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PL
Matematyczna wiedza dydaktyczna nauczyciela wczesnej edukacji potocznie postrzegana jest jako zestaw instruktażowych metod przekazywania uczniom podstawowych pojęć. Studenci wczesnej edukacji dysponują osobistymi doświadczeniami szkolnymi oraz skonstruowanymi na tej podstawie matematycznymi przekonaniami. Umiejętność (lub jej brak) rozwiązywania zadań matematycznych z poziomu klas początkowych przez przyszłych nauczycieli również odsłania określone ich rozumienie, czym jest wiedza matematyczna oraz jej rozwijanie w szkole. Wyniki badań studentów wczesnej edukacji ukazują ich potoczne koncepcje związane z nauczaniem matematyki najmłodszych uczniów. Badani studenci rozumieją ten proces przede wszystkim jako przekaz pojęć i gotowych strategii postępowania. Odsłaniają również niewielkie zaufanie do uczniowskich możliwości samodzielnego poznawania matematyki, Oprócz niskiej wiedzy merytorycznej, ujawniane w badaniach przekonania wskazują również na ich znacząco ograniczone kompetencje dydaktyczne w zakresie wczesnej edukacji matematycznej.
EN
The paper undertakes research meant to identify the teacher’s violent behaviour towards students during early school math lessons. The research conducted in grade one during the math class was used as an aid to deeper understanding of the phenomenon of violence in school. It was found that some lesson procedures, mathematical formulations, and cognitive situations can be seen from the perspective of teacher violence. Their effects can reduce pupils’ self-esteem, limit understanding of mathematics and hinder full participation in culture now and in the future.
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EN
One day, Jean-Jacques Rousseau, who was known mainly as a philosopher and a pedagogue, told a deer hunting story. In doing so, he managed to play a small role in the development of the branch of maths called ‘game theory’. Later his story was converted into a game. Initially game theory was used to explain exchange in the field of economics. Over time, the mathematical modeling was found to be useful in the social sciences. A game theory describes diverse and cognizant participants forced to make decisions. In regards to the game based on cooperation, a choice is at the same time a dilemma. It can be viewed as a moral or philosophical predicament and in addition it gives as an inside into the human psyche and behaviour. Game theory has the potential to offer an attractive mathematical model, useful in analyzing social interactions. Though currently unappreciated by pedagogy, it has the potential to be successfully used in pedagogical studies analyzing conflict of interest of all participants in an educational process.
EN
The digital world is becoming accessible to ever younger children, who are increasingly looking for and building their presence in it. The school seems to be a place that should respond to these trends by incorporating digitality into its educational proposals. Research into the content of textbooks for the first year of primary school shows infantile character and inadequacy in time and cognition of content related to the digital world. First-grade students are unlikely to encounter (in the currently offered school’s curriculum) a reflection on the dangers it poses or proposals to use digital skills. The contents of the textbooks constitute a world existing alongside the digital natives.
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