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1
Content available Wolne aplikacje webowe wspierające wykorzystanie klocków w edukacji matematycznej
Zuziak Wojciech Jan, Zuziak Mikołaj Wojciech
Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej
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2019
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Nr 65
131--134
PL
Realizowany w Bielsku-Białej i okolicy – w roku szkolnym 2018/2019 – projekt edukacyjny pod nazwą „Klockiem w matematykę!” dostarczył nowych pomysłów na wykorzystanie klocków w edukacji matematycznej w klasach 1-4 szkoły podstawowej. Artykuł opisuje proces powstania wolnych aplikacji webowych na tablice lub monitory interaktywne. Aplikacje te mają ułatwić prowadzenie zajęć warsztatowych z klockami. Zaprezentowano wymagania przyjęte wobec aplikacji, wskazano obszary zastosowań aplikacji podczas zajęć z uczniami, omówiono etapy i przyczyny wyboru front-endowych technologii webowych, w których one powstają. W podsumowaniu wskazano na nowy projekt „Edukacja klockiem po(d)parta”, którego koordynatorem jest RODN „WOM” w Bielsku-Białej. Projekt ten ma dostarczyć obudowy dydaktyczno-metodycznej, opisującej pomysły na pracę z wykorzystaniem klocków i powstających aplikacji.
EN
An educational project called “With a building block at Math!” (“Klockiem w matematykę!”) realized in Bielsko-Biała and the surrounding area during the school year of 2018-2019 has provided new ideas for the usage of building blocks in mathematics education in grades 1-4 of primary school. The article describes the process of creating free web applications for interactive whiteboards or interactive monitors. These applications have been created to support workshop classes with the usage of the building blocks. The requirements regarding the selected applications have been presented, possible usage of applications has been indicated during classes with students, the stages and reasons for selecting front-end web technologies in which they were created were also discussed. In conclusion, the new project “Education supported by building blocks” (“Edukacja klockiem po(d)parta”) coordinated by the Regional In-Service Teacher Training Centre "WOM" in Bielsko-Biala (Poland) has been indicated. This project has been created to provide a didactic and methodological support for working with the building blocks with the above proposed applications.
2
Content available Problems of expert evaluation in terms of the use of variative models of a computer-oriented learning environment of mathematical and natural science disciplines in schools
Hrybiuk Olena
Zeszyty Naukowe Politechniki Poznańskiej. Organizacja i Zarządzanie
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2019
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Nr 79
101--118
EN
The article discusses the concept of mathematical education of pupils of a school and the results of pedagogical research. Being trained to solve the simplest tasks without a deep (thorough) understanding of the meaning of mathematical relationships is not conducive to the development of intellectual abilities and is quickly lost after completing the topic. It is experimentally confirmed that a student aspiring to attain a higher technical education, in addition to computational skills, needs to have an idea about mathematics and its methods, possess logical development, a graphic culture, develop a spatial imagination, independent work skills, the ability, if necessary, to use the appropriate directory to restore specific facts and obtain the necessary information. The research also looks into ways of solving problems with designing the learning environment and elaborating variable models of studying the natural and mathematical sciences with application of certain components of a computer-oriented learning system with the aim of upgrading pupils’ performance (a mass model, the main model and the creative model – an advanced level). The structuring of knowledge and the correct correlation of the selected types of knowledge develop the content of profile education, taking into account significant differentiation and the possibility of building an individual educational curriculum for schoolchildren, and also contributes to the filling of the three most important components of the content of profile training: basic invariant, profile variational and additional ones.
