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PL
W artykule chciałem zwrócić uwagę na potrzebę właściwego przygotowania informatycznego przyszłego nauczyciela, ponieważ w zmieniającej się rzeczywistości uczniowie coraz częściej korzystają z komputera oraz innych urządzeń multimedialnych i należy im pokazać, jakie są możliwości wykorzystania tych urządzeń do wspomagania procesu nauczania i uczenia się.
EN
In this article I would like to draw attention to the need for proper IT preparation of the future teacher since in the changing reality pupils more often use both computer and also other multimedia appliances. That is why it is essential to show them what possibilities of these appliances are to assist the process of teaching and learning itself.
EN
The use of Information and Communication Technology (ICT) in education during a pandemic has become a fact and a must. Before COVID-19 (for decades), the need to use ICT in education was po[1]stulated and suggested. Research carried out in this area resulted from the need to understand what technologies are potentially available for use in education, including the teaching and learning of mathematics. One important issue still to be resolved is whether and how to support children in their mathematical education using technology. This publication, referring to selected recent studies con[1]ducted worldwide, gives examples and arguments for technological support of mathematics learning.
EN
The problem of school readiness of Polish children takes up lots of space in social debates. This has been associated with big changes in the national curriculum, and lowering the school start threshold. It is the first time that going to school at the age of 6 will be made compulsory in September 2014. It seems to be very important to assess the school readiness of 5-year-old children from the perspective of primary school beginning at the age of 6. There was an attempt in the research to answer the question whether 5-year-old children were ready to start their mathematical school education. Their level of mathematical competences was assessed using the Scale LPC6 (Oszwa 2005). It consisted of 3 parts and 36 items, referring to the ability to use numbers, to be oriented in time and in space. The subjects were 5-year-olds in the target group (n=30) and 6-year-olds in the control group (n=30). The attained results did not indicate relevant statistical differences between two groups of subjects. The level of mathematical competences of 5-year-old children was equally high as that one of 6-year-old subjects. The obtained data permit a conclusion that the assessed 5-year-old subjects were ready to start their mathematical education at school.
PL
Problem gotowości szkolnej dzieci polskich zajmuje sporo miejsca w społecznych debatach. Jest to związane z ogromną zmianą w systemie edukacji, polegającą na obniżeniu progu obowiązku szkolnego. Od września 2014 roku po raz pierwszy obowiązkowo poszły do szkoły polskie dzieci sześcioletnie. Osiągnięcie gotowości szkolnej przez dzieci 5-letnie wydaje się zatem niezwykle istotne przed rozpoczęciem edukacji szkolnej w wieku lat sześciu. W badaniach własnych podjęto próbę odpowiedzi na pytanie: czy badane 5-latki są gotowe do rozpoczęcia edukacji matematycznej? Poziom ich kompetencji arytmetycznych oceniano przy użyciu Skali LPC6 (Oszwa 2005). Składa się ona z 3 części i 36 stwierdzeń, odnoszących się do zdolności posługiwania się liczbami, orientacji w czasie i przestrzeni. Badane były dzieci pięcioletnie (n=30) w grupie docelowej oraz sześcioletnie (n=30), które stanowiły grupę kontrolną. Otrzymane rezultaty nie ujawniły istotnych statystycznie różnic między dwiema porównywanymi grupami. Uzyskane wyniki pozwalają zatem sądzić, że badane dzieci 5-letnie osiągnęły gotowość do rozpoczęcia edukacji matematycznej w szkole podstawowej.
PL
W artykule zwrócono uwagę na zmiany zachodzące w edukacji matematycznej pod wpływem ekspansji technik informacyjnych. Rozwój technologii informacyjnej i kreowane przez nią metody zbierania i dystrybuowania informacji otwierają drogę do alternatywnych form kształcenia w powstającym społeczeństwie wiedzy. Wskazano na rolę i przygotowanie informatyczne nauczycieli i nowy sposób przekazywania wiedzy, a w szczególności wiedzy matematycznej. Interakcja pomiędzy uczniem a nauczycielem stanowi najważniejszy element dydaktyczny i wychowawczy.
