Displaying similar documents to “Kształtowanie odruchów”

Przykłady zagadnień z różnych działów matematyki niezbędnych do studiowania teorii miary

Antoni Chronowski, Zbigniew Powązka (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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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...

Współczesne cele i metody kształcenia w świetle koncepcji Wacława Nałkowskiego

Magdalena Misztalska (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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An important task of geographical education is thought to be the formulation of teaching objectives, the selection of contents and development of teaching methods. The primary task is then to define teaching objectives since the formulation of objectives is thought to be a decisive factor in the selection of contents and methods. All these topics constitute the subject matter of the special branch of geography distinguished by Nałkowski, namely the „school geography”, which was seen...

Komputer jako narzędzie badania sytuacji zadaniowej w długoterminowej pracy domowej ucznia

Renata Wojtuś (2009)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In the article I submit a fragment of my research carried out in 2004-2007, which was connected with the role of mathematical computer programs in the independent extracurricular work of the pupil. These examinations were conducted in a group of 119 pupils from the second grade of secondary schools. The article concerns the specific form of homework in mathematics – a long-term homework. The purpose of this homework was to answer the questions: a) In what mathematical situations do pupils...

Atrakcyjność turystyczna regionów na przykładzie Francji

Sławomir Dorocki, Małgorzata Zdon-Korzeniowska, Anna Delekta (2012)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Technological and economic transformation of the past few decades resulted in a significant re-evaluation of the factors affecting the location of economic activity. General trend in these changes is the declining importance of the so-called “hard factors”, “cost factors” (such as transport costs, labour costs and the amount of taxes), as opposed to the so-called “soft factors”; special emphasis among these factors is placed on human capital. An important aspect of the human factor in...

Analiza błędów z geometrii elementarnej popełnianych przez kandydatów na studia matematyczne w Akademii Pedagogicznej w Krakowie dokonana na podstawie wyników egzaminów wstępnych na kierunek matematyka w latach 2003 i 2004

Ewa Lubaś (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In the article the errors in the solutions of geometry problems made by the candidates for the first year of the mathematical studies at the Pedagogical University of Cracow during the entrance examinations in 2003 and 2004 are analysed. Every geometry problem is provided with the examples of its solutions, and the detailed conclusions are drawn from the analysis. In the final part of the article a general didactic analysis of the errors is carried out as well as some aspects of teaching...

Praktyka kształtowania matematycznej twórczości uczniów

Antoni Pardała (2009)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The subject of this work, teacher’s practice forming mathematical activity and creativity of the gifted pupils, is submerged in the issue of one of the contemporary trends in researching the methodology of teaching maths, which is called: creativity in teaching mathematics – theory, diagnosis and methodology, prospects. In this work I refer to certain synthesis of the knowledge to that point, see A. Pardała (2003; 2004; 2006), and I also articulate one of its aspects – the crucial importance...

Aktywności matematyczne studentów inspirowane grami Penneya

Maciej Major, Barbara Nawolska (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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This paper proposes a way to adapt theories of countable probabilistic spaces in order to use them to educate mathematical students trained to be teachers. It presents many examples of how to develop students’ mathematical activities using stochastic games called Penney games. Introducing chance games delivers the opportunity of creating and examining probabilistic spaces. The fairness of games is a problem that inspires and motivates mathematicians to formulate problems and tasks of...

Schüler/innen- und Lebensweltorientierung einschließlich ökonomischer Kompetenzentwicklung im Unterrichtsgegenstand „Geographie und Wirtschaftskunde” an österreichischen Schulen

Christian Fridrich (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The main focus of the curriculum of the subject area “Geography and Economic Education” in Austria is the action of humans in natural space, economy and society. This includes various aspects and consequences of these human actions in our world. Moreover, humans are also in the focus of didactics and teaching in the classroom. That means an orientation towards pupils and their ideas, previous knowledge, everyday life, interim competences etc. Since the great change of the Austrian curriculum...

