Why do they study in Israel using old Soviet textbooks?

2024 Author: Seth Attwood | [email protected]. Last modified: 2023-12-16 15:55

In the early 30s of the last century, the world's best textbooks on Mathematics of the "outdated" "pre-revolutionary" Kiselev, returned to socialist children, instantly raised the quality of knowledge and improved their psyche. And only in the 70s did the Jews manage to change "excellent" for "bad".

Academician V. I. Arnold

The call to "return to Kiselev" has been ringing for 30 years. It arose immediately after the reform-70, which expelled excellent textbooks from the school and launched the process progressive degradation of education … Why does this appeal not subside?

Some people explain this by "nostalgia" [1, p. 5]. The inappropriateness of such an explanation is obvious if we recall that the first who, back in 1980, on the fresh trail of reform, called for a return to the experience and textbooks of the Russian school, was Academician L. S. Pontryagin. Having professionally analyzed the new textbooks, he convincingly, using examples, explained why this should be done [2, p. 99-112].

Because all new textbooks are focused on Science, or rather, on pseudoscience and completely ignore the Pupil, the psychology of his perception, which the old textbooks knew how to take into account. It is precisely the "high theoretical level" of modern textbooks that is the root cause of the catastrophic decline in the quality of teaching and knowledge. This reason has been valid for more than thirty years, not allowing to somehow rectify the situation.

Today, about 20% of students master mathematics (geometry - 1%) [3, p. 14], [4, p. 63]. In the 1940s (right after the war!) 80% of schoolchildren who studied "according to Kiselev" mastered all sections of mathematics.[3, p. 14]. Is this not an argument for returning it to children?

In the 1980s, this appeal was ignored by the ministry (M. A. Prokofiev) under the pretext that "new textbooks must be improved." Today we see that 40 years of "perfecting" bad textbooks have not produced good ones. And they could not give birth.

A good textbook is not "written" in one or two years by order of the ministry or for a competition. It will not be "written" even at ten years old. It is developed by a talented practicing teacher together with students throughout their pedagogical life (and not by a mathematics professor or academician at a writing desk).

Pedagogical talent is rare - much less often than mathematics itself (there are a lot of good mathematicians, there are only a few authors of good textbooks). The main property of pedagogical talent is the ability to sympathize with the student, which allows you to correctly understand the course of his thought and the causes of difficulties. Only under this subjective condition can the correct methodological solutions be found. And they must still be checked, corrected and brought to a result by long practical experience - careful, pedantic observations of the numerous mistakes of students, their thoughtful analysis.

This is how, for more than forty years (the first edition in 1884), the teacher of the Voronezh real school A. P. Kiselev created his wonderful, unique textbooks. His highest goal was the understanding of the subject by students. And he knew how this goal was achieved. That is why it was so easy to learn from his books.

AP Kiselev expressed his pedagogical principles very briefly: “The author … first of all set himself the goal of achieving three qualities of a good textbook:

accuracy (!) in the formulation and establishment of concepts, simplicity (!) in reasoning and

conciseness (!) in the presentation "[5, p. 3].

The deep pedagogical significance of these words is somehow lost behind their simplicity. But these simple words are worth thousands of modern dissertations. Let's think about it.

Modern authors, following the instructions of A. N. Kolmogorov, strive "for a more rigorous (why? - IK) from the logical point of view, the construction of a school course in mathematics" [6, p. 98]. Kiselev cared not about "rigor", but about the accuracy (!) Of the formulations, which ensures their correct understanding, adequate to science. Accuracy is consistency with meaning. The notorious formal "rigor" leads to distance from meaning and, in the end, completely destroys it.

Kiselev does not even use the word "logic" and does not speak about "logical proofs" that seem to be inherent in mathematics, but about "simple reasoning". In them, in these "reasoning", of course, there is logic, but it occupies a subordinate position and serves a pedagogical goal - intelligibility and persuasiveness (!)reasoning for the student (not for the academician).

