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    Wyświetlanie 1-14 z 14
    Tytuł:
    O liczbach ujemnych z perspektywy historycznej i dydaktycznej
    On the Negative Numbers from the Historical and Educational Perspective
    Autorzy:
    Błaszczyk, Piotr
    Sajka, Mirosława
    Powiązania:
    https://bibliotekanauki.pl/articles/1791026.pdf
    Data publikacji:
    2018-06-01
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    Negative numbers
    History of mathematics
    Mathematics education
    Opis:
    We identify two ways of introducing negative numbers. In the first one, a totally ordered set (L, $\prec $) is presupposed, an element 0 in L is arbitrarily taken, and a number a is negative when a 0. In the second one, a negative number is defined by the formula a + (−a) = 0. From a mathematical perspective, the first method involves the idea of a totally ordered group (G,+, 0,<), while the second one considers the idea of the algebraic group (G,+, 0) alone. Through the analysis of source texts, we show that the first model originates in John Wallis’ 1685 Treatise of Algebra, while the second one comes form the theory of polynomials, as developed by Descartesin his 1637 La Géométrie. In mathematical education, the first model is applied in the overwhelming majority. Still, we identify a theory that applies to the second model. We show how to develop it further and simplify the representation of the operation a + (−a) = 0 by turning the second modelin to a tablet game.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2017, 9; 5-36
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Znaczenie i możliwości kształcenia matematycznego w studiowaniu kierunków ekonomicznych
    The importance and opportunities of mathematics education in the course of economics studies
    Autorzy:
    Dąbrowa, Maria
    Powiązania:
    https://bibliotekanauki.pl/articles/1790993.pdf
    Data publikacji:
    2017-07-05
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    mathematical culture
    the usefulness of mathematics
    mathematics
    education
    Opis:
    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 universities. In this paper, we present the results of research on determining the significance of mathematics education from the perspective of economics students and graduates, as well as lecturers of economics. We also discuss the problem of how to introduce mathematics courses into teaching economics. We conclude that the mathematical skills of economics students do not meet the prerequisites of mathematics education in economics teaching.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2014, 6; 61-71
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Leonardo Pisano called Fibonacci, between advanced mathematics, history of mathematics and mathematics education: three examples drawn from Liber Quadratorum
    Od matematyki wyzszej, przez historie do dydaktyki. Trzy przykłady zaczerpniete z Liber Quadratorum Leonarda z Pizy zwanego Fibonaccim
    Autorzy:
    Bussotti, Paolo
    Powiązania:
    https://bibliotekanauki.pl/articles/1791019.pdf
    Data publikacji:
    2017-07-04
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    Fibonacci
    Enriques
    Liber Quadratorum
    Paradigmatic examples
    Medieval mathematics
    Diophantine analysis
    Lagrange
    Genochhi
    Number theory and mathematics education
    Relation history of mathematics-mathematics education
    Opis:
    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 relationshistory of mathematics-mathematics education-advanced mathematics. Last, but notthe least, a further aim is to offer a specific series of interesting material to the teacherin order to develop stimulating lessons. The material here expounded is conceived forpupils frequenting the third and the fourth years of the high school, but, with minormodifications, it can be adapted to the fifth year of the high school and to the initialyears of the scientific faculties at the university.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2015, 7; 5-25
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The role of visualisation in the process of generalisation
    Rola wizualizacji w procesie uogólniania
    Autorzy:
    Zaręba, Lidia
    Powiązania:
    https://bibliotekanauki.pl/articles/1790999.pdf
    Data publikacji:
    2017-07-04
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    generalisation
    visualisation in mathematics
    Opis:
    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’ strategies of generalizing. Presumably, visual thinking produces a positive effect on the pupils’ process of generalizing and abilities to describe regularity with the aid of a letter symbol.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2015, 7; 111-128
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Inspiring pre-service teachers of early years education to create an inquiry environment for children to learn mathematics
    Autorzy:
    Bojarska-Sokołowska, Agnieszka
    Powiązania:
    https://bibliotekanauki.pl/articles/32443987.pdf
    Data publikacji:
    2023
    Wydawca:
    Uniwersytet Komisji Edukacji Narodowej w Krakowie
    Tematy:
    Mathematics education
    early years mathematics
    motivation of pre-
    service teachers
    interactive education
    Opis:
    The paper presents a~teaching proposal for the Mathematics Education course for university students of Education with a specialisation in Early Childhood Education, in order to motivate pre-service teachers to self-discovery and to encourage individual mathematical problem solving. The proposal was pre-tested in practice. Interactive activities were carried out in which pre-service teachers individually solved mathematical problems at thematic stations and had the opportunity to learn by manipulating objects and discovering solutions to problems. The study was conducted using an action research approach. The results of the study are described in four areas of the researcher's activity: preparing the learning environment (organising the research), observing the subjects, communicating with the subjects (interviewing the pre-service teachers) and using the results.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2023, 14; 159-171
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Popularyzacja matematyki na polskich uniwersytetach dziecięcych
    Popularizaton of mathematics at the polish Children’s Universities
    Autorzy:
    Bojarska-Sokołowska, Agnieszka
    Powiązania:
    https://bibliotekanauki.pl/articles/1790990.pdf
    Data publikacji:
