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Mathematische Bildung im Klagenfurter Doktorand(inn)enkolleg
67-84Views:80In 2003 we set up a programme for PhD-studies ("Doktorand(inn)enkolleg") at the University of Klagenfurt which should promote and support PhD-studies in the field of mathematics education.Within this programme it is worked on the topic "general mathematics education" from different perspectives.
In the first part of this paper intentions, the fields of work and the form of organisation are briefly demonstrated. The second and main part considers in detail the work in one of the four fields of work, and finally, the third and last part presents some experiences with regard to the contents as well as general ones. -
Analogous programming with a template class library
135-152Views:142In this paper, a template class library and its usage can be read. The classes of the library contain the C++ code of the algorithm of programming theorems. This library supports the implementation of the programs that are planned by analogous programming but the primary aim of its usage is to introduce the object-oriented programming style to show how a reusable code can be written with inheritances, overriding virtual methods, composition of objectcs and template parameters. -
Report of the conference "Connecting Tamás Varga’s Legacy and Current Research in Mathematics Education": November 6-8, 2019, Budapest, Hungary
5-8Views:327On the occasion of the 100th anniversary of the birth of the Hungarian mathematics educator, didactician and reform leader Tamás Varga, a conference on mathematics education has been organized in November 2019 and held at the Hungarian Academy of Science.
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Building a virtual framework to exploit multidisciplinary project workshops – peaks & pits
147-164Views:103Multidisciplinary project work in connection to industry is highly favoured at University education, since it prepares students to envision their spectrum of profession, to be able to participate in production projects in co-operation with partners out of campus, and learn to communicate between disciplines. An effctive combination presumes selection of right partners, set-up of proper virtual platform to bridge time, space, and diffrences in working styles. The set-up process requires several phases of design-based research proofing the melding process to produce a productive workshop that is sustainable. The paper describes the review of literature, the platform and set-up established, a first phase in bridging Art and Computer Science through the description of MOMELTE project, a critical evaluation in order to learn from mistakes, and a new list of design principles to improve the next phase of the workshop process. -
A first course in computer science: languages and goals
137-152Views:73The College Board Advanced Placement exam in computer science will use the language Java starting in fall 2003. The language chosen for this exam is based on the language commonly taught in introductory computer science courses at the university level. This article reviews the purpose of an introductory course and the various suggestions for the curriculum of introductory courses published by the Association for Computing Machinery. It then proposes that such a course stress foundational concepts over specific language syntax, and then provides a list of such foundational concepts and related topics. Based on this fundamental curriculum, the article recommends C++ as the most appropriate language. An appendix provides a sample syllabus. -
The "Teaching Mathematics and Computer Science" Journal logo's mathematical background
55-65Views:53In the present contribution we give an elementary technology for drawing the geodesics, paracycles and hypercycles on the pseudosphere. -
Facilitating class attendance to improve student achievements
77-90Views:78Many studies have revealed that attendance is strongly associated with students' achievements, and have proposed different strategies to improve students' attendance. However, there are few studies investigating how to efficiently take students' attendance – the key component to improve students' attendance. Taking attendance manually is inefficient since it will consume part of the limited class time. This paper describes the design and the implementation of an online attendance system that is currently used in classes at West Virginia University and California University of Pennsylvania. Examples of the system are provided online. Implementation codes of the system are shared, which can be used to teach computer science courses such as Web Programming or Client-Server Script Languages. -
Introductory Computer Programming Courses in Mathematics Curriculum
19-30Views:217We present the results of surveys and curricular research on introductory computer programming courses that are required or recommended for mathematics degrees at U.S. colleges and universities. Our target schools were those with populations between 5,000 and 20,000 undergraduate students. A key result is a synopsis of programming languages in use in these introductory courses with Java, Python and C + + holding the top three spots. We found that 85% of the 340 schools in our pool require or recommend an introductory programming course as a component of a mathematics degree. Furthermore, most of these introductory programming courses are taught by faculty outside of the mathematics department. These results indicate that mathematics faculty value computer programming and should be actively involved in setting learning outcomes, incorporating skills and concepts learned in introductory programming courses into subsequent mathematics courses, and determining programming languages in use.