Finally, conciseness. Please note - not brevity, but conciseness! How subtly Andrei Petrovich felt the secret meaning of the words! Brevity presupposes contraction, throwing away something, perhaps essential. Compression is lossless compression. Only what is superfluous is cut off - distracting, clogging, interfering with concentration on the meanings. The purpose of brevity is to reduce volume. The goal of conciseness is purity of essence! This compliment to Kiselev sounded at the conference "Mathematics and Society" (Dubna) in 2000: "What purity!"

The remarkable Voronezh mathematician Yu. V. Pokorny, "sick of the school", found that the methodological architecture of Kiselev's textbooks is most consistent with the psychological and genetic laws and forms of the development of young intelligence (Piaget-Vygotsky), ascending to Aristotle's "ladder of soul forms". "There (in Kiselev's geometry textbook - IK), if anyone remembers, initially the presentation is aimed at sensorimotor thinking (we will superimpose, since the segments or angles are equal, the other end or the other side coincide, etc.) …

Then the worked out schemes of actions, providing the initial (according to Vygotsky and Piaget) geometric intuition, by combinations lead to the possibility of guesses (insight, aha-experience). At the same time, argumentation in the form of syllogisms is growing. Axioms appear only at the end of the planimetry, after which more rigorous deductive reasoning is possible. It was not for nothing that in the past it was precisely geometry according to Kiselev that instilled in schoolchildren the skills of formal logical reasoning. And she did it quite successfully "[7, pp. 81-82].

Here is another secret of Kiselev's wonderful pedagogical power! He not only psychologically correctly presents each topic, but builds his textbooks (from junior grades to senior grades) and chooses methods according to age-specific forms of thinking and children's understanding capabilities, slowly and thoroughly developing them. The highest level of pedagogical thinking, inaccessible to modern certified methodologists and successful textbook authors.

And now I want to share one personal impression. While teaching the theory of probability at the technical college, I always felt discomfort when explaining to students the concepts and formulas of combinatorics. The students did not understand the conclusions, they were confused in the choice of formulas for combinations, placements, and permutations. For a long time it was not possible to clarify, until the thought dawned on me to turn to Kiselev for help - I remembered that at school these questions did not cause any difficulties and were even interesting. Now this section has been thrown out of the secondary school curriculum - in this way the Ministry of Education tried to solve the problem of overload, which it created itself.

So, after reading Kiselev's presentation, I was amazed when I found in him a solution to a specific methodological problem, which for a long time did not work out for me. An exciting connection between times and souls arose - it turned out that A. P. Kiselev knew about my problem, thought about it and solved it a long time ago! The solution consisted in a moderate concretization and psychologically correct construction of phrases, when they not only correctly reflect the essence, but take into account the student's train of thought and direct it. And it was necessary to suffer pretty much in the long-term solution of a methodological problem in order to appreciate the art of A. P. Kiselev. Very inconspicuous, very subtle and rare pedagogical art. Rare! Modern scholarly educators and authors of commercial textbooks should start researching the textbooks of the gymnasium teacher A. P. Kiselev.

A. M. Abramov (one of the reformers-70 - he, according to his admission [8, p. 13], participated in writing "Geometry" Kolmogorov) honestly admits that only after many years of studying and analyzing Kiselev's textbooks began to understand a little hidden pedagogical "secrets" of these books and the "deepest pedagogical culture" of their author, whose textbooks are a "national treasure" (!) of Russia [8, p. 12-13].

And not only Russia, - all this time in Israeli schools they have been using Kiselev's textbooks without any complexes. This fact is confirmed by the director of the Pushkin House, Academician N. Skatov: “Now more and more experts argue that, experiments, clever Israelis taught algebra according to our textbook Kiselev. " [9, p. 75].

We have obstacles coming up all the time. The main argument: "Kiselev is outdated." But what does that mean?

