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• Radio Frequency Identification from the viewpoint of students of computer science

  241-250

  Miklós Hoffmann

  Tibor Juhász

  Tünde Taskó

  Views:

  8

  This paper aims at creating the right pedagogical attitudes in term of teaching a new technology, Radio Frequency Identification (RFID) by evaluating the social acceptance of this new method. Survey of future teachers, students of teacher master studies and students from informatics oriented secondary schools were surveyed comparing their attitudes in terms of RFID to other recent technologies. Consequences of this survey are incorporated into the curriculum of the new RFID course at our institution.

• Some thoughts on a student survey

  41-59

  István Molnár

  Views:

  26

  The paper analyzes a survey of college students and describes its major findings. The object of the survey, involving 154 students, was to discover and highlight the problems that arise in taking the course Economic Mathematics I. The paper, as the summary of the first phase of a research project, wishes to present these problems, ways that may lead out of them, and possible means of help that can be offered to those taking the course.

• Constructing the disk method formula for the volume obtained by revolving a curve around an axis with the help of CAS

  363-376

  Muharrem Aktümen

  Tolga Kabaca

  Views:

  26

  Calculus concepts should have been taught in a carefully designed learning environment, because these concepts constitute a very important base for almost all applied sciences. The integral, one of the fundamental concepts of Calculus, has a wide application area. This paper focuses on constructing the disk method formula for the volume obtained by revolving a curve around an axis with the help of a CAS.
  In this study, a semi-structured interview was carried out. In this interview, we tried to construct the disk method formula.
  The levels of constructing the disk method formula in this study are:
  • Introducing the concept: evaluating the volume of an Egyptian pyramid.
  • Evaluating the volume of a cone obtained by revolution (using Maple worksheet).
  • Designing their own ring and evaluating its price (using Maplet).
  In this study, the interview has been presented as a dialog between teacher and students. When we look at feedback from students, we see that such a teaching method effects students in a positive way and causes them to gain conceptual understanding directed towards the concepts of approximation and volume.

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

  139-164

  Ildikó Kozákné Székely

  Views:

  7

  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.

• Why some children fail? Analyzing a test and the possible signs of learning disorders in an answer sheet: dedicated to the memory of Julianna Szendrei

  251-268

  Katalin Fried

  Views:

  12

  Teachers and educators in mathematics try to uncover the background of the mistakes their students make for their own and their students' benefit. Doing this they can improve their teaching qualities, and help the cognitive development of their pupils. However, this improvement does not always support their students with learning disorders, since their problem is not caused by wrong attitude or lack of diligence. Therefore, it is the interest of a conscientious teacher to recognize whether the weaker performance of a student is caused by learning disorders, so the helping teacher can give useful advices. Although the teacher is not entirely responsible for the diagnosis, but (s)he should be be familiar with the possible symptoms in order to make suggestions whether or not to take the necessary test of the learning disorders.
  In this article, through examining a test and the answer sheet of a single student, I show some signs that might be caused by learning disorders.

• Teaching of old historical mathematics problems with ICT tools

  13-24

  Tünde Kántor

  Anna Tóth

  Views:

  15

  The aim of this study is to examine how teachers can use ICT (information and communications technology) tools and the method of blended learning to teach mathematical problem solving. The new Hungarian mathematics curriculum (NAT) emphasizes the role of history of science, therefore we chose a topic from the history of mathematics, from the geometry of triangles: Viviani's Theorem and its problem field. We carried out our teaching experiments at a secondary school with 14-year-old students. Students investigated open geometrical problems with the help of a dynamic geometric software (GeoGebra). Their research work was similar to the historical way.

• Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 25-27, 2013 Oradea, Romania

  123-143

  E. Herendiné Kónya

  E. Debrenti

  Views:

  9

  The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Oradea, Romania from the 25th to the 27th of January, 2013 at the Partium Christian University. It was organized by the PhD School of Mathematics and Computer Sciences of the University of Debrecen and the Partium Christian University in Oradea. The meeting was supported by the project: TAMOP-4.2.2/B/10/1-2010-0024.
  The 61 participants – including 50 lecturers and 21 PhD students – came from 5 countries, 22 cities and represented 35 intstitutions of higher education.

