Argumentacja w edukacji: postulaty badań edukacyjnych w polskiej szkole argumentacji

Uwzględniając dotychczasową działalność Polskiej Szkoły Argumentacji, w szczególności jej działalność edukacyjną wyeksponowaną podczas XV konferencji ArgDiaP, sformułowaliśmy postulaty dotyczące dalszej działalności edukacyjnej Szkoły. Ich realizacja w ciągu najbliższych lat mogłaby stanowić grunt dla długoterminowych celów edukacyjnych, takich jak (1) opracowanie spójnego programu nauczania sztuki argumentowania i krytycznego myślenia w szkołach podstawowych i średnich oraz (2) zaprojektowanie ogólnopolskich standardów i ram nauczania przedmiotów powiązanych z argumentacją i krytycznym myśleniem na poziomie studiów uniwersyteckich

Geometry in the first years of school education in the context of selected curricula and methodological guides for teachers in the years 1773 – 2020

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

What do we mean by mean?

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

Students' mental manipulation of a shape at the early educational level

In this article we present results of research aiming at describing the strategies used by 10-year-old children while solving one geometric task. The research was lead through three different stages. In May 2015 the Educational Research Institute in Poland carried out a survey titled Competences Of Third Grades. One task, related to the domain "the geometric imagination", solved by 199 361 students, achieved a low degree of solvability, also among students achieving good results in other educational domains. To identify the strategy for solving this task, about 3000 submitted solutions were reviewed. One of them was based on imagination of action. We were interested to which extent such dynamic thinking is present in children's solutions, therefore, in the next stage, individual observations of a child working on this task were carried out. 35 children aged 10 years participated in this stage. The results of all stages are briefly presented in this study, with particular attention to the result of the third stage. This last stage supports our opinion that dynamic reasoning is possible to trigger, but requires special teaching methodology and specially designed tasks

Analysis of students’ solutions to geometry questions forming a bundle

One of the main goals of mathematical education is to develop the skills for problem solving as well as skills that help carry out mathematical reasoning and argumentation.Geometric problems play here a special role. These require the person solving them to act with an inquiry attitude and a ‘specific vision’. The ‘specific vision’ is the ability one can manipulate with geometric objects in ones’ mind and perceive, separate and focus on the important information only. However, it is not enough to “see” it is also necessary to know how to interpret what is being seen. Although many researchers have dealt with the problem and many establishments have been made in this scope, the question of how to develop the skills of the “specific vision” stays still open.Herein article presents the research results which aimed at, among others, verification to what degree the combination of geometry problems formed into a bundle helps the secondary school students ‘notice’ and understand the presented situation and as a consequence to find the answer to few questions about this situation. We wanted to establish whether such an organised educational environment entails students natural thinking over the subsequent bundle of problems solved, or maybe makes them return to questions already solved, or by the usage of knowledge acquired helps students to find the problem solution for the next question or a correction for the committed mistakes. The analysis was based on some results coming from the survey School of Independent Thinking conducted by the Institute for Educational Research in 2011