EN
The article is about changes in education of mathematics impacted by information technologies expansion. Development of information technologies together with created methodologies of gathering and distributing information opens alternative routes of education in knowledge society. There is pointed out the role and preparation of a teacher, the new way of transferring the knowledge – especially mathematical knowledge. Interaction between teacher and student is the most important didactical and educational element.
EN
Very recent studies show that a cognitive-motor interference can expose people not only to a motor danger but also weaken their cognitive capabilities. This effect is called the dual-task cost. One of the most popular examples of it nowadays is the smartphone use while walking, which is well examined. Yet, there are no studies that would analyse to what extent the other high-popular dual-task situation – shopping at the supermarket, weakens cognitive processes. To shed some light on this issue, we investigated a behavioral experiment on everyday mental calculations. Methods: Twenty mathematical-ly-educated adults took part in this study. We used stimuli in the form of shop labels. The participant’s task was to add two prices or state the price after a discount. They carried out the tasks by turns, either by standing (single-task) or walking with a shopping basket (dual-task). EEG controlled level of their attention. Results: We found that a cognitive-motor interference do not affected the everyday mental calculations. But, such familiar mental arithmetic as calculating prices after discounts was frighteningly difficultfor the participants. Conclusions: While our findingdoes not confirmthe occurrence of dual-task costs in everyday mental calculations, it has profound consequences for a mathematical education, which effects turn out to be useless in real life.
EN
Mathematical education at the pre-primary stage sets out its aims which are predominantly focussed on the area of developing the cognitive side of the child’s personality. This area becomes the focus of relevant curricular documents for mathematical education, on the one hand, and influences the actual teaching of mathematics in practice, on the other. Meaningful and effective cross-curricular mathematical education opens a new space for developing the emotional and social skills of the child. The above aspect of mathematical education has the potential to become a determining factor in creating a positive attitude towards mathematics.
EN
The article points out the need to reform higher education associated with the preparation of future mathematics teachers. The impact of information technologies on the learning process, the rapid development and continuous updating of software in the field of mathematics, which leads to a shift in emphasis toward competency is indicated. The conclusions about the necessity of developing and implementing new integrated courses on computer mathematics and special courses for the study of computer mathematics systems (CMS) are made. The transition of the society to a new stage of its development requires mathematics teaching reforming, which is adequate to the logic of the computer revolution. In other words, we should organize a system of mathematical preparation of young people for life in the modern world, that they not only have some knowledge in mathematics, but can operate this knowledge on the production of new knowledge with the help of methods of mathematics and drawing on the potential of information technologies. The author shows the growing contradiction between the paradigm of mathematical training that changes in the conditions of transition to the information society, the increased capacity of tools and applied information technologies to work in the sphere of mathematics and mathematics education, modern tendencies of reforming the system of education, on the one hand, and the real state of the methodological system, which does not fully provide for the development of a modern level of mathematical, technological and methodological competence of future teachers of mathematics in their active expression, on the other hand. CMS in the modern information society has become a popular tool in solving many problems of life, and together with deepening the knowledge and practical skills of work with computer facilities «the density» of the use of specialized mathematical computer tools will grow. It makes to fill more and more both traditional school mathematics and a subject base of teachers of mathematics with courses, methods, and skills of using CMS through a separate compulsory training course.
EN
The article presents an analysis of data gathered to assess the package “Playing with pictograms”. The package is intended as support for the development of symbolic language skills by influencing the way teachers teach mathematics during the first years of primary school. The research was conducted using a cluster-randomised repeated measures experimental design with a control group. The main research problem investigated change in the level of relevant student skills, specifically associated with the package. IRT modeling and multilevel regression were employed in the analysis. Results demonstrated significant improvement in the use of symbolic language derived from the package.
