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.
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.
Zbigniew Powązka (2006)
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
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This article presents the author’s research results concerning the teaching of introductory notions and theorems of mathematical analysis. The research was carried out among the first-year students of mathematics. The main objects of the research were: – the observation of the degree of assimilation of the basic notions and theorems by the students; – the investigation of the students’ progress in proving theorems and constructing suitable examples and counterexamples. The final part...
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...
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,...
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...
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
Tatyana Kirillova (2012)
Annales Universitatis Paedagogicae Cracoviensis Studia Geographica
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Antoni Pardała (2009)
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
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The subject of this work, teacher’s practice forming mathematical activity and creativity of the gifted pupils, is submerged in the issue of one of the contemporary trends in researching the methodology of teaching maths, which is called: creativity in teaching mathematics – theory, diagnosis and methodology, prospects. In this work I refer to certain synthesis of the knowledge to that point, see A. Pardała (2003; 2004; 2006), and I also articulate one of its aspects – the crucial importance...
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.
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...
Jan Rodzik, Mirosław Krukowski, Piotr Zagórski (2010)
Annales Universitatis Paedagogicae Cracoviensis Studia Geographica
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The article presents the development of a small, midfield form of road, which cuts the side of a loessic valley. The contemporary shape of the surface was determined by GPS measurements (Leica System 500), set together in ArcView and ArcGIS. Changing of its position was determined by a field analysis of the construction of 50 profiles of the Luvisols with varying degrees of erosion or aggradation. Calculation and visualization were performed in the ‘Surfer’ program. The results are interpreted...
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...
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...
Владимир В. Афанасьев (2012)
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
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In the paper, the author presents the basic concepts and theorems concerning methods of mathematical statistics and its application in the domain of empirical research. Several examples presented in the paper can be useful as patterns of using statistical tool in didactic research.
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...
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.
Jan Reder, Józef Superson, Tadeusz Król (2010)
Annales Universitatis Paedagogicae Cracoviensis Studia Geographica
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The article analyzed the impact of old (prehistoric, medieval) and modern settlement on the nature of the Holocene alluvial sediments at the bottom of the Bystra valley. It was shown that the transition from peat to mineral deposits was the result of Neolithic farming. Nomadic culture of the late Neolithic and early Bronze Age have helped to stop the denudation slope sand increasing erosion in the bottom of the river valley. Restarting the denudation in the basin and the beginning of...
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...
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...
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...
Antoni Chronowski (2019)
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
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In this article, I analyze the theoretical foundations of the division with remainder in the arithmetic of natural numbers. As a result of this analysis I justify that the notation a:b=c r s, where a, b, c, s are natural numbers and r denotes, is correct at school mathematics level and does not lead to a contrediction suggested by the author of the article (Semadeni, 1978). As a generalization of the division with remainder of natural numbers, I consider the division with remainder of...
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...
Agnieszka Świętek (2014)
Annales Universitatis Paedagogicae Cracoviensis Studia Geographica
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Roma people are one of the most colourful minorities in Poland and arouse interest and controversy among contemporary Polish society, nearly monolithic in terms of ethnic origin and nationality. At present, the socio-economic situation of Roma people in Poland and in other European countries is difficult and marked with social exclusion. In the article the author identifies and describes the following symptoms of social exclusion experienced by Roma people in Poland: lack of tolerance...
Agnieszka Świętek (2013)
Annales Universitatis Paedagogicae Cracoviensis Studia Geographica
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Professor Jan Flis began his collaboration with the Higher College of Teacher Training in 1951, and since 1960 he has become its full-time employee, which he remained until the end of his long teaching and academic career. One of the most important record of his research activity (especially in the area of teaching), is an extensive collection of his publications that can be found in the Library of the Institute of Geography of the Pedagogical University of Cracow, which the author compiled...
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...
Elżbieta Choinkowska (2011)
Annales Universitatis Paedagogicae Cracoviensis Studia Geographica
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The article attempts to explain the scientific and social phenomenon that was constituted by the figure of Wacław Nałkowski. With comprehensive knowledge concerning his life, the author undertook the characterization of his personality with the use of the special psychological method of transactional analysis. It is a method developed by American psychiatrist Eric Berne during 1960s. It explains the way people think and behave, offering many tools to understand human functioning, social,...
Mariola Tracz (2013)
Annales Universitatis Paedagogicae Cracoviensis Studia Geographica
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The study shows the role of professor Jan Flis in the development of geography education in the post-war era. His academic input into the discipline is expressed in 134 publications, out of which 40 concern the topic of the didactics of geography. Professor’s interest in the field of geography education focused on: the selection and structure of geographical material, forming of theories in teaching and learning geography, function of geography in education and cognitive development,...
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. ...
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...
Witold Warcholik, Konrad Leja (2012)
Annales Universitatis Paedagogicae Cracoviensis Studia Geographica
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Urban games and other forms of field games, such as Questing, are innovative ideas for presentation, disclosure and interpretation of natural and cultural heritage. The results of the survey presented in the study show that soon urban games can become an alternative to a traditional guided sightseeing of an urban area. There may be several reasons for such a choice: an interesting way of exploring a city, aspects of play and physical activity, better memorization of information, as well...
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...
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...
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...
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...
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...
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...
Bożena Olik-Pawlik (2015)
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
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In this paper, we identify the phenomenon of false conviction. Weanalyze the definition of false conviction and provide the typology of falseconvictions, including their logical, geometric, cognitive and methodologicaltypes. Every type of false conviction is exemplified by empirical data.
Tomasz Parusel, Dominik Karkosz (2010)
Annales Universitatis Paedagogicae Cracoviensis Studia Geographica
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The town Mysłowice is located in the southern mesoregions of the Silesian Upland: Katowice Upland (341.13) and Jaworzno Hills (341.14). Mysłowice terrain has been intensively used by man for centuries and still is nowadays. This process left permanent signs on the natural environment; the mosaic forms of land use are the effect of this activity, among others. In the town area contrasts are frequent – direct proximity of various land use forms is observed. Initial characterization of...
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...
Viaczeslav Sukhorukov, Bożena Wójtowicz (2014)
Annales Universitatis Paedagogicae Cracoviensis Studia Geographica
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The modern world is characterized by rapid changes in all spheres of social life. These changes are amplified by extremely rapid dissemination of information, knowledge, values, tastes, and ideas from one society to another. Some values are invisible to the eye, other can be noticed quickly and easily. The result is a new cultural phenomena, which are called “civilization“ and “ the modern way of life.” To change the values and ideological climate in today’s world it is necessary to...
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.
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...
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...
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.
Zbigniew Powązka (2009)
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
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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”.
Mateusz Wierciński (2011)
Annales Universitatis Paedagogicae Cracoviensis Studia Geographica
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Wacław Nałkowski is certainly an outstanding figure for Polish geography. In many publications he has also been classified as positivist, anti-metaphysician, evolutionist, anticleric and socialist. Perhaps these designations are not always right, since in his works one can also find the ideas that do not quite match the labels conferred. His broad interests, diligence, criticism in selecting arguments, and the ability to see the essence of complex phenomena of different nature (both...
Martina Škodová, Alfonz Gajdoš (2010)
Annales Universitatis Paedagogicae Cracoviensis Studia Geographica
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Forest edges generally represent a very important element of ecological stability. The goal of this paper is to classify the types of anthropogenic forest edges in the area of Starohorské Mountains and to analyze anthropogenic impacts on the selected attributes of forest edges. We evaluated the attributes of a biocomplex, type of forest edge, its structure, consistence, species composition and other factors. The differences in environment variables and anthropic impact were influenced...
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.