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| Description
| - On the basis of an extensive questionnaire survey mapping the respondents' initial reactions and quite a large number of interviews investigating individuals' ideas by means of inducing the cognitive conflict the following main sources of obstacles in understanding infinity have been identified: the conception of the existence of objects (the creator?s principle) and the horizon, and its positions. Further we have distinguished a total number of 17 epistemological obstacles in the process of creating the infinity concept and divided them into four groups: knowledge about finite sets, replacement of an object for its model, knowledge about finite processes and potential perception of the infinite process and knowledge about the set of natural numbers. These obstacles are commented on from the point of view of the genetic parallel and illustrated in greater detail by selected extracts from the interviews. Significant is also the description of the development of overcoming individual obstacles within time with the examined population sample (9 ? 19 years old pupils and students). A very surprising fact that is commented on in this article is a strong defect of the expected development of the success rate in the age categories of 14- and 16-year old students. After classifying the respondents? perception of infinity in greater detail, we identified an intermediate stage between the potential and actual conception of infinity, we call the omega position. The questions and tasks that were developed in the course of our research and serve the diagnostics of these obstacles in pupils are also considered a significant contribution to this article.
- On the basis of an extensive questionnaire survey mapping the respondents' initial reactions and quite a large number of interviews investigating individuals' ideas by means of inducing the cognitive conflict the following main sources of obstacles in understanding infinity have been identified: the conception of the existence of objects (the creator?s principle) and the horizon, and its positions. Further we have distinguished a total number of 17 epistemological obstacles in the process of creating the infinity concept and divided them into four groups: knowledge about finite sets, replacement of an object for its model, knowledge about finite processes and potential perception of the infinite process and knowledge about the set of natural numbers. These obstacles are commented on from the point of view of the genetic parallel and illustrated in greater detail by selected extracts from the interviews. Significant is also the description of the development of overcoming individual obstacles within time with the examined population sample (9 ? 19 years old pupils and students). A very surprising fact that is commented on in this article is a strong defect of the expected development of the success rate in the age categories of 14- and 16-year old students. After classifying the respondents? perception of infinity in greater detail, we identified an intermediate stage between the potential and actual conception of infinity, we call the omega position. The questions and tasks that were developed in the course of our research and serve the diagnostics of these obstacles in pupils are also considered a significant contribution to this article. (en)
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| Title
| - Overcoming obstacles in understanding infinity
- Overcoming obstacles in understanding infinity (en)
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| skos:prefLabel
| - Overcoming obstacles in understanding infinity
- Overcoming obstacles in understanding infinity (en)
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| skos:notation
| - RIV/44555601:13440/11:43881270!RIV12-GA0-13440___
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| http://linked.open...avai/predkladatel
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/44555601:13440/11:43881270
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - cognitive conflict; epistemological obstacle; Infinity (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...v/mistoKonaniAkce
| - Technická univerzita Liberec
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| http://linked.open...i/riv/mistoVydani
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| http://linked.open...i/riv/nazevZdroje
| - International Conference Presentation of Mathematics 11
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...vavai/riv/projekt
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| http://linked.open...UplatneniVysledku
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| http://linked.open...iv/tvurceVysledku
| - Cihlář, Jiří
- Eisenmann, Petr
- Krátká, Magdaléna
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| http://linked.open...vavai/riv/typAkce
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| http://linked.open.../riv/zahajeniAkce
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| number of pages
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| http://purl.org/ne...btex#hasPublisher
| - Technická univerzita v Liberci
|
| https://schema.org/isbn
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| http://localhost/t...ganizacniJednotka
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| is http://linked.open...avai/riv/vysledek
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