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• Regula falsi in lower secondary school education

  169-194

  Zsolt Fülöp

  Views:

  35

  The aim of this paper is to offer some possible ways of solving word problems in lower secondary school education. Many studies have shown that pupils in lower secondary school education (age 13-14) encounter difficulties with learning algebra. Therefore they mainly use arithmetical and numerical checking methods to solve word problems. By numerical checking methods we mean guess-and-check and trial-anderror. We will give a detailed presentation of the false position method. In our opinion this method is useful in the loweer secondary school educational processes, especially to reduce the great number of random trial-and-error problem solving attempts among the primary school pupils. We will also show the results of some problem solving activities among 19 grade 8 pupils at our school. We analysed their problem solving strategies and compared our findings with the results of other research works.

• The single-source shortest paths algorithms and the dynamic programming

  25-35

  Zoltán Kátai

  Views:

  30

  In this paper we are going to present a teaching—learning method that help students look at three single-source shortest paths graph-algorithms from a so called "upperview": the algorithm based on the topological order of the nodes, the Dijkstra algorithm, the Bellman-Ford algorithm. The goal of the suggested method is, beyond the presentation of the algorithms, to offer the students a view that reveals them the basic and even the slight principal differences and similarities between the strategies. In order to succeed in this object, teachers should present the mentioned algorithms as cousin dynamic programming strategies.

• Interactive web portals in mathematics

  347-361

  Róbert Vajda

  Zoltán Kovács

  Views:

  18

  Many of the recent problems in higher education (less contact seminars, the heterogeneity and the increasing number of our students) call for new instructional methods. At University of Szeged we have developed a mathematical web portal which can offer a solution for such problems among the changing circumstances. This freely available, easy-to-use web-surface supports interactive mathematical problem-solving and student self assessment. Our computer program cooperates with a lot of free software (computer algebra systems, formula parsers, converters, word processors). WebMathematics Interactive has been available for the public since June 2002 on its web page http://wmi.math.u-szeged.hu.

• 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:

  140

  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

• Learning and Knowledge: The results, lessons and consequences of a development experiment on establishing the concept of length and perimeter

  119-145

  Margit Tarcsi

  Views:

  33

  In the paper the four main stages of an experiment are described focusing on the question as to how much measuring the length and perimeter of various objects such as fences, buildings by old Hungarian units of measurements and standards contribute to the establishment of the concept of perimeter.
  It has also been examined in what ways and to what extent the various forms of teaching such as frontal, group and pair and individual work contribute to the general knowledge, thinking, creativity and co-operation in this area.
  It will also be shown to what extent folk tales, various activities and games have proved to be efficient in the teaching of the particular topic.
  Every stage of the experiment was started and closed with a test in order to find out whether the development was successful and children managed to gain lasting knowledge in this particular area.

• Methodological questions of digital teaching material development made in the subject of mathematics

  25-41

  András Lénárd

  Judit Szitányi

  Views:

  37

  In the methodology of mathematics teaching, the selection and the manner of using applicable digital teaching materials appeared as a new element. As the number of digital teaching materials applicable in education is constantly increasing, their purposeful use is rarely discussed. In what areas digital teaching materials can be used in mathematics? What are the problems for which they could provide a solution? Shall we use them besides traditional solutions, or instead?
  The authors of this article have had the opportunity to participate in projects aiming to develop digital learning materials on various occasions. During the implementation of the projects, they needed to make methodological compromises at various points.
  In