Rola programu komputerowego CABRI w rozwiązywaniu matematycznych problemów

Henryk Kąkol, Witold Pająk (2009)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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CABRI is a didactic program which has won a very stable position and is probably the most popular one in teaching mathematics. The program is constructed in such a way that it not only accepts and carries out tasks but it emits and stimulates certain behaviors itself, communicating them to the user. Program CABRI, using automatic means, allows undertaking activities corresponding to the so - called Platonian geometric constructions which are usually made with a pair of compasses and...

Przyczynek do badań nad twórczą postawą studentów podczas rozwiązywania zadań matematycznych

Joanna Major, Zbigniew Powązka (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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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...

Antropopresja turystyki wysokogórskiej na przykładzie Kilimandżaro

Michał Apollo (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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This article outlines the negative impact on the environment of the Kilimanjaro Mountain which is a result of commercial approach to mountaineering and change of the climber’s profile. Kilimanjaro, which was called “trampled mountain” in the years 1977–2007, has been visited by 627,974 tourists. The National Park of Kilimanjaro pocketed 25.7 millions USD from admission fees in 2006 only. Officials of the Park are more interested in the commercial aspect than the environmental one. A...

O pewnym sposobie kontroli rozumienia wybranych pojęć z analizy matematycznej przez studentów studiów matematycznych

Danuta Ciesielska, Zbigniew Powązka (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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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...

Innowacyjność w hotelarstwie z uwzględnieniem adaptacji obiektów zabytkowych na bazę noclegową

Kamila Ziółkowska-Weiss (2012)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Nowadays, tourism is a crucial sector of national economy, and for many countries and regions it is one of the goals of economic activity, at the same time being a means of social and economic revival. Therefore, in order to professionally present the tourist potential and offer, and to attract tourists, tourist products should be organized, promoted and introduced in a relevant way. It is necessary to bear in mind that tourism is a service sector, a sector in which different kinds of...

Gry miejskie jako innowacyjne produkty turystyczne

Witold Warcholik, Konrad Leja (2012)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Urban games and other forms of field games, such as Questing, are innovative ideas for presentation, disclosure and interpretation of natural and cultural heritage. The results of the survey presented in the study show that soon urban games can become an alternative to a traditional guided sightseeing of an urban area. There may be several reasons for such a choice: an interesting way of exploring a city, aspects of play and physical activity, better memorization of information, as well...

Od hipotezy do twierdzenia

Jan Górowski, Maciej Klakla, Adam Łomnicki (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In the paper, on the basis of elementary geometrical content, the authors present examples of students' reasoning, which permits, in the first place, to formulate a hypothesis, and further to find a proof. The essential fact here is that the same hypothesis can lead students to follow different possible ways of reasoning.

Kontekst Przekazu w Matematyce

Jerzy Pogonowski (2016)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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We introduce the concept of the context of transmission. It coversthe ways in which mathematical knowledge and mathematical abilities aretransmitted in education and popularization of mathematics. We stress therole of intuitive explanations in these processes. Several examples of suchexplanations are presented, related to: linguistic explanations, perception,empirical models, and internal explanations inside mathematics itself.

Uwagi dotyczące pojęcia wartości bezwzględnej liczby rzeczywistej

Joanna Major, Zbigniew Powązka (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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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.

O badaniach nad kształtowaniem się u studentów matematyki podstawowych pojęć analizy matematycznej

Zbigniew Powązka (2013)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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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...

Kompetencje geometryczne nauczycieli matematyki

Monika Czajkowska (2016)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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Practice proves that students tend to face difficulties in learninggeometry. This observation is partially confirmed by the results of educationalresearch as well as external exams. It happens repeatedly that studentsget lower marks in arithmetic or algebra tasks. The causes of such situationare complex. One of the reasons is that teaching geometry requires specialteaching skills characteristic for this specific teaching branch as well as theneed for “specific vision”. Therefore, I decided...

