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Teaching geometry using computer visualizations
259-277Views:20In this work we study the development of students' creativity using computer-aided-teaching during IT classroom. Teaching geometry in Bolyai Grammar School specialized natural science classes is not an easy task. Here is introduced a new didactic means of teaching geometry which nevertheless requires the same effort to understand the material, but uses a different more active method to familiarize students with the topics. Traditional methods, and the use of compasses and rulers are not omitted either, as they develop the students' motor skills. -
Methods of teaching programming
247-257Views:47Programming methodology is one of the oldest fields of IS education, and thus various methods have evolved for its teaching. While some of them could be used effectively in primary or secondary education, others are more suited for students in higher education. The methods themselves determine the structure and curricula of courses such as Programming methodology, Data types and algorithms, Programming technology. -
Teaching XML
317-335Views:31The author has been teaching XML at the Faculty of Informatics, University of Debrecen since the end of the nineties. This paper gives an overview of XML technology from an educators viewpoint that is based on the experience that the author has gained teaching XML over the years. A detailed description of the XML course is provided. Methodological issues are also discussed. -
Taking learning styles into consideration in e-learning based education
385-396Views:38In improving electronic teaching material processes we should take the student's learning styles or methods into consideration. The ways learners receive information may be shared into three categories (modalities): visual, auditory, kinesthetic (tactile). In this paper I present some pedagogical questions of the electronic teaching-learning environment, offer a brief survey of the different learning style theories and emphasise the importance of the modalities in encoding information. The electronic teaching material should encourage the learner to choose an appropriate form of syllabus by which his knowledge can become more efficient. -
Die Stichprobe als ein Beispiel dafür, wie im Unterricht die klassische und die bayesianische Auffassung gleichzeitig dargestellt werden kann
133-150Views:30Teaching statistics and probability in the school is a new challenge of the Hungarian didactics. It means new tasks also for the teacher- and in service-teacher training. This paper contains an example to show how can be introduced the basic notion of the inference statistics, the point- and interval-estimation by an elementary problem of the public pole. There are two concurrent theories of the inference statistics the so called classical and the Bayesian Statistics. I would like to argue the importance of the simultaneously introduction of both methods making a comparison of the methods. The mathematical tool of our elementary model is combinatorial we use some important equations to reach our goal. The most important equation is proved by two different methods in the appendix of this paper. -
Forming the concept of congruence II.
1-12Views:31This paper is a continuation of the article Forming the concept of congruence I., where I gave theoretical background to the topic, description of the traditional method of representing the isometries of the plane with its effect on the evolution of congruence concept.
In this paper I describe a new method of representing the isometries of the plane. This method is closer to the abstract idea of 3-dimensional motion. The planar isometries are considered as restrictions of 3-dimensional motions and these are represented with free translocations given by flags.
About the terminology: I use some important concepts connected to teaching of congruence, which have to be distinguished. My goal is to analyse different teaching methods of the 2-dimensional congruencies. I use the term 3-dimensional motion for the orientation preserving (direct) 3-dimensional isometry (which is also called rigid motion or rigid body move). When referring the concrete manipulative representation of the planar congruencies I will use the term translocation. -
Teachers and the interactive whiteboards
281-298Views:27The spread of IWB (Interactive WhiteBoard) around the world changes, reforms and modernizes the traditional teaching methods. We can find these new ICT devices in more and more schools in Hungary as well and the use of it is getting widespread in everyday teaching. The teachers have the greatest role in the proper use of IWB during the lessons and they are also responsible for providing students with creative and motivating tasks lesson by lesson. In the following research, the advantages of the IWB are highlighted, the difficulties of its usage and the teachers' attitude towards the new ICT devices by asking 205 teachers from different primary and secondary schools. The results are mainly based on questionnaires. -
Shall we use one more representation? Suggestions about establishing the notion of recursion in teaching informatics in primary schools
209-229Views:27Among the most prominent developmental tasks of primary school education one finds increasing pupils' cognitive capacity with especial regard to observing, interpreting, coding and proving skills, which form an integral part of information and communication culture.
Info-technology (problem solving with the tools and methods of informatics), a subject matter within informatics, provides outstanding opportunities to reach the aims outlined above.
