It is put on display in Russian most prominent galleries “Tretiakovka” so anyone can check it there by themselves. It shows a scene from a study process in a village school back then. There is a teacher and a bunch of children. Then all attention goes to the blackboard: It has some task for the kids that seem to puzzle them, but that’s just a temporary confusion. They all look to be ready for the challenge. The name of this art masterpiece is something like “Oral maths test in village school”. It gets what it means - no calcs involved, just mind skills of counting, even without any piece of paper and pencil. So now the question - can any contemporary city school kid do that? I am not sure.I can't vouch for any of the above, but the Tretyakov Gallery has an immense collection of Russian fine arts, and I see no reason for the painting not to be valid.
But I can vouch for the math puzzle. You can click to enlarge the painting, but it's probably easier to reproduce it here:
Found at English Russia.
Update: I am recurrently astounded by the breadth of knowledge of TYWKIWDBI readers. Today Hexmaster identified the painting and the artist - "The painting is called "Counting in their heads". It was made by Nikolay Bogdanov-Belsky in 1895" - and provided a link to the painting's entry in the Russian Wikipedi: The painting on the Russian Wikipedia.