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• Forming the concept of congruence I.

  181-192

  Éva Szeredi

  Views:

  9

  Teaching 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.

• Various systems in a single mathematical model

  1-13

  Gábor Geda

  Views:

  4

  Our aim is to study differential equations and systems described by them which have great historical importance and are considered to be fundamental on different levels of education.
  Due to their simplicity these are suitable for those who deal with this topic and want to gain useful experience in this field.
  Furthermore, our aim is to give these equations a general form which facilitates the studying of the different models by computer even for an individual programmer. At the same time it facilitates the use of different mathematical auxiliary-programmes.
  By giving the equations this way we get a chance of studying the relations between the individual systems.

• Analysis of a problem in plane geometry discussed in an 11th grade group study session

  181-193

  Richárd Rakamazi

  Views:

  27

  The main aim of this paper is to show those strategies and proof methods we try to teach in secondary maths education through an interesting geometric problem: Find a relation for the sides of a triangle where an angle is the double of another angle. Is the converse also true? Is it possible to generalize the problem? We try to answer these questions while discussing the upcoming difficulties in detail and presenting more possible solutions. Hopefully the paper can be successfully used in study group sessions and problem solving seminars in secondary schools.

• Fostering engineering freshmen’s shifts of attention by using Matlab LiveScript for solving mathematical tasks

  1-14

  Giovannina Albano

  Agnese Ilaria Telloni

  Views:

  104

  We designed an experimental path including a summative assessment phase, where engineering freshmen are involved in solving mathematical tasks by using Matlab LiveScripts. We analyzed the students’ answers to a questionnaire about their perceived impact of the use of Matlab on their way to solve mathematical tasks. The main result is that students show shifts of attention from computations to other aspects of problem solving, moving from an operational to a structural view of mathematics.

  Subject Classification: 97U70, 97H60

• Metadata formats and the new markup language from library field

  85-102

  Marianna Salgáné Medveczki

  Views:

  6

  Using new communication technologies libraries must face continuously new questions, possibilities and expectations. This study discusses some library-related aspects of our electronic era and how computer-related data formats affect bibliographic dataprocessing to give a survey of the most important results.
  Altough library systems have been supporting the creation and maintenance of MARC records for decades, the need to create other forms of metadata is relatively new. In higher education it is important that students get acquainted with these new aspects of bibliographic description and bibliographic dataprocessing.
  In our department I launched the BDML development project in order to standardize bibliographic description (based on Hungarian standard 3424/1) with the help of XML. The development aims at the creation of a set of standards that provides information about the structure of bibliographic description in XML form. In the second part of the paper I give a brief presentation and summary of BDML.

• How to teach testing?

  215-232

  Tibor Gregorics

  Krisztián Mózsi

  Rudolf Szendrei

  Views:

  22

  Testing methodology is an important part of IT education. It is desired to show the beginner programmer students the advantage of testing by having them do only a small amount of work. In this paper, we will show how to make testing as a part of programming in simple exercises. These exercises are solved with the analogous programming technique, which is based on programming theorems over enumerators. We have elaborated grey-box test cases for the programs which have been developed based on programming theorems. These test cases can be taught together with the programming theorems, and they can serve as a standard testing procedure for programmers. We also suggest a test tool to automatize test runs, and we will discuss its usage in a short case study.

• Heuristic arguments and rigorous proofs in secondary school education

  167-184

  Zsolt Fülöp

  Views:

  31

  In 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.

• Teaching word processing – the practice

  247-262

  Mária Csernoch

  Views:

  20

  I compared two surveys, which were aimed to check the word processing ability of students in high schools and universities. The surveys were carried out ten years apart from one another, in 1997 and 2006. The results clearly show that most of the students are not able to use word processors properly. In the survey of 1997 I found explanation for this underperformance in the lack of computers and teachers. However, the results of the second survey did not prove any better than the results of the first, and in 2006 neither the number of computers nor the number of teachers can be blamed. What else then? I suggest that the reason for this general ignorance, for this `modern illiteracy' is the ignorance of the teachers. Until the teachers are not prepared and the senior students of the universities leave the education system without a proper knowledge of the required subjects, there is little chance that they would be able to teach word processing at a satisfactory level.

• Teaching multiparadigm programming based on object-oriented experiences

  171-182

  Zoltán Porkoláb

  Viktória Zsók

  Views:

  25

  Multiparadigm programming is an emerging practice in computer technology. Co-existence of object-oriented, generic and functional techniques can better handle variability of projects. The present paper gives an overview of teaching multiparadigm programming approach through typical language concepts, tools in higher education. Students learning multiparadigm-oriented subjects would gain considerable expertise, which is highly needed by the industrial side in large-scale application development.

