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Remarks on the Sixteenth Slovak-Polish-Czech Mathematical School, IMEM Congress and the Seventh Nitrianska Mathematical Conference
Remarks on the Sixteenth Slovak-Polish-Czech Mathematical School, IMEM Congress and the Seventh Nitrianska Mathematical Conference
Wokół twierdzenia Picka
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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...
Calculus without the concept of limit
There are two different approaches to nonstandard analysis: semantic(model-theoretic) and syntactic (axiomatic). Both of these approachesrequire some knowledge of mathematical logic. We present a method basedon an ultrapower construction which does not require any mathematical logicprerequisites. On the one hand, it is a complementary course to a standardcalculus course. On the other hand, since it relies on a different intuitivebackground, it provides an alternative approach. While in standard...
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.
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.
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.
O roli prac dyplomowych z dydaktyki matematyki w kształceniu przyszłych nauczycieli matematyki
In the training process of students – future teachers of mathematics, an important role is played by, among others, participation in the diploma seminar, during which the student (being at the final stage of studies)is tasked with preparing a bachelor’s or master’s thesis. This dissertation may be purely mathematical in nature or refer to problems in didactics of mathematics. The article aims to develop and illustrate some thoughts from previous works of the authors (Zaręba, 2009; Major, Olik-Pawlik,...
Wybrane uwagi na temat roli zadań matematycznych w procesie nauczania-uczenia się matematyki
The paper presents the comments relating to the role of tasks in theprocess of teaching and learning of mathematics in the context of educationof students studying to become teachers. In the considerations part, referencewas made to the fragments of undergraduate and postgraduate works, madeat seminars of didactics of mathematics.
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