This study presents methodological ideas related to the subfield Algorithmization and data modelling of Info-technology. More specifically, it presents teaching methods to be applied while establishing the notion of recursion in grades 3–8 of primary education, and at the same time it also focuses on various realization possibilities of the prominent developmental tasks mentioned above. -
Young women's barriers to choose IT and methods to overcome them - A case study from Hungary
77-101Views:175Women's scarcity in the STEM, especially in the IT sector is pronouncedly evident. Young women are obstructed from entering and remaining in IT by a broad range of social, educational, and labor market factors. In our paper, we would like to analyze the main barriers girls face in choosing IT, while also proposing potential methods to help them overcome these obstacles. In the second part of the paper, we will present a case study to illustrate in detail how the combination of the above methods can be put into practice to address and tackle the complex set of barriers girls face. We will first introduce a Hungarian annual program, Girls' Day ("Lányok napja"), specifically aimed to promote STEM to girls, then we will present two specific events organized for the 2020 edition of the program and designed with the above principles in mind. The interactive presentation, exposing girls to female role models of the field in a gamified way, and a game development exercise, building Scratch programming skills, have attempted to provide young women both with positive perspectives and experiences in IT, which are instrumental in helping them to surmount entrenched obstacles and raise their interest in the field.
Subject Classification: 97P10, 97U30
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Linear clause generation by Tableaux and DAGs
109-118Views:31Clause generation is a preliminary step in theorem proving since most of the state-of-the-art theorem proving methods act on clause sets. Several clause generating algorithms are known. Most of them rewrite a formula according to well-known logical equivalences, thus they are quite complicated and produce not very understandable information on their functioning for humans. There are other methods that can be considered as ones based on tableaux, but only in propositional logic. In this paper, we propose a new method for clause generation in first-order logic. Since it inherits rules from analytic tableaux, analytic dual tableaux, and free-variable tableaux, this method is called clause generating tableaux (CGT). All of the known clause generating algorithms are exponential, so is CGT. However, by switching to directed acyclic graphs (DAGs) from trees, we propose a linear CGT method. Another advantageous feature is the detection of valid clauses only by the closing of CGT branches. Last but not least, CGT generates a graph as output, which is visual and easy-to-understand. Thus, CGT can also be used in teaching logic and theorem proving. -
Expressiveness of programming languages and environments: a comparative study
111-141Views:31In written and oral communication tools, the support of the understanding of our message have an important role: we can increase the expressiveness and the level of understanding of our topic by approaching it in several ways, i.e. in written methods by highlighting the important parts; in oral by changing tone and other elements of non-verbal communication. In this paper programming languages and developing environments are compared with each other in terms of their methods and their level of support to the solution of programming tasks.
There is a need to have these tools in programming and, of course, in teaching programming. What are the factors that define the distinctness and the legibility of a program? What are the basic principles which give an instrument in programmers' and students' hands in order to create a properly working program from already existing algorithms in the most efficient way? We search for the answers to these questions in this paper. -
Heads or Tails gambling — what can be learned about probability?
15-41Views:23During the teaching of probability theory, a problem may appear whose solution requires the use of methods that are unfamiliar to secondary school students. In this paper, examples of methods that can resolve this difficulties are demonstrated, which could in future allow school students to tackle and solve a wide variety of problems involving probability. -
Numerical mathematics with GeoGebra in high school
363-378Views:41We have prepared a suite of motivational examples which illustrate numerical methods for equation solving. Fixed point iteration, Newton's method, secant method and regula falsi method are implemented as GeoGebra tools. Our experience in teaching of numerical mathematics in "Jovan Jovanovic Zmaj" high school in Novi Sad is presented. We have tested pupil proficiency in numerical equation solving with and without use of a computer and the results are presented. -
Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 20 - January 22, 2012, Levoča, Slovakia
205-230Views:27The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Levoca, Slovakia from the 20th to the 22th of January, 2012. The 66 participants – including 54 lecturers and 25 PhD students – came from 6 countries, 20 cities and represented 33 institutions of higher and secondary education. The abstract of the talks and the posters and also the list of participants are presented in this report. -
Forming the concept of congruence I.
181-192Views:9Teaching isometries of the plane plays a major role in the formation of the congruence-concept in the Hungarian curricula.
In the present paper I investigate the way the isometries of the plane are traditionally introduced in most of the textbooks, especially the influence of the representations on the congruence concept, created in the teaching process.
