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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Propozycja wykładu na temat argumentu głównego liczb zespolonych

100%
Chronowski A.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2010
|
tom 3
41-48
PL
--
2
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Teoretyczne podstawy dzielenia z resztą liczb naturalnych wraz z uwagami o dzieleniu z resztą liczb całkowitych, wymiernych i rzeczywistych

100%
Chronowski A.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2019
|
tom 11
63-72
EN
In this article, I analyze the theoretical foundations of the division with remainder in the arithmetic of natural numbers. As a result of this analysis I justify that the notation a:b=c r s, where a, b, c, s are natural numbers and r denotes, is correct at school mathematics level and does not lead to a contrediction suggested by the author of the article (Semadeni, 1978). As a generalization of the division with remainder of natural numbers, I consider the division with remainder of integers, rational and real numbers.
3
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Teoretyczne i dydaktyczne aspekty nauczania o największym wspólnym dzielniku i najmniejszej wspólnej wielokrotności w zbiorze liczb naturalnych

100%
Chronowski A.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2006
|
tom 1
31-56
PL
This article contains a collection of didactic ideas concerning teaching the elementary arithmetic. Although they are firmly based on abstract mathematics, they can be realized at different levels of teaching school mathematics. The source of these didactic propositions is the fact that using the set of natural numbers and suitable relations it is possible to construct the models of structures which are called lattices. In this paper we consider the two models of lattices: the lattice of natural numbers with the divisibility relation and the lattice of hereditary sets with the inclusion relation. These lattices are abstract models describing the theoretical foundations of the intuitive process of teaching the greatest common divisor and the least common multiple in the school mathematics. The properties of these lattices inspire considerations of interesting mathematical problems using the elementary notions of the school mathematics. In this paper the didactic propositions are directed to the work with pupils who are interested in mathematics and who will probably choose mathematics as a subject of their studies
4
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Przekształcenia wykresów funkcji

100%
Chronowski A.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2006
|
tom 1
13-30
PL
This article is concerned with some topics of the transformationsof the graphs of functions. It is designated to serve as a text for thestudents of mathematics (prospective teachers) and the teachers of ma-thematics.In this paper we give the answer to the following problem:Given the graph of the function f:R Df
5
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Uporządkowane struktury liczbowe

100%
Chronowski A.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2013
|
tom 5
5-37
PL
In this article we consider the ordered algebraic structures of thesystems of natural numbers, integers, rational and real numbers. We presentthe ordered algebra of natural numbers, the ordered ring of integers, and theordered fields of rational and real numbers. The main problem considered forordered number structures is the categoricity of these systems determined bya suitable isomorphism. First of all, this article is addressed at Mathematicsstudents of pedagogical studies and at teachers of Mathematics.
6
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Ułamki algebraiczne i funkcje wymierne

100%
Chronowski A.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2009
|
tom 2
5-27
PL
The subject-matter of this article can be divided into three main parts. The first one includes the theoretical problems concerning the fields of algebraic fractions and rational functions. In the second part we deal with didactic questions of algebraic fractions and rational functions in some chosen school textbooks. In the third part deep ideas and formal models of algebraic fractions and rational functions are discussed.
7
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Twórcza aktywność matematyczna uczniów związana z rozwiązywaniem pewnych zadań na zastosowanie wzorów Viète’a

64%
Chronowski A., Powązka Z.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2016
|
tom 8
25-49
PL
In this article we propose ways of developing the active and creativeattitude of students towards solving mathematical problems. The taskswere sourced from various mathematical competitions for secondary schoolstudents, such as the so-called Mathematical Olympiad, and require theuse of Vieta’s formulas for third-degree polynomials. These problems inspirestudents to conduct their own elementary research work and foster theircreative attitude towards mathematics. This article is dedicated mainly tostudents who are pre-service mathematics teachers, but may also be of useto in-service teachers.
8
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Wstęp

64%
Chronowski A., Klakla M.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2006
|
tom 1
5-7
PL
--
9
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Przykłady zagadnień z różnych działów matematyki niezbędnych do studiowania teorii miary

64%
Chronowski A., Powązka Z.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2012
|
tom 4
31-60
PL
In the education of mathematicians, including teachers of mathematics, the measure theory plays an important role. From the experience in and research on teaching the measure theory it follows that on of the important reasons why students encounter difficulties in the subject is their insufficient ability to apply their knowledge of other branches of mathematics, especially of the set theory and topology. In this article we propose a series of problem analyses and exercises aimed at preparing students to study the measure theory, especially to understand the proofs of theorems on properties of the measure, including the Lebesgue measure. Most of these problems and exercises are presented with solutions, outlines of solutions, hints, didactic remarks and comments. In this paper we point out, in a practical way, the significance of active reading of mathematical texts and skilful use of mathematical literature. This article is dedicated to both students of mathematics and their academic teachers.
10
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O różnych sposobach definiowania wartość bezwzględnej

51%
Chronowski A., Major J., Powązka Z.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2009
|
tom 2
29-36
PL
In this article we present some didactic ideas of introducing theabsolute value of a real number by means of functional equations and aninequality. The basic properties of the absolute value of a real number arewritten as functional equations and an inequality. The function "absolutevalue" is a solution of a suitable functional equation or an inequality.
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