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Signum Temporis
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2012
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vol. 5
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issue 2
28-37
EN
Mathematics takes a specific place in the education of any country because the opportunities and success of youth in contemporary society are often dependent on their knowledge and skills exactly in the sphere of mathematics. Information about the status quo of mathematics education in the country is gained in international comparative research on education. The goal of the present research is to reflect the outcomes of the international project “Non-cognitive skills and Singapore learners - international comparison” organized by Singapore National Education Institute about the achievement of 2828 Latvian school learners of grade 9 in doing 12 mathematical sums. These outcomes were compared with Programme for International Student Assessment (PISA) 2003 research outcomes that, in turn, made it possible to predict the outcomes of PISA 2012 research in mathematics education as well as evaluate the efficiency of the new standard of education in Latvia in the first six years. The article will also regard the causes of the low achievement of Latvian learners in doing sums in mathematics.
EN
Effective mathematics education of the visually impaired people and full accomplishment of the core curricular of this course is challenging, especially due to the current obligation of passing mathematics on a school-leaving examination. The transfer of knowledge in this field is primarily based on visual and spatial communication, which is a major barrier in the process of teaching/learning of the blind and visually impaired pupils. Research presented in this article was conducted in order to collect the specifics of teaching mathematics in Polish schools attended by visually disabled students as well as the opinions of teachers, students and their parents regarding their needs in this respect. The results confirmed the lack of friendly technologies tailored to identified needs, supporting the teaching process, including effective communication between the teacher (parent) and a student in the class (at home). Respondents' answers showed a high level of informatic culture - all use the computer, and 71% of teachers and 64% of students use it on daily basis. 90% of teachers were interested in learning about new technologies that are useful in teaching mathematics, and 79% of the students would like to use a computer, tablet or any other device to learn mathematics if properly adapted. This is a friendly environment for the development of the new assistive technologies in the field of mathematics education. One of them is an innovative educational platform PlatMat whose functional adaptation to the needs of users was obtained, among others, based on the results of this research.
EN
In the era of information technology and general digitization of society, invasion of every kind of software is evident. No matter how laudable is the existence and development of educational software, taking into account its role, its quality and whether it achieves the desired goal is very important. In addition to programming experts it is necessary to include educational experts in certain fields when developing educational software. Those who should take an active part and be able to distinguish good from bad educational software are certainly teachers. Especially as they should be the most competent persons from which parents will seek the advice and opinion when searching for appropriate educational software.
EN
Content and Language Integrated Learning (CLIL) can support the use of a minority language in different subjects. In our paper we present this method in the case of school mathematics. First, we describe the process of gaining knowledge in teaching mathematics. We will then present some students’ work who will be future Slovak minority teachers.
EN
The paper describes the results of a study whose aim was to explore correlations among the components of the construct Culture of problem solving (mathematical intelligence, reading comprehension, creativity and ability to use existing knowledge) and six dimensions of Scientific reasoning, which was tested by the Lawson’s Classroom Test. The total of 180 pupils from the Czech Republic aged 14-15 took part in this study. The results show that the dimensions proportional reasoning, control of variables and probability reasoning strongly correlate with the components mathematical intelligence, reading comprehension and ability to use existing knowledge.
EN
A good quality education is an essential tool for achieving a more sustainable world. According to the UNESCO, mathematics is an instrument for sustainable development and particular attention should be paid to mathematics education. For that reason, the objective of this study was to create a framework for transforming mathematics studies at the university into education for sustainable development and describe a change project which includes three steps: assessment of existing practice, how university is meeting demands of sustainable development as well as description of the change project idea. The article describes factors influencing the development of maths education at Latvia University of Life Sciences and Technologies, compliance of maths education with the demands of sustainable challenges, as well as initiatives to transform maths education into education for sustainable development which is based on UNECE Strategy for ESD.