In science, the term "obsolete" is applied to theories, the fallacy or incompleteness of which is established by their further development. What is "obsolete" for Kiselev? Pythagorean theorem or something else from the content of his textbooks? Perhaps, in the era of high-speed calculators, rules for actions with numbers that many modern high school graduates do not know (cannot add fractions) are outdated?

For some reason, our best modern mathematician, Academician V. I. Arnold does not consider Kiselev "obsolete". Obviously, in his textbooks there is nothing wrong, not scientific in the modern sense. But there is that highest pedagogical and methodological culture and conscientiousness that have been lost by our pedagogy and which we will never reach again. Never!

The term "obsolete" is just sly receptioncharacteristic of modernizers of all times. A technique that affects the subconscious. Nothing truly valuable becomes obsolete - it is eternal. And it will not be possible to "throw him off the steamer of modernity," just as the RAPP modernizers of Russian culture did not manage to throw off the "obsolete" Pushkin in the 1920s. Kiselev will never be outdated, nor will Kiselev be forgotten.

Another argument: the return is impossible due to a change in the program and the merging of trigonometry with geometry [10, p. 5]. The argument is not convincing - the program can be changed again, and trigonometry can be disconnected from geometry and, most importantly, from algebra. Moreover, this "connection" (as well as the connection of algebra with analysis) is another gross mistake of the reformers-70, it violates the fundamental methodological rule - difficulties to separate, not connect.

Classical teaching "according to Kiselev" presupposed the study of trigonometric functions and the apparatus of their transformations in the form of a separate discipline in the X grade, and at the end - the application of the learned to the solution of triangles and to the solution of stereometric problems. The latter topics have been remarkably methodically worked out through a sequence of common tasks. The stereometric problem "in geometry with the use of trigonometry" was a compulsory element of the final examinations for the certificate of maturity. The students did well with these tasks. Today? MSU applicants cannot solve a simple planimetric problem!

Finally, another killer argument - "Kiselev has mistakes" (Prof. N. Kh. Rozov). I wonder which ones? It turns out - omissions of logical steps in the proofs.

But these are not mistakes, these are deliberate, pedagogically justified omissions that facilitate understanding. This is a classic methodological principle of Russian pedagogy: "one should not strive immediately at a strictly logical substantiation of this or that mathematical fact. For the school," logical leaps through intuition "are quite acceptable, providing the necessary accessibility of educational material" (from the speech of a prominent methodologist D. Mordukhai-Boltovsky at the Second All-Russian Congress of Teachers of Mathematics in 1913).

Modernizers-70 replaced this principle with the anti-pedagogical pseudoscientific principle of "rigorous" presentation. It was he who destroyed the technique, gave rise to misunderstanding and disgust of students for mathematics … Let me give you an example of pedagogical deformities to which this principle leads.

Remembers the old Novocherkassk teacher V. K. Sovaylenko. "On August 25, 1977, a meeting of the UMS of the USSR MP was held, at which Academician A. N. Kolmogorov analyzed mathematics textbooks from the 4th to 10th grades and ended the examination of each textbook with the phrase:" After some correction, this will be an excellent textbook, and if you understand this question correctly, then you will approve this textbook. "A teacher from Kazan who was present at the meeting said with regret to those sitting next to them:" This is necessary, a genius in mathematics is a layman in pedagogy. He doesn't understand that these are not textbooks, but freaksand he praises them."

The Moscow teacher Weizman spoke in the debate: "I will read the definition of a polyhedron from the current geometry textbook." Kolmogorov, after listening to the definition, said: "Right, all right!" The teacher answered him: "Scientifically, everything is correct, but in the pedagogical sense, it is blatant illiteracy. This definition is printed in bold, which means that it is necessary to memorize, and it takes half a page. ? While in Kiselev this definition is given for a convex polyhedron and takes less than two lines. This is both scientific and pedagogically correct."