• Learning and teaching combinatorics with Sage

  389-398

  István Vajda

  Views:

  44

  Learning Mathematics is not an easy task, since this subject works with especially abstract concepts and sophisticated deductions. Many students lose their interest in the subject due to lack of success. Computer algebra systems (CAS) provide new ways of learning and teaching Mathematics. Numerous teachers use them to demonstrate concepts, deductions and algorithms and to make learning process more interesting especially in higher education. It is an even more efficient way to improve the learning process, if students can use the system themselves, which helps them to practice the curriculum.
  Sage is a free, open-source math software system that supports research and teaching algebra, analysis, geometry, number theory, cryptography, numerical computation, and related areas. I have been using it for several years to aid the instruction of Discrete Mathematics at Óbuda University. In this article I show some examples how representations provided by this system can help in teaching combinatorics.

• Teaching of problem-solving strategies in mathematics in secondary schools

  139-164

  Ildikó Kozákné Székely

  Views:

  8

  In the Hungarian mathematics education there is no explicit teaching of problem-solving strategies. The best students can abstract the strategies from the solutions of concrete problems, but for the average students it is not enough. In our article we report about a developmental research. The topic of the research was the explicit teaching of two basic strategies (forward method, backward method). Based on our experiences we state that it is possible to increase the effectivity of students' problemsolving achievement by teaching the problem-solving strategies explicitly.

• Würfel und Augensummen – ein unmögliches Paar

  71-88

  Stefan Götz

  Views:

  26

  It is well known that the values 2, 3, ..., 12 of the sum of eyes that appear when throwing two regular dice are not equally distributed. It can also be shown that no matter how the dice are falsified (or if only one of them is being manipulated) they can never reach the same probability concerning the sum of eyes ([8], 91 et seq.). This discovery can be generalized for n ≥ 2 dice. Various results of algebra and (real) calculus are used, so that a connection between two different mathematical fields can be realized. Such a connection is typical and often provides a large contribution for mathematics (because it frequently leads to a successful attempt of solving a special problem) and therefore examples of this sort should also be included in the mathematical education at schools as well as in the student teachers' university curriculum for the study of mathematics.

• Young women's barriers to choose IT and methods to overcome them - A case study from Hungary

  77-101

  Anna Szlávi

  Péter Bernát

  Views:

  175

  Women'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

• A role of geometry in the frame of competencies attainment

  41-55

  Ivan Anić

  Neda Bokan

  Tijana Šukilović

  Srdjan Vukmirović

  Views:

  29

  We discuss aspects of the Education Reform from teaching to educational system. In this context we recognize some problems in recognition of some competencies that students need to achieve and we present how we have developed the measurement method of spatial abilities and problem solving competence. Especially, we investigate how students use spatial visualization abilities in solving various problems in other mathematical course. We have tested how students use their spatial abilities previously developed in geometry courses based on conceptual approach to solve a test based on procedural concept in Mathematical Analysis course.

• Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 28 – January 30, 2011, Satu Mare, Romania

  159-179

  T. Baranyai

  E. Herendiné Kónya

  Views:

  12

  The 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.

• Mathematical Laboratory: Semiotic mediation and cultural artefacts in the mathematics classroom

  183-195

  Maria G. Bartolini Bussi

  Views:

  91

  Aim of this presentation is to summarize the influence of Tamas Varga on the Italian research and practice concerning didactics of mathematics since the 70s of the 20th centuries. While being in Budapest for the Conference I noticed that this influence was not known by most Hungarian mathematics educators. I guess that also in Italy, only the teacher educators of my generation know Varga’s influence on the teaching and learning of mathematics in primary school. Hence I start from a brief summary of development of mathematics curriculum in Italy (mainly in primary school) in the last decades of the 20th century. I focus some elements that may be connected with Varga’s influence and, later, some recent development of them.

  Subject Classification: 97G20, 97-U6, 97A40

• Teaching model-based testing

  1-17

  Gábor Árpád Németh

  Views:

  1205

  Different testing methodologies should play an important role in the education of informatics. In the model-based testing (MBT) approach, the specification of the system is described with a formal model. This model can be used to revise the correctness of the specification and as a starting point for automatic test generation. The main problem with MBT is however, that there is a huge gap between theory and practice and that this approach has a high learning curve. To cope with these problems, current paper shows, how the MBT approach can be introduced to students through a small scale example.