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EN
Aim. The aim of this paper is to present the results of a pilot validation of an artificial intelligence chatbot for mathematics tutoring. The subject of the analysis is the behaviour of the students in the course, in particular their approach to solving problems without external motivation through scoring or other assessment. Methods. The analysis of student behaviour was carried out on the basis of records in the application database. The subject of the analysis was not only the pupils' responses, but also the time taken to produce them and the overall trajectory through the course. Results. The results of the analysis show that students who choose to join the course, work intensively in the lessons. Most pupils solve more than one basic task. A significant proportion of pupils also use the prepared help and instructional videos. The analysis of the solution time allowed identification of a group of pupils who do not even read the problems and only confirm the results. Conclusion. The pilot validation confirmed that the chat-bot format is close to the learners, and they are able to use the courses created in this environment. Solution time analysis suggests that this parameter can be used to analyse learner behaviour and system control. Further analyses in this area are needed.
EN
This article describes the theoretical foundations of cultural and historical part of modern mathematics education. The concept of educational paradigm of the philosophy and pedagogy is interpreted. Classification of educational paradigms is made. Humanization and liberalization of education are described. Components of cultural and historical components of mathematics education are characterized. Analysis of the scientific work of researchers who determine what educational principles and humanization reform covering all educational sectors at different stages of the didactic process and are important landmarks of modern didactics is made. The analysis of school textbooks in mathematics that clearly shows the level of use of cultural and historical components now is made. The substantive components and goals of cultural and historical constituent are described, the review of literature is made, the analysis of the proposed use in teaching mathematics cultural and historical component of mathematics education. The cultural approach is considered as a set of methodological techniques that provide analysis of education, in terms of cultural concepts such as culture, cultural patterns, norms and values, cultural activities and interests. The key components of mathematics education: theoretical, practical, technological, cultural and historical are examined. These components perform specific functions and tasks and are interconnected. The basic elements that make up all paradigms are the following: understanding of the system of knowledge necessary to a person; understanding the type of culture and means of human development in the process of mastering the subject; principles of coding and transmission of information; public awareness of the importance of education; awareness of the cultural development of a person; the role of education in society; understanding of the character and place of the teacher as a carrier of knowledge and culture in the educational process; image and place of the child in the structures of education and training.
PL
Twierdzenie Jeana Piageta, że rozwój poznawczy dziecka jest podstawą nabywania i rozwijania pojęcia liczby oraz umiejętności operowania liczbami, wywarło ogromny wpływ na sposób nauczania matematyki. Od czasu pojawienia się wyników badań wskazujących na istnienie biologicznych podstaw operowania liczbami koncepcja Piageta zaczęła być szeroko krytykowana przez przedstawicieli neuropsychologii poznawczej. Dowody na to, że istnieje wrodzone, niezależne od systemu językowego i edukacji podłoże powstawania i rozwoju reprezentacji liczbowej, wpłynęły na sposób tworzenia programów kształcenia i zaleceń metodycznych w Europie Zachodniej i Stanach Zjednoczonych. Pomimo że dyskusja na temat możliwości nabywania i rozwoju pojęcia liczby przez dzieci toczy się od wielu lat, nadal trudno mówić o jednoznacznych rozstrzygnięciach w tej kwestii. Celem tego artykułu jest krytyczna analiza obu stanowisk teoretycznych oraz formułowanych w ich ramach zaleceń dotyczących praktyki edukacyjnej.
EN
Piaget’s claim that the cognitive development of a child is the basis for acquiring and developing the concept of numbers as well as the ability to work with numbers, had a huge impact on the methods of teaching mathematics in Poland and the world. Since the appearance of research results indicating the existence of a biological basis for the ability to work with numbers, the Piaget’s theory has been widely criticized by representatives of cognitive neuropsychology. The evidence that there is an innate foundation for the formation and development of numerical representation, independent of language and education, has influenced the manner of constructing educational curricula and methodological recommendations in Western Europe and the United States. Although the discussion on the possibility of children acquiring and developing number sense has been ongoing for many years, it is still difficult to point to a conclusive resolution of this issue. The aim of this paper is to present a critical analysis of the two theoretical concepts and recommendations for educational practice, formulated within their frameworks.
