Przyczynek do badań nad przygotowaniem absolwentów szkół ponadgimnazjalnych do studiowania matematyki na Uniwersytecie Pedagogicznym w Krakowie
--
O fałszywych przekonaniach obserwowanych na zajęciach z analizy matematycznej
In this paper we present the results of our research carried out among the students of the first, second and third years of mathematical studies in the years 2003-2006. The research was focused on the difficulties these students faced in understanding the fundamental notions of the mathematical analysis such as: a limit, continuity, differentiability and integrability. These special problems, described in this paper, are called ”false beliefs”.
Z badań nad trudnościami studentów w rozumieniu pojęcia miary i całki
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...
Z badań nad wprowadzeniem podstawowych treści analizy matematycznej podczas zajęć na I roku studiów matematycznych
This article presents the author’s research results concerning the teaching of introductory notions and theorems of mathematical analysis. The research was carried out among the first-year students of mathematics. The main objects of the research were: – the observation of the degree of assimilation of the basic notions and theorems by the students; – the investigation of the students’ progress in proving theorems and constructing suitable examples and counterexamples. The final part of the article...
O badaniach nad kształtowaniem się u studentów matematyki podstawowych pojęć analizy matematycznej
This paper is a reflection on the process of forming the basic concepts of mathematical analysis in students. These studies were conducted in the years 2002-2011 and they coincided with the period of major educational reforms in our country. These reforms had an impact on the level of Mathematics teaching in various schools and on anticipatory preparing of young people to study this subject. Thus, this work is an attempt to summarize the results of the already described various stages of the research....
Uwagi o polsko-czesko-słowackich konferencjach z dydaktyki matematyki w roku 2007
Od wielu lat między Polską a jej sąsiadami Czechami i Słowacją, owocnie rozwija się wymiana wyników badań naukowych z dydaktyki matematyki. Organizowane są liczne konferencje naukowe dotyczące tej tematyki. Niniejsza publikacja zawiera uwagi dotyczące trzech takich konferencji, które odbyły się w roku 2007.
Researches on the use of a concept of continuity of a function for the defining a derivative of a function at a point
The article contains no abstract
Przykłady zagadnień z różnych działów matematyki niezbędnych do studiowania teorii miary
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...
Przyczynek do badań nad twórczą postawą studentów podczas rozwiązywania zadań matematycznych
In this paper, we understand the term ''creative attitude'' to denote an action of the learner which consists in undertaking creative activity. This activity can take different forms, such as: discovery, invention, a creative act, etc. We understand ''discovery'' to denote a fact which already exists but was unknown to the discoverer. While teaching mathematics, we deal with such an understanding of ''discovery'' e.g. when we use the problem method. Thence, subjectively new theorems can emerge...
Z badań nad analizą rysunku i odkrywaniem własności funkcji
The article presents remarks regarding analysis of drawings and the use of the data contained therein in resolving mathematical tasks. A particular type of drawing is considered, which is a graph of a function. The presented findings are the result of several years of research conducted among the Mathematics students at the Pedagogical University of Cracow.
O pewnym sposobie kontroli rozumienia wybranych pojęć z analizy matematycznej przez studentów studiów matematycznych
In the last years in Poland new standards for the matriculation examination have been established, especially in mathematics. Subsequently, for many years at the Pedagogical University of Krakow research has been conducted on difficulties that students experience in understanding the basic concepts of mathematical analysis. For the results of this research see: Powązka, Z. (2006, 2009); these are the reports of research conducted in the academic years: 2003/2004 and 2006/2007. Our main goal was...
Twórcza aktywność matematyczna uczniów związana z rozwiązywaniem pewnych zadań na zastosowanie wzorów Viète’a
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...
Uwagi dotyczące pojęcia wartości bezwzględnej liczby rzeczywistej
This paper deals with some studies of understanding the absolute value of real numbers. This article is divided into two parts. The first one contains the conclusions drawn from the analysis of the solutions of the mathematical problems with the absolute value which were solved by the secondary school pupils. The second part of the article contains the didactic proposition of teaching the concept of absolute value at various levels of mathematical education.
Remarks on the Fifteenth Slovak-Polish-Czech Mathematical School and the Sixth Nitrianska Mathematical Conference
The article summarises the Fifteenth Polish-Czech-Slovak Mathematical School and the Sixth Nitrianska Mathematical Conference (Nitrianska matematicka konferencja) - the meetings of Polish, Czech and Slovak mathematicians and mathematics teachers that took place this year.
O zastosowaniu sumowania według Eisensteina do pewnej sumy podwójnej
The lattice sum S_2 for the square array conditionally converges. Having used physical arguments, Rayleigh chose an order of summation in such a way that S_2 = π. The Eisenstein summation method applied to S2 yields the same result. This paper is devoted to a rigorous proof of S_2 = π for the Eisenstein summation method. The study can be used in class for students as an interesting example which illustrates different types of convergence.
Z badań nad sylwetką absolwenta matematycznych studiów w Akademii Pedagogicznej w Krakowie w latach 2001-2007
The main goal of our studies was eliciting the opinion of graduates and students of the last year of Master studies on the course for teachers of mathematics at the Pedagogical University of Cracow. The research method was a survey questionnaire.We were interested in opinions on the level of studies at the college, and professional skills acquired in the study process. Moreover, we asked the questions concerning the professional career.In the article we present the analysis of the replies of respondents...
O różnych sposobach definiowania wartość bezwzględnej
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.
Page 1