Subject Classification: 97D30, 97P20, 97P40
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Development of classification module for automated question generation framework
89-102Views:130Automatic question generation is in the focus of recent researches which includes bordering disciplines like education, text mining, knowledge-engineering. The elaborated system generates multi-choice questions from textbooks without using an external semantic database. One of the base modules of the system is the classification module defining the extracted word. This paper describes modules of the framework including a detailed analysis of the classification part. We show the operability of the elaborated system through a practical test. -
Mobile devices in Hungarian university statistical education
19-48Views:164The methodological renewal of university statistics education has been continuous for the last 30 years. During this time, the involvement of technology tools in learning statistics played an important role. In the Introduction, we emphasize the importance of using technological tools in learning statistics, also referring to international research. After that, we firstly examine the methodological development of university statistical education over the past three decades. To do this, we analyze the writings of statistics teachers teaching at various universities in the country. To assess the use of innovative tools, in the second half of the study, we briefly present an online questionnaire survey of students in tertiary economics and an interview survey conducted with statistics teachers.
Subject Classification: 97-01, 97U70, 87K80
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The effect of augmented reality assisted geometry instruction on students' achiveement and attitudes
177-193Views:239In this study, geometry instruction's academic success for the students and their attitudes towards mathematics which is supported by education materials of Augmented Reality (AR) and its effect on the acceptance of AR and its usage by teachers and students have been researched. Under this research, ARGE3D software has been developed by using augmented reality technology as for the issue of geometric objects that is contained in the mathematics curriculum of 6th class of primary education. It has been provided with this software that three-dimensional static drawings can be displayed in a dynamic and interactive way. The research was conducted in two different schools by an experiment and control group. In the process of data collection, Geometry Achievement Test (GAT), Geometric Reasoning Test (GRT), Attitudes Scale for Mathematics (ASM), students' math lecture notes, semi-structured interviews with teachers and students and observation and video recordings were used. Results showed that geometry instruction with ARGE3D increased students' academic success. In addition, it was found that geometry instruction with ARGE3D became more effective on students' attitudes that had negative attitudes towards mathematics and it also provided support to reduce fear and anxiety. -
E-learning management systems in Hungarian higher education
357-383Views:69Computers, informatics, and information technology have an ever-increasing role in the establishment and spread of new educational forms and methods. The role of e-learning as a new educational model is increasing in the world of computer networks, because of a widespread access to the net and a growing demand for learning beside work.
Technological elements of e-learning can be separated as Learning Management System, authoring system, course material and a browser. Learning Management System is the software package that creates the structure of the whole educational process: course organisation, course material presentation, tracking student work, recording results, and the completion of the program.
This publication shows examples of Learning Management Systems used in Hungarian higher education. Summarizing and systematizing expectations and demands expressed in connection with learning management systems, the present work tries to help the reader orientate on an ever-expanding market. -
Practice based course of Information Technology Service Management for BSc students
229-246Views:78Currently 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. -
Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: January 24-26, 2020 Sárospatak, Hungary
243-271Views:195The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Sárospatak, Hungary, on the Comenius Campus of the Eszterházy Károly University, from the 24th to the 26th of February, 2020. It was organized by the Doctoral School of Mathematical and Computational Sciences of University of Debrecen and the Eszterházy Károly University. The 76 participants – including 15 PhD students – came from 9 countries, 23 cities and represented 33 institutions of higher and secondary education. There were 4 plenary, 48 session talks and 4 poster presentations in the program.