Czym jest zmysł geograficzny?

Witold Wilczyński (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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„Geographical sense” is one of the original ideas of Wacław Nałkowski. He defined it as oneof the characteristics of human perception and thinking, which manifests itself in such a way, that the whole variety of human experience is transformed in the act of perception to shape the overall, general and comprehensive situations or figures. It is a process based on a spontaneous, unconscious selection of incoming sensory data and its evaluation, interpretation and synthesizing, to create...

Roma ethnic minority risk of social exclusion in Poland

Agnieszka Świętek (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Roma people are one of the most colourful minorities in Poland and arouse interest and controversy among contemporary Polish society, nearly monolithic in terms of ethnic origin and nationality. At present, the socio-economic situation of Roma people in Poland and in other European countries is difficult and marked with social exclusion. In the article the author identifies and describes the following symptoms of social exclusion experienced by Roma people in Poland: lack of tolerance...

Wyniki badań nad stanem nauczania statystyki opisowej w Polsce

Zofia Aleksandra Tomaszewska (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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This article presents the results of the study of teaching descriptive statistics in Poland nowadays. After a short review of the history of teaching this branch of school mathematics in the second part of the 20th century, I made an attempt at diagnosing the stage of teacher’s preparation for teaching descriptive statistics. The diagnosis was based on the analysis of: - the survey conducted among working teachers; - teaching standards for mathematics at universities; - curriculum and...

Badania nad osobowością Wacława Nałkowskiego

Elżbieta Choinkowska (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The article attempts to explain the scientific and social phenomenon that was constituted by the figure of Wacław Nałkowski. With comprehensive knowledge concerning his life, the author undertook the characterization of his personality with the use of the special psychological method of transactional analysis. It is a method developed by American psychiatrist Eric Berne during 1960s. It explains the way people think and behave, offering many tools to understand human functioning, social,...

Náměty na globální rozvojové vzdělávání dětí mladšího školního věku

Petra Karvánková, Dagmar Popjaková, Vlasta Kovaříková (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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This paper initially deals with the origins of the idea of global education. It points to the multitude of internationally existing concepts and business terms of global education which makes it difficult to implement the global dimension into real-life education. This “international” multitude is, as a result, obvious in the Czech terminology of global development education (GRV in the Czech text) where it originates as particular authors followed one or the other concept of global...

Co zostało z idei jedności geografii?

Witold Wilczyński (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Trying to analyze and assess particular scientific, educational and philosophical concepts of Wacław Nałkowski, one should not lose sight of what is his greatest achievement, what was his main concern and care throughout all his scientific career. It is the idea of geography as an autonomous and coherent science, covering the whole of reality that is perceived and experienced in the course of the everyday life. Among the contemporary Polish geographical circles there are very limited...

Leonardo Pisano called Fibonacci, between advanced mathematics, history of mathematics and mathematics education: three examples drawn from Liber Quadratorum

Paolo Bussotti (2015)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In this research, three problems faced by Leonardo Pisano, called Fibonacci,are dealt with. The main purpose is to show that history of mathematics can offerinteresting material for mathematics education. The approach to the use of history ofmathematics in mathematics education cannot be merely historical, but adapted to theneeds of the explanations in a classroom. In the course of this paper, the meaning ofsuch assertion will be clarified. A further purpose is a trying to explore the...

Z badań nad wprowadzeniem podstawowych treści analizy matematycznej podczas zajęć na I roku studiów matematycznych

Zbigniew Powązka (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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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...

Twórcza aktywność matematyczna uczniów związana z rozwiązywaniem pewnych zadań na zastosowanie wzorów Viète’a

Antoni Chronowski, Zbigniew Powązka (2016)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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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...

