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Introduction
Ján Gunčaga currently works at the Department of Science Education, Comenius University in Bratislava. Ján does research in Mathematics Education, Teaching Methods and Pedagogic Theory. Their current project is 'Geometric conceptions and misconceptions of pre-school and school age children', History of Mathematics Education, ICT in Education
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Publications
Publications (89)
Microlearning brings a number of advantages that make it an attractive tool for education. Short and clear lessons minimize the risk of information overload, promote better understanding of the material, and enable quick and easy retention of information. The relevance of microlearning lies in its ability to respond to current educational needs and...
Applications of augmented reality are gradually being integrated into teaching at various levels and types of schools. Augmented reality has the potential to transform the training of future teachers in the context of developing their mathematical knowledge, digital skills, and teaching competencies. The paper focuses on researching the impact of a...
This research delves into the influence of Augmented Reality (AR) on Science, Technology, Engineering, Arts, and Mathematics (STEAM) education within the domain of primary school teacher training at the university level. The core aim is to augment digital literacy within the primary education framework through inquiry-based teaching methods. This i...
The aim of the monograph is to present the results of the research carried out within the project VEGA 1/0033/22 Inquiry-oriented teaching in mathematics, sciences, and technical education with students of the study programme Teacher Training for Primary Education in mathematical subjects.
Different forms of evaluation of achieved students’ knowledge are an important component of the educational process. They provide important information about the level of acquired knowledge and skills to the student, his parents, and the school organization, and also represent important feedback for teachers. Knowing the real situation. Teachers ca...
Education is a constantly evolving field that encompasses various approaches to teaching and learning. In our paper, we focused on qualitative research conducted with future primary level teachers using a STEAM (Science, Technology, Engineering, Arts and Mathematics) approach. The research involved classroom observation, analysis of the student wor...
The research focused on the issue of physics subject matter in higher education of primary education teachers. It explained students’ misconceptions on an example of the subject matter about a pulley. The research aimed to study on a sample of 79 students the effectiveness of the designed IBI in eliminating misconceptions in favour of scientificall...
An innovative approach to delivering pre-service teacher training to student teachers in individual areas is considered crucial in the smooth digital transformation of education in Slovakia. One of the major shortcomings of the current pre-service training of student teachers is the fact that not all higher education institutions involved in the te...
Digital technologies have entered our daily lives and into schools. Computers, tablets, smartphones are a part of today’s generation of children from birth; therefore they appear naturally also in education. Besides interactive whiteboards and notebooks in classrooms, children also often possess tablets and smartphones. For the teacher, it is a ver...
The COVID-19 pandemic situation has adversely affected mobility and international cooperation of students and workers throughout Europe. The transfer of knowledge from foreign experts who can point out the issue in another point of view is an integral part of university studies. However, the reaction of international agency CEEPUS have been greatly...
Teachers' digital literacy is an essential prerequisite for them to be able to use technology-enhanced teaching effectively in their pedagogical practice. In 2018, the National Institute of Certified Educational Measurements of the Slovak Republic launched the PIAAC – Programme for the International Assessment of Adult Competencies project, which i...
The twenty-first century presents fundamental challenges for education systems focused on skills development. With this requirement, the training of teachers is changing little by little. Where the learning of the knowledge to be taught seeks to articulate itself in different modalities. Teachers can use various resources, from manipulative materia...
2019 marked the two-hundredth anniversary of elementary-level teacher training for the German minority in Hungary. A systemic review of regulations, laws and curricula enable an examination of the changes in teacher training institutions, including the language of instruction in teacher training, beginning from the period of the Kingdom of Hungary...
The rapid changes in information and communication technology (ICT), the increasing availability of processing power, and the complexity of mathematical software demand a radical re-thinking of science, technology, engineering, arts, and mathematics (STEAM), as well as mathematics education. In the transition to technology-based classrooms, the con...