• Sequenced problems for functional equations

  179-192

  Zsolt Ádám

  Károly Lajkó

  Gyula Maksa

  Fruzsina Mészáros

  Views:

  9

  There are many possible methods to solve equations of the form H(f(x + y), f(x − y), f(x), f(y), x, y) = 0 (x, y 2 R), where H is a known function and f is the unknown function to be determined. Here we will create a sequence of problems for equations of type (1) (see on the next page). These sequenced problems are appropriate for the fostering of talented students on different level of mathematical education.

• Report of Meeting Researches in Didactics of Mathematics and Computer Sciences, April 1-3, 2022 Baja, Hungary

  135-155

  E. Kónya

  M. Kiss

  Views:

  151

  The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Baja, Hungary, at Eötvös József College, from the 1st to the 3th of April, 2022. It was organized by the Doctoral School of Mathematical and Computational Sciences of the University of Debrecen and by Eötvös József College. The 62 participants - including 18 PhD students - came from 8 countries and represented 26 institutions of higher and secondary education. There were 3 plenary and 40 session talks in the program.

• 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:

  9

  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.

• Zbigniew Michalewicz - Matthew Michalewicz: Puzzle Based Learning: An introduction to critical thinking, mathematics, and problem solving. Hybrid Publishers Melbourne 2008 (Book review)

  415-420

  András Ambrus

  Views:

  30

  Based on their experiences with engineering, mathematics, computer science, business students concerning the puzzle based learning in different countries the authors summarize their main problem solving teaching ideas. With help of interesting, motivating, nice problems they analyze the main mathematical principles and problem types. The review gives an overview about the main ideas, results of an interesting book.

• Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 20 - January 22, 2012, Levoča, Slovakia

  205-230

  E. Herendiné Kónya

  Views:

  20

  The 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.

• 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:

  6

  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.

• Maximum and minimum problems in secondary school education

  81-98

  Zsolt Fülöp

  Views:

  29

  The aim of this paper is to offer some possible ways of solving extreme value problems by elementary methods with which the generally available method of differential calculus can be avoided. We line up some problems which can be solved by the usage of these elementary methods in secondary school education. The importance of the extremum problems is ignored in the regular curriculum; however they are in the main stream of competition problems – therefore they are useful tools in the selection and development of talented students. The extremum problem-solving by elementary methods means the replacement of the methods of differential calculus (which are quite stereotyped) by the elementary methods collected from different fields of Mathematics, such as elementary inequalities between geometric, arithmetic and square means, the codomain of the quadratic and trigonometric functions, etc. In the first part we show some patterns that students can imitate in solving similar problems. These patterns could also provide some ideas for Hungarian teachers on how to introduce this topic in their practice. In the second part we discuss the results of a survey carried out in two secondary schools and we formulate our conclusion concerning the improvement of students' performance in solving these kind of problems.

• The investigation of students' skills in the process of function concept creation

  249-266

  Gyöngyi Szanyi

  Views:

  17

  Function is a basic concept of mathematics, in particular, mathematical analysis. After an analysis of the function concept development process, I propose a model of rule following and rule recognition skills development that combines features of the van Hiele levels and the levels of language about function [11]. Using this model I investigate students' rule following and rule recognition skills from the viewpoint of the preparation for the function concept of sixth grade students (12-13 years old) in the Ukrainian and Hungarian education system.

• Online tests in Comprehensive Exams – during and after the pandemic

  77-93

  Adrienn Vámosiné Varga

  Views:

  67

  The Covid-19 pandemic accelerated the development of electronic (e-learning) assessment methods and forced their use worldwide. Many instructors and students had to familiarize themselves with the form of distance education. During and since Covid-19 in Hungary, at the Faculty of Engineering of the University of Debrecen, the written part of the Comprehensive Exam in Mathematics is organized in a computer lab of the university using an online test. Our goal is that the results of the tests may be as reliable as possible in terms of measuring the students’ knowledge, and thus the grades given based on the test results would be realistic. In this paper, we show the analysis of a sample written exam and compare the real exam results of students who were prepared for the comprehensive exam during Covid-19 and who have participated in face-to-face education since then. The tools provided by the Moodle system necessary for comparison are also presented.