EN
This article provides information about publications and speeches of the Jagiellonian University Professor, Stanisław Zaremba, covering the years of 1900-1935. It includes a list of papers presented by him during meetings of the Academy of Learning in Kraków, international mathematical congresses, conventions and meetings of the Kraków department of the Polish Mathematical Society and conventions of mathematicians of Slavic countries. Moreover, there is a comprehensive list of Zaremba’s lectures delivered at the Jagiellonian University. The article includes also the first list of his publications, including articles and books on mathematics and its applications, mathematical education, philosophy, mathematical physics, mechanics and crystallography. The list includes numbers of reviews, which appeared in „Jahrbuch über die Fortschritte der Mathematik”, „Zentralblatt für Matematik” and „Mathematical Reviews”.
PL
W artykule zwrócono uwagę na zmiany zachodzące w edukacji matematycznej pod wpływem ekspansji nowych technologii edukacyjnych. Przedstawiono analizę wyników ankiety dotyczącej wykorzystania ich w praktyce pedagogicznej (w nauczaniu matematyki). Opis projektu – „Nowe metody nauczania w matematyce”. Rozwój technologii edukacyjnych i kreowane metody zbierania i dystrybuowania informacji otwierają drogę do alternatywnych form kształcenia w społeczeństwie wiedzy. Oddają one nieocenione zasługi w rozpoznawaniu, zgłębianiu i konstruktywnym wypracowaniu rozwiązań problemów w różnych dziedzinach naszego życia. Matematyka, informatyka, komputery są w dużej korelacji, zarówno współcześnie, jak i historycznie. Nowe technologie zmieniają styl nauczania i uczenia się matematyki.
EN
The article is about changes in teaching mathematics under the influence of expansion of new educational technologies. Presents an analysis of the results of the questionnaire form concerning exploiting them in practice pedagogic (in teaching mathematics). Project description – „New Methods of Teaching in Mathematics”. Development of education technologies together with new methodologies of gathering and distributing information opens alternative forms of education in an educated society. They have been providing substantial contribution to identification, exploration and constructive solutions to various questions of our lives. Mathematics, information technology, computers – remain in strict correlation both now and in the past. New technologies have been changing the style of teaching and learning mathematics.
PL
W niniejszym artykule zwraca się uwagę na rolę, jaką odgrywa edukacja matematyczna studentów kierunków ekonomicznych w przygotowaniu ich do studiowania przedmiotów ekonomicznych oraz przyszłej pracy zawodowej. W części wstępnej zaprezentowano poglądy wybranych filozofów i ekonomistów na temat znaczenia matematyki w rozwoju nauk, w szczególności – ekonomii. Następnie, w oparciu o teorię dydaktyki matematyki oraz badania i przemyślenia własne, przedstawiono cele kształcenia matematycznego, sygnalizując jednocześnie problemy związane z ich realizacją.
EN
This article puts emphasis on the role played by teaching mathematics to students of economics department while preparing them for studying economics subjects andtheir professional work. In the introduction the views of some selected philosophers and economists on the importance of teaching mathematics in the development of science in particular economics are shown. Then on the basis of didactic theory of mathematics, research and individual reflections the aims of teaching mathematics are introduced signalling the problems of their realization.