Mathematik ist in Ungarn traditionell von hoher kultureller und wissenschaftlicher Bedeutung.
Intention der Buchreihe „Mathematiklehren und -lernen in Ungarn“ ist es, die beispielgebende Rolle des Landes und den inspirativen Austausch über Grenzen hinweg zum Ausdruck zu bringen.
Als Schulfach und als Wissenschaftsdisziplin gleichermaßen hat Math...
The article points out some of the challenges faced by students at the University of Ostrava, Comenius University in Bratislava and Al-Farabi Kazakh National University, who had almost no previous practice in online teaching during the COVID-19 pandemic situation. The students from the mentioned universities were interviewed to share their experien...
We focus on mapping, analysis and capturing the life and work of some personalities of Slovak mathematics in the 20th century in our contribution. They are mathematicians, teachers and their knowledge and experience can be useful in teacher training of the future maths teachers and as an added value to education knowledge of these group of students...
We prepare in the frame of the project KEGA "Prominent personality of Slovak Mathematics - idols for future generations". Biographies of Slovak mathematicians as inspiration for students - future teacher of mathematics at secondary schools. In our contribution will be presented personality of prof. L. Bukovsky, prof. M. Hejny, prof. S. Jendrol, pro...
Mathematik ist in Ungarn traditionell von hoher kultureller und wissenschaftlicher Bedeutung. Intention der Buchreihe „Mathematiklehren und -lernen in Ungarn“ ist es, die beispielgebende Rolle des Landes und den inspirativen Austausch über Grenzen hinweg zum Ausdruck zu bringen. Als Schulfach und als Wissenschaftsdisziplin gleichermaßen hat Mathema...
2020 will be remembered for COVID-19, a pandemic that forced the world to lock down and urged most educational providers to promptly implement e-learning solutions. In this paper, we point out some challenges faced by university teachers who had almost no earlier practice in online teaching. Nine lecturers working in different universities from Bra...
The aspect of visualization plays an important role in the calculus teaching. The notion of the function is basic notion at the lower secondary level and in the teacher training of future mathematics teachers. The notion of the graph of the function and his graphical and visual representation is important at upper secondary level and university lev...
Die Präsentation wurde von den beiden Autoren im Rahmen des 6. Treffens des AK "Mathematiklehren und lernen in Ungarn" an der Eötvös Loránd Universität Budapest, Institut für Mathematik, online am 2.10.2021 gehalten um umfasste: Im ersten Teil des Beitrags wird die Bedeutung des Algorithmischen Denkens unter Beiziehung aktueller fachdidaktischer Pu...
Karl Josef Fuchs, Salzburg und Ján Gunčaga, Bratislava
Algorithmisches Denken in der Talenteförderung
Im ersten Teil des Beitrags wird die Bedeutung des Algorithmischen Denkens unter
Beiziehung aktueller fachdidaktischer Publikationen als Fundamentale Idee diskutiert. Den Hauptteil des Beitrags bilden ausgewählte Beispiele im Kontext von Wettbew...
Mathematik ist in Ungarn traditionell von hoher kultureller und wissenschaftlicher Bedeutung. Intention der Buchreihe „Mathematiklehren und -lernen in Ungarn“ ist es, die beispielgebende Rolle des Landes und den inspirativen Austausch über Grenzen hinweg zum Ausdruck zu bringen. Der vorliegende Band enthält – ganz in diesem Sinne – Artikel aus mehr...
This article focuses on Smart Education – Evolution in Digital World in Conditions of Internationalisation of Higher Education as viewed by experts from different countries: the Czech Republic, Poland, Portugal, Slovakia, Spain, Russia and Ukraine. The article aims to provide opinions, views and reflections on important topics addressed by Internat...
The overall aim of education is to train proactive, motivated, and independent citizens to face and overcome continuous challenges. Critical thinking—finding solutions to problems—is of primary importance in the 21st century to handle challenging situations and deal with obstacles in careers. A critical literature review approach was used to assess...
