Z badań nad trudnościami studentów w rozumieniu pojęcia miary i całki

Zbigniew Powązka

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia (2012)

  • Volume: 4, page 139-154
  • ISSN: 2080-9751

Abstract

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Measurement is an important form of human activity. It appears at all levels of secondary school education, while discussing the length of a segment, the area of a plane figure and the volume of a solid. The definition of a measure, understood as a non-negative real function defined on a σ-field of set of a space, is taught during the classes on mathematical analysis. It is observed that the concept of measurement causes great difficulties to students. This paper presents the results of research on students' difficulties in understanding and using the basic concept of measure theory and integral. The research conducted in years 2006-2009 shed some light on the causes of those difficulties. The study involved students of the third year of the Mathematics Department at the Pedagogical University of Krakow.

How to cite

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Zbigniew Powązka. "Z badań nad trudnościami studentów w rozumieniu pojęcia miary i całki." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 4 (2012): 139-154. <http://eudml.org/doc/296384>.

@article{ZbigniewPowązka2012,
abstract = {Measurement is an important form of human activity. It appears at all levels of secondary school education, while discussing the length of a segment, the area of a plane figure and the volume of a solid. The definition of a measure, understood as a non-negative real function defined on a σ-field of set of a space, is taught during the classes on mathematical analysis. It is observed that the concept of measurement causes great difficulties to students. This paper presents the results of research on students' difficulties in understanding and using the basic concept of measure theory and integral. The research conducted in years 2006-2009 shed some light on the causes of those difficulties. The study involved students of the third year of the Mathematics Department at the Pedagogical University of Krakow.},
author = {Zbigniew Powązka},
journal = {Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia},
keywords = {measure; integral; problems},
language = {pol},
pages = {139-154},
title = {Z badań nad trudnościami studentów w rozumieniu pojęcia miary i całki},
url = {http://eudml.org/doc/296384},
volume = {4},
year = {2012},
}

TY - JOUR
AU - Zbigniew Powązka
TI - Z badań nad trudnościami studentów w rozumieniu pojęcia miary i całki
JO - Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
PY - 2012
VL - 4
SP - 139
EP - 154
AB - Measurement is an important form of human activity. It appears at all levels of secondary school education, while discussing the length of a segment, the area of a plane figure and the volume of a solid. The definition of a measure, understood as a non-negative real function defined on a σ-field of set of a space, is taught during the classes on mathematical analysis. It is observed that the concept of measurement causes great difficulties to students. This paper presents the results of research on students' difficulties in understanding and using the basic concept of measure theory and integral. The research conducted in years 2006-2009 shed some light on the causes of those difficulties. The study involved students of the third year of the Mathematics Department at the Pedagogical University of Krakow.
LA - pol
KW - measure; integral; problems
UR - http://eudml.org/doc/296384
ER -

References

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  1. Chronowski, A., Powązka, Z.: 2012, Przykłady zagadnień z różnych działów matematyki niezbędnych do studiowania teorii miary, Annales Academiae Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia IV, 31-59. 
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  3. Gunčaga, J.: 2009, Regulated functions and integrability, Annales Academiae Paedagogicae Cracoviensis. Studia Mathematica 8, 43-56. 
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  7. Major, J., Powązka, Z.: 2006, Pewne problemy dydaktyczne związane z pojęciem wartości bezwzględnej, Annales Academiae Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia I, 163-185. 
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  9. Major, J., Powązka, Z.: 2008, Utváranie pojmu obsah rovinného útvaru na rôznych stupňoch vzdelávania, Acta Mathematica 11, 135-140. 
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  11. Major, J., Powązka, Z.: 2009, From research on student difficulties in using the properties of functions while solving equations and inequalities, w: M. Billich (red.), Mathematica III, Catholic University in Ružomberok, Faculty of Education, 69-76. 
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  13. Łojasiewicz, S.: 1973, Wstęp do teorii funkcji rzeczywistych, PWN, Warszawa. 
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  15. Powązka, Z.: 2009a, From research on developing concept of different types of integrals in students of peagoical studies, w: M. Billich, M. Papčo, Z. Takáč (red.), Teaching Mathematics. Innovation, new trends, Catholic University in Ružomberok, Faculty of Education, 217-227. 
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  17. Powązka, Z.: 2009b, Uwagi o kształtowaniu rozumienia pojęcia miary na różnych poziomach edukacji, Prace monograficzne z dydaktyki matematyki, Współczesne problemy nauczania matematyki 2, 141-149. 
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  19. Powązka, Z., Zaręba, L.: 2007, Teachers studies students difficulties concerning the generalization of the concept of the Riemann integral, w: J. Povstenko (red.), Scientific Issues J. Długosz University of Częstochowa. Mathematics XII, Częstochowa, 347-354. 
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  21. Siwek, H.: 2005, Dydaktyka matematyki. Teoria i zastosowania w matematyce szkolnej, WSiP, Warszawa. 
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  23. Turnau, S.: 1990, Wykłady o nauczaniu matematyki, PWN, Warszawa. 

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