EN
The article is devoted to the formation of mathematical ideas of junior schoolchildren by means of game method of teaching. The educational process at school today has been transformed and filled with new content. It is not just a process of interaction between a teacher and a student but a new level of educational process organization, an integral part of which includes educational technology, advanced methods, techniques and tools (special interactive whiteboards, projectors, consoles, etc.), approaches (personal, qualified, active) and the variety of activities (communication, playing, working, teaching). The period of primary school should create an enabling environment for children, providing them successful development, training and education. Understanding of the mathematics serves as a means of intellectual development of the child's cognitive and creative abilities. The effectiveness of the mathematical development of the child in the first form strongly influences the success of teaching mathematics in future. The choice of the game method as a first object of creative analysis and practical development is dictated by the fact that it can act a crucial role in gaining of cognitive interest, facilitating the complex process of teaching, accelerating development. In the article the didactic opportunities and pedagogical conditions of the game method of teaching in the formation of understanding of the mathematics among junior schoolchildren are detected. Providing comprehensive mathematical training of children is possible in case of pedagogically skillful combination of game methods in teaching junior schoolchildren. The analysis of the theory and practice of problems in formation of mathematical skills among children gave the opportunity to identify educational conditions which contributes to the formation of the foundations of the mathematics education: the use of competence-based approach; promotion of self-fulfillment of children within games and other activities; using of game techniques for intensification of the cognitive activity of children. Along with the extension of mathematical horizons and experiences of children, shaping their communicative skills and education of personal qualities, special attention is paid to the development of mathematical speech of children, their general logic development.
EN
The acquisition of educational experiences by children from grades 1-3 may be enhanced by means of the use of various didactic aids. Undoubtedly, one of them may be printed materials therefore, the subject matter of the presented text is the Świerszczyk magazine published in the 20th century. The objective of the analysis was to show the magazine as a didactic aid for teachers of grades 1-3 in the course of teaching mathematics. In this context, special attention was paid to the presence of tasks, games and exercises which offer an incentive for taking an interest in mathematics for early-school pupils. The quantity, type, and also the quality of the Świerszczyk content referring to mathematics varied, depending on the decade of the 20th century. However, the diversity of texts and also tasks addressed to young readers was a support at the beginning of their educational path. It could also provide an inspiration for teachers of grades1-3 with respect to preparing interesting and activating lessons. In particular, board games and card games included in the magazine contributed to the formation of a number of vital competences in children (especially in the area of mathematics), encouraged them to modify the presented ideas and stimulated the development of creativity and imagination.
XX
Zdobywanie doświadczeń edukacyjnych dzieci klas I-III można wzbogacić wykorzystując różnorodne środki dydaktyczne. Niewątpliwie jednym z nich mogą stać się materiały drukowane, dlatego przedmiotem prezentowanego tekstu uczyniono czasopismo „Świerszczyk” w okresie XX wieku. Celem dokonanej analizy było ukazanie magazynu jako pomocy dydaktycznej dla nauczycieli klas I-III w toku realizacji zajęć z zakresu edukacji matematycznej. W tym kontekście zwrócono szczególną uwagę na obecność w tygodniku zadań, gier i ćwiczeń stanowiących impuls do zainteresowania się matematyką uczniów w wieku wczesnoszkolnym. Ilość, rodzaj, a także jakość treści „Świerszczyka” odnoszących się do matematyki różniła się w zależności od dekady XX wieku. Jednak wielorakość tekstów, a także zadań kierowanych do młodych czytelników była wsparciem na początku ich edukacyjnej drogi. Mogła stać się również inspiracją dla nauczycieli uczniów klas I-III do realizacji ciekawych i aktywizujących zajęć. Szczególnie zamieszczane w magazynie gry planszowe oraz karciane przyczyniały się do kształtowania u dzieci wielu kompetencji kluczowych (zwłaszcza z zakresu matematyki), pobudzały do modyfikacji zamieszczonych pomysłów przyczyniając się tym samym do rozwijania kreatywności i wyobraźni.
15
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Komunikacja na zajęciach z edukacji matematycznej

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EN
The language of school mathematics is specific as it combines the elements of natural language and the language of mathematics. Practice shows that sometimes the language, instead of becoming a tool for communication of information, may be an obstacle in the way of communication between the speaker and the listener. Frequently during mathematical education classes there is no proper communication between the teacher and the learners. The students do not understand what the teacher says, and the teacher does not try to understand the meaning of the students’ utterances. For the last decade there has been a new source of information in the lesson – a computer, thus a new way of communication. In the paper we will present and discuss some of the difficulties associated with communication between teacher – students and computer – students, illustrating them with examples from the school practice.