PL
Matematyka jest przedmiotem, który sprawia uczniom najwięcej problemów nieraz przez całe życie szkolne. Od lat obserwuje się na całym świecie niezadawalające wyniki nauczania tego przedmiotu, a brak lub zbyt niski poziom umiejętności matematycznych nie pozwala wielu uczniom sprostać rosnącym wymaganiom życiowym. Taka niepokojąca sytuacja implikuje podejmowanie ustawicznych prób modyfikacji i reformowania programów edukacji matematycznej zmierzających w kierunku większej ich skuteczności. W pracy podjęto problem trudności dzieci w uczeniu się matematyki. Zwrócono uwagę na rodzaje i skutki niepowodzeń w edukacji matematycznej. W kontekście tych zagadnień, jako alternatywę zakomenderowano edukację metodą M. Montessori. Omówiono główne założenia pedagogiki montessoriańskiej ze szczególnym uwzględnieniem materiału rozwojowego. Największą uwagę poświęcono materiałom sensorycznym i matematycznym, dokonując krótkiej ich charakterystyki oraz wskazując wysoką skuteczność edukacyjną. W celu przybliżenia specyfiki montessoriańskich form pracy ucznia przedstawiono trzystopniową lekcję nazw dotyczącą charakterystycznej dla metody Montessori pomocy rozwojowej, zwanej „złotym materiałem”. W zakończeniu wskazano efektywność dydaktyczną pedagogiki Montessori w obszarze edukacji matematycznej. Podkreślono, że uczniowie w placówkach montessoriańskich chętnie i samodzielnie pracują z materiałami matematycznymi. Doświadczają sukcesów, nabywają nowe umiejętności i przekonują się, że matematyka może być łatwa i przyjemna.
EN
Mathematics is a school subject which causes students the greatest problems, sometimes throughout their entire school experience. Unsatisfactory learning outcomes in mathematics have been observed worldwide for a number of years, and the lack of or poor mathematical skills make it impossible for many students to cope with the ever increasing demands of modern life. In view of this alarming situation, constant attempts are being made to modify and reform mathemati­cs education curricula in order to improve their effectiveness. The present study explores the difficulties faced by students in learning mathematics. Attention is given to the types and effects of failures in mathematics education. In the context of these problems, the Montessori method is recommended as an alternative. The main assumptions of the Montessori pedagogy are presented, with a special emphasis on the development material. The greatest prominence is given to sensory and mathematical materials, providing their brief characterization and pointing to their high educational effectiveness. In order to bring the characteristics of Montessori’s organizational forms closer (forms of students’ work) the three-stage-lesson is presented. The lesson involves presenting the names connected with the typical developmental Montessori method with the use of Golden Bead Material. The concluding section highlights the didactic effectiveness of Montessori pedagogy in the domain of mathematics education. It is stressed that students who have been educated in Montessori schools work eagerly with mathematical materials and independently. They achieve educational success, acquire new skills and see that mathe­matics can be easy and pleasant to learn.
EN
Developmental dyscalculia is characterized by decreased numerical and finger skills. In general, dyscalculia affects children with learning disabilities in mathematics and is usually associated with problems that prevent effective acquisition of mathematical competence. There are different ways of supporting children with dyscalculia, but there is no single therapeutic approach to it. Among the available publications we can find some that discuss the possibility of supporting the therapy of children with dyscalculia by new technological solutions. The present study verified this issue by means of a review of English language literature. Research on the use of new technologies in working with children with dyscalculia is noted and several potentially used technological tools and their benefits of this type of assistance are pointed out. The literature review shows that technology can enhance educational therapy for children with dyscalculia and that there is a need for intensified research on this topic, as well as a need to standardize the terminology used in this area.
