Displaying similar documents to “Atrakcyjność turystyczna regionów na przykładzie Francji”

Rola portów morskich w rozwoju cruisingu na Karaibach

Renata Rettinger, Anna Urbańska (2012)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Sea tourism brings huge profits to the Caribbean. The cruise market is set mainly for tourists coming from North America. Low travel costs, high income and the long-lasting tradition of sailing excursions are the main reasons. More and more European tourists can also be seen in the Caribbean thanks to numerous air connections. The cruise routes follow the most attractive ports. The ongoing competition causes the increase of quality of passenger’s service and goods. The investment of...

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...

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...

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...

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....

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...

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...

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...

Park miejski – zielone serce Sanoka

Piotr Kutiak (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The Municipal Park is located in the centre of Sanok, on the slope of the Park Mount (height 364 m asl), which is an essential dominant in the town’s panorama. The park was established in 1909 on a “beautifully located, but completely inaccessible and entirely mountainous ground” and donated by Dr. Aleksander Tchorznicki. Nowadays it is one of the most attractive places in the town; it is said to be one of the most beautiful parks in Poland and it is the biggest mountain park in the...

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.

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...

Housing conditions in selected metropolitan areas in Poland

Piotr Raźniak, Anna Winiarczyk-Raźniak (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Housing conditions are considered an element reflecting the living standard of the population. In addition, it is also an important index illustrating advancement of suburbanisation processes. The article presents diversification of housing conditions in two selected metropolitan areas: Warsaw, Kraków and Potential Rzeszów Metropolitan Area. Two indexes are analysed in the paper: the number of persons per apartment and the average floor space of apartments, in two time periods:1995 and...

Industrial and commercial suburbanization in post-socialist city: the Kraków Metropolitan Area (Poland)

Sławomir Kurek, Tomasz Rachwał, Mirosław Wójtowicz (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The subject of this paper is the issue of urban sprawling in the Kraków Metropolitan Area (Poland). Particular attention is paid on the changing role of industry as one of the key elements of development and metropolization of cities in post-socialist, emerging economies. The role of the industry in terms of activation of labor resources has been diminishing, which is connected to the automation of manufacturing processes and relocations of labor-intensive activities to regions with...

Dynamics of changes in the structure of the forest edge in Slovakia

Martina Škodová, Alfonz Gajdoš (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Forest edges generally represent a very important element of ecological stability. The goal of this paper is to classify the types of anthropogenic forest edges in the area of Starohorské Mountains and to analyze anthropogenic impacts on the selected attributes of forest edges. We evaluated the attributes of a biocomplex, type of forest edge, its structure, consistence, species composition and other factors. The differences in environment variables and anthropic impact were influenced...

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...

Main issues concerning drinking water supply in the Angara River watershed

Elena A. Rush (2012)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Main issues concerning drinking water supply in the Angara River watershed. Water supply for drinking and communal-general purposes plays an important role in every economy all over the world as water is not only widely used for people’s everyday purposes, but is also essential for people’s vital functions. The principle concerning the priorities of supplying drinking and communal water, stipulated in relevant norms and regulations, presumes that in the first place people should be provided...

Innowacyjność w rozwoju przestrzeni turystycznej

Janusz Ustupski (2012)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Critical socio-political changes that have happened in Europe during the last twenty years, particularly in East-Central Europe, have had a great influence on the development of cities and the surrounding areas. The state welfare structure of West European countries has influenced the socioeconomic development of their cities. On the other hand, the state–managed economy in East-Central Europe controlled the local communities, which had great impact on their undertakings. The changes...

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,...

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...

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...

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...

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...

Development and present situation of slovenian didactics of geography

Tatjana Resnik-Planinc (2013)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The paper presents the development of Slovenian didactics of geography in the frame of the development of geographical education from the Middle Ages until nowadays. Important milestones are discussed through the prism of the work of important men who influenced the development of geographical education from its very beginning.

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...

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...

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...

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...

Koncepcja kształcenia nauczycieli

Bogdan J. Nowecki (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The article constitutes a written version of the Author’s presentation during the special session of the Senate Science Committee held in December 2003. The session was devoted to teacher training. It contains important general ideas concerning teacher training, criticism of the current system and regulations as well as proposals for improving the situation.

Nauka i ewolucja w myśli Wacława Nałkowskiego

Mateusz Wierciński (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Wacław Nałkowski is certainly an outstanding figure for Polish geography. In many publications he has also been classified as positivist, anti-metaphysician, evolutionist, anticleric and socialist. Perhaps these designations are not always right, since in his works one can also find the ideas that do not quite match the labels conferred. His broad interests, diligence, criticism in selecting arguments, and the ability to see the essence of complex phenomena of different nature (both...

Ocena wykształcenia kompetencji przedmiotowych z geografii społeczno-gospodarczej a wybrane aspekty innowacyjności w edukacji i kształceniu nauczycieli

Wiktor Osuch (2012)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Although Poland has gone through a period of many various trials regarding the introduction of different changes in the educational system (involving everything from types of schools, through levels of teaching, changes in curricula for each school subject, syllabuses and textbooks, to the modification of teaching aims and content for each subject), very little, in fact, has been done to promote the necessary remodelling of work that would ensure the shaping of a truly modern teacher....