In primary and secondary geometry education, some problems exist with pupils’ space thinking and understanding of geometric notions. Visualisation plays an important role in geometry education, and the development of pupils’ visualisation skills can support their spatial imagination. The authors present their own thoughts on the potential of includ...
mathematical competencies of Slovak students
Historische Materialien sind wichtige Dokumente menschlicher Kultur. Sie sind deshalb auch wertvoll für den Mathematikunterricht.
Eine sinnstiftende Verwendung von Softwaresystemen im Unterricht erfordert Veränderungen in der Aus- und Fortbildung von Lehrkräften (siehe Gunčaga, 2011).
Im Bereich der Mathematikdidaktik können wir folgende Fragen s...
Methods of stock market analysis have undergone long-term development. In particular, stock market failures and financial crises were the driving forces behind the search for new methods and forecasts. We are currently living in a time of digital boom that has greatly helped advance science in all areas. This fact was also reflected in the area of...
The study is aimed to describe the using of geometrical educational software oriented to develop geometrical spatial thinking. This software is available on the webpage www.delmat.info. We would like to show his functions, propose concrete thematic areas in Slovak and Polish curriculum in the elementary level useful for this software. Future resear...
Acronym STEM (Science, Technology, Engineering, and Mathematics) has become very frequently word among many stakeholders in the school policy. Mathematical and computational thinking are important for STEM Education. There are common thinking skills, but computational thinking focuses more on automation. Mathematical thinking focuses more on proofi...
Learning is a complex phenomenon. Contemporary theories of education underline active participation of learners in their learning processes. One of the key arguments supporting this approach is the learner’s simultaneous and unconscious development of their ability of “learning to learn”. This ability belongs to the soft skills highly valued by emp...
Beitrag Guncaga/Fuchs: COMPUTER ALGEBRA SYSTEME IM MATHEMATIKUNTERRICHT-INSTRUMENTE ZUR BEGRIFFSBILDUNG SOWIE EINER „MODERNISIERUNG“ HISTORISCHER MATERIALIEN
Zusammenfassung: Computer Algebra Systeme (CAS) wie GeoGebraCAS und andere an den Schulen verwendeten Hand-Held-Systeme wie TI-Nspire oder Casio ClassPad II sind nicht nur Instrumente zur Visu...
The paper deals with educational traditions in mathematics education in Austrian-Ugrian monarchy in the nineteenth century. This country as a multinational and multicultural territory is an inspirable example of cultural diversity. There is lack of university courses in the teacher training study, which shows cultural diversity as a heritage of Cen...
Abstract. In unserem Beitrag wollen wir einige Beispiele von Schwellenkonzepten im Mathematik-unterricht vorstellen. Diese Konzepte können eine Barriere im Verständnis für viele Schüler/innen darstellen. Die Aufgabe für Mathematiklehrer/innen ist es, passende Modelle für seine/ihre Klasse zu suchen, die helfen, diese mentale Barriere im Verständnis...
Visualisation is an important part of the cognitive process in mathematics. Pedagogical-psychological theoretical frameworks concerning cognitive processes consider perception and visualisation as basic conditions for the creation of correct mental imagery. This study examined visualisation as a key factor in the development of geometric concepts f...
Visual imagery has been an effective tool to communicate ideas connected with basic mathematics concepts since the dawn of mankind. The development of educational visualisation technology allows these ideas to be demonstrated with the help of some educational software. In this paper, we specifically consider the use of GeoGebra, a free, open-source...
The aim of the mathematical publication „Young Children‘s Conceptions of Geometric Shapes“ was to present findings of the three years long research project supported by the Scientific grant agency of the Ministry of Education of Slovak republic and the Slovak Academy of Sciences VEGA 1/0440/15 named „Geometric conceptions and misconceptions of chil...