PL
Dyskalkulia rozwojowa charakteryzuje się obniżonymi umiejętnościami numerycznymi i palcowymi. Na ogół dyskalkulia dotyczy dzieci z trudnościami w uczeniu się matematyki i zwykle wiąże się z problemami uniemożliwiającymi efektywne nabywanie kompetencji matematycznych. Istnieją różne sposoby wspierania dzieci z dyskalkulią, nie ma jednak w stosunku do nich jednego podejścia terapeutycznego. Wśród dostępnych publikacji odnajdujemy takie, które omawiają możliwości wsparcia terapii dzieci z dyskalkulią przez nowe rozwiązania technologiczne. W niniejszym opracowaniu zweryfikowano to zagadnienie za pomocą przeglądu najnowszej literatury anglojęzycznej. Odnotowano badania dotyczące wykorzystania nowych technologii w pracy z dziećmi z dyskalkulią i wskazano na kilka potencjalnie wykorzystywanych narzędzi technologicznych oraz ich korzyści wynikające z tego typu pomocy. Przegląd literatury pokazuje, że technologia może wzmocnić terapię edukacyjną dzieci z dyskalkulią oraz że istnieje potrzeba zintensyfikowanych badań na ten temat,jak i potrzeba ujednolicenia stosowanej w tym zakresie terminologii.
EN
The article discusses the development, improvement and research opportunities for application of methodological system of teaching math correspondence students of engineering specialties of technical universities, which contributes to higher motivation to learn mathematics, can improve the quality of teaching part-time students mathematics, but also enhances the creative and intellectual potential of students through self-organization, optimizes the ability to work with computers and allow themselves to make responsible decisions. Distance education is a form of training and retraining of specialists with higher and secondary special education, as well as a form of education on the job. In modern conditions the solution to the problem concerning the use of information and communication technologies (ICT), particularly program-methodological in educational process is complex. Methodological system of teaching mathematics correspondence students of higher technical school is of practical importance because it helps during the learning process to increase the level of mathematical training of students and to form independent work skills. The paper presents a practical implementation of the developed methodological system, in particular, created program-methodological complex of teaching mathematics correspondence students of engineering specialties. By requirements of teaching mathematics the students of technical universities are features of each component of the guidance system: objectives, content, organizational forms, methods and means of education. The research results can be used in the practice of teaching mathematics in high school while preparing engineering students, distance learning, as well as during the study of other disciplines (physics, chemistry, special subjects) during the development of computer learning tools. The study does not fully solve the problem of improving the methods of teaching mathematics correspondence students of technical universities using program-methodological complex system of distance learning, which enables the prospect of further scientific understanding of the raised issue, particularly in terms of creation of methodological maintenance of the mathematics and the development and use of software tools for the effective use of ICT.
PL
Podczas gdy współczesny dyskurs naukowy oraz debaty edukacyjne są przesycone nie zawsze efektywnymi pytaniami o treści i metody nauczania matematyki, fundamentalne z punktu widzenia jednostki pytania o cel, sens i wartość nauczania i uczenia się matematyki zdają się pozostawać w cieniu. W artykule podjęto temat humanistycznych aspektów matematyki. Zaproponowano przyjęcie wielowymiarowej perspektywy w badaniu zagadnień związanych z edukacją matematyczną: ontologicznej, epistemologicznej oraz aksjologicznej. Nacisk został położony na ostatni wymiar. Przywołano cele kształcenia matematycznego w ujęciu Zofii Krygowskiej, a także przedstawiono definicje i klasyfikacje wartości odgrywających istotną rolę w aktywności matematycznej zarówno ucznia, jak i nauczyciela. Artykuł kończy refleksja na temat potrzeby spojrzenia na edukację matematyczną z perspektywy aksjologiczno-teleologicznej i prowadzenia w Polsce badań z zakresu dydaktyki matematyki, które by ten wymiar uwzględniały.