    2017-07-05
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    popularization of mathematics
    children’s university
    Opis:
    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.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2014, 6; 41-60
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Intuitive explanations of mathematical ideas
    Autorzy:
    Pogonowski, Jerzy
    Powiązania:
    https://bibliotekanauki.pl/articles/1791043.pdf
    Data publikacji:
    2020-01-27
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    mathematical intuition
    understanding in mathematics
    intuitive explanation
    Opis:
    This short note is devoted to the role played by intuitive explanations in mathematical education. We provide a few examples of such explanations. They are related to: verbal commentaries, perception, physical models. We recall also some examples of internal explanations, inside mathematics itself.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2018, 10; 123-137
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Geometria w pierwszych latach szkolnej edukacji w świetle wybranych programów nauczania i poradników metodycznych dla nauczycieli z lat 1773 – 2020
    Geometry in the first years of school education in the context of selected curricula and methodological guides for teachers in the years 1773 – 2020
    Autorzy:
    Zambrowska, Małgorzata
    Powiązania:
    https://bibliotekanauki.pl/articles/1789257.pdf
    Data publikacji:
    2020-12-31
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    the history of teaching
    geometry
    mathematics education
    Opis:
    Currently there is little geometry content in the early years of school. In my doctoral thesis Geometry in teaching children since the times of the Commission of National Education until today. Analysis of the succession of education concepts, supervised by Prof. Edyta Gruszczyk-Kolczynska, I examined how the teaching of geometry to younger children has changed since the time of KEN. In the article, I discuss curricula and methodological guide books for teachers in terms of the geometric content they cover in the first years of school education. I focus on three periods: the second half of the 19th century, the 1920s and the 1970s. These periods stand out from the others I studied n that there was a lot of geometric content in the first years of school. However, in the first one of these, the content was mainly included in the subject “drawings”, while in the others the main aim of teaching was to develop pupils’ computational skills. To a large extent, geometry has also served this purpose.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2020, 12; 250-259
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Mathematics education for students with Autism Spectrum Disorder: Where are we now?
    Autorzy:
    Carr, Monica
    Seah, Wee Tiong
    Powiązania:
    https://bibliotekanauki.pl/articles/1791047.pdf
    Data publikacji:
    2020-01-27
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    autism spectrum disorder
    behavior
    mathematics
    pedagogy
    values
    Opis:
    Individuals diagnosed with Autism Spectrum Disorder (ASD), the fastest growing disability group, exhibit varying degrees of intellectual ability. Students with ASD are increasingly held accountable to academic standards comparable to their peers. Applied Behavior Analysis (ABA) is widely considered best practice for supporting these students. Twenty-six single-case design (SCD) mathematics classroom teaching interventions, conducted with students diagnosed with ASD, were systematically located and reviewed in detail. Most interventions were conducted in special education mathematics classrooms involving low ability students. Interventions typically targeted simple mathematics skills, and a paucity of research addressing more complex mathematical skills was noted. Elsewhere in the literature, teachers who have students with ASD in their classrooms reported having received no autism training, and described subsequent stress and potential to burn-out as a result. A need for future research with high ability mathematics students is observed, and the relevance of a values paradigm approach is proposed.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2018, 10; 17-39
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    English and Swedish year one teachers' perspectives on the role of homework in young children's learning of number
    Autorzy:
    Marschall, Gosia
    Sayers, Judy M.
    Andrews, Paul
    Powiązania:
    https://bibliotekanauki.pl/articles/1791046.pdf
    Data publikacji:
    2020-01-27
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    early number
    early mathematics
    homework
    year one
    comparative
    education
    Opis:
    This paper draws on data from semi-structured interviews undertaken with year one teachers in England and Sweden. The broad aim was to explore how teachers construe their own and parents' roles in supporting year one children's learning of early number. The role of homework within those efforts, surfaced as a key theme. The two data sets were an\-a\-lysed independently by means of a~constant comparison process and yielded perspectives that were, cross culturally, both similar and different. The similarities related to the importance teachers placed on the role of homework in supporting children who struggle academically. The differences were several and included teachers' views on the necessity, or even the desirability, of homework, the purpose of homework, the role of parents in the completion of~homework and the nature of the tasks set. The results, which are discussed against the literature, highlight the extent to which teachers' perceptions of the role of homework in support of young children's learning of number are culturally determined.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2018, 10; 109-121
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Geometria kół Otta Reichela jako przykład pracy z uczniem zdolnym na lekcjach matematyki w II połowie XIX wieku
    The Otto Reichels geometry of circles as an example of work with a gifted student in mathematics lessons in the second half of the 19th century
    Autorzy:
    Karpińska, Karolina
    Klemp-Dyczek, Bogumiła
    Powiązania:
    https://bibliotekanauki.pl/articles/1789261.pdf
    Data publikacji:
    2020-12-24
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    history of mathematics education
    mathematics education on the Polish
    territories in the 19th c.