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Teaching multiparadigm programming based on object-oriented experiences
171-182Views:111Multiparadigm 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. -
Comparing the IT skills and the programming knowledge of Hungarian students specialized in informatics with Romanian students attending a science course or a mathematics-informatics course
21-40Views:115The goal of this research is an analysis of the IT skills and programming knowledge of Hungarian and Romanian students attending a Science course or a Mathematics-Informatics course. Analysed was how effectively can students from different grades answer questions dealing with different subjects. After having evaluated the test results correctness of the original presumption emerged. Significance level was 5% through the analysis. Significant divergency in knowledge of Hungarian students and Romanian students of Humanities (Profil Uman) was found in 11th and 12th grades too. Romanian students attending a science course (Profil Real) and a Mathematics-Informatics course scored higher in programming than their Hungarian counterparts specialized in Informatics in the 11th grade. After the evaluation a final conclusion can be made: Romanian students of the Real Profile have the same or more practice in programming than Hungarian students specialized in Informatics, though the latters have the same or better IT skills. Unfortunately, Hungarian teachers concentrate on word processing and spreadsheet calculation and teach programming just for the students specialized in Informatics, although algorithm thinking would be important for every student before finishing secondary school. -
Psychology - an inherent part of mathematics education
1-18Views:233On the chronology of individual stations of psychology and their effect on mathematics education designed as working document for use in teacher training.
The article is structured as a literature survey which covers the numerous movements of psychology towards mathematics education. The current role of psychology in mathematics education documented by different statements and models of mathematics education should provide a basis for the subsequent investigations. A longitudinal analysis pausing at essential marks takes centre of the continuative considerations. The observed space of time in the chapter covers a wide range. It starts with the separation of psychology from philosophy as a self-contained discipline in the middle of the 19th and ends with the beginning of the 21st century. Each stop states the names of the originators and the branches of psychology they founded. These stops are accompanied by short descriptions of each single research objective on the one hand, and their contributions to mathematics education on the other hand. For this purpose, context-relevant publications in mathematics education are integrated and analysed. The evaluation of the influence of concepts of psychology on teaching technology in mathematics is addressed repeatedly and of great importance. The layout of this paper is designed for the use as a template for a unit in teacher-training courses. The conclusion of the article where the author refers to experiences when teaching elements of psychology in mathematics education courses at several universities in Austria is intended for a proof on behalf of the requested use.Subject Classification: 01A70, 01-XX, 97-03, 97D80
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Report of conference XXXVIII. National Conference on Teaching Mathematics, Physics and Computer Sciences: August 25-27, 2014 Pécs, Hungary
281-303Views:89The XXXVIII. National Conference on Teaching Mathematics, Physics and Computer Sciences (MAFIOK) was held in Pécs, Hungary between 25 and 27 August, 2014 at the Pollack Mihály Faculty of Engineering and Information Technology. It was organized by the Engineering Mathematics Department. The 65 participants – including 4 invited lecturers and 53 lecturers – came from 2 countries and represented 14 institutions of higher education. -
Programming theorems on enumerator
89-108Views:131This paper deals with the examination of the programming patterns best known by programmers: the programming theorems. It is a significant issue that in what way these patterns can be formulated in order to solve a relatively broad spectrum of problems using a small number of patterns. In this paper, the well known programming theorems are applied to the processing of enumerators. To this end, the robustness of patterns gained this way will be presented, and it will be also pointed out how the programs thus constructed can be implemented in the modern object-oriented programming environments: in language C++, Java and C#. -
Interdisciplinary Secondary-School Workshop: Physics and Statistics
179-194Views:135The paper describes a teaching unit of four hours with talented students aged 15-18. The workshop was designed as a problem-based sequence of tasks and was intended to deal with judging dice whether they are regular or loaded. We first introduced the students to the physics of free rotations of rigid bodies to develop the physics background of rolling dice. The highlight of this part was to recognise that cubes made from homogeneous material are the optimal form for six-sided objects leading to equal probabilities of the single faces. Experiments with all five regular bodies would lead to similar results; nevertheless, in our experiments we focused on regular cubes. This reinsures that the participants have their own experience with the context. Then, we studied rolling dice from the probabilistic point of view and – step-by-step – by extending tasks and simulations, we introduced the idea of the chi-squared test interactively with the students. The physics and the statistics part of the paper are largely independent and can be also be read separately. The success of the statistics part is best described by the fact that the students recognised that in some cases of loaded dice, it is easier to detect that property and in other cases one would need many data to make a decision with small error probabilities. A physical examination of the dice under inspection can lead to a quick and correct decision. Yet, such a physical check may fail for some reason. However, a statistical test will always lead to reasonable decision, but may require a large database. Furthermore, especially for smaller datasets, balancing the risk of different types of errors remains a key issue, which is a characteristic feature of statistical testing.
