Displaying similar documents to “Praktyka kształtowania matematycznej twórczości uczniów”

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...

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,...

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 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.

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...

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...

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

Antoni Chronowski, Zbigniew Powązka (2016)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In this article we propose ways of developing the active and creativeattitude of students towards solving mathematical problems. The taskswere sourced from various mathematical competitions for secondary schoolstudents, such as the so-called Mathematical Olympiad, and require theuse of Vieta’s formulas for third-degree polynomials. These problems inspirestudents to conduct their own elementary research work and foster theircreative attitude towards mathematics. This article is dedicated...

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...

Przyczynek do badań nad twórczą postawą studentów podczas rozwiązywania zadań matematycznych

Joanna Major, Zbigniew Powązka (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In this paper, we understand the term ''creative attitude'' to denote an action of the learner which consists in undertaking creative activity. This activity can take different forms, such as: discovery, invention, a creative act, etc. We understand  ''discovery'' to denote a fact which already exists but was unknown to the discoverer. While teaching mathematics, we deal with such an understanding of  ''discovery'' e.g. when we use the problem method. Thence, subjectively new theorems...

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...

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...

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...

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...

Kontekst Przekazu w Matematyce

Jerzy Pogonowski (2016)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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

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....

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...

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...

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...

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....

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.

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.

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...

Innowacyjność w hotelarstwie z uwzględnieniem adaptacji obiektów zabytkowych na bazę noclegową

Kamila Ziółkowska-Weiss (2012)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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

Atrakcyjność turystyczna regionów na przykładzie Francji

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

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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

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...

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...

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...

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....

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...

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...

Refleksje na temat określania wiedzy przedmiotowej nauczycieli matematyki

Mirosława Sajka (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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This article presents the author’s reflections, comments and problems that arise in relation to the issue of defining the subject matter knowledge a teacher should have in the context of Even’s theoretical framework. They incline to start working on a considerable modification of this conception in order to explore its adaptability in other contexts. This paper also includes initial results of this modification.

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.

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...

Przyszli nauczyciele wobec modelowania matematycznego

Anna Pyzara (2014)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The term mathematical modelling covers a wide range of activities. These are not only purely mathematical skills but also skills referring toa framework of modelled situation. For this reason, acquiring the skills of mathematical modelling brings a number of teaching benefits. This ability is connected with necessary competencies related to mathematical modelling. Mathematics students – prospect teachers of mathematics, should acquire these skills before they start teaching mathematical...

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

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...

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:...

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. ...

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 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,...

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...

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...

Komputer jako narzędzie badania sytuacji zadaniowej w długoterminowej pracy domowej ucznia

Renata Wojtuś (2009)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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

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...

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.

Teoretyczne i dydaktyczne aspekty nauczania o największym wspólnym dzielniku i najmniejszej wspólnej wielokrotności w zbiorze liczb naturalnych

Antoni Chronowski (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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This article contains a collection of didactic ideas concerning teaching the elementary arithmetic. Although they are firmly based on abstract mathematics, they can be realized at different levels of teaching school mathematics. The source of these didactic propositions is the fact that using the set of natural numbers and suitable relations it is possible to construct the models of structures which are called lattices. In this paper we consider the two models of lattices: the lattice...