Displaying similar documents to “Human geographical ideas of Eugeniusz Romer”

Przestrzenne zróżnicowanie migracji w Polsce w ujęciu miast i gmin na przełomie XX i XXI wieku

Dariusz Nowotnik (2012)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Total permanent migration in Poland at the turn of the 21st century was influenced by the political and economic events (economic transformation and the change of the political system in 1989, and accession to the European Union). Among the types of international migration, temporary emigration prevailed. Emigrants were usually aged between 18 and 39,and came mostly from urban areas. Until the year 2000, the prevailing direction in internal migration was the movement from rural to urban...

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...

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...

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...

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....

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...

Akademik W. M. Monachow - niezwykły człowiek, uczony, dydaktyk i organizator nauki

Roza A. Utiejewa, Antoni Pardała (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The authors refer to the atmosphere, the issues and the results of this year international conference in Togliatti '2010 dedicated to 75 years of the academician W. M. Monachow. The authors remind his way to creative development of didactics subjects and educational technology and point out and analyze his selected achievements.  In particular, they express gratitude to himself, his collaborators and supervisors for support and scientific cooperation with Poland in the field of education...

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...

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...

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...

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...

Waloryzacja środowiska geograficznego Nadleśnictwa Rymanów pod kątem atrakcyjności turystycznej

Piotr Skóra, Wanda Wilczyńska-Michalik, Maciej Szpiech (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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A sudden increase in various tourism forms in Poland in the second half of the twentieth century brought development of natural environment evaluation methods for tourist purposes. Natural and cultural environment values and slight anthropogenic transformations of the Forestry Rymanów created tourists’ interest in this region. The paper presents the scope and ways of evaluating individual components of the natural environment in connection with historical and political changes. Evaluating...

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...

Publikacje prof. Jana Flisa w zbiorach Biblioteki Instytutu Geografii Uniwersytetu Pedagogicznego im. KEN w Krakowie

Agnieszka Świętek (2013)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Professor Jan Flis began his collaboration with the Higher College of Teacher Training in 1951, and since 1960 he has become its full-time employee, which he remained until the end of his long teaching and academic career. One of the most important record of his research activity (especially in the area of teaching), is an extensive collection of his publications that can be found in the Library of the Institute of Geography of the Pedagogical University of Cracow, which the author compiled...

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...

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...

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...

Wacław Nałkowski jako prekursor konstruktywistycznego podejścia do edukacji geograficznej

Teresa Sadoń-Osowiecka (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Although the very term “constructivism” appeared rather recently, its concept was knownin science long before now. According to modern cognitive psychology, the reality is created individually in person’s mind. An individual transforms and interprets the flow of information which he receives in his own way, depending on cultural, social, biological or situational context. Nałkowski’s statements concerning perception and thinking from the beginning of the twentieth century, connected...

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...

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...

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...

Monitoring ruchu turystycznego w Pienińskim Parku Narodowym

Witold Warcholik, Marcin Semczuk, Marcin Baranowski (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The paper presents the results of tourist traffic monitoring carried out in the years 2007–2009 by SKNG UP in the Pieniny National Park. The study included a survey of 25612 visitor sand allowed estimating the intensity and spatial variability of tourist traffic in the Pieniny National Park, as well as determining the main routes and the most popular marked paths within the Park. The questionnaires helped to determine the types and preferences of the visitors to the Pieniny National...

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...

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...

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.

Wybrane aspekty pedagogizacji nauczycielskiego kierunku studiów geograficznych

Wiktor Osuch (2013)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The issue of initial and further training of geography teachers seems to be relevant everywhere where teaching faculty is currently offered. This paper presents discussion, reflection and research results on the widely understood process of initial and further training of future geography teachers in the context of academic work of professor Jan Flis, especially regarding the problem of pedagogization of teaching faculty at universities (Flis 1984) understood as supplementing the faculty...

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...

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...

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...