PL
Omówiono koncepcję edukacji matematycznej uczniów szkoły oraz wyniki pedagogicznych badań naukowych. Wyćwiczenie w rozwiązywaniu najprostszych zadań bez głębszego (świadomego) rozumienia sensu zasad matematycznych nie sprzyja rozwojowi zdolności intelektualnych i jest szybko zapominane po zakończeniu przerobionego tematu. Uczeń zamierzający uzyskać wyższe wykształcenie techniczne oprócz nawyków obliczeniowych powinien zdobyć wiedzę o matematyce i jej metodach, osiągnąć rozwój logiczny, kulturę graficzną, rozwiniętą wyobraźnię przestrzenną, nawyki samodzielnej pracy, umiejętność pozwalającą, w koniecznym przypadku, skorzystać z odpowiedniego źródła w celu ustalenia konkretnych faktów i otrzymać niezbędne informacje. Strategia realizacji nauczania profilowanego przewiduje oddzielenie poziomu ogólnokształcącego od poziomu profilowanego. W badaniu zostały również omówione sposoby rozwiązania zadań projektowania środowiska uczenia się i tworzenia modeli z zastosowaniem poszczególnych składników komputerowo-zorientowanego systemu kształcenia w celu poprawy wyników uczniów. Przeprowadzona strukturyzacja wiedzy i prawidłowe zestawienie wydzielonych typów wiadomości pozwalają na opracowanie treści nauczania profilowego, zakładającego znaczne zróżnicowanie i możliwość ułożenia dla uczniów indywidualnego programu nauczania (model masowy, model podstawowy i model twórczy – wyższy). W badaniu biorą udział metodycy w celu przeprowadzenia eksperymentów w szkolnej praktyce dla określenia zdolności intelektualnych, rezultaty są również analizowane na podstawie badań eksperymentalnych.
3
Content available Mathematical contests as seen by participants
Szczepański J.
Tarnowskie Colloquia Naukowe. Nauki Techniczne i Ścisłe
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2017
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T. 4, nr 3
49--54
EN
Motivation to take part in mathematical competitions and sources of information concerning the competitions is analysed on a basis of a questionnaire presented to a group of students.
4
Content available How Hungarian teachers think about combinatorics and its teaching
Ambrus G., Rácz N. K., Vancsó Ö.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2017
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Vol. 22
11--22
EN
Teachers’ attitudes and beliefs have a fundamental influence on the way of teaching and the efficiency of learning. This topic was also brought up in the didactic research in recent years, in connection with mathematics teachers as well.– To the best of our knowledge, however, a study that investigates this specific area (combinatorics) was not included. As combinatorics has a special role in connecting the development of mathematical thinking and teaching different areas, our short-time Project (Didactics Grant of the Hungarian Academy: Complex Mathematics Education in the 21st Century) focused on the teaching of combinatorics in Hungary. Our aim was to examine some aspects of this field in connection with Tamás Varga’s method and also teachers’ beliefs towards combinatorics with the help of a questionnaire. The main results of this survey are discussed below.
5
Wirtualizacja pisemnej techniki obliczeń arytmetycznych dostępnej dla uczniów z dysfunkcją wzroku
Brzostek-Pawłowska J., Rubin M., Mikułowski D., Terlikowski G.
Elektronika : konstrukcje, technologie, zastosowania
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2016
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Vol. 57, nr 1
33--39
PL
W artykule przedstawiono założenia wirtualizacji pisemnej techniki obliczeń arytmetycznych dostępnej dla uczniów z dysfunkcją wzroku z uwzględnieniem wymagań i zindywidualizowanych potrzeb odbiorców odnośnie interfejsu użytkownika. Aplikacja KUBARYTMY jest jednym z narzędzi składowych innowacyjnej platformy edukacyjnej PlatMat wspomagającej edukację matematyczną uczniów z dysfunkcją wzroku, opracowanej w ramach projektu badawczego przez Instytut Maszyn Matematycznych w Warszawie.
EN
The article presents the premises of the virtualization of written arithmetic calculations available to visually impaired pupils. The CUBARYTHMS application takes into account the requirements of the user interface tailored to the diverse needs of end users resulting from the type of possessed visual disability. It is one of the tools of innovative educational PlatMat platform. PlatMat supports math education of visually impaired pupils and is elaborated under a research project in the Institute of Mathematical Machines in Warsaw.
6
Content available Workshops as a significant vocational education component of students specializing in teaching fields
Korcz M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
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Vol. 19
95--99
EN
The post modern social processes have somehow destroyed the institutional role of teachers over the past two decades. It is currently necessary to give would-be teachers new, different competencies than the present ones. The tendency to make the teacher education adequate for contemporary needs imposes a number of new tasks on the institutions of teacher education. There is, among other things, a need for organizing innovative classes in terms of both their content and form. The article will contain a practically verified concept of workshops as an important form of improving and completing the education of mathematics teachers.