PL
W artykule przedstawiono analizę wyników badania sprawdzającego skuteczność zastosowania pakietu edukacyjnego „Gramy w piktogramy”. Jest on przeznaczony do wspierania rozwoju umiejętności posługiwania się językiem symbolicznym na etapie edukacji początkowej. Ma on na celu uruchomienie procesu zmiany sposobu nauczania matematyki. Badanie zostało przeprowadzone w schemacie eksperymentalnym z pomiarem powtarzanym i grupą kontrolną, przy randomizacji przeprowadzonej oddziałami wewnątrz szkół. Głównym problemem badawczym poddanym analizie była zmiana w poziomie ogólnego wskaźnika umiejętności posługiwania się językiem symbolicznym uczniów, związana z wdrożeniem pomocy dydaktycznej. W analizach wykorzystano modelowanie IRT oraz regresję wielopoziomową. Wyniki wskazują na istotny statystycznie wzrost umiejętności posługiwania się językiem symbolicznym w grupie eksperymentalnej, związany specyficznie z zastosowaniem badanego pakietu edukacyjnego.
EN
The article presents the analysis of data gathered to assess the package “We play pictograms”. The package is intended as support for the development of symbolic language skills by influencing the way teachers teach mathematics during the first years of primary school. The research was conducted using a cluster-randomized repeated measures experimental design with a control group. The main research problem investigated change in the level of relevant student skills, specifically associated with the package. IRT modeling and multilevel regression were employed in the analysis. Results demonstrated significant improvement in the use of symbolic language derived from the package.
PL
Celem opracowania jest charakterystyka koncepcji edukacji matematycznej na kierunku geodezja i kartografia, na przykładzie kształcenia WSBiP w Ostrowcu Świętokrzyskim. W grudniu 2010r. przeprowadzono badania sondażowe; ich celem było zebranie opinii, sugestii i oczekiwań osób wykładających przedmioty podstawowe i kierunkowe na temat programu matematyki, jego treści oraz umiejętności studentów koniecznych dla efektywnego studiowania. Analizę jakościową i ilościową wypowiedzi respondentów prowadzono w zakresie przydatności materiału z zakresu matematyki, oczekiwanego sposobu jego opracowania (formalno – logiczny , aplikacyjny, algorytmiczny), pożądanych osiągnięć studentów (rozumienie i sprawne operowanie pojęciami, umiejętnościami ich stosowania w sytuacjach spoza matematyki, sprawne posługiwanie się systemami symbolicznymi – rachunek algebraiczny, macierzowy, pochodny). W efekcie badań wydzielono te zagadnienia, dla których współczynnik przydatności jest większy niż 60%, oraz mniejszy niż 35%. Uzasadniono, że podejście aplikacyjne nakierowane na kształtowanie obrazów pojęć spełnia potrzeby oraz oczekiwania studentów i wykładowców. Wnioski z badań wykorzystano przy konstrukcji kursu matematyki typu on – line.
EN
The purpose of this paper is characteristic of the concept of mathematical education in geodesy and cartography on the example of training in WSBiP in Ostrowiec Świętokrzyski. In December 2010 surveys were carried out; their aim was to gather opinions, suggestions and expectations of people teaching foundational and directional core subject on the program of mathematics, its content as well as students’ skills necessary for effective studying. Qualitative and quantitative analysis of expression of the respondents was conducted in the usability of the material in the field of mathematics, the expected pattern of its development (formal – logical, application, algorithmic), the desired students’ achievement (understanding an efficient handling of concepts, skills, their use in situations outside mathematics, efficient use of symbolic systems – matrix algebra, differential calculus tc). As a result, the studies allowed to separate these issues, for which the ratio of usefulness is greater than 60% and less than 35%. It was justified that the application approach oriented t image concepts meet the needs and expectations of students and faculty educators. The conclusions of the studies used in the construction of an on – line math course.