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...

Motives for the choice of geography in Matura examinations in the context of Poland’s examination policy

Mariola Tracz (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The educational reform in 1999 introduced external examinations into the Polish system of education. The examinations are carried out on the basis of educational standards for individual subjects and subject groups. External examinations, especially new Matura examination, changed diametrically previous solutions which is a challenge to teachers, students and parents. Being frequently chosen by students out of the group of optional subjects, geography has a large contribution to Matura...

The concept of geographical space

Zbigniew Zioło (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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In the process of shaping the geography as a science there appeared two research trends. One of them is reflected in ongoing scientific specialization and isolation of new disciplines, while the other is characterized by making attempts to synthesize the results achieved by the specialized disciplines. Against this background, this paper is trying to find a frame to synthesize the phenomena through the relations between the natural, socio-economic and cultural elements of geographical...

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...

Współczesne problemy i praktyka kształcenia matematycznego studentów

Antoni Pardała (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The subject matter of this paper relates to one of the modern research trends in teaching mathematics: the problems of quality of mathematical education of pupils and students in the twenty-first century in different countries and cultural traditions. This analysis throws light on the literature, research results, and observations from the Polish perspective of practice, and outlines the intentions of the range. The work also discusses some theoretical bases for the concept of improving...

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...

Актуальные проблемы обучения математике в школе и вузе в свете идей Л. С. Выготского

Людмила Боженкова, Марина Егупова (2016)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The article gives a brief overview of the scientific results of the III  International Conference held in Moscow State Pedagogical University in November 2016. The main directions of the development of ideas of L. S. Vygotsky, presented in the reports of leading Russian and foreign scientists – participants of the conference.

Dokształcanie i doskonalenie nauczycieli na studiach podyplomowych

Bogdan J. Nowecki (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The project presents an outline of a general concept of teacher training and self-improvement in the postgraduate courses. The general proposals are illustrated with an example of postgraduate Studies in Mathematics.

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...

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...

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,...

Gotowa wiedza i aktywność w matematycznym kształceniu na przykładzie kątów Langleya

Maciej Klakla (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The article contains a didactic project of classes with mathematics students – future teachers. On the example of problems related to Langley’s angles, the author presents differences between two styles of teaching mathematics. One style is based on existing mathematical knowledge, and the second requires active participation of the students in creating this knowledge during the problem solving process.

Idea czynnościowego wprowadzania pojęć geometrii elementarnej z pomocą kursu e-learningowego

Magdalena Kucio, Tadeusz Ratusiński (2009)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The present article introduces a didactic proposal of supporting the process of teaching mathematics with blended learning. The authors discuss both benefits and dangers of this idea. Also, the concept of functional method of teaching mathematics is brought closer, as it is naturally inscribed in the concept of blended learning. In the second part of the article, the authors describe the materials processed for employment of the discussed foundation in teaching elementary geometry. Estimate...

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...

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...

Struktura odpadów komunalnych w jednostkach organizacyjnych Uniwersytetu Pedagogicznego w Krakowie

Joanna Ćwiąkała, Paweł Kramarz (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Wastes as a result of civilizational impact on the environment pose a major threat, not only to our lives, but also those of other living creatures. Therefore, current state’s policy sets some strict rules for administering wastes by minimizing their production, reusing them in various technological processes and neutralizing their harmful effects. Waste segregation is essential in the process of their reusage for the production of new materials. The study presents monthly reports concerning...

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...

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....

Rodzinny i społeczny kontekst twórczości Wacława Nałkowskiego

Marzena Kubacz (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The author reveals previously unknown details of the Nałkowskis’ family life which affected the development of Wacław’s character and his interests. These details were also decisive as factors which influenced his scientific and social commitment. Social relationships of his parents and their affinities were also analyzed in order to explain the origins of his worldview. Wacław’s combative nature was already developed in the Russian school, where every symptom of Polish patriotism as...