7
Content available Using graphic display calculator in solving some problems with polynomials
Jureczko J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
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Vol. 19
83--93
EN
A graphic display calculator (GDC) is becoming more and more popular in teaching mathematics as it is used to examine some mathematical activities of students of almost all ages. Various modes of GDC are considered to be a useful tool in understanding of particular parts of mathematics. In most cases the properties of functions are examined by observation of their graphs. However, there are some properties of the functions which one cannot see during the graphs analysis (for example properties concerning complex roots of polynomials). The aim of this paper is to analyse how 17-and-18-year-old students for whom GDC is an obligatory device can generalize some relations between polynomials and so called “shadows” of these functions. The whole paper is concerned with in investigation of properties of quadratic, cubic and quartic functions with both real and complex roots.
8
Content available Some remarks on fluid flow in hourglasses
Bryll A., Sochacki R.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
|
Vol. 19
29--36
EN
In the paper the authors analyse different shapes of an hourglass for the linearity of their graduation. We also assume that any hourglass (more precisely, each of the two congruent parts) has the shape of a solid of revolution and any cross section at height h of this hourglass depends on the base radius r, i.e. h = ƒ(r).
9
Content available Non-standard tasks in mathematical education
Major J., Major M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
|
Vol. 19
115--119
EN
Mathematical knowledge and skills have been playing a more and more important role in our daily lives. At the same time, solving tasks is the essence of mathematics understood as a field of human activity. The subject of this paper are selected issues concerning some atypical tasks which play important role in mathematical education. Presented task is related to the elementary knowledge of probability theory.
10
Content available Many faces of mathematical modelling
Pyzara A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
|
Vol. 19
129--141
EN
Mathematical modelling is a concept that covers a wide range of activities. Mathematical modelling can be understood both as formulation of an equation, a function, etc., describing a given situation and as a whole process of creating a model, starting from the real-world situation to the creation of a ready-to-use optimized tool. The work presents different approaches to mathematical modelling from the point of view of teaching mathematics. It presents the results of the research conducted on students (future teachers) regarding their theoretical knowledge and skills related to mathematical modelling.
11
Content available Is math a gift?
Bartošová B.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
|
Vol. 19
25--28
EN
“I am just not a math person” is a sentence we can hear very often these days. Students use it as an excuse any-time they do not know or understand anything. But is Maths really some gift a person gets or is not? Or is it more like ability which can be improved if practised enough? This is a brief preview of what do the Czech, Slovak and also foreign authors think of this issue.
12
Content available Inquiry based mathematics education (IBME) and its reflection by primary school teachers
Novák B., Nováková E.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
|
Vol. 19
121--127
EN
In the paper we present selected outcomes of a research into possible acceptance of inquiry based mathematics education as a method used by primary school teachers. We suggest some objective as well as subjective reasons for explaining its so far low level of usage and aim at identifying obstacles, which prevent the enquiry based techniques in the primary school educational environment.
13
Content available Geometric terminology and imagination
Grebeň R., Molnár J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2014
|
Vol. 19
37--49
EN
How do pupils and students understand geometric terminology, symbols and phraseology? Using the same designation for a particular object, feature or link, allows the use of the same “language” to communicate about topics related to these concepts. The fact that everyone will equally understand the same term depends on how well the definitions are introduced. The objective of this article is one of the surveys, which is a part of the research, aimed to contribute to updating the geometric terminology in the Czech education system.
14
Content available Elements of mathematical epistemology - elements of the philosophy of teaching mathematics
Pawlak R. J., Korczak-Kubiak E.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
|
Vol. 19
11--24
EN
In the paper we present the main idea of the concept which we have called confrontational concept of mathematical epistemology. We refer it to philosophy of mathematics (in the context of epistemology of research) as well as to didactic problems (in the context of teacher preparation). Although we tried not to involve our discussion directly with any existing concepts of the philosophy of mathematics, however, in the paper one can notice some elements of modern formalism as well as Lakatos quasi-empiricism or a modern approach to structuralism.