Znaczenie i możliwości kształcenia matematycznego w studiowaniu kierunków ekonomicznych

Maria Dąbrowa (2014)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The aims and functions of mathematics education differ depending on the level of education. Moreover, the role of mathematics itself differs depending on the domain of its application. In this paper, we focus on mathematics education in the course of economics studies. Unfortunately, while mathematical methods prove useful in building economic models and the importance is still growing, the mathematics education plays increasingly smaller role in the course of economics studies at Polish...

Vývoj didaktiky geografie a nové trendy výuky zeměpisu v Česku

Petra Karvánková (2013)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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This paper deals with the issue of the didactics of the Czech lands geography process and the position of geography as a scientific branch in its system. It describes new trends and styles in teaching geography in the Czech Republic. At the same time, it mentions some current teaching difficulties at Czech primary and secondary schools. The first stage of teaching developing theory, the period from 1948 to 1965, is tagged “applied period” (Hájek, 2003). The theory of teaching geography...

Geography in Russia: education and public interest

Valery Solomin, Viaczeslaw Suchorukov (2013)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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In the article, the terms of the public interest in Russia are discussed, among which are the natural resources and the humanitarian component, including the geographic entity, the state plays an important role.

Edukacja ekologiczna w szkole i społeczeństwie a rozwój regionalny

Wiktor Osuch (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Raising and developing ecological awareness is a great challenge to modern societies in many countries. This article presents examples of ecological education at Polish schools. Ecological education at the beginning of the 21st century plays an important role in the education of young generations. It depends on education if we encourage a young person to choose the lifestyle which will be environment-friendly, or not. The raising and developing of ecological awareness is therefore a...

Dekadencja geografii i zapomniane idee Wacława Nałkowskiego

Jacek May (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The article is inspired by Wacław Nałkowski’s writings and is a reflection on the nature of geography and its place in the system of knowledge. Moreover, the author considers the status of geography and its social relevance. The article seeks to justify the thesis that the low prestige of geography in social consciousness is an outcome of the attitudes of scholars and teachers of geography themselves, the media propaganda and also the state policy. The main objective of the paper is...

Актуальные проблемы современной методики обучения математике

Роза А. Утеева (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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This article analyzes the development of the concept of methodical system of teaching mathematics. Various approaches (A. Pyshkalo, G. Sarantsev, T. Ivanova, N. Stefanova, etc.) to the concept of methodical system of teaching mathematics are analyzed.

Twórczość i kontekst ideologiczny w poglądach Wacława Nałkowskiego

Karol Wilczyński (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Nałkowski lived in times of rapid transformation of civilization and during the period of ideological ferment, in a colonized country which at that time was Poland. Clearly disappointed with social and political reality, he turned his interest towards the trendy socialist ideas, seeing in them the hope for improving the living conditions of the society. The discerning analysis of the Nałkowski’s Social Writings (ed. 1951), allowed the author to assess the influence of the intellectual...

Idee Wacława Nałkowskiego a współczesna dydaktyka

Elżbieta Szkurłat (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The answer to the question whether teaching of geography nowadays respects the universal ideas of the great geographer, is not clear. A critical look at teaching achievements of Wacław Nałkowski, as well as at the contemporary state of geographical teaching, seems to be difficult due to the individual views and personal experiences. This paper is an attempt to assess the extent to which the important educational concepts of Nałkowski are respected in contemporary educational practice....

Koncepcja geografii malowniczej

Katarzyna Mentel (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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„Picturesque geography” is an original expression of Wacław Nałkowski, which probably has no counterpart in the whole history of geographical thought. It clearly shows Nałkowski’s belief that the materials utilized in the process of education should have a beautiful shape. This is also a very convincing expression of his romantic sensibility and the testimony of his great literary talent. Romantic aspects in works of Nałkowski are thought to be very important, since geography is a field...

Calculus without the concept of limit

Piotr Błaszczyk, Joanna Major (2014)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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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...

