Displaying similar documents to “Dokształcanie i doskonalenie nauczycieli na studiach podyplomowych”

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.

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.

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,...

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.

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.

Kształcenie przyszłych nauczycieli matematyki - wyzwanie edukacyjne

Anna K. Żeromska (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The purpose of this paper is to draw attention to the still current (as compared to the reform of higher education) issue: how should we train mathematics teachers in order to attain the desired outcomes? The article presents an extensive range of thought-provoking questions about what knowledge of well-educated mathematics teachers should be. References to the already existing didactic literature are included. Reflections on this question, containing some arguments as to the direction...

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...

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...

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...

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...

Zastosowanie technologii informacyjnej w kursie rachunku prawdopodobieństwa z elementami statystyki opisowej dla przyszłych nauczycieli matematyki

Jarosław Leżański (2009)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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This paper shows the concept of a probability theory course with elements of descriptive statistics for future Mathematics teachers. This course is backed up by electronic materials provided via the Internet. An e-learning platform extends the communication opportunities and offers a wide access to educational materials available there. The contents available on the platform show the presented material in a new way, which limits its passive reception and makes the user an active participant...

Analiza błędów z geometrii elementarnej popełnianych przez kandydatów na studia matematyczne w Akademii Pedagogicznej w Krakowie dokonana na podstawie wyników egzaminów wstępnych na kierunek matematyka w latach 2003 i 2004

Ewa Lubaś (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In the article the errors in the solutions of geometry problems made by the candidates for the first year of the mathematical studies at the Pedagogical University of Cracow during the entrance examinations in 2003 and 2004 are analysed. Every geometry problem is provided with the examples of its solutions, and the detailed conclusions are drawn from the analysis. In the final part of the article a general didactic analysis of the errors is carried out as well as some aspects of teaching...

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...

Gotowa wiedza i aktywność w matematycznym kształceniu na przykładzie kątów Langleya

Maciej Klakla (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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

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...

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.

Wybrane aspekty pedagogizacji nauczycielskiego kierunku studiów geograficznych

Wiktor Osuch (2013)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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

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.

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...

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....

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.

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...

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...

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...

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’...

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...

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...

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...

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’...

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...

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...

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...

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.

Założenia koncepcji Ekologicznego Śladu i przykłady obliczeń dla dużych miast

Wanda Wilczyńska-Michalik, Karolina Świder (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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

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.

Popularyzacja matematyki na polskich uniwersytetach dziecięcych

Agnieszka Bojarska-Sokołowska (2014)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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We discuss the popularization of science, in particular, mathematics.We focus on the contemporary methods and forms of popularization ofmathematics at Children’s Universities in Poland: lectures, workshops andseminars.

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...

O ciałach uporządkowanych

Piotr Błaszczyk (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In this paper, we present some basic facts concerning ordered fields. We review definitions of an ordered field, give an example of a field that admits many orderings, and present equivalent definitions of the axiom of Archimedes and the continuity axiom. We show how to extend an ordered field by means of an ultrapower construction and formal power series.

O nieskończonych ciągach liczb naturalnych, parami względnie pierwszych

Jan Górowski, Adam Łomnicki (2009)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In the first part of the paper the authors, using general formulas, determine and describe a class of infinite series of natural numbers pairs of which are relatively prime. The second part of the paper contains - as a proposition - a set of problems concerning prime numbers and pairs of relatively prime numbers suggested for use during the process of work with Mathematics students, as well as some didactic comments concerning these problems.

Human geographical ideas of Eugeniusz Romer

Witold Wilczyński (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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Eugeniusz Romer’s contribution to the development of Polish geography has been extensively appreciated. Historians of geography emphasized however his contribution in the field of physical geography and map making. Meanwhile, Romer’s human geographical concepts seem to be no less original and valuable. One of the most popular ones is the geopolitical controversy between Romer and Wacław Nałkowski concerning the individual character of Polish lands. This broadly commented dispute has...

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...

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...

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...

Wykorzystanie prac Stanisława Drózdza jako srodków dydaktycznych w nauczaniu

Agata Hoffmann (2015)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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As far as teaching practice in mathematics is concerned, we usedifferent methods, forms and tools, which enable pupils to acquire both theoreticalknowledge and practical skills more efficiently. Stanisław Drózdz(1939-2007) was a concrete poet, who, in his work, used not only words, butalso visual art. Poetry, art and mathematics are apparently distant domains,yet when I saw Drózdz‘s works, I noticed the opportunity to use them asoriginal tools in teaching mathematics. I will show his...

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...

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. ...

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...