Subject Classification: F90, K90, M50, R30
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The role of computer in the process of solving of mathematical problems (results of research)
67-80Views:119We 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. -
Nice tiling, nice geometry!?!
269-280Views:100The squared papers in our booklets, or the squared (maybe black and white) pavements in the streets arise an amusing problem: How to deform the side segments of the square pattern, so that the side lines further remain equal (congruent) to each other? More precisely, we require that each congruent transformation of the new pattern, mapping any deformed side segment onto another one, leaves the whole (infinitely extended) pattern invariant (unchanged).
It turns out that there are exactly 14 types of such edge-transitive (or so-called isotoxal) quadrangle tilings, sometimes with two different forms (e.g. black and white) of quadrangles (see Figure 2). Such a collection of tiling can be very nice, perhaps also useful for decorative pavements in streets, in flats, etc.
I shall sketch the solution of the problem that leads to fine (and important) mathematical concepts (as barycentric triangulation of a polygonal tiling, adjacency operations, adjacency matrix, symmetry group of a tiling, D-symbol, etc). All these can be discussed in an enjoyable way, e.g. in a special mathematical circle of a secondary school, or in more elementary form as visually attractive figures in a primary school as well.
My colleague, István Prok [11] developed an attractive computer program on the Euclidean plane crystallographic groups with a nice interactive play (for free download), see our Figures 3-5.
A complete classification of such Euclidean plane tilings (not only with quadrangles) can be interesting for university students as well, hopefully also for the Reader (Audience). This is why I shall give some references, where you find also other ones.
Further problems indicate the efficiency of this theory now. All these demonstrate the usual procedure of mathematics and the (teaching) methodology as well: We start with a concrete problem, then extend it further, step-by-step by creating new manipulations, concepts and methods. So we get a theory at certain abstraction level. Then newer problems arise, etc.
This paper is an extended version of the presentation and the conference paper [7]. The author thanks the Organizers, especially their head Professor Margita Pavlekovic for the invitation, support and for the kind atmosphere of the conference. -
Report of Meeting Researches in Didactics of Mathematics and Computer Sciences, April 1-3, 2022 Baja, Hungary
135-155Views:254The 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.
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Radio Frequency Identification from the viewpoint of students of computer science
241-250Views:94This 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. -
Using the computer to visualise graph-oriented problems
15-32Views:106The computer, if used more effectively, could bring advances that would improve mathematical education dramatically, not least with its ability to calculate quickly and display moving graphics. There is a gap between research results of the enthusiastic innovators in the field of information technology and the current weak integration of the use of computers into mathematics teaching.
This paper examines what exactly the real potentials of using some mathematics computer software are to support mathematics teaching and learning in graph-oriented problems, more specifically we try to estimate the value added impact of computer use in the mathematics learning process.
While electronic computation has been used by mathematicians for five decades, it has been in the hands of teachers and learners for at most three decades but the real breakthrough of decentralised and personalised micro-computer-based computing has been widely available for less than two decades. And it is the latter facility that has brought the greatest promise for computers in mathematics education. That computational aids overall do a better job of holding students' mathematical interest and challenging them to use their intellectual power to mathematical achievement than do traditional static media is unquestionable. The real question needing investigation concerns the circumstances where each is appropriate.
A case study enabled a specification of advantages and obstacles of using computers in graph-oriented questions. Individual students' interviews revealed two less able students' reactions, difficulties and misinterpretations while using computers in mathematics learning.
Among research outcomes is that the mathematical achievement of the two students observed improved and this makes teaching with computers an overriding priority for each defined teaching method.
This paper may not have been realised without the valuable help of the Hungarian Eötvös State Grant.
