a student in the right direction: go there, see something interesting, become interested, maybe this is your life path?

Okay, end of retreat. No, it's not over yet! “I have to” is another thing. In the 70s of the last century, they tried to teach teachers and students by giving them - from kindergarten - a summary of the university course in mathematics. And how was it supposed to end?

Let's return to our tasks and Lego. An eye is drawn on the white block - this will be the snake's eye, which we will now decompose (that is, the children will decompose it). The first 6 lengths are easy. Then 10 lengths (here you need to break the snake). This is followed by a controversial but very interesting task: to make the longest snake.

Why controversial? The suggested answer is 44, which means you should turn them all on and roll the snake into a ball. Yes, a snake can curl up like that. But both I and about half of my “respondents” believe that the snake should not contact itself. Why can I be right? Is a snake a line, or at least something oblong, and a square is oblong? Second question: if the snake looks like this photo 2аwhere is the tail? In what direction does the tail go behind the head? Of course, these may be inappropriate questions, especially since the case is live and you can immediately clarify your doubts ...

Photo 5. You see the central symmetry here, right?

Task 1. (difficult, and certainly difficult for first-year students). Do what we see on photo 2аis it a snake? What does it mean that he is a "serpent"? This means that you can make this shape a polyline. Let's try (photo 2b). I wrote a minute ago that "maybe I'm right." I do not need, I understand that I do not need. I do not want to enter into a discussion that may be of interest to professional educators. But I asked myself, is it a good effect? Do I like the pattern? And, of course, I started collecting the rest. It is impossible to measure which puzzle will be more beautiful than the other. But you can ask the question: which snake is the most beautiful. Let's vote.

Task 2. Make the most beautiful snake. Use almost all bricks. But why limit yourself to snakes?

Task 3. Assemble the most beautiful puzzle using all the blocks (with or without the snake eye). i like that(photo 4, 5). They have symmetry - the first is axial, the second is central.

Task 4. Make a symmetrical ornament so that there are no “holes” like on mine PHOT. one.

Photo 6. Symmetry "with holes"

Is it possible to create an ornament that would have axial symmetry, but with respect to the x-axis, i.e. horizontal? What about vertical? This puzzle also has central symmetry. The next puzzle in the LEGO Education XNUMXst grader set is very interesting... and not many people know. In the Western Tatras there is a not very ambitious Gzhes peak, where tourists come for half a day from the Chocholowska Valley during the season. It is enough to turn west from it, towards the Personal, and in ten minutes you will find yourself in another world. But let's not dream. The mission of the company is to:

Task 5. Use six bricks to build hose 14.

The problem can be solved in many ways. The snake must have a head. Therefore, there are five blocks left to make a tail of length 13. Which blocks from our set should we take? There are only two possibilities: 13 = 4 + 3 + 2 + 2 + 2 = 3 + 3 + 3 + 2 + 2. So there are only two possibilities to stack the snake!

Photo 7. Different arrangements of the same snake

Oh, are you really just the two? So we only have two snakes? It depends on your point of view. snakes on PHOT. one Should we be different or the same? We can say that this is the same snake, only coiled differently. You say so Here you go, quest: Task 6. In how many ways can a snake be seen on PHOT. one?

Task 7. Arrange ... the following tasks. No, this is not a mistake. Arrange it yourself. I will give some advice.

Task 8. When you let your imagination run wild, imagine that the snakes are the same species as PHOT. one they are men. The male is characterized by the presence of a tail of such colors as there: red, light green and dark green. The order of the colors is arbitrary, but there cannot be “spots”, i.e. the combination of light green-dark green-light green is not allowed. How many types of males are possible?

Task 9. And when will we allow “patches”?

Task 10. Well, consider female snakes of type 3 + 3 + 3 + 2 + 2. Arrange such a snake. In how many ways can it become broken? How many types of women are there?

Task 11. Repeat the previous steps for other hose lengths.

Task 12. Surprise the teacher with the question: how long is the hose laid? fig. 1. He folded his back in a figure eight and sleeps contentedly. If the teacher says: “for the body (tail) you used five tubular bricks, four two-mouthed bricks, one four-mouthed, and including the head - 28, then the snake has a length of 28” - then answer: “Let's count like in the game Chinaman. How many steps are needed to complete the cycle (fig. 1)? I take off from my head and after 29 steps I find myself in a field from which I still have a step to close the loop. This means the length is 30. 1. Snake, "calculated" in blocks or steps

Task 13. Na PHOT. one ignore the colors. How many buttons do you see in subsequent layers? What are these numbers called? Add them all. You got 36, which is six times six. Make a 6 by 6 square.

Photo 8. Do you see 6 by 6 here?

Task 14. What do you see in photo 9? 

Photo 9. Do we have anything interesting here?