Search

Search Results

• 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:

  14

  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.

• Outstanding mathematicians in the 20th century: András Rapcsák (1914-1993)

  99-110

  Tünde Kántor

  Views:

  5

  In this paper we commemorate the life and work of András Rapcsák on the occasion of the centenary of his birth. He was an outstanding professor and a scholar teacher. He was head of the Department of Geometry (1958-1973) and the director of the Institute of Mathematics at the University of Debrecen (Hungary). He played an important role in the life of the University of Debrecen. He was the rector of this university between 1966 and 1973.
  At the beginning of his career he taught at secondary schools in several towns. He wrote mathematical schoolbooks with coauthors. He also taught at Teacher's College in Debrecen and in Eger.
  He became to interested in differential geometry under the influence of Ottó Varga. The fields of his research were line-element spaces and related areas. He was elected an Ordinary Member of the Hungarian Academy of Science in 1965. He wrote 21 papers, 8 school and textbooks and 3 articles in didactics of mathematics.

• Veranschaulichung der Lehrstoffstruktur durch Galois-Graphen

  217-229

  László Fatalin

  Views:

  19

  In this article we compare the process diagram with the Galois-graph, the two hierarchical descriptions of the curriculum's construction from the point of didactics. We present the concrete example through the structure of convex quadrangles. As a result of the analysis it is proved that the process diagram is suitable for describing the activity of pupils, still the Galois-graph is the adequate model of the net of knowledge. The analysis also points out that in teaching of convex quadrangles the constructions of curriculum based only on property of symmetry and only on metrical property are coherent. Generalizing concept is prosperous if the pupils' existing net of knowledge lives on, at most it is amplified and completed. Teaching of convex quadrangles in Hungarian education adopts this principle.

• The time spent on board games pays off: links between board game playing and competency motivation

  119-131

  András Ferenc Dukán

  Katalin Fried

  Csaba Szabó

  Views:

  112

  The impact playing has on the development of thinking is an important topic of psychology of learning, brain research and mathematics didactics.
  Our research is also connected to the aforementioned topic. We investigated the effects of playing board games on competence motivation and the development of mathematical competencies.
  In this paper, we present the results of an experiment carried out in a secondary school class.
  The experimental group spent one of three weekly mathematics lessons playing board games.
  Apart from the several advantages of playing games in general, we can conclude that, based on the results of the national competence measurement, the mathematical competence of the students developed properly.
  The readiness and the progress of the pupils were compared on the basis of input and output tests and an initial knowledge measurement and, at the same time, we compared their level of mathematical competence with the results of the national competence
  measurement.

  Subject Classification: 97C70, 97D40

• Über einen allgemeinen Übungsbegriff bei verschiedenen Unterrichtsmethoden in der Planung des Mathematikunterrichtes

  175-201

  Gabriella Ambrus

  Views:

  14

  Practice is important in the education of mathematics but is neclected in the didactic of mathematics. One of the reasons is that practice is often defined too "narrowly" and the definitions of practice have in most cases an obscure background theory. In the article a general definition of practice is given, which – in contrast to the usual definitions – views practice from the point of the pupils (practice means activity of pupils). By utilising this definition consequences will be drawn. These consequences serve as for the more exact planning of practice in education as for the analysis of the dependency of practice from teachingsmethods.
  In the second part an example will be presented for planning together practice and lesson, in two different teachingsmethods (traditionel, problemsolving). The analysis of both worksheets (one for each method, identical teachingsmaterial) was made on the basis of authors practise in lessons i.e. her own concepts and the experience with pupils at a class 5. On the basis of the expectable solutions is specified – using a criteriacatalog – what was practised.
  The analysis of practice leads further to the examination of above mentioned dependency from teachingsmethods.

• Wichtige Momente aus der ungarischen Geschichte des Analysisunterrichts

  57-76

  Ödön Vancsó

  Hana Burian

  Views:

  64

  Törner et al. (2014) paper gives an outstanding review about teaching analysis at high school level in (Western) Europe. We tried to extend this paper with some results from the Hungarian Math History (Beke and Rátz 1897-1924, after second World War 1949-1960, the current situation-first of all based on schoolbooks, and we also included an experiment from 1984-1989 by E. Deák, which was interrupted and partially forgotten). In summary, this paper deals with the turning points of the brief history of teaching secondary school analysis in the XXth century in Hungary, including some conclusions at the end.

  Subject Classification: 97A30, 97C30, 97D30, 97E50, 97I20, 97I40, 97U20

• Some logical issues in discrete mathematics and algorithmic thinking

  243-258

  Viviane Durand-Guerrier

  Views:

  85

  The role of logic in mathematics education has been widely discussed from the seventies and eighties during the “modern maths period” till now, and remains still a rather controversial issue in the international community. Nevertheless, the relevance of discrete mathematics and algorithmic thinking for the development of heuristic and logical competences is both one of the main points of the program of Tamás Varga, and of some didactic teams in France. In this paper, we first present the semantic perspective in mathematics education and the role of logic in the Hungarian tradition. Then, we present insights on the role of research problems in the French tradition. Finely, we raise some didactical issues in algorithmic thinking at the interface of mathematics and computer science.

  Subject Classification: 97E30

• A didactic analysis of merge sort

  195-210

  Christian Rinderknecht

  Views:

  4

  Due to technical difficulties, educators teaching merge sort often avoid the analysis of the cost in the general and average cases. Using basic discrete mathematics, elementary real analysis and mathematical induction, we propose a self-contained derivation of bounds αn log_2 n + βn + γ in all cases. Independent of any programming language or pseudo-code, supported by intuitive figures, it is suitable for informatics students interested in the analysis of algorithms. It is also a good exercise in showing that induction allows us to actually discover constants, instead of simply checking them a posteriori.