Other teachers said the same in their speeches. Summing up, A. N. Kolmogorov said: “Unfortunately, as before, unnecessary criticism continued instead of a business conversation. You did not support me. But it doesn’t matter, since I reached an agreement with Minister Prokofiev and he fully supports me. This fact is stated by V. K. Sovailenko in an official letter to the FES dated 25.09.1994.

Another interesting example of profanation of pedagogy by specialist mathematicians. An example that unexpectedly revealed one truly "secret" of the Kiselev books. About ten years ago I was present at a lecture by our prominent mathematician. The lecture was devoted to school mathematics. At the end I asked the lecturer a question - how does he feel about Kiselev's textbooks? Answer: "The textbooks are good, but they are outdated." The answer is banal, but the continuation was interesting - as an example, the lecturer drew a Kiselevsky drawing for the sign of parallelism of two planes. In this drawing, the planes bent sharply in order to intersect. And I thought: "Indeed, what a ridiculous drawing! Drawn what cannot be!" And suddenly I clearly remembered the original drawing and even its position on the page (bottom-left) in the textbook, which I had studied almost forty years ago. And I felt a feeling of muscular tension associated with the drawing, as if I were trying to forcibly connect two non-intersecting planes. By itself, a clear formulation arose from memory: "If two intersecting lines" of the same plane are parallel -.. ", and after it all the short proof" by contradiction."

I was shocked. It turns out that Kiselev imprinted this meaningful mathematical fact in my mind forever (!).

Finally, an example of Kiselev's unsurpassed art in comparison with contemporary authors. I am holding in my hands a textbook for the 9th grade "Algebra-9", published in 1990. The author - Yu. N. Makarychev and K0, and by the way, it was the textbooks of Makarychev, as well as Vilenkin, who cited LS Pontryagin as an example of "poor quality, … illiterately executed" [2, p. 106]. First pages: §1. "Function. Domain of definition and range of values of a function".

The heading states the goal of explaining to the student three interrelated mathematical concepts. How is this pedagogical problem solved? First, formal definitions are given, then a lot of motley abstract examples, then a lot of chaotic exercises that do not have a rational pedagogical goal. There is overload and abstractness. The presentation is seven pages long. The form of presentation, when they start from out of nowhere "strict" definitions, and then "illustrate" them with examples, is stencil for modern scientific monographs and articles.

Let us compare the presentation of the same topic by A. P. Kiselev (Algebra, Part 2. Moscow: Uchpedgiz. 1957). The technique is reversed. The topic begins with two examples - everyday and geometric, these examples are well known to the student. The examples are presented in such a way that they naturally lead to the concepts of variable, argument, and function. After that, definitions and 4 more examples are given with very brief explanations, their purpose is to test the student's understanding, to give him confidence. The last examples are also close to the student, they are taken from geometry and school physics. The presentation takes two (!) Pages. No overload, no abstractness! An example of "psychological presentation", in the words of F. Klein.

Comparison of volumes of books is significant. Makarychev's textbook for grade 9 contains 223 pages (excluding historical information and answers). Kiselev's textbook contains 224 pages, but is designed for three years of study - for grades 8-10. The volume has tripled!

Today, regular reformers are trying to reduce overload and "humanize" education, ostensibly taking care of the health of schoolchildren. Words words… In fact, instead of making mathematics understandable, they destroy its core content. First, in the 70s. "raised the theoretical level", undermining the psyche of children, and now "lower" this level by the primitive method of discarding "unnecessary" sections (logarithms, geometry, etc.) and reducing the teaching hours[11, p. 39-44].