EN
While contemporary scientific discourse and educational debates are suffused with, not always effective, questions on both the content and methods of teaching mathematics, questions about the aim, meaning and value of mathematics education, fundamental from the perspective of the learner, seem to remain in the background. This article addresses the humanistic aspects of mathematics. It proposes the adoption of a multidimensional perspective in the study of issues related to mathematics education, encompassing ontological, epistemological and axiological dimensions, with an emphasis on the latter. Zofia Krygowska’s objectives of mathematics education are recalled together with definitions and classifications of the values playing an important role in mathematics related activities of students and teachers. The article concludes with a reflection on the urgent need of looking at mathematics education from the axiological and teleological perspectives, and the importance of conducting research on mathematics education in Poland that would take these dimensions into account.
PL
W artykule przeanalizowano strukturę, funkcje i metody zarządzania jakością kształcenia we współczesnej szkole oraz zaproponowano system zarządzania szkołą na bazie tradycji, który może być wprowadzony do modelu organizacyjnego zarządzania. Propozycję oparto na wynikach badań przeprowadzonych w szkołach Polski i Ukrainy. Zwrócono również uwagę na fakt, że w większości placówek wysoka efektywność systemu zarządzania oświatą nie zawsze idzie w parze z jego wysoką skutecznością. Jednak w odniesieniu do oceny efektywności systemu zarządzania oświatą może mieć zastosowanie tylko rozszerzona formuła tej efektywności. Uzyskanie nowych rezultatów kształcenia jest niemożliwe bez zmiany treści kształcenia, rozwoju zawodowych kompetencji pedagogów, stworzenia warunków dla rozwoju zasobów i środowiska edukacyjnego. Artykuł ma charakter teoretyczno-empiryczny.
EN
The article’s aim is to analyse the structure, functions and methods of quality management in modern schools and educational institutions. The author proposes the school management system based on traditions that can be incorporated into the organisational management model. The proposition is based on the results of research carried out in Polish and Ukrainian schools. It is also noted in this article that in most institutions, the high effectiveness of the education management system does not always go hand in hand with its high efficiency. However, with regard to the assessment of the effectiveness of the education management system, only the extended formula of this effectiveness may be applied. Moreover, the article contains considerations on organisational effectiveness. Obtaining new educational results is impossible without changing the content of education, developing professional competencies of teachers, creating conditions for the development of resources and educational environment. This article is theoretical and empirical.
EN
W artykule zasygnalizowano znaczenie kompetencji matematycznych, społeczno- komunikacyjnych, informatyczno-medialnych, informacyjnych oraz w kształceniu on-line. Zaprezentowano wyniki badań własnych na podstawie internetowego konkursu matematycznego „Internetowa przygoda z matematyką”. Wskazano na zależność między wynikami osiąganymi przez uczniów szkół średnich w konkursach matematycznych on-line a stopniem rozwoju społecznych zainteresowań matematycznych.
EN
The number of students with the experience of migration has been growing year by year in Polish schools. They need to learn Polish relatively fast for educational purposes. This paper presents, based on a pilot glottodidactic experiment, the observations of how foreign children could be helped to learn Polish using simple math exercises. The demonstrated outline of the didactic innovation is aimed at showing how the repeatability of language sequences in the narration of the exercises affects the development of students’ grammatical and lexical competence.
PL
Na podstawie Raportu Liczą się nauczyciele o stanie edukacji 2013 opublikowanego przez Instytut Badań Edukacyjnych przedstawiono zarys drogi, jaką pokonują adepci, aby zdobyć zawód nauczyciela. W artykule wskazano na niski poziom przygotowania merytorycznego i pedagogicznego nauczycieli do tego zawodu pomimo „dobrego” (czytaj: wyższego) wykształcenia. Podkreślono słabe strony organizacji i zakresu studiów nauczycielskich. Zaproponowano możliwości poprawy aspektu dydaktycznego oraz organizacyjnego kształcenia nauczycieli.
EN
The Institute for Educational Research published report about the state of education in 2013 – named Teachers are important. Article outlines the path that adepts must overcome to become teachers. There is pointed low level of preparation both substantial and pedagogical of teachers to the profession despite academic degree education. There are outlined weaknesses of organization and scope of the studies. It was offered opportunities to improve the educational aspect of teacher’s training and organizational solutions.
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