  Subject Classification: 97D40, 97D70, 97U50

• Concept systematization with concept maps in data modelling

  149-166

  Márta Czenky

  János Kormos

  Views:

  36

  An important goal of concept learning is that students can allocate concepts in the hierarchical system of concepts. In the data modelling course, first, we supported concept systematization with worksheets in which the students had to fill in the blank hierarchical figures of classification of the concepts or blank Venn diagrams describing the relationships between concepts. The hierarchical systems, however, are somewhat restricted to the description of connections. The filling in Venn diagrams did not deliver the expected result, so our attention turned to concept maps. In this paper we introduce the concept maps we drew. Then we evaluate the results of concept mapping survey conducted among students. The survey was done in three courses. We compare the results of our survey with the result of an earlier concept systematising survey.

• Teaching probability theory by using a web based assessment system together with computer algebra

  81-95

  Anna Takács Klingné

  Views:

  33

  In the course of Maths Basics 2, the Faculty of Economic Science students of Kaposvár University learn the classical chapters of Probability Theory, namely random variables and the well-known probability distributions. Our teaching experiences show that students' achievement is weaker in case of problems concerning continuous random variables. From school year 2012/13 we have had an opportunity to take Maple TA, the web-based test- and assessment system, into the course of education. It is sufficient for the users of Maple TA to have a browser. Maple computer algebra system, which runs on the server, assesses students' answers in an intelligent way, and compares them with the answers that are considered correct by the teacher. In our presentation we introduce some elements of Maple TA system, the didactic considerations the test sheets were made by, as well as our research results concerning the use of Maple TA.

• The role of computer in the process of solving of mathematical problems (results of research)

  67-80

  Henryk Kąkol

  Tadeusz Ratusiński

  Views:

  30

  We would like to present results of an almost two years investigations about the role computer in the process of solving of mathematical problems. In these investigations took part 35 students of the secondary school (generalists) in the age 17–19 years. Each of these students solved following problem:
  Find all values of the parameter m so that the function
  f(x) = |mx + 1| − |2x − m| is:
  a) bounded,
  b) bounded only from the bottom,
  c) bounded only from above,
  first without a computer and next with a special computer program. We would like to show results of these researches.

• Examining continuity/discontinuity of a function by using GeoGebra

  241-257

  Ljubica Dikovic

  Views:

  24

  The possibility to visualize the things with the help of today's dynamic software (GeoGebra being one of them), enables the students to see and explore mathematical relations and concepts that were difficult to be presented in the past, prior to the state-of-the-art technologies. In methodological sense, the contribution of this paper lies in the presentation of a set of visualizations designed to help students better understand and explore the basic calculus concepts such as continuity at a point, to examine discontinuity at a point, to display discontinuities and the relations between continuity and differentiability of single variable functions. In technical sense, this paper presents creative GeoGebra applets which offer new possibilities that could be of a vital importance for the future development of e-learning of College mathematics.

• The hyperbola and Geogebra in high-school instruction

  277-285

  Eugen Ljajko

  Milan Mihajlović

  Zlatka Pavličić

  Views:

  30

  In this article the results of teaching/learning hyperbola and its characteristics in high-school using computers and GeoGebra are shown. Students involved in the research attend Engineering School "Nikola Tesla" in Leposavic, Serbia. The aim of the research was to define ways and volume of computer and GeoGebra usage in mathematics instruction in order to increase significantly students' mathematical knowledge and skills.

• Comparative geometry on plane and sphere: didactical impressions

  81-101

  Ágnes Makara

  István Lénárt

  Views:

  2

  Description of experiences in teaching comparative geometry for prospective teachers of primary schools. We focus on examples that refer to changes in our students' thinking, in their mathematical knowledge and their learning and teaching attitudes. At the beginning, we expected from our students familiarity with the basics of the geographic coordinate system, such as North and South Poles, Equator, latitudes and longitudes. Spherical trigonometry was not dealt with in the whole project.

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

  1-14

  Giovannina Albano

  Agnese Ilaria Telloni

  Views:

  94

  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

• Group Work at High School According to the Method of Tamás Varga

  167-176

  Eszter Kovács-Kószó

  József Kosztolányi

  Views:

  74

  The 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

• Why do we complicate the solution of the problem? reflection of Finnish students and teachers on a mathematical summer camp

  405-415

  András Ambrus

  István Hortobágyi

  Marjatta Näätänen

  Riitta Liira

  Maija Salmela

  Views:

  29

  This paper deals with reactions and reflections of Finnish secondary school students and teachers on Hungarian mathematics teaching culture. The experiences were collected at a mathematics summer camp in Hungary.