Studia geograficzne w Uniwersytecie Jagiellońskim w XIX wieku

Mariola Tracz (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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In time of Wacław Nałkowski’s studies in Kraków (1871–1876), the chair of geography at the Jagiellonian University did not exist. Despite this, in addition to mathematics, astronomy and physics, he attended lectures in geography, astronomy and cartography. Geographical learning opportunities within the Faculty of Philosophy were enabled there as early as1765, thanks to the reform of the University made by Hugo Kołłątaj. In late 1811 and 1812among 12 departments in the Faculty of Philosophy...

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...

Walory turystyczne wybranych regionów Spitsbergenu

Piotr Dolnicki, Łukasz Gawor (2012)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The paper presents different attractions of Spitsbergen: geological, geomorphological and glaciological objects and processes, as well as industrial sites especially connected with coalmining, which constitute the group of geotourist attractions in Hornsund, Isfjorden and North East Land. It also describes logistic and infrastructure conditions in Svalbard. The evaluation of possibilities to develop geotourism in Spitsbergen is included as well.

Ścieżka dydaktyczna jako forma poznania najbliższej przestrzeni geograficznej ucznia – na przykładzie ścieżki dydaktycznej w miejscowości Zalas

Renata Gasek (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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An important, but underestimated method of teaching geographic themes in elementary and junior high schools are strolls, organized on didactic routes appointed near schools. They enable merging the knowledge on multiple topics, show its application in practice, and enables expanding students’ interests. The project of a didactic route created for Zalas shows the possibilities of using local potential to teach geography, with special consideration of human activities. Usage of students’...

Ski and spa tourism as local development strategy – the case of Krynica Zdrój (Poland)

Sławomir Dorocki, Paweł Brzegowy (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The socio-economic, cultural and technological transformations, characteristic features of the globalization era, result in altering the ways in which tourist and recreational services are rendered, leading to the formation of the so-called mega-tourism trends. At present, tourism has become one of the fastest developing economic branches in many countries around the world. This dynamic development includes, among others, SPA and wellness and outdoor physical activity sectors. Slowly...

Koncepcja nauczycielskich studiów geograficznych według Jana Flisa

Danuta Piróg, Mariola Tracz (2013)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The study shows the evolution of plans of teaching and curriculums of geography studies at the Pedagogical University of Cracow (former Wyższa Szkoła Pedagogiczna) in Cracow in 1946–2001. On the basis of literature and their own research, the authors distinguished some stages of changes introduced into geography-teachers training, taking into account formal and curricular aspects and professor Jan Flis’ contribution to the notion of geography-teachers’ training. The first chapter illustrates...

Założenia koncepcji Ekologicznego Śladu i przykłady obliczeń dla dużych miast

Wanda Wilczyńska-Michalik, Karolina Świder (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The article presents the concept of Ecological Footprint (EF), which is a quantitative indicator of human impact on the environment. The idea of EF has originated from the concept of carrying capacity. The Ecological Footprint measures how much of the land and water area a human population requires to produce the resource it consumes and to absorb its wastes, using the prevailing technology. The methodology was developed by Rees and Wackernagel (1996). The Ecological Footprint Assessment...

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...

O fałszywych przekonaniach obserwowanych na zajęciach z analizy matematycznej

Zbigniew Powązka (2009)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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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”.

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...

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...

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....

Geograficzny bieg dziejów

Piotr L. Wilczyński (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The expression „geographical course of history”, currently seen as old-fashioned or obsolete, seems to be typical in geographical works of Nałkowski. It combines two fields that were very close to him just from the very beginning of his scientific career: geography, to which he has devoted his whole life, and history, which was for him a source of information necessary to explain the diversity of landscapes. The origins of the concept can be found in works of German geographer, educator...

Przekształcenia wykresów funkcji

Antoni Chronowski (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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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

Kontrasty w użytkowaniu przestrzeni jako wynik wielowiekowej degradacji środowiska przyrodniczego – na przykładzie obszaru miasta Mysłowice (Wyżyna Śląska)

Tomasz Parusel, Dominik Karkosz (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The town Mysłowice is located in the southern mesoregions of the Silesian Upland: Katowice Upland (341.13) and Jaworzno Hills (341.14). Mysłowice terrain has been intensively used by man for centuries and still is nowadays. This process left permanent signs on the natural environment; the mosaic forms of land use are the effect of this activity, among others. In the town area contrasts are frequent – direct proximity of various land use forms is observed. Initial characterization of...

Nowe spojrzenie na gry Penneya

Maciej Major, Barbara Nawolska (2013)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The problem of gaming is an important part of the educational process on all levels of Mathematics teaching. In this work, we present certain stochastic problems, based on the so-called Penney games. It provides the opportunity to formulate new problems and to construct the tools needed to solve them. This process is accompanied by a variety of mathematical activities.

High School Identities

Katarzyna Słomczyńska (2015)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In 1969, Polish mathematician and logician, Alfred Tarski asked ifall the identities true in the set of natural numbers involving the constant 1,addition, multiplication, and exponentiation can be derived from the elevenaxioms that are taught at the high school level (High School Identities). In1981 Alex Wilkie negatively solved this problem by constructing an identitythat cannot be proved using these axioms. In this paper we survey resultsconnected with Tarski’s problem.

Kształtowanie odruchów

Jan Górowski, Adam Łomnicki (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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This article attempts to single out actions performed by a person while solving a mathematical task that lead to the acquisition of desired habits towards solving such tasks. The examples of tasks, which are presented here with their solutions, stress the importance of reflection that follows a completed process of solving a task.

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...