I am going to publish a second part on this topic about a non-traditional approach (Forming the concept of congruence II). The main idea is to introduce the isometries of the two dimensional plane with the help of concrete, enactive experiences in the three dimensional space, using transparent paper as a legitimate enactive tool for building the concept of geometric motion. I will show that this is both in strict analogy with the axioms of 3-dimensional motion and at the same time close to the children's intuitive concept of congruence. -
Group Work at High School According to the Method of Tamás Varga
167-176Views:78The aim of our research is to develop students’ logical thinking. For this reason, Hungarian mathematics teachers need to be encouraged to try new methods which induce greater student involvement. Research all over the world prove that self-instruction or self-verbalizing has high effect on the learning process. This was one of the key elements of Tamás Varga’s experiment in high school. In our classroom experiments we are using a special cooperative method from Kagan among 14-18 years old students, called Sage and Scribe structure. We are looking for the answers to the following question: Does this method make mathematics lessons more enjoyable and more comfortable for students? Furthermore, we assume this structure could open the gate toward other collaborative and cooperative teaching technics.
Subject Classification: 97D40
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Dynamic methods in teaching geometry at different levels
1-13Views:37In this paper we summarize and illustrate our experiences on DGS-aided teaching geometry of the courses "Computer in mathematics" and "Mathematical software" held for students at Juhász Gyula Teacher Training College of University of Szeged. Furthermore, we show examples from our grammar school experiences too. The figures in this paper were made by using Cinderella ([19]) and Euklides ([21]). -
Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 28 – January 30, 2011, Satu Mare, Romania
159-179Views:12The meeting Researches in Didactics of Mathematics and Computer Science was held in Satu-Mare, Romania from the 28th to the 30th of January, 2011. The 46 Hungarian participants – including 34 lecturers and 12 PhD students – came from 3 countries, 14 cities and represented 20 institutions of higher education. The abstract of the talks and the posters and also the list of participants are presented in this report. -
Integrating Didactic Games in Higher Education: Benefits and Challenges
1-15Views:448In our paper, we study the reasons for the introduction of didactic games and the way of their application in higher education, especially in teaching mathematics. After describing the main characteristics and needs of Generation Z students, we outline the advantages and drawbacks of gamification and game-based learning, followed by some new aspects to their classification. The idea of device-based grouping arose because the most commonly used methods require IC tools. Gen Zs naturally accept gamified learning materials available on digital and mobile platforms, but we must not forget about traditional games either. In higher education, especially in the case of small-group teaching there should also be room for traditional, specialized didactic games, of which we focus on the benefits of card games.
Subject Classification: 97C70, 97D20, 97D40, 97U70
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What does ICT help and does not help?
33-49Views:114Year by year, ICT tools and related teaching methods are evolving a lot. Since 2016, the author of the present lines has been looking for a connection between them that supports the development of mathematical competencies and could be integrated into Transcarpathian minority Hungarian language education too. As a doctoral student at the University of Debrecen, I experienced, for example, how the interactive whiteboard revolutionized illustration in Hungarian mathematics teaching, and how it facilitated students' involvement. During my research of teaching in this regard, in some cases, the digital solution had advantageous effects versus concrete-manipulative representation of
Bruner's too.
At the same time, ICT "canned" learning materials (videos, presentations, ...) allow for a shift towards repetitive learning instead of simultaneous active participation, which can be compensated for by the "retrieval-enhanced" learning method.
I have conducted and intend to conduct several research projects in a Transcarpathian Hungarian primary school. In the research so far, I examined whether, in addition to the financial and infrastructural features of the Transcarpathian Hungarian school, the increased "ICT-supported" and the "retrieval-enhanced" learning method could be integrated into institutional mathematics education. I examined the use of two types of ICT devices: one was the interactive whiteboard, and the other was providing one computer per student.
In this article, I describe my experiences, gained during one semester, in the class taught with the interactive whiteboard on the one hand, and in the class taught according to the "retrieval-enhanced" learning method on the other hand.
