On convincing and non-convincing solutions of mathematical problems
The article discusses a question of what a solution of mathematical problem should be if we want this solution to be not only mathematically strict and correct, but also convincing for the student. Sometimes mathematical textbooks contain non-natural and original (as they think) solutions to longer but at the same time more natural and convincing solutions. This phenomenon contradicts to the basic principles of pedagogy and can be considered as a kind of" snobbery". For the illustration of the ideas the article considers two geometric problems.