A return to Kiselev would be a genuine humanization. He would make mathematics understandable to children and beloved again. And there is a precedent for this in our history: in the early 30s of the last century, the "outdated" "pre-revolutionary" Kiselev, returned to "socialist" children, instantly raised the quality of knowledge and improved their psyche. And maybe he helped to win the Great War

The main obstacle is not the arguments, but clans that control the Federal set of textbooks and profitably multiply their educational products … Such figures of "public education" as the recent chairman of the FES G. V. Dorofeev, who put his name on, probably, a hundred educational books published by "Bustard", L. G. Peterson [12, p. 102-106], I. I. Arginskaya, E. P. Benenson, A. V. Shevkin (see the site "www.shevkin.ru"), etc., etc. Evaluate, for example, a modern pedagogical masterpiece aimed at the "development" of the third grader:

"Problem 329. To determine the values of three complex expressions, the student performed the following actions: 320-3, 318 + 507, 169-3, 248: 4, 256 + 248, 231-3, 960-295, 62 + 169, 504: 4, 256 + 62, 126 + 169, 256 + 693. 1. Complete all the indicated actions. 2. Reconstruct complex expressions if one of the actions occurs in two of them (??). 3. Suggest your continuation of the task. " [thirteen].

But Kiselev will return! In different cities there are already teachers who work "according to Kiselev." His textbooks begin to be published. The return is coming invisibly! And I remember the words: "Long live the sun! Let the darkness hide!"

Reference:

It is generally accepted that the well-known reform of mathematics in 1970-1978. ("Reform-70") was invented and implemented by Academician A. N. Kolmogorov. It's a delusion. A. N. Kolmogorov was put in charge of the 70 reform already at the last stage of its preparation in 1967, three years before its start. His contribution is greatly exaggerated - he only concretized the well-known reformist attitudes (set-theoretic content, axioms, generalizing concepts, rigor, etc.) of those years. He was meant to be "extreme." It has been forgotten that all the preparatory work for the reform was carried out for more than 20 years by an informal group of like-minded people, formed back in the 1930s, in the 1950s-1960s. strengthened and expanded. At the head of the team in the 1950s. Academician A. I. Markushevich, who conscientiously, persistently and effectively carried out the program outlined in the 1930s. mathematicians: L. G. Shnirelman, L. A. Lyusternik, G. M. Fichtengoltz, P. S. Alexandrov, N. F. Chetverukhin, S. L. Sobolev, A. Ya. Khinchin and others [2. S. 55-84]. Being very talented mathematicians, they did not know the school at all, had no experience in teaching children, did not know child psychology, and therefore the problem of raising the “level” of mathematical education seemed simple to them, and the teaching methods they proposed did not raise doubts. In addition, they were self-confident and dismissive of the warnings of experienced teachers.

In 1938, Andrei Petrovich Kiselev said:

I am happy that I have lived to see the days when mathematics became the property of the widest masses. Is it possible to compare the scanty print runs of pre-revolutionary times with the present. And it’s not surprising. After all, the whole country is studying now. I am glad that in my old age I can be useful to my great Motherland

Morgulis A. and Trostnikov V. "The legislator of school mathematics" // "Science and Life" p.122

Textbooks by Andrey Petrovich Kiselev:

"Systematic course of arithmetic for secondary educational institutions" (1884) [12];

"Elementary Algebra" (1888) [13];

"Elementary Geometry" (1892-1893) [14];

"Additional articles of algebra" - the course of the 7th grade of real schools (1893);

"Brief arithmetic for urban schools" (1895);

"Brief algebra for women's grammar schools and theological seminaries" (1896);

"Elementary Physics for Secondary Educational Institutions with Many Exercises and Problems" (1902; withstood 13 editions) [5];

Physics (two parts) (1908);

"Principles of Differential and Integral Calculus" (1908);

"The elementary doctrine of derivatives for the 7th grade of real schools" (1911);

"Graphic representation of some functions considered in elementary algebra" (1911);

"On such questions of elementary geometry, which are usually solved with the help of limits" (1916);

Brief Algebra (1917);

"Brief arithmetic for city district schools" (1918);

Irrational numbers regarded as infinite non-periodic fractions (1923);

"Elements of algebra and analysis" (parts 1-2, 1930-1931).

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