This paper presents some results achieved with carefulness for pupils with larger interest in mathematics in the 4th class at elementary school. We gave attention to two subjects - teacher and his (her) pupils. We mention the first one in this paper. We have found out certain reserves at work with these pupils including gifted pupils, mainly at out of educational time. Research shows needs to improve the quality of preparation for pupils interested more in mathematics. It is also connected with preparation of next teachers at universities.
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