Displaying similar documents to “Z badań nad trudnościami studentów w rozumieniu pojęcia miary i całki”

The concept of geographical space

Zbigniew Zioło (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

Similarity:

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...

Współczesne problemy i praktyka kształcenia matematycznego studentów

Antoni Pardała (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

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...

Wyniki badań nad stanem nauczania statystyki opisowej w Polsce

Zofia Aleksandra Tomaszewska (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

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...

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

Similarity:

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...

O badaniach nad kształtowaniem się u studentów matematyki podstawowych pojęć analizy matematycznej

Zbigniew Powązka (2013)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

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...

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

Similarity:

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...

Znaczenie i możliwości kształcenia matematycznego w studiowaniu kierunków ekonomicznych

Maria Dąbrowa (2014)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

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...

Kompetencje geometryczne nauczycieli matematyki

Monika Czajkowska (2016)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

Practice proves that students tend to face difficulties in learninggeometry. This observation is partially confirmed by the results of educationalresearch as well as external exams. It happens repeatedly that studentsget lower marks in arithmetic or algebra tasks. The causes of such situationare complex. One of the reasons is that teaching geometry requires specialteaching skills characteristic for this specific teaching branch as well as theneed for “specific vision”. Therefore, I decided...

Dekadencja geografii i zapomniane idee Wacława Nałkowskiego

Jacek May (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

Similarity:

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...

Актуальные проблемы современной методики обучения математике

Роза А. Утеева (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

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.

Koncepcja nauczycielskich studiów geograficznych według Jana Flisa

Danuta Piróg, Mariola Tracz (2013)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

Similarity:

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...

Tourism development in small cities on the example of Pistoia in Tuscany

Małgorzata Bajgier-Kowalska, Renata Rettinger (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

Similarity:

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...

Dynamics of changes in the structure of the forest edge in Slovakia

Martina Škodová, Alfonz Gajdoš (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

Similarity:

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...

Housing conditions in selected metropolitan areas in Poland

Piotr Raźniak, Anna Winiarczyk-Raźniak (2014)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

Similarity:

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...

Przekształcenia wykresów funkcji

Antoni Chronowski (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

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

Different ways of solving quadratic equations

Barbara Pieronkiewicz, James Tanton (2019)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

In this paper we explore different ways of solving quadratic equations. Our main goal is to review traditional textbooks methods and offer an alternative, often side-stepped method based on the area model. We conclude that whereas traditional methods offer effective algorithms that quickly lead to the desired results, alternative methods may enhance meaningful and joyful learning.

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

Similarity:

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.

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

Similarity:

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...

Nowe spojrzenie na gry Penneya

Maciej Major, Barbara Nawolska (2013)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

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.

O fałszywych przekonaniach obserwowanych na zajęciach z analizy matematycznej

Zbigniew Powązka (2009)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

In this paper we present the results of our research carried out among the students of the first, second and third years of mathematical studies in the years 2003-2006. The research was focused on the difficulties these students faced in understanding the fundamental notions of the mathematical analysis such as: a limit, continuity, differentiability and integrability. These special problems, described in this paper, are called ”false beliefs”.

Założenia koncepcji Ekologicznego Śladu i przykłady obliczeń dla dużych miast

Wanda Wilczyńska-Michalik, Karolina Świder (2010)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

Similarity:

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...

Czym jest zmysł geograficzny?

Witold Wilczyński (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

Similarity:

„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...

Calculus without the concept of limit

Piotr Błaszczyk, Joanna Major (2014)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

There are two different approaches to nonstandard analysis: semantic(model-theoretic) and syntactic (axiomatic). Both of these approachesrequire some knowledge of mathematical logic. We present a method basedon an ultrapower construction which does not require any mathematical logicprerequisites. On the one hand, it is a complementary course to a standardcalculus course. On the other hand, since it relies on a different intuitivebackground, it provides an alternative approach. While...

Geograficzny bieg dziejów

Piotr L. Wilczyński (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

Similarity:

The expression „geographical course of history”, currently seen as old-fashioned or obsolete, seems to be typical in geographical works of Nałkowski. It combines two fields that were very close to him just from the very beginning of his scientific career: geography, to which he has devoted his whole life, and history, which was for him a source of information necessary to explain the diversity of landscapes. The origins of the concept can be found in works of German geographer, educator...

Z badań nad analizą rysunku i odkrywaniem własności funkcji

Joanna Major, Zbigniew Powązka (2013)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

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.

Kontekst Przekazu w Matematyce

Jerzy Pogonowski (2016)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

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 geografii malowniczej

Katarzyna Mentel (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

Similarity:

„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...

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

Similarity:

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.

Geometria i kształcenie geometryczne we współczesnej szkole średniej i wyższej - praktyka i problemy

Roza A. Utiejewa, Antoni Pardała (2013)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

The present article presents the genesis of the international conference: andhighGeometry and geometrical education in the current second high school, which took place on November 22-25, 2012 in Togliatti StateUniversity. This conference was dedicated to the 70th jubilee of professorW.A. Gusiew (В.А. Гусев), world-wide famous professor of Mathematicseducation, author and co-author of Geometry textbooks and methodologicalguidebooks for teachers of Maths, published for the need of students’...

Z badań nad wprowadzeniem podstawowych treści analizy matematycznej podczas zajęć na I roku studiów matematycznych

Zbigniew Powązka (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

This article presents the author’s research results concerning the teaching of introductory notions and theorems of mathematical analysis. The research was carried out among the first-year students of mathematics. The main objects of the research were: – the observation of the degree of assimilation of the basic notions and theorems by the students; – the investigation of the students’ progress in proving theorems and constructing suitable examples and counterexamples. The final part...

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

Similarity:

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...

Development and present situation of slovenian didactics of geography

Tatjana Resnik-Planinc (2013)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

Similarity:

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.

Praktyka kształtowania matematycznej twórczości uczniów

Antoni Pardała (2009)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

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...

Atrakcyjność turystyczna regionów na przykładzie Francji

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

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

Similarity:

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...

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

Similarity:

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...

Применение методов математической статистики в научных исследованиях

Владимир В. Афанасьев (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

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.

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

Similarity:

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...

Symbolika matematyczna związana z pojęciem funkcji

Izabela Jóźwik, Małgorzata Terepeta (2016)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

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....

Rola portów morskich w rozwoju cruisingu na Karaibach

Renata Rettinger, Anna Urbańska (2012)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

Similarity:

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...

Ziarnista przestrzeń probabilistyczna w stochastyce dla nauczyciela - dydaktyczne osobliwości

Adam Płocki (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

The paper deals with the notion of a probability space as a mathematical object, and also as a mathematical model of a real nonmathematical situation. A construction of probability spaces with the tools of mathematical analysis and geometry is proposed. Geometrical and physical interpretations of the discrete probability space are offered as well.

Idee Wacława Nałkowskiego a współczesna dydaktyka

Elżbieta Szkurłat (2011)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

Similarity:

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....