Articles

• Approximated Poncelet configurations

  163-176

  Örs Nagy

  Szilárd András

  Views:

  39

  In this short note we present the approximate construction of closed Poncelet configurations using the simulation of a mathematical pendulum. Although the idea goes back to the work of Jacobi ([17]), only the use of modern computer technologies assures the success of the construction. We present also some remarks on using such problems in project based university courses and we present a Matlab program able to produce animated Poncelet configurations with given period. In the same spirit we construct Steiner configurations and we give a few teaching oriented remarks on the Poncelet grid theorem.

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  6

• The effect of augmented reality assisted geometry instruction on students' achiveement and attitudes

  177-193

  Emin İbili

  Sami Şahin

  Views:

  77

  In 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.

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  33

• Live & Learn: When a wrong program works

  195-208

  Tibor Gregorics

  Views:

  28

  In this paper an interesting and surprising case study of my programming education practice is presented. This case underlines the importance of methods, standards and rules of thumb of the programming process. These elements of the programming technology can be taught well in education and they can guarantee the quality of the implemented programs. However the case described in this paper brings an anomaly when a programming standard is violated during the programming process and, although it should imply that the implemented program code works badly, the program works perfectly. This anomaly is caused by a typical implementation problem: the boundary and rules of the machine representation of numbers. This anomaly is going to be analyzed and the appropriate conclusions of our case study will be deducted.

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  2

• Number theory vs. Hungarian high school textbooks: the fundamental theorem of arithmetic

  209-223

  Petra Csányi

  Kata Fábián

  Csaba Szabó

  Zsanett Szabó

  Views:

  21

  We investigate how Hungarian highschool textbooks handle basic notions and terms of number theory. We concentrate on the presentation of the fundamental theorem of arithmetic, the least common multiple and greatest common divisor. Eight families of textbooks is analyzed. We made interviews with the authors of four of them. We conclude that a slightly more precise introduction would not be harmful for pupils and could bring basic number theory closer to them.

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  13

• Transition from arithmetic to algebra in primary school education

  225-248

  Zsolt Fülöp

  Views:

  38

  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.

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  7

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

  249-266

  Gyöngyi Szanyi

  Views:

  27

  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.

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  1

• Application of a color education software to improve color aptitude

  267-285

  Erika Perge

  Views:

  16

  The ability to handle colors smoothly and consciously may be vital to professionals in various fields, including engineers specializing in architecture or design. Education in sciences related to colors and a developed color aptitude are essential. In our experience, many secondary school graduates in Hungary exhibit inadequate competence and need to be trained in both fields by college instructors, thereby laying the foundations for their future professional work. In our paper, we introduce a computer-based method to teach color theory using a self-developed interactive educational software. We also demonstrate the results of a test measuring the efficiency of the software. Our method was shown to be capable of familiarizing students with the basic fields of visual computing, e.g. graphics and image processing.

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  2

• Zoltán Szvetits (1929-2014): legendary teacher, Zoltán Szvetits passed away

  287-288

  István Gaál

  Views:

  13

  The legendary mathematics teacher of Secondary School Fazekas in Debrecen, Zoltán Szvetits passed away on 5th November 2014, at the age of 84. Beginning in 1954 he had been teaching here almost forty years. His pupils and the society of teachers have lost an outstanding teacher character. This secondary school has been well known for decades about its special mathematics class with 10 math lessons a week. This special class was designed and established by Zoltán Szvetits.

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  4

• On the psychology of mathematical problem solving by gifted students

  289-301

  Sandor M. Veres

  Views:

  40

  This paper examines the nature of mathematical problem solving from a psychological viewpoint as a sequence of mental steps. The scope is limited to solution processes for well defined problems, for instance, which occur at International Mathematical Olympiads. First the meta-mathematical background is outlined in order to present problem solving as a well defined search problem and hence as a discovery process. Solving problems is described as a sequence of elementary steps of the so called "relationship-vision" introduced here. Finally, non-procedural aspects of the psychology of problem solving are summarized, such as the role of persistence, teacher-pupil relationship, the amount of experience needed, self-confidence and inspiration at competitions.

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  3

• Some thoughts concerning power sums

  303-308

  Gábor Nyul

  Views:

  18

  In this note we present an elementary way to derive directly closed-form expressions for power sums. Applying this method, we deduce some general results on power sums with arbitrary exponents. Finally, we give an outlook on higher mathematical connections between power sums, Stirling and Bernoulli numbers.

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  7

• Report of Conference XXXIX. National Conference on Teaching Mathematics, Physics and Computer Science-August 24-26, 2015 Kaposvár, Hungary

  309-331

  Eleonóra Stettner

  Anna Klingné Takács

  Views:

  11

  The XXXIX. National Conference on Teaching Mathematics, Physics and Computer Sciences (MAFIOK) was held in Kaposvár, Hungary between 24 and 26 August, 2015 at the Faculty of Economic Sciences of Kaposvár University. It was organized by the Department of Mathematics and Physics. The 67 participants – including 5 invited lecturers and 54 lecturers – came from 5 countries and represented 16 institutions of higher education.

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  2