    geometry
    geometric constructions
    gifted education
    Otto Reichel
    Opis:
    Niniejszy artykuł jest poswiecony omówieniu zadan zwiazanych ze znajdowaniem miejsca geometrycznego punktów, które zostały umieszczone w artykule Beiträge für den Unterricht in der Geometrie („Przyczynki do nauczania geometrii”) Otta Reichela (Thorn, 1866), nauczyciela gimnazjum w Toruniu w latach 60. XIX wieku. Rozwiazanie wiekszosci tych zadan wykraczało poza ramy programowe wyznaczone przez ówczesne władze oswiatowe. Jest to przykład samodzielnego rozszerzenia programu nauczania matematyki przez nauczyciela w szkole dla uczniów zdolnych, w celu lepszego przygotowania młodziezy do egzaminów maturalnych, studiow uniwersyteckich oraz pózniejszej pracy zawodowej.
    The paper is devoted to the discussion of the tasks related to finding the geometric locus of points. These tasks were included in the article Beiträage fäar den Unterricht in der Geometrie (“Contribution to the teaching of geometry”) by Otto Reichel (Thorn, 1866), a teacher of Torun gymnasium in the 1860s. The solution of most of these tasks went beyond the curricula determined by the then educational authorities. It is an example of self-extension of the mathematics curriculum by a teacher in a school for gifted students in order to better prepare young people for matriculation examinations, university studies, and later professional careers.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2020, 12; 173-196
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    PISA, TIMSS and Swedish students’ knowledge of linear equations: A ‘telling’ case of a system fixing something that may not be broken
    Autorzy:
    Andrews, Paul
    Palm Kaplan, Kristina
    Powiązania:
    https://bibliotekanauki.pl/articles/1789253.pdf
    Data publikacji:
    2020-12-31
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    Linear equations
    Mathematics achievement
    PISA critique
    Sweden
    ’Telling’ case
    TIMSS critique
    Opis:
    In this paper, we construct a ‘telling’ case to highlight a problematic inconsistency between the results of international large-scale assessments (ILSAs) and other studies of Swedish students’ knowledge of linear equations. In this context, a ‘telling’ case, based on the scrutiny of appropriately chosen cases, is presented as a social science counter-example to the prevailing view that ILSAs’ assessments are not only valid but should underpin systemic reform. Our ‘telling’ case comparison of the different forms of study shows that Swedish students, in contrast with the summative assertions of the different ILSAs, have a secure and relational understanding of linear equations that persists into adulthood. We conclude with a cautionary message for the curriculum authorities.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2020, 12; 5-29
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Актуальные проблемы обучения математике в школе и вузе в свете идей Л. С. Выготского
    Actual problems of teaching mathematics at school and university in the light of the ideas of L. S. Vygotsky
    Autorzy:
    Боженкова, Людмила
    Егупова, Марина
    Powiązania:
    https://bibliotekanauki.pl/articles/1789268.pdf
    Data publikacji:
    2017-07-05
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    Moscow State Pedagogical University
    international scientific conference
    education
    ideas of L. S. Vygotsky
    mathematics
    Opis:
    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.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2016, 8; 179-183
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    O roli prac dyplomowych z dydaktyki matematyki w kształceniu przyszłych nauczycieli matematyki
    On the role of dissertations in didactics of mathematics in the training process of future teachers of mathematics
    Autorzy:
    Major, Joanna
    Olik-Pawlik, Bożena
    Ratusiński, Tadeusz
    Zaręba, Lidia
    Powiązania:
    https://bibliotekanauki.pl/articles/1791033.pdf
    Data publikacji:
    2018-06-01
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    educating students – future teachers
    the teaching-learning process of
    mathematics
    thesis
    mathematical activities
    generalization
    Opis:
    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, Olik-Pawlik, Ratusiński, Zaręba, 2016), pointing to the legitimacy of the preparation of teacher diploma theses in the field of didactics of mathematics by students.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2017, 9; 111-138
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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