I compare the effectiveness of the classes to their previous achievements, to each other, and to a class in Hungary.Subject Classification: 97U70
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Heuristic arguments and rigorous proofs in secondary school education
167-184Views:31In this paper we are going to discuss some possible applications of the mechanical method, especially the lever principle, in order to formulate heuristic conjectures related to the volume of three-dimensional solids. In the secondary school educational processes the heuristic arguments are no less important than the rigorous mathematical proofs. Between the ancient Greek mathematicians Archimedes was the first who made heuristic conjectures with the methods of Mechanics and proved them with the rigorous rules of Mathematics, in a period, when the methods of integration were not known. For a present day mathematician (or a secondary school mathematics teacher) the tools of the definite integral calculus are available in order to calculate the volume of three dimensional bodies, such as paraboloids, ellipsoids, segments of a sphere or segments of an ellipsoid. But in the secondary school educational process, it is also interesting to make heuristic conjectures by the use of the Archimedean method. It can be understood easily, but it is beyond the normal secondary school curriculum, so we recommend it only to the most talented students or to the secondary schools with advanced mathematical teaching programme. -
Transition from arithmetic to algebra in primary school education
225-248Views:35The main aim of this paper is to report a study that explores the thinking strategies and the most frequent errors of Hungarian grade 5-8 students in solving some problems involving arithmetical first-degree equations. The present study also aims at identifying the main arithmetical strategies attempted to solve a problem that can be solved algebraically. The analysis focuses on the shifts from arithmetic computations to algebraic thinking and procedures. Our second aim was to identify the main difficulties which students face when they have to deal with mathematical word problems. The errors made by students were categorized by stages in the problem solving process. The students' written works were analyzed seeking for patterns and regularities concerning both of the methods used by the students and the errors which occured in the problem solving process. In this paper, three prominent error types and their causes are discussed. -
Many paths lead to statistical inference: Should teaching it focus on elementary approaches or reflect this multiplicity?
259-293Views:76For statistics education, a key question is how to design learning paths to statistical inference that are elementary enough that the learners can understand the concepts and that are rich enough to develop the full complexity of statistical inference later on. There are two ways to approach this problem: One is to restrict the complexity. Informal Inference considers a reduced situation and refers to resampling methods, which may be completely outsourced to computing power. The other is to find informal ways to explore situations of statistical inference, also supported with the graphing and simulating facilities of computers. The latter orientates towards the full complexity of statistical inference though it tries to reduce it for the early learning encoun-ters. We argue for the informal-ways approach as it connects to Bayesian methods of inference and allows for a full concept of probability in comparison to the Informal Inference, which reduces probability to a mere frequentist concept and – based on this – restricts inference to a few special cases. We also develop a didactic framework for our analysis, which includes the approach of Tamás Varga.
Subject Classification: 97K10, 97K70, 97K50, 97D20
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Implementation opportunities of the Moodle learning management system in virtual environment the Sloodle project
275-293Views:30Using e-learning was firstly appeared in companies' sphere. It should be very useful if learning management systems were applied. Nowadays e-learning is used in different fields and gives useful informations in case of basics and its knowledge. It is essential to know the arranging technics and applicated handling methods of some supporting learning management systems of e-learning. The Moodle is the best-known learning management system.
The Second Life is one of the virtual environments which is useful in learning-teaching methods that is used in most educational institute all over the world. Sloodle is an open source project which connects the Second Life with Moodle learning management system. Sloodle is a kind of "bridge" in which different kind of activities and registering and provided in both Moodle and Second Life.
In our department, University of Debrecen Health Faculty of Nyíregyháza ILIAS learning management system has operated since February, 2008. In the interest of higher level education we decided to use and made available some courses through Moodle learning management system.
Some tools of Sloodle will be presented in our article. It will be the first study for our research in which we would use the Moodle learning management system, the virtual environment of Second Life and the project of Sloodle itself. Our article will contain the starting details and its statistical confirmation of our Sloodle project. We like to demonstrate that the results of the Sloodle-aided group are significantly better than the results of the control group in the most cases. -
Cultivating algorithmic thinking: an important issue for both technical and HUMAN sciences
107-116Views:28Algorithmic thinking is a valuable skill that all people should master. In this paper we propose a one-semester, algorithm-oriented computer science course for human science students. According to our experience such an initiative could succeed only if the next recipe is followed: interesting and practical content + exciting didactical methods + minimal programming. More explicitly, we suggest: (1) A special, simple, minimal, pseudo-code like imperative programming language that integrates a graphic library. (2) Interesting, practical and problem-oriented content with philosophical implications. (3) Exciting, human science related didactical methods including art-based, inter-cultural elements.