Articles

• Solving Diophantine equations with binomial coefficients in study group sessions using both elementary and higher mathematical methods

  1-12

  Richárd Rakamazi

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  13

  The paper can be considered as the continuation of [4] in the sense that we are studying Diophantine equations containing binomial coefficients. It was an important aspect that one should be able to discuss these problems — even if not in complete depth — also in high school study group sessions with the most talented students. We present various methods through several examples, which help the successful handling of other questions too, including problems in math competitions. Our discussion starts with the elementary treatment of easier problems, and then proceed gradually to more difficult questions which require higher mathematical methods.

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• Teaching of old historical mathematics problems with ICT tools

  13-24

  Tünde Kántor

  Anna Tóth

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  4

  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.

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• Developing a method to determine teachers’ and pupils’ activities during a mathematics lesson

  25-43

  Maija Ahtee

  Erkki Pehkonen

  Anu Laine

  Liisa Näveri

  Markku S. Hannula

  Pirjo Tikkanen

  Views:

  12

  Third-graders from nineteen classrooms (N = 316) were asked to draw a picture on a mathematics lesson. Based on these drawings we have developed a data analysing method that allows us to find out how pupils present both their teacher's and their classmates' activities in their drawings. Two inventories were formed that contain, respectively, teachers' and pupils' activities during a mathematics lesson as seen in the pupils' drawings. The first inventory contains 14 separate items organized into six groups that contain teacher activities like asking questions and giving feedback on mathematics. Ten of the items are related to teaching and the rest contain items like keeping order in addition to the teacher's location in the classroom. Respectively, pupils' activities are organized into five groups that contain altogether 22 items. These contain the activities of a single pupil, and also pupil-teacher and pupil-pupil discussions on mathematics.

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  5

• An interactive animation for learning sorting algorithms: How students reduced the number of comparisons in a sorting algorithm by playing a didactic game

  45-62

  Ladislav Végh

  Veronika Stoffová

  Views:

  8

  Learning programming and understanding algorithms is one of the hardest tasks for novice computer science students. One of the basic algorithms they learn during the introductory programming and algorithms courses are the sorting algorithms. Students like learning these and other algorithms by animations and didactic games, however, these animations are not educationally useful in every case. In this article, we present our educational sorting game, which can be used to introduce the topic of sorting algorithms. The didactic game can be used later too, as a demonstrative tool for explaining the more efficient, quicksort algorithm. We conducted a pedagogical experiment, in which we examined the process of development of sorting algorithms by students while they used the mentioned didactic game. The results showed that students were able to create an algorithm to solve the sorting problem, and they improved its effectiveness by reducing the number of comparisons in the algorithm. They were also able to understand the importance of the efficiency of algorithms when we demonstrated them the quicksort algorithm using the same tool after the experiment.

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• The efficiency of written final exam questions in mathematics based on voluntary data reports, 2012–2015

  63-81

  Csaba Csapodi

  Levente Koncz

  Views:

  11

  The efficiency of each question in the mathematics written final exam is not recorded by the institutions organizing the graduation exam. In order to overcome this deficiency the committee of final exams in mathematics and the Hungarian Educational Authority ask schools to send – beyond the total marks obtained on the paper – the scores of each question of all individual candidates to the Authority every year since 2012. Because a high proportion of schools complied with this request between 2012 and 2015, the researchers were provided valuable information for a deeper analysis on the effectiveness of exams. In this paper we have carried out an analysis of the efficiency of questions set in the written examination papers both on the intermediate and on the higher level in the last four years, on the basis of these voluntary data reports.

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• Fehleranalyse beim Lösen von offenen Aufgaben Ergebnisse einer empirischen Studie in der Grundschule

  83-113

  Gabriella Ambrus

  Kinga Szűcs

  Views:

  5

  Open problems play a key role in mathematics education, also in primary school. However, children in primary school work in many relations in a different way from learner in secondary school. Therefore, the (possibly) first confrontation with an open task could be problematical. Within the framework of an international paper and pencil test it was examined how far children of primary school notice the openness of a task and which mistakes they do during working on that task. In particularly are meant by openness different interpretations of the task, which all lead to a set of numbers with more than one element as a result. For evaluation, a common classification system was adapted by slightly modification of the original system.

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  2

• Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: January 22-24, 2016 Bratislava, Slovakia

  115-137

  E. Herendiné Kónya

  L. Korenová

  E. Partová

  Views:

  10

  The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Bratislava, Slovakia from the 22th to the 24th of January, 2016 at Comenius University in Bratislava. It was organized by the Doctoral School of Mathematical and Computational Sciences of University of Debrecen and the Faculty of Education of Comenius University.
  The 60 participants – including 47 lecturers and 15 PhD students – came from 5 countries, 23 cities and represented 32 institutions of higher and secondary education.

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