Auch wenn A falsch ist, kann B wahr sein. – Diese aussagenlogische Feststellung soll als Leitsatz für das vorliegende Buch nicht in wörtlicher, sondern in metaphorischer Bedeutung den Erkenntnisgang der Mathematik zum Ausdruck bringen – und zwar in doppelter Weise. Auf dem Weg zu gesicherten Erkenntnissen sind Irrtümer und Fehler, Lücken und Unvoll...
This article describes two heuristic strategies for problem solving: the use of false assumption strategy and the use of double false assumption strategy. Both of these strategies have their roots deep in history. In this article, we define these two strategies and illustrate their use in a problem developed by Frances Pellos. The article provides...
The Use of Computer Algebra Systems in variable context.
Presentation at the GDM & DMV Conference at the University of Paderborn, 5.-9.3.2018
The aim of this chapter is to present a study focused on exploring the process of teaching mathematics with mobile technologies in classrooms in the lower secondary level (pupils aged nine to 14 years old) in Slovakia. This scientific study was based on the realization of inquiry-based learning in concrete topics from school mathematics. During the...
New technologies with modern method of teaching must be implemented in the university studies. Important part is teacher training study. These technologies make the study more attractive and also it brings bigger motivation an understanding of notions by students. We present in our contribution augmented reality technology as a part of using of mob...
Misconceptions in geometry are an essential problem in the understanding of geometric terms by primary and pre-primary aged children. Present research shows some misconceptions in geometry demonstrated in the understanding of circles, squares, triangles and oblongs for children in the last year of kindergarten and pupils in the last year of primary...
The aim of this article is to give an overview about the mathematics education in primary schools in Hungary and Slovakia (both parts that time of the Habsburǵs Empire) at the end of the XVIIIth and in the first part of XIXth century. Besides describing the educational historical circumstances, which give a background to the study of the mathematic...
The main aim of the paper is to describe educational activities in the Teacher's Institutes in Spišská Kapitula and Eger in the 19th century. These institutes were the first in contemporary Hungary to provide training for future teachers at primary level. They were founded by Johann Ladislaus Pyrker (1772-1847), bishop of Spiš in 1819-1820 and arch...
The aim of this chapter is to analyse the development of achieved level of mathematical competence in Slovak lower secondary schools over the past six years. Special attention is given to the analysis of the pupils’ knowledge in different thematic units, gender analysis and comparison of pupils’ achievements according to the founder of the school....
Significant development of information and communication technologies and especially the Internet boom bring new possibilities in education of different subjects of STEM (Science, Technology, Engineering, and Mathematics). Information technology has provided new innovations to sustain constructing an artifical educational environment by means of co...
We would like to present some excerpts of historical mathematical textbooks from the Teachers' Institute in Spisska Kapitula, because this institute is at the roots of primary education in Central Europe. The methodological approaches used in these textbooks contain suitable motivation and models for explaining basic mathematical notions in primary...
During the last reform, Slovakia has reduced geometry in curriculum in primary mathematics education. Preschool education schools devote more time to geometry in curriculum, but this is not mandatory for all the children. In the primary schools, teachers devote very little lessons time to this problem. These lessons are mainly focused on technology...
In this article we present several possibilities of the use of educational software as a motivational tool in education. We show some examples of computer aided education in subjects of mathematics and computer science. This teaching is connected to the goals described in the new Slovak Curriculum ISCED 2 for education of these subjects at the seco...
Teacher training in Slovakia as a member of European Union is mostly influenced by the European tendencies. The European values are inserted on the base of explanation of European dimension of understanding of Europe, as an association of time, space and culture and explanation of the context.
The aim of this work is to describe educational activities at the Teachers Institute in Spisska Kapitula. As the frst Teachers Institute in the area of Slovakia, it provided Training of the future teachers in order to perform primary education. Jan Ladislav Pyrker (1772-1847), a Bishop of the Spis Diocese, made a decision to establish an institute...