PL
W artykule autor zwraca uwagę na potrzebę właściwego przygotowania informatycznego przyszłego nauczyciela, bowiem w zmieniającej się rzeczywistości uczniowie coraz częściej ko-rzystają z komputera oraz innych urządzeń multimedialnych i należy im pokazać, jakie są możli-wości wykorzystania tych urządzeń do wspomagania procesu nauczania i uczenia się.
EN
In this article I would like to draw attention to the need for proper IT preparation of the future teacher since in the changing reality pupils more often use both computer and also other multime-dia appliances. That is why it is essential to show them what possibilities of these appliances are to assist the process of teaching and learning itself.
XX
In connection with introduction of modern standards the process of mathematical training of students needs constant improvements. Use of information technologies in solving mathematical problems provides process control at all stages of the solution, the possibility of dialogue interaction, in which can be discussed not only the correctness of certain actions, but also finding solutions strategy, planning and optimization of performing tasks by students in general. Effective use of information technologies help to facilitate solutions to complex problems in the study of Mathematics at the Technical Universities, remove psychological barrier to study mathematics and make this process more interesting and easy. Distance education as an innovative educational project using of information technologies helps students realize their educational goals aimed at personality development. The widespread introduction of information technologies will permit to enrich the content and diversity forms and methods of acquisition of new topics, to increase the motivation of educational and creative activities of students during their studies. It will give a possibility for students to learn definite topics independently, get fundamentally new knowledge and use it in future practical work. In this article some aspects of competent use of applied mathematics programs in process of teaching of Mathematics are considered. The examples of use of programs MathCAD, MathLab, Maple presented in this article help to intensify educational process. This makes it possible to improve the competitive ability of future specialists. However, applications are not considered able to maintain control over the sequence of actions in dealing with the student, identify its weaknesses, and provide detailed descriptions of errors. Without this training program is unable to replace the teacher. Control of knowledge in such systems is limited to checking the final answer, no reason errors on a particular step solution. To work with similar programs the user himself should know the methods and ways of solving problems.
EN
Numbers have cognitive (mental) representations that have neuronal underpinnings and are shaped in development and strengthened based on experience. It is also known that neuroplasticity allows the effective training (and therefore development or improvement) of both cognitive and motor functions. Can motor training have anything to do with the effectiveness of cognitive training? Are cognitive processes embodied, and can we influence cognitive ability through movement? The dynamic development of modern technology that is applied in education and therapy has made computerassisted training of cognitive and motor functions increasingly popular. As many studies indicate, cognitive training and cognitive-motor training using computer games are very effective not only in education and development of mathematical competency, but also in overcoming deficits in people suffering from problems with maths. This article provides a review of the most important research results on this issue.
PL
Liczby posiadają poznawcze reprezentacje w umyśle człowieka, które kształtują się w toku rozwoju jednostki i są utrwalane na bazie doświadczenia oraz mają dobrze udokumentowane neuronalne podstawy. Wiadomo również, że neuroplastyczność pozwala na efektywne ćwiczenie (a więc rozwój lub poprawę) zarówno funkcji poznawczych, jak i ruchowych. Czy trening motoryczny może mieć jednak coś wspólnego z rozwojem poznawczym? Czy procesy poznawcze są „ucieleśnione” i czy przez ruch możemy wpływać na poziom zdolności poznawczych? Dynamiczny rozwój nowoczesnych technologii, które znalazły zastosowanie w edukacji i terapii, spowodował, że wspierane komputerowo metody rozwijające zdolności matematyczne stają się coraz bardziej popularne. Wyniki licznych badań wskazują na to, że programy ćwiczeń z wykorzystaniem gier komputerowych doskonale sprawdzają się nie tylko w edukacji i rozwijaniu zdolności poznawczych istotnych w kształtowaniu kompetencji matematycznych czy utrwalaniu umysłowych reprezentacji liczb. Okazują się one również skuteczną metodą pokonywania deficytów u osób z problemami w zakresie matematyki.
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