Displaying similar documents to “Application of certain properties of matrices over GF(2) to the description of linear switching networks”

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...

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.

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.

Introduction to E. Nelson’s internal set theory

Taras Kudryk (2015)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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An axiomatic approach to Non-standard Analysis by E. Nelsonis presented in a simplified form. The main aim of the article is strictly thepopularization of NSA, and not its foundations. No special preparation inmathematical logic is required from the reader but it is assumed that he(she) is familiar with elementary calculus and linear algebra.

Wybrane problemy zadań konstrukcyjnych na płaszczyźnie euklidesowej i wykorzystanie do ich rozwiązywania twierdzeń geometrii rzutowej

Ewa Lubaś (2009)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The article gives examples of construction tasks of first and second degree on a Euclidean plane, which can be solved with the use of a simple ruler. For this purpose, the theoretical backgrounds of projective geometry have been used. It has been proved that in the projective approach some constructions on a Euclidean plane become linear constructions. In particular, a linear construction of this type may be the typical operation of inversion in respect of a circle and an arbitrary conic...

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...

Применение методов математической статистики в научных исследованиях

Владимир В. Афанасьев (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In the paper, the author presents the basic concepts and theorems concerning methods of mathematical statistics and its application in the domain of empirical research. Several examples presented in the paper can be useful as patterns of using statistical tool in didactic research.

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.

Wybrane uwagi na temat roli zadań matematycznych w procesie nauczania-uczenia się matematyki

Joanna Major, Bożena Olik-Pawlik, Tadeusz Ratusiński, Lidia Zaręba (2016)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The paper presents the comments relating to the role of tasks in theprocess of teaching and learning of mathematics in the context of educationof students studying to become teachers. In the considerations part, referencewas made to the fragments of undergraduate and postgraduate works, madeat seminars of didactics of mathematics.

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.

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...

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...

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....

Wielomiany Fibonacciego stopnia k

Jan Górowski, Adam Łomnicki (2014)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In this paper, we give formulas determining the Fibonacci polynomials of order k using the so-called generalized Newton symbols, i.e., the coefficients in the expansion of (1+z +z^2 +. . .+z^{k−1})n with respect to the powers of z.

“Nature of Saint-Petersburg” electronic educational edition as a mean of shaping ecological awareness in schoolchildren

T.V. Vileyto, E.M. Rebko (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The article discusses in detail the contents of electronic educational edition of “Nature of St. Petersburg”. It shows the scientific and methodological benefits, as well as the principles underlying the publication. Much attention is paid to the analytic section of the manual, especially to enable the development of ecological awareness of schoolchildren.

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

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...

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...

Znaczenie i możliwości kształcenia matematycznego w studiowaniu kierunków ekonomicznych

Maria Dąbrowa (2014)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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

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...

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’...

O elementach logiki erotetycznej w edukacji matematycznej

Tadeusz Rams (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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Asking questions is one of the most common activities of mathematics teachers at various levels of education. Moreover, the way the teachers formulate questions has profound impact on the results of teaching, especially on their pupils' reasoning process. Erotetic logic is frequently presented in a very formal manner. In this paper, we restrict our attention to these aspects of erotetic logic that can turn it into a useful framework to describe various didactic situations. In particular,...

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’...

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...

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

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

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In the training process of students – future teachers of mathematics, an important role is played by, among others, participation in the diploma seminar, during which the student (being at the final stage of studies)is tasked with preparing a bachelor’s or master’s thesis. This dissertation may be purely mathematical in nature or refer to problems in didactics of mathematics. The article aims to develop and illustrate some thoughts from previous works of the authors (Zaręba, 2009; Major,...

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,...

O pewnej implikacji

Jan Górowski, Adam Łomnicki (2016)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The purpose of this paper is to show how the process of provinga theorem in different ways or proving generalized versions of the theorem,after learning one its proofs, influences the development of the skills of provingtheorems and analysing proofs by the students of mathematics. Toillustrate this process we use an elementary theorem about numbers and itsgeneralizations, giving fourteen proofs. Proving theorems we use methodsand facts which are available to high school students. ...

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.

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...

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,...

Aktywności matematyczne studentów inspirowane grami Penneya

Maciej Major, Barbara Nawolska (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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

Информационно-коммуникационные технологии в образовании студентов специальности >>5В010900-Математика<< педагогического вуза

Бакыткуль Р. Каскатаева, Назира С. Баймулдина (2013)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In the paper the authors discuss educational usefulness of special applied software (Mathematica) in the process of studying Mathematics at the pedagogical university. The authors also present the levels of thecompetences connected with using an educational electronic means, necessaryfor the students of mathematics.

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...

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...

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...

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...

O potrzebie dokształcania nauczycieli akademickich

Bogdan J. Nowecki (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In this paper author underlines the necessity of continuing education of young academic teachers in the domain of methods of students’ activity during their studies.

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...

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....

Z badań nad analizą rysunku i odkrywaniem własności funkcji

Joanna Major, Zbigniew Powązka (2013)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The article presents remarks regarding analysis of drawings and the use of the data contained therein in resolving mathematical tasks. A particular type of drawing is considered, which is a graph of a function. The presented findings are the result of several years of research conducted among the Mathematics students at the Pedagogical University of Cracow.

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...

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...

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...

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.

Różne reprezentacje liczb rzeczywistych

Barbara Pieronkiewicz (2017)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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This article is devoted to the different representations of real numbers. In particular, the following types are distinguished and discussed: (1)representations based on theorems referring to the axiomatic characterization of the field of real numbers, (2) genetic representations – related to the construction of real numbers, (3) visual representations – mainly related to the geometrical way of presenting numbers. The paper addresses different representations of real numbers from a higher...