In our contribution we would like to show how is possible to use GeoGebra in some historical - mathematical textbook. We show some examples from the textbook Václav Posejpal: Aritmetika pre ústavy učitel'ské (Arithmetic for Teachers' Institutes) with using GeoGebra. This textbook is from Library of Teachers Academy in Spišská Kapitula and we have S...
In this paper, the authors describe some activities which might be implemented within the framework of Slovak and Polish GeoGebra Institute. It's presented new goals defined in new Slovak curriculum ISCED 3 for Mathematics at secondary schools. Several students' works, which use the GeoGebra software, become a concrete example for motivation during...
In this article we present several possibilities of the use of GeoGebra in education. We present Slovak GeoGebra Wiki as a tool to share teaching materials. We show some examples of this use in subjects of mathematics, physics and computer science. These works are connected to the goals described in new Slovak Curriculum ISCED 2 for education at th...
In this article we describe some activities which we propose to implement within the framework of Slovak GeoGebra Institute. We present new goals defined in new Slovak curriculum ISCED 3 for Mathematics at secondary schools. Several students' works those use the GeoGebra software (by the students of Pedagogy at Catholic University in Ružomberok) wi...
https://ggijro.files.wordpress.com/2011/07/6geogebraguncaga1507antohe.pdf
Properties of functions defined on a bounded closed interval, weaker than continuity, have been considered by many mathematicians. Functions having both sides limits at each point are called regulated and were considered by J. Dieudonné [2], D. Fraňková [3] and others (see for example S. Banach [1], S. Saks [8]). The main class of functions we deal...
This paper contains the results of a pedagogical research devoted to the
understanding of the notions of finite limit and derivative of a function at a point. In
case of teaching limits, the effort spent by a teacher is not effective because for
students the notion of a limit is very formal. This claim is supported by our
pedagogical research u...
A renowned Slovak mathematician Professor Igor Kluvánek (1931 -1993) during his affiliation with the University of Adelaide in Australia (1968 -1990) has worked out a unique course of mathematical analysis for future high school teachers of mathematics. The course has been tested in its conceptual form but, as a whole, it still awaits its publicati...
Resumé Tematický celok "Prirodzené čísla, násobenie a delenie prirodzených čísel" patrí podľa učebných osnov do 4. a 5. ročníka základnej školy. K hlavným zručnostiam, ktoré žiak musí pri jeho preberaní zvládnuť, patrí algoritmus delenia. Často je zvládnutý len povrchne a formálne, čo sa prejavuje aj u budúcich učiteľoch matematiky, ktorí často nev...
Kľúčové slová: inovácia, vyučovanie, matematika, informatika, projekt , Európsky sociálny fond 1 Ďalšie vzdelávanie učiteľov V súčasnosti je v školstve viditeľná snaha o zefektívnenie a zmodernizovanie vyučovania a o zavádzanie informačno – komunikačných technológií do vyučovacieho procesu. Aj v predmetoch matematika a informatika je nutné neustále...
ZUSAMMENFASSUNG: Dieser Beitrag beschreibt die Benutzung der Ungleichung von Jensen bei der Lösung einigen Extremalaufgaben. Diese Ungleichung formulierte J. L. W. V. Jensen in seinem Beitrag "Sur les fonctions convexes et les inégalités entre les valeurs moyennes" (Sehe [6]). Im Beitrag sind die Lösungen der konkreten Beispielen gezeigt, die konve...
This time in Slovakia a transmissive type of teaching is very widespread. In this type it is typical that students learn accomplished facts, algorithms, formulas an so on. For constructivist type of teaching it is typical that students are more active in the teaching process. The teacher had a position of a presenter who presents and guides the dis...
This paper describes the problems with limits of sequences and sum of series. Teaching of this part of mathematics at the grammar school is oft very formal. History of mathematics brings a lot of examples, which can motivate the students in the teaching process. This paper shows a part of the work from Archimedes about parabolas. 1 Úvod Tematický c...
