# We discussed at Stanford what to do with the mathematical and engineering education of Ukrainian schoolchildren

“What can America learn from Ukraine in the field of education?” - This question arose during the meeting at Stanford. It turns out that there is something, for example, the traditions of teaching mathematics, which Ukraine has in common with other CIS countries. “How does the Ukrainian government support the orientation of students towards engineering professions?” - There was another question from the audience, which included employees from SAP, Facebook, MIPS and other well-known technology companies.

But let's start the story in order. March 8 at Stanford held a round table "Education Reforms in Ukraine: Breakthroughs and Challenges." The organizer was the charity Nova Ukraine, which supplies Ukrainian libraries with computers. The main participants:

- Co-founder of the Lviv Teacher Training Center Enlighten Julia Vasilieva;
- Former Minister of Education of Ukraine Sergey Kvit;
- Study.com educational content strategy expert Svetlana Kostenko.

Among those present were specialists from Silicon Valley companies, students of local colleges, representatives of public and cultural organizations of Ukrainian Americans. The organizers mainly talked about improving school administration, as well as expanding teaching in Ukrainian and English. However, both in the subsequent discussion and in the conversations after the event, less humanitarian issues arose:

- On the continuity of the traditions of teaching mathematics. In Soviet times, Ukrainian mathematicians led circles and published many advanced books for physics schools.
- On the continuity of the traditions of teaching engineering disciplines. In Soviet times, there were enterprises in Kiev producing analogs DEC PDP-11 and Intel 8080. In general, the first computer in the USSR and the fastest computer in continental Europe in 1950 (MESM) were designed and built in Kiev, by the team of S.A. Lebedeva from the Kiev Polytechnic Institute.
- About modern experiments in KPI in the field of teaching design of digital devices on FPGAs to schoolchildren. In this Ukraine has a chance to get ahead of California.

Why math? How does this relate to programming? From the point of view of most non-technical people, all programmers are the same. But we all know that within the programming profession there are specializations that require different levels of mathematical thinking. Algorithms for machine learning or to automate the design of microchips are usually created by people who have trained their brains with math from school. This will be discussed in our post.

So, in order. The round table at Stanford was held on March 8. The room had many mimosas, tulips, hyacinths and small talk:

Before the round table, the musicians sang:

Finally, everyone began to sit down:

Here is the main trinity, from left to right: Svetlana Kostenko (study.com), Julia Vasilyeva (economist, teacher training center, administration), Sergey Kvit (journalist, philologist, Ministry of Education):

Here are the cribs of Julia and Sergey:

- Secondary school reform begins with higher education reform
- Decentralization and autonomy
- Lack of money
- Who will be the agent of change - the state or civil society?

Sergey Kvit emphasized various humanitarian issues, which is natural, since he is a journalist and philologist. I will not describe this part, but you can listen to the video that is on Facebook Nova Ukraine. Then came a talk about what Ukraine can teach America in the field of school education. Then I felt that humanitarian comrades needed help, and added to their reasoning this:

*I studied in the 1980s in Kiev, in three schools, including physics school number 145. My three children were already born in California and attended local schools, including three public schools, including Homestead High, the school Steve Jobs attended. Therefore, I can fairly accurately assess the difference in the programs of schools in the USSR and in modern California. Although American schools have better programs in chemistry and biology, they are less advanced in mathematics. In particular, statement reasoning is introduced much later and in smaller numbers.*

A group of school teachers from the CIS countries (including Ukraine) understood this difference and created a network of additional schools in the USA called the Russian School of Mathematics (RSM). This network now includes 45 schools. RSM is an unambiguous business success, and not only and not so much among Russians, as among other nationalities - Indians, Chinese, Americans. Education at school is in English and children solve problems on the proof of theorems. For example, here is a piece of homework for 13-year-olds:

Such a seemingly uncomplicated transfer of Soviet teaching methods to American soil gives a very concrete effect: here is a quote from the prestigious Johns Hopkins University, which among the RSM graduates is “the most talented young people in the world”:

The average SAT among RSM graduates is 774, and the state average is 518. The Boston Globe newspaper called RSM "The Russian Solution to the American Problem of Education." And now you can imagine - on Wikipedia about RSM there is an article in English only. There are no articles about RSM in Russian, Ukrainian and Belarusian:

In addition to basic school education in Ukraine in the 1980s, there was a group of mathematicians who organized school groups and published a series of talentedly written books for physics schools. For example:

One of the books, about the Dirichlet principle, began with a comic task: “there are 800,000 Christmas trees in the forest, each of which has no more than 500,000 needles. Prove that at least two Christmas trees have the same number of needles. ” Then it was tied to other branches of mathematics - irrational numbers, congruence theory, even probability theory and set theory

(!)

Here is a reference to irrational numbers, also in an accessible way. “Ditches were made across the road with step A, where A is an irrational number. On the road there is a person with a step of 1 meter. Prove that no matter how narrow the ditches are, a person will eventually fall into one of them ”:

Very popular in the 1980s was popular science literature for schoolchildren. Here is an excerpt from A. Konforovich, M. Soroka. By the roads of Unіkursalії. 1981. About the Skuse number, which is written in unit with 10

^{ 10000000000000000000000000000000000000000 }zeros. What this number means: there is a Chebyshev formula that gives an approximate number of primes in the range from 1 to N. And now, before the Skewes number, the Chebyshev formula gives a larger estimate of the number of primes than the true one, and after the Skewz number it is less:

The text was for schoolchildren 5-7 classes:

It is not surprising that in the 1980s in Ukraine they developed and produced their microprocessors, for example, an analog of Intel 8080 at the Kiev factory Crystal. Also in Kiev, at the VUM plant in the 1970s, they released SM-4, an analogue of DEC PDP 11/34. So I photographed the PDP-11 at the Computer History Museum in Mountain View, California, next to my classmate girl, Irina, with whom I did lab work when I was studying chemistry courses at a local college as a hobby:

Sergey Kvit and other Ukrainian philologists and education reformers are probably interested in the development of Ukrainian literature. But Ukrainian literature is not only Lina Kostenko’s love lyrics (“I want to know, who love me, who still have a dream, who don’t even dream of? My share was baked quietly, my very own self!”), But also for example novel by Ukrainian writer Vadim Sobko "Key". The protagonist of the novel is a mathematics student at Kiev State University, who works at the Kiev VUM factory in parallel with studies. The novel describes how the hero designed and assembled a laptop from microcircuits of a small degree of integration at his home on Borshchagovka, as a result of which he found a girl.

I note that microcircuits with a small degree of integration are still an ideal means of teaching schoolchildren the basics of digital logic (logical elements AND-OR-NOT, D-triggers, etc.). In particular, last year we from California helped to conduct a seminar for schoolchildren in Kiev, at which they first trained on microcircuits of small degree of integration of the CMOS 4000 series, originally from the 1970s, and then switched to 2017 technologies - FPGA / FPGA Xilinx Artix -7:

It is worthwhile to dwell on FPGAs in more detail, because teaching FPGAs to schoolchildren is an area in which Ukraine can become ahead of California. See the result of the Kiev experiment on teaching FPGAs to schoolchildren in an article on Geektimes “I took a video interview from Vice President Arduino and discussed with her teaching schoolchildren FPGAs / FPGAs and Verilog . ”

Excerpt from a post on Geektimes with the rationale why this kind of additional education can be useful:

В картине мира, представляемой школьным образованием, существует "слепое пятно" в области принципов проектирования цифровой электроники, между физикой и программированием. Курсы роботики и ардуино это слепое пятно не закрывают, так как сводятся к программированию готовых чипов. Упражнения с дискретными элементами и микросхемами малой степени интеграции, хотя и эффективны во введении в основные принципы, базируются на технологиях 1960-1970-х годов и не содержат привязки к современному проектированию. Слепое пятно можно закрыть с помощью введения элементов языков описания аппаратуры (ЯОА) и доступные для школьного экспериментирования микросхемы ПЛИС (программируемые логические интегральные схемы) — матрицы реконфигурируемых логических элементов. Тем самым картина мира становится цельной, и способствует созданию среды для появления большого количества молодых инженеров, имеющих представление о всех сторонах современных микросхем для приложений типа самоуправляемых автомобилей, и способных в будущем специализироваться для проектирования того или иного аспекта таких устройств.

Введение ЯОА и ПЛИС в школьную программу также хорошо привязывается к курсу математики и физики физматшкол — булевская алгебра, арифметические схемы, конечные автоматы.

Заметим, что ЯОА и ПЛИС, несмотря на поверхностное сходство с программированием, используют другие базовые концепции:

Программирование: последовательное исполнение, ветви выбора, циклы, переменные, выражения, массивы (c моделью плоской адресуемой памяти), функции (на основе использования стека), рекурсия.

Проектирование цифровой логики: комбинационный логический элемент; построение из этих элементов облаков комбинационной логики, включающей примитивы выбора с помощью мультиплексоров, а также блоки для реализации арифметических выражений; концепция тактового сигнала для синхронизации вычислений и повторения, концепция D-триггера для хранения текущего состояния между тактами; конечный автомат; параллельность операций, иерархия модулей, концепция конвейера (не только для процессора, но и для арифметических блоков).

In addition to the Kiev experiment, there was also a very interesting experiment in teaching FPGAs at the Summer School of Young Programmers in Novosibirsk. Although usually advanced FPGA principles can only be understood by advanced students of grade 9 and older, there were two fifth graders at the Novosibirsk school who were able to figure out how to connect the blocks designed at the register transfer level and create simple projects for them. Here is one of them - this is undoubtedly a schoolboy with a great future, a combination of early intelligence, accuracy and initiative:

I discussed FPGAs at a meeting in Stanford, and there they asked me how this differs from Arduino. To this I gave an explanation from the presentation at the round table on the education of schoolchildren at Moscow State University. The round table at Moscow State University took place last October. Here is one of the slides of that presentation:

Eugene Korotky and his Laboratory Lamp at the Kiev Polytechnic Institute last year won a grant from the Kiev municipality to create a laboratory for teaching children electronics. They will probably try to conduct an even more detailed seminar this year than they did in the past. We will see if they can demonstrate higher results than those of Novosibirsk. At the Novosibirsk Summer School of Young Programmers there was a girl of grade 9 who learned how to modify the synthesized processor core (see the post on Habr “Severe Siberian and Kazakhstan Microelectronics of 2017: Verilog, ASIC and FPGA in Tomsk, Novosibirsk and Astana” ).

In general, in Ukraine, schoolchildren are smart, and there are very advanced gymnasiums, for example, the group in the photo below from the ORT center in Kiev, shot on a hatacon in the Kiev-Mohyla Academy. However, in order to develop the potential of these students to the maximum, it is necessary to plan not only measures for better school administration, but also to create an optimal curriculum. For this optimal program, it is worth collecting the best finds of American, Asian and European schools, as well as choosing a good part of the traditions of the CIS. To figure out how to optimally educate future developers of processors for artificial intelligence, and geneticists, bioengineers, and economists, and journalists, and authors of love lyrics in Ukrainian. This is, as the Americans say, Challenge. But it is achievable.