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Displaying similar documents to “Przyrodnicze i antropogeniczne uwarunkowania rozwoju systemów wąwozowych w okolicy Rogowa (Wyżyna Lubelska)”

Z badań nad sylwetką absolwenta matematycznych studiów w Akademii Pedagogicznej w Krakowie w latach 2001-2007

Danuta Ciesielska, Joanna Major, Zbigniew Powązka (2009)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The main goal of our studies was eliciting the opinion of graduates and students of the last year of Master studies on the course for teachers of mathematics at the Pedagogical University of Cracow. The research method was a survey questionnaire.We were interested in opinions on the level of studies at the college, and professional skills acquired in the study process. Moreover, we asked the questions concerning the professional career.In the article we present the analysis of the replies...

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...

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:...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

Geografia na maturze – zróżnicowanie merytoryczne i ocena zadań… z arkuszy egzaminacyjnych w latach 2005–2011

Jan Wójcik (2013)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The paper presents a substantive and methodological assessment of the tasks and the trends in changes in the scope of knowledge and skills tested during the final examinations (matura) at Polish high schools in the years 2005–2011. The examination sheets contained a various number of tasks (27–38). They included open-ended and closed-ended tasks. With a total of 14 sheets, closed-ended tasks predominated in 9 sheets, open-ended tasks prevailed in 4 sheets, while the number of open-ended...

The role of visualisation in the process of generalisation

Lidia Zaręba (2015)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In my paper, I discuss the results of individual observations of pupils aged 13-14. These children undertook an attempt to solve problems which were designed in order to bring about an inductive type of generalizing. The main aim of the study was to classify typical methods of proceeding, which represent the pupils’ ways of reasoning and to determine what influence a particular method of proceeding may have on the final outcome of their work. These results indicate the general pupils’...

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...

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...

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...

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.

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...

Etapy rozwoju osadnictwa zachodniej części Płaskowyżu Nałęczowskiego i ich zapis w osadach dna doliny Bystrej

Jan Reder, Józef Superson, Tadeusz Król (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The article analyzed the impact of old (prehistoric, medieval) and modern settlement on the nature of the Holocene alluvial sediments at the bottom of the Bystra valley. It was shown that the transition from peat to mineral deposits was the result of Neolithic farming. Nomadic culture of the late Neolithic and early Bronze Age have helped to stop the denudation slope sand increasing erosion in the bottom of the river valley. Restarting the denudation in the basin and the beginning of...

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...

Maksymalne sumy dobowe opadów w Ojcowie (Dolina Prądnika)

Eligiusz Brzeźniak (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The analysis of multiannual variability of maximum sums of daily precipitation was based on a 20 years-long observation series (1990–2009) from Ojców-Park Zamkowy observation point, situated in the Prądnik river valley, and maintained by the Ojców National Park. Methods of descriptive statistics, namely average values, including 5-days and 5-hours moving averages, extremal values and dispersion indices were used in the analysis (Fig. 1, 2).An attempt at determining the basic characteristics...

Jan Flis – współtwórcą współczesnej polskiej dydaktyki geografii

Mariola Tracz (2013)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The study shows the role of professor Jan Flis in the development of geography education in the post-war era. His academic input into the discipline is expressed in 134 publications, out of which 40 concern the topic of the didactics of geography. Professor’s interest in the field of geography education focused on: the selection and structure of geographical material, forming of theories in teaching and learning geography, function of geography in education and cognitive development,...

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...

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...

Droga profesora Jana Flisa do geografii

Krystyna Banaśkiewicz-Cabaj, Wacław Cabaj (2013)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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In the study, the authors presented Jan Flis’ road to geography. They emphasized four significant facts in the Professor’s biography which had, in their opinion, impact on his choice of future field of study and professional career. He attended an eight-year Jan Długosz public middle school in Nowy Sącz; a classical school with Greek and Latin courses. The school education provided him with excellent knowledge of Polish, which resulted in conciseness of his works, as well as in uncompromising...

Rozwój śródpolnego wąwozu drogowego w świetle badań pedologicznych i pomiarów GPS

Jan Rodzik, Mirosław Krukowski, Piotr Zagórski (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The article presents the development of a small, midfield form of road, which cuts the side of a loessic valley. The contemporary shape of the surface was determined by GPS measurements (Leica System 500), set together in ArcView and ArcGIS. Changing of its position was determined by a field analysis of the construction of 50 profiles of the Luvisols with varying degrees of erosion or aggradation. Calculation and visualization were performed in the ‘Surfer’ program. The results are interpreted...

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...

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...

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.

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....

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...

Profesor Jan Flis – mistrzem dla uczestników studiów doktoranckich z dydaktyki geografii

Michalina Lubelska (2013)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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In the first part of this paper the author presents her own path as a teacher. During her professional career she has met the Professor numerous times. The first time was when she was a geography student at the Jagiellonian University. The subsequent occasions occurred when she was a geography teacher in primary school and also as a PhD student of the didactics of geography. In main part of the paper the author presented the curriculum of the PhD studies in the field of didactics of...

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....

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...

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...

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...

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...

Z badań nad trudnościami studentów w rozumieniu pojęcia miary i całki

Zbigniew Powązka (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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Measurement is an important form of human activity. It appears at all levels of secondary school education, while discussing the length of a segment, the area of a plane figure and the volume of a solid. The definition of a measure, understood as a non-negative real function defined on a σ-field of set of a space, is taught during the classes on mathematical analysis. It is observed that the concept of measurement causes great difficulties to students. This paper presents the results...

Diagnoza wiedzy uczniów szkół ponadgimnazjalnych i studentów matematyki na temat związku twierdzenia z jego dowodem

Halina Pieprzyk, Anna Żeromska (2009)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The paper presents results of research carried out on the two following levels of mathematics education: the high school level and the level of pre-service Mathematics teachers training. The subject of the research was understanding the relations between mathematical theorem and its proof by the study participants.

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.

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...

Nowe cechy równobocznych trójkątów

Michał Biesiada, Jan Górowski, Adam Łomnicki (2014)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In this paper the authors formulate and prove several conditions fortriangle to be equilateral. These conditions are associated with Gergonne,Nagel and Torricelli points and were obtained by composing and solvingthe so-called ‘enforcement tasks’. Both, the method and the results, can beused to trigger some mathematical student activities at different levels ofeducation or even some teacher activities.

Spatial structure transformations in small towns in view of rehabilitation and gentrification processes

Agnieszka Kwiatek-Sołtys, Krzysztof Wiedermann (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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During the time of centrally controlled economy Polish cities were shaped by processes and structures typical of a socialist state. When changes in the economic, social and political system in Poland begun, Polish cities and towns entered a transformation process. The aim of the paper is to answer the question whether and to what extent spatial transformations of small towns in Poland show symptoms of gentrification. Authors analyse the problems of towns genesis, population changes,...