An Ordinary Problem, But a Difficult One...

Abstract. The present article contains an analysis of the Russian experience of working with difficult problems in the classroom. Certain examples of such problems are examined, as well as the purpose of using them and the ways in which they can be used. Also discussed are issues related to preparing teachers who are capable of organizing the solving of such problems in the classroom. The article concludes by looking at the experience of employing such problems in teacher education outside of Russia. This article has three aims. First, it represents an attempt to describe and analyze the Russian tradition of solving difficult problems in the classroom. The problems in question are not those of mathematics Olympiads (although the distinction is sometimes a difficult one to make), but plain, ordinary problems—problems that can be solved in ordinary classes and appear on ordinary tests. The origin and character of such problems, as well as the development of methods for solving them and techniques for working with them in the classroom, are of considerable interest. The second aim of this article is to analyze what kind of preparation a teacher requires in order to be able to organize the solving of such problems in the classroom. Finally, the third aim is an attempt to look at the traditions that hav