O pewnej implikacji

Jan Górowski; Adam Łomnicki

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia (2016)

  • Volume: 8, page 77-86
  • ISSN: 2080-9751

Abstract

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The purpose of this paper is to show how the process of provinga theorem in different ways or proving generalized versions of the theorem,after learning one its proofs, influences the development of the skills of provingtheorems and analysing proofs by the students of mathematics. Toillustrate this process we use an elementary theorem about numbers and itsgeneralizations, giving fourteen proofs. Proving theorems we use methodsand facts which are available to high school students.

How to cite

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Jan Górowski, and Adam Łomnicki. "O pewnej implikacji." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 8 (2016): 77-86. <http://eudml.org/doc/296382>.

@article{JanGórowski2016,
abstract = {The purpose of this paper is to show how the process of provinga theorem in different ways or proving generalized versions of the theorem,after learning one its proofs, influences the development of the skills of provingtheorems and analysing proofs by the students of mathematics. Toillustrate this process we use an elementary theorem about numbers and itsgeneralizations, giving fourteen proofs. Proving theorems we use methodsand facts which are available to high school students.},
author = {Jan Górowski, Adam Łomnicki},
journal = {Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia},
keywords = {homographic function; inequality},
language = {pol},
pages = {77-86},
title = {O pewnej implikacji},
url = {http://eudml.org/doc/296382},
volume = {8},
year = {2016},
}

TY - JOUR
AU - Jan Górowski
AU - Adam Łomnicki
TI - O pewnej implikacji
JO - Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
PY - 2016
VL - 8
SP - 77
EP - 86
AB - The purpose of this paper is to show how the process of provinga theorem in different ways or proving generalized versions of the theorem,after learning one its proofs, influences the development of the skills of provingtheorems and analysing proofs by the students of mathematics. Toillustrate this process we use an elementary theorem about numbers and itsgeneralizations, giving fourteen proofs. Proving theorems we use methodsand facts which are available to high school students.
LA - pol
KW - homographic function; inequality
UR - http://eudml.org/doc/296382
ER -

References

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  1. Bednarek, W.: 2006, Prostsze rozwiązanie, Matematyka 8, 464. 
  2.  
  3. Górnicki, J.: 1995, Okruchy matematyki, PWN, Warszawa. 
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  5. Górowski, J., Łomnicki, A.: 2012, Cechy równoboczności trójkątów, Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia IV, 83–92. 
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  7. Guzicki, W.: 2013, Rozszerzony program matematyki w gimnazjum. Poradnik nauczyciela matematyki, Ośrodek Rozwoju Edukacji, Warszawa. 
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  9. Janowicz, J.: 2006, Oznaczenie ma znaczenie, Matematyka 2, 88–89. 
  10.  
  11. Kourliandtchik, L.: 2002, Słynne nierówności, Aksjomat, Toruń, 9–40, 187–206. 

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