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EN
Currently there is little geometry content in the early years of school. In my doctoral thesis Geometry in teaching children since the times of the Commission of National Education until today. Analysis of the succession of education concepts, supervised by Prof. Edyta Gruszczyk-Kolczynska, I examined how the teaching of geometry to younger children has changed since the time of KEN. In the article, I discuss curricula and methodological guide books for teachers in terms of the geometric content they cover in the first years of school education. I focus on three periods: the second half of the 19th century, the 1920s and the 1970s. These periods stand out from the others I studied n that there was a lot of geometric content in the first years of school. However, in the first one of these, the content was mainly included in the subject “drawings”, while in the others the main aim of teaching was to develop pupils’ computational skills. To a large extent, geometry has also served this purpose.
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What do we mean by mean?

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EN
In order to be successful with a certain concept at school, it is often sufficient to master some types of tasks, without having to be aware of the different perspectives that a concept can be viewed from. It is, however, definitely not enough when the goal is to understand mathematics and become flexible and creative in solving mathematical tasks. Not only school students, but also prospective teachers should be encouraged to reflect on what particular concepts actually mean and how they can be thought of. In this article we focus our attention on the concept of mean. In the introduction we outline the gaps that our paper partially fills. Then we provide a brief review of how the Polish core curriculum and two very popular mathematics textbook series (one each for primary and secondary school) treat the topic of means. Next, we present results from a study conducted on a group of first-year students of mathematics and a group of teachers undertaking postgraduate studies qualifying for teaching mathematics as a second subject. We show the results obtained in two tasks concerning the arithmetic and geometric mean. The paper ends with several teaching suggestions and recommendations for mathematics teachers’ educators.
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