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Edukacja
|
2017
|
issue 5(2017)
72–83
EN
Mathematics uses a wide range of representations, but the mathematical symbol is not the only way to code information. Different ways of representing mathematical concepts and relationships are used, especially in the early stages of learning. Generally, the teacher decides on the choice of representational forms to use. But in the process of solving mathematical problems, it is the pupils – not the teacher – who are engaged in the problem-solving, and the coding used should support their cognitive work. This paper analyses how different representations can influence the results of work on an untypical mathematical problem. The task was solved by a group of 7–8 year-old pupils participating in a mathematics club. The examples selected for analysis indicate a strong relationship between the choice of representations and the final result of the pupils’ work.
Edukacja
|
2017
|
issue 1(2017)
27–38
PL
Matematyka w szerokim zakresie posługuje się zapisem symbolicznym, ale symbol matematyczny nie jest jedynym sposobem kodowania informacji. Zwłaszcza na etapie nauczania wczesnoszkolnego stosuje się różne sposoby reprezentowania pojęć i relacji matematycznych. Na ogół to nauczyciel decyduje o wyborze formy reprezentacji. Jednak w procesie rozwiązywania matematycznych problemów jest zaangażowany uczeń, a zastosowany sposób kodowania związków powinien wspierać jego pracę umysłową. W badaniu opisanym w tym artykule sprawdzono, w jaki sposób różne reprezentacje mogą wpłynąć na efekt pracy nad nietypowym zadaniem matematycznym. Zadanie było rozwiązywane przez uczniów 7–8-letnich w ramach kółka matematycznego. Wybrane do analizy przykłady wskazują na silny związek między wyborem reprezentacji, a końcowym wynikiem pracy ucznia.
EN
Mathematics uses a wide range of representations, but the mathematical symbol is not the only way to code information. Different ways of representing mathematical concepts and relationships are used, especially in the early stages of learning. Generally, the teacher decides on the choice of representational forms to use. But in the process of solving mathematical problems, it is the pupils – not the teacher – who are engaged in the problem-solving, and the coding used should support their cognitive work. This paper analyses how different representations can influence the results of work on an untypical mathematical problem. The task was solved by a group of 7–8 year old pupils participating in a mathematics club. The examples selected for analysis indicate a strong relationship between the choice of representations and the final result of the pupils’ work.
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