  Subject Classification: P50

• Transition from arithmetic to algebra in primary school education

  225-248

  Zsolt Fülöp

  Views:

  35

  The 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.

• Comments on the remaining velocity project with reports of school-experiments

  117-133

  Ödön Vancsó

  Attila Komzsík

  Csaba Csapodi

  Views:

  14

  The aim of this article is to introduce different possible solutions to the exercise referring to the calculation of "remaining velocity". We explain the possible approaches to the problem with the help of either using the tools of mathematics or other subjects. During the past few years, we have made Hungarian and Slovakian secondary school students solve the exercise, choosing from both children of average and of high abilities. The experince has shown that very few students were able to solve the problem by themselves, but with the help of their teachers, the exercise and the solution has been an eye-opener experience to all of them. A lot of students were even considering to drive more carefully in the future after getting their driving licenses.

• CALIBRATE and CAS/DGS resources

  267-279

  Vladimir Batagelj

  Iztok Kavkler

  Matija Lokar

  Views:

  28

  The CALIBRATE project was initiated by the EU with the goal of expanding the use of ICT in education by increasing the amount of available learning resources via resource exchange. Although CAS/DGS can be used to easily create high quality learning resources which are also easily adaptable across national boundaries, such resources are difficult to find at CALIBRATE portals. We believe that this is due to CAS/DGS still being rather exotic to most of the people as well as with the common problem of finding existing appropriate resources. A possible solution is for CALIBRATE portals to properly equip existing and forthcoming CAS/DGS resources with suitable metadata and to provide some integration with CAS/DGS tools, enabling both beginners and power users to create and exchange CAS/DGS resources.

• 14 to 18-year-old Hungarian high-school students' view of mathematicians appearing in the media - a case study

  183-194

  Orsolya Dóra Lócska

  Zoltán Kovács

  Views:

  10

  One way to develop positive attitude toward STEM subjects that popular media, including movies and films can be engaged to promote more positive and inclusive STEM images. The movie Hidden numbers offers an opportunity to explore the representations of scholars, especially mathematicians within a biographical drama. Focusing on 5 characters, this article first discusses whether these characters fit into stereotypical scientist image or not. Secondly, we examine how high school students evaluate these characters. We argue that this movie is suitable to promote positive attitude toward STEM subjects.

• Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 24-26, 2014 Eger, Hungary

  117-134

  E. Herendiné Kónya

  I. Oláhné-Téglási

  Views:

  13

  The meeting Researches in Didactics of Mathematics and Computer Sciences
  was held in Eger, Hungary from the 24th to the 26th of January, 2014 at the
  Eszterházy Károly College. It was organized by the PhD School of Mathematics and Computer Sciences of the University of Debrecen and the Eszterházy Károly College in Eger.
  The 58 participants – including 43 lecturers and 18 PhD students – came from 7 countries, 15 cities and represented 22 institutions of higher education.

• Practice based course of Information Technology Service Management for BSc students

  229-246

  Krisztina Erdélyi

  Views:

  11

  Currently IT systems are primarily observed as sets of services, for example finance services can be accessed via the Internet. The IT background of an enterprise has strategic importance in its activity, but it is also important, that IT helps the enterprise supporting course of business really from the background. To implement this kind of conception, IT Infrastructure Library (ITIL) provides practical advices.
  The paper describes the topic of an optional course which introduces BSc students to the subject of IT Service Management the way that it can be used as a practice supplement beside theory courses of IT Service Management.

• Teaching polygons in the secondary school: a four country comparative study

  29-65

  Éva Szeredi

  Judit Török

  Views:

  38

  This study presents the analysis of four sequences of videotaped lessons on polygons in lower secondary schools (grades 7 and 8) taught by four different teachers in four different countries (Belgium, Flanders, England, Hungary and Spain). Our study is a part of the METE project (Mathematics Educational Traditions in Europe). The aims and methodology of the project are described briefly in the introduction. In the next section of this paper we describe various perspectives on teaching and learning polygons which were derived from the literature, concerning the objectives, conceptual aspects and didactic tools of the topic. The next two sections introduce the main outcomes of our study, a quantitative analysis of the collected data and a qualitative description linked to the perspectives on teaching polygons. We conclude by discussing some principal ideas related to the theoretical and educational significance of this research work.

• Gaussian iteration of mean values and the existence of 2^(1/2)

  35-42

  Zoltán Daróczy

  Views:

  33

  We propose a method for proving the existence of √2 and finding its approximate value in secondary education.