Jezioro Aralskie – największa katastrofa ekologiczna minionego stulecia

Rafał Bielecki (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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One of the best examples of environmental risk arising as a result of inefficient management of environmental resources is the disappearance of the Aral Sea. Aral Sea extends into the territories of Kazakhstan and Uzbekistan. About 10 thousand years ago, this vast body of water was under the influence of water from melting mountain glaciers, flowing directly into the Aral Basin. However, the climate change which started about 3500 years ago contributed to the drying process of the tank....

Winter tourism of Davraz Mountain

Ahmet Tokgözlü, Kadir Temurçin, Kamile Uysal (2012)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Winter tourism comprises activities such as traveling to snowy and sloping areas in ski centers, accommodation in these areas and other services. For winter tourism, the climate is a major factor. However, a particular altitude and slopes are required. A site could be defined as an available territory for winter tourism if there are places that are suitable for climbing and trekking and have appropriate snow for skiing. In addition to the abovementioned issues, the period during which...

Symbolika matematyczna związana z pojęciem funkcji

Izabela Jóźwik, Małgorzata Terepeta (2016)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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Mathematical texts are characterised by the occurrence of specificsymbols. They may be letters (as applied, for example, by Euclid), numbersymbols or graphic signs with context-independent meaning. Mathematicalsymbols store knowledge of previous generations that provides frameworkswith which to examine history of mathematical problems. In this paper, wedeal with symbols related to the concept of function and related concepts likelimit, and some other set theoretical or logical concepts....

O roli prac dyplomowych z dydaktyki matematyki w kształceniu przyszłych nauczycieli matematyki

Joanna Major, Bożena Olik-Pawlik, Tadeusz Ratusiński, Lidia Zaręba (2017)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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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,...

Tourism development in small cities on the example of Pistoia in Tuscany

Małgorzata Bajgier-Kowalska, Renata Rettinger (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The dynamic development of tourism in many regions of the world causes competition boost which, in turn, leads to a variety of changes in tourist offers. Tourism is an alternative for other types of economic activity, this relates to spatial units of diverse area, including cities. The tourist function can become the mechanism of local development for cities and the protection of the cultural and natural heritage. The main goal of the article is to present the tourist potential of a...

System komputerowy Mizar narzędziem do komputerowego wspomagania nauczania w szkole wyższej

Ewa Borak (2010)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The MIZAR system is a computer system for representing mathematical proofs in such a way that the computer checks their correctness. The texts written in the MIZAR language are called Mizar articles and are organized into the Mizar Mathematical Library (MML). Since the very beginnig of the development of the MIZAR system, experiments using MIZAR as a tool for teaching mathematics have been conducted. Numerous courses were organized which were based on different versions of the system:...

Teoretyczne podstawy dzielenia z resztą liczb naturalnych wraz z uwagami o dzieleniu z resztą liczb całkowitych, wymiernych i rzeczywistych

Antoni Chronowski (2019)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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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...

Dokształcanie i doskonalenie zawodowe nauczycieli geografii… jako instrument dostosowania się do aktualnych wyzwań rynku pracy

Danuta Piróg, Renata Jania (2013)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Facing a deteriorating situation on the job market for teachers (including geographers), one should expect even heavier commitment of the professional group to their additional training. Therefore, it is necessary to take actions on the central level for creating wider range of offer adequate for the teachers’ needs and supporting them in that. The current system of methodological guidance and additional training for teachers is based on local arrangements and diverse organizational...

The problem of human development and liberal education

Viaczeslav Sukhorukov, Bożena Wójtowicz (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The modern world is characterized by rapid changes in all spheres of social life. These changes are amplified by extremely rapid dissemination of information, knowledge, values, tastes, and ideas from one society to another. Some values are invisible to the eye, other can be noticed quickly and easily. The result is a new cultural phenomena, which are called “civilization“ and “ the modern way of life.” To change the values and ideological climate in today’s world it is necessary to...

Z badań nad analizą rysunku i odkrywaniem własności funkcji

Joanna Major, Zbigniew Powązka (2013)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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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.