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Elements of theory of divisibility are present in many various interesting mathematical tasks, especially in tasks that are addressed to talented pupils taking part in mathematical competitions. Good understanding of it lets solve very interesting and difficult (at first glance) issues. On the other hand, there are a lot of problems with understanding such terms as: multiple, divisor, divisibility,...
The current core curriculum in mathematics for lower secondary school (3-rd educational level in Poland) omits formal definitions of concepts related to geometric transformations in the plane and is based on their intuitive sense. Practice shows that the current approach makes teaching very difficult and the students solve the typical tasks, not understanding the meaning of geometrical concepts. The...
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