15
Content available Divisibility and its application in teaching mathematics in the third educational level
Jędrzejewski J., Ziółkowski M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2014
|
Vol. 19
71--82
EN
Elements of theory of divisibility are present in many various interesting mathematical tasks, especially in tasks that are addressed to talented pupils taking part in mathematical competitions. Good understanding of it lets solve very interesting and difficult (at first glance) issues. On the other hand, there are a lot of problems with understanding such terms as: multiple, divisor, divisibility, prime number, LCM, GCD etc. The purpose of the article is presenting the base terms of theory in the language understood for pupil of the gymnasium (3-rd educational level, 13-16 years old). In addition, we present some algorithms that are used to solve problems from the theory of divisibility and we discuss the influence the choice of the algorithm on its effectiveness (so we analyse its complexity). Presented algorithms let us create computer programs that solve the problems mechanically. We also enlarge a bit some topics for those ones which can be taught in the class of pupils which are interested in Mathematics.
16
Content available Central Limit Theorem visualized in Excel
Hodaňová J., Zdráhal T.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2014
|
Vol. 19
51--55
EN
The Central Limit Theorem states that regardless of the underlying distribution, the distribution of the sample means approaches normality as the sample size increases. This paper describes the steps in MS Excel to help students’ better understanding of this theorem.
17
Content available Can information technology change attitude of the student in the teaching of mathematics?
Kowalski J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2014
|
Vol. 19
101--110
EN
The article shows a specific example of extracurricular activities conducted in secondary school, how the graphing calculator helped the first class student in learning mathematics to solve a very difficult task (math problem): How many elements has the equation: a x = log a x. The article describes the reasoning and attitude of the student who voluntarily of his own accord, inspired by other students to experiment, putting, generalizing and verifying hypotheses coped with the solution of this task. It describes the impact of this teaching mean that triggered activity and aroused student’s interest with the task on the degree of knowledge and skills in mathematics, the student’s skills in the use of mathematical language, self-reliance in solving a mathematical problem.
18
Content available Blended learning in Polish schools
Stróżyk J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2014
|
Vol. 19
165--171
EN
Development in technology, changing labour market and the need for lifelong learning necessitate the evolution in the education of children and youth. Blended learning is about combining the online learning and traditional methods in order to personalize the learning process. The intensive application of this teaching method in the United States seems to make the American students more engaged in solving the tasks assigned to them. It is believed that it has a positive impact on their final exam results. The article describes the basic principles of blended learning from the perspective of the theory of hybrid. It also includes some personal experience of working with this method.
19
Content available A mistake in definition of a limit of a function and some consequences
Jędrzejewski J. M., Kostrzewski T.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2014
|
Vol. 19
61--65
EN
Many times our students make some errors in definitions, especially when we must apply some quantifiers. The definition of a limit is one of the definition with many quantifiers, so one can observe many mistakes in it. We want to present one of possible mistakes and show how to improve the understanding of this difficult but one of most important notions.
20
Content available remote The role of Czech mathematicians in the Balkans (1850‒1900)
Bečvářová M.
Czasopismo Techniczne. Nauki Podstawowe
|
2014
|
R. 111, z. 1-NP
37--57
EN
From 1860s, the number of mathematicians, teachers and authors of monographs, textbooks and papers in Bohemia increased noticeably. This was due to the improvement of education and the emergence of societies. During 1870s and 1880s many candidates for teaching mathematics and physics were without regular position and income. Some of them went abroad (especially to the Balkans) where they obtained better posts and started to play important roles in the development of "national" mathematics and mathematical education. The article describes this remarkable phenomenon from the history of the Czech mathematical community and analyzes its influence on other national communities.
PL
Od lat 60. XIX w. w Czechach wyraźnie wzrosła liczba matematyków, nauczycieli matematyki, autorów monografii, podręczników i artykułów. Było to spowodowane rozwojem matematycznej edukacji i powstaniem towarzystw. W latach 70. i 80. XIX w. wielu czeskich kandydatów na nauczycieli matematyki i fizyki w szkołach średnich nie miało stałej posady i dochodów. Część z nich udawała się za granicę (szczególnie na Bałkany), gdzie zajmowali lepsze stanowiska i znacząco przyczynili się do rozwoju "narodowej" matematyki i edukacji matematycznej. Artykuł prezentuje ten niezwykły fenomen w historii czeskiego środowiska matematycznego i poddaje analizie jego wpływ na inne społeczności narodowe.
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