In my previous question I suggested using the Research Gate platform to launch large-scale spatio temporal comparative researches.
The following is the description of one of the problems of pressing importance for humanitarian and educational sectors.
For the last several decades there has been a gradual loss in quality of education on all its levels . We can observe that our universities are progressively turning into entertaining institutions, where students parties, musical and sport activities are valued higher than studying in a library or working on painstaking calculations.
In 1998 Vladimir Arnold (1937 – 2010), one of the greatest mathematicians of our times, in his article “Mathematical Innumeracy Scarier Than Inquisition Fires” (newspaper “Izvestia”, Moscow) stated that the power players didn’t need all the people to be able to think and analyze, only “cogs in machines,” serving their interests and business processes. He also wrote that American students didn’t know how to sum up simple fractions. Most of them sum up numerator and denominators of one simple fraction with the ones of the other, i.e. as they did it, 1/2+ 1/3 according to their understand is equal to 2/5 . Vladimir Arnold pointed out that with this kind of education, students can’t think, prove and reason – they are easy to turn into a crowd, to be easily manipulated by cunning politicians because they don’t usually understand causes and effects of political acts. I would add, for myself, that this process is quite understandable and expected because computers, internet and consumer society lifestyle (with its continuous rush for more and newer commodities we are induced to regard as a healthy behavior) have wiped off young people’s skills in elementary logic and eagerness to study hard. And this is exactly what the consumer economics and its bosses, the owners of international businesses and local magnates, need.
I recall a funny incident that happened in Kharkov (Ukraine). One Biology student was asked what “two squared” was. He answered that it was the number 2 inscribed into a square.
The level and the scale of education and intellectual decline described can be easily measured with the help of the Research Gate platform. It could be appropriate to test students’ logic abilities, instead of guess-the-answer tests which have taken over all the universities within the framework of Bologna Process which victorious march on the territories of former Soviet states. Many people can remember the fact that Soviet education system was one of the best in the world. I have therefore suggested the following tests:
1. In a Nikolai Bogdanov-Belsky (1868-1945) painting “Oral accounting at Rachinsky's People's school”(1895) one could see boys in a village school at a mental arithmetic lesson. Their teacher, Sergei Rachinsky (1833-1902), the school headmaster and also a professor at the Moscow University in the 1860s, offered the children the following exercise to do a mental calculation (http://commons.wikimedia.org/wiki/File:BogdanovBelsky_UstnySchet.jpg?uselang=ru
(10 х 10 + 11 х 11 + 12 х 12 + 13 х 13 + 14 х 14) / 365 = ?
(there is no provision here on Research Gate to write square of the numbers,thats why I have writen through multiplication of the numbers )
19th century peasant children with basted shoes (“lapti”) were able to solve such task mentally. This year, in September, this very exercise was given to the senior high school pupils and the first year students of a university with major in Physics and Technology in Kyiv (the capital of Ukraine) and no one could solve it.
2. Exercise of a famous mathematician Johann Carl Friedrich Gauss (1777–1855): to calculate mentally the sum of the first one hundred positive integers:
1+2+3+4+…+100 = ?
3. Albrecht Dürer’s (1471-1528) magic square (http://en.wikipedia.org/wiki/Magic_square
The German Renaissance painter was amazed by the mathematical properties of the magic square, which were described in Europe firstly in Spanish (the 1280s) and Italian (14th century) manuscripts. He used the image of the square as a detail for in his Melancholia I painting , which was drawn in 1514, and included the numbers 15 and 14 in his magic square:
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
Ask your students to find regularities in this magic square. In case this exercise seems hard, you can offer them Lo Shu (2200 BC) square, a simpler variant of magic square of the third order (minimal non-trivial case):
4 9 2
3 5 7
8 1 6
4. Summing up of simple fractions.
According to Vladimir Arnold’s popular articles, in the era of computers and Internet, this test becomes an absolute obstacle for more and more students all over the world. Any exercises of the following type will be appropriate at this part:
3/7 + 7/3 = ? and 5/6 + 7/15=?
I think these four tests will be enough. All of them are for logical skills, unlike the tests created under Bologna Process.
Dear colleagues, professors and teachers,
You can offer these tasks to the students at your colleges and universities and share the results here, at the Research Gate platform, so that we all can see the landscape of the wretchedness and misery resulted from neoliberal economics and globalization.