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Early mathematical education in narrative contexts and the local environment

100%
Bilewicz-Kuźnia B.
Problemy Opiekuńczo-Wychowawcze
|
2020
|
vol. 587(2)
54-63
EN
The article describes the implementation of the project that took the form of a teaching experiment. The “Myśleć jak architect” [en. “Think like an Architect”] project was aimed at developing children's spatial, mathematical and creative skills, integrating the social environment: academic, educational, family and cultural, and promoting science. Its essence was to design and conduct a mathematical and creative didactic cycle in the university space and in the local cultural space. The essence of educational meetings were: play, tasks, games and mathematical problems undertaken and solved by children in active and creative action, also using innovative teaching materials. The workshop didactic program was designed as a cycle of 12 hours of didactic classes, in which there was a deliberate use of rhymes, poems, fairy tales and mathematical narratives. The project lasted from November 2018 to May 2019. The beneficiaries of the project were the oldest pre-schoolers and younger students from grades I-III, in 9 groups, each consisting of 12 people. The study confirmed the effectiveness and attractiveness of integrating literature with mathematics and learning mathematics in various areas. The study has shown that the strategies for teacher management of construction play using narration are an important and effective ways of supporting the development of a child's mathematical thinking.
2
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Stworzenie świata według Leibniza

88%
Heller M.
Zagadnienia Filozoficzne w Nauce
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2008
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issue 42
3-14
PL
Leibniz's idea of creation is best epitomized by a note written by him on the margin of his work entitled 'Dialogus'. The note reads:'When God thinks things through and calculates, the world is made'. Simple calculations are almost mechanical. The true mathematical thinking begins when one is confronted with a problem that has to be solved, when starting from the known mathematical structure one has to construct a new structure, to comprehend its intricacies, the ways of its functioning, and its connections with other mathematical structures. And when one successfully applies the new mathematical structure to a physical theory, the new world is made. This was Leibniz's experience when he was discovering calculus and tried to apply it to mechanical problems. Leibniz's doctrine that our world is the best of all possible words is often ridiculed, but this attitude is the result of a very superficial reading of Leibniz's texts. In fact, God's calculations to choose the best possible world are similar to solving the variational problem in mathematics. Leibniz claims that in mathematical reasoning if there is neither 'maximum' nor 'minimum' nothing can happen. Similarly, if there were no world better that other possible worlds, God's wisdom would have not been able to create anything. Some consequences of this doctrine, concerning the nature of space, time and causality, are also considered.
3
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Mathematical Thinking and Verifying Erroneous Intuition within the Context of Security. A Case Study

75%
Piwowarski J., Ratusiński T.
Security Dimensions: International & National Studies
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2017
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vol. 23(23)
165-174
EN
The article presents an example which demonstrates how misconceptions and erroneous intuition of a subject can have an influence on making incorrect decisions. A simple case study demonstrates that being familiar with basic mathematical principles constitutes a tool sufficient to verify the correctness of reasoning by a subject and, as a result, to make decisions.
4
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Kognitywne aspekty w edukacji matematycznej

63%
Kandzia J.
Edukacja Humanistyczna
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2021
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issue 2
9-20
PL
W opracowaniu przedstawiono konstruktywistyczne ujęcie procesu uczenia się matematyki, komunikowania się w matematyce, o matematyce i z użyciem matematyki, w aspekcie dynamicznie rozwijającej się nauki, jaką jest kognitywistka. Matematyka odgrywa ogromną rolę w poznaniu naukowym, stwarza szerszą perspektywę opisu rzeczywistości. Istotna, zatem jest: umiejętność zadawania pytań i udzielania odpowiedzi na zadany temat, w ramach i z wykorzystaniem środków matematycznych; rozumienie i stosowanie matematycznego języka i narzędzi matematycznych.
EN
The study presents a constructivist approach to the process of learning mathematics, communicating in mathematics, about mathematics and with the use of mathematics, in the aspect of the dynamically developing science of cognitive science. Mathematics plays a huge role in scientific cognition; it creates a broader perspective for describing reality. Essential, therefore, is the ability to ask questions and answer a given topic, within and with the use of mathematical means; understanding and use of mathematical language and mathematical tools.
5
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Language as a Necessary Condition for Complex Mental Content: A Review of the Discussion on Spatial and Mathematical Thinking

63%
MIRSKI R., GUT A.
Roczniki Filozoficzne
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2018
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vol. 66
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issue 3
33-56
EN
In this article we review the discussion over the thesis that language serves as an integrator of contents coming from different cognitive modules. After presenting the theoretical considera­tions, we examine two strands of empirical research that tested the hypothesis—spatial cognition and mathematical cognition. The idea shared by both of them is that each is composed of two separate modules processing information of a specific kind. For spatial thinking these are geo­metric information about the location of the object and the information about the object’s pro­perties such as color or size. For mathematical thinking, they are the absolute representation of small numbers and the approximate representation of numerosities. Language is said to integrate the two kinds of information within each of these domains, which the reviewed data demon­strates. In the final part of the paper, we offer some comments on the theoretical side of the discussion.
PL
W niniejszym artykule dokonujemy przeglądu badań z zakresu psychologii poznawczej, które skupiają się na hipotezie języka jako integratora treści zaczerpniętych z oddzielnych modułów po­znawczych. W pierwszej kolejności przedstawiamy teoretyczną stronę badań, a następnie prze­chodzimy do prezentacji dwóch obszarów badan empirycznych eksplorujących hipotezę języka jako integratora treści. Punktem wyjścia tych badań jest fakt, że w obydwu przypadkach mamy do czynienia z dwoma rodzajami informacji, przetwarzanych przez dwa oddzielne moduły. Dla myślenia przestrzennego są to informacja geometryczna na temat lokacji przedmiotu w prze­strzeni oraz informacja na temat właściwości inherentnych przedmiotowi, takich jak kolor czy wielkość. W przypadku matematycznego myślenia, dwa moduły przetwarzają kolejno informację na temat absolutnych ale małych ilości oraz przybliżonych wielkości. Celem badań w tych dwóch obszarach jest wykazanie, że język jest koniecznym warunkiem ku temu, aby informacja z oby­dwu modułów została zintegrowana. W końcowej części artykułu oferujemy kilka komentarzy na temat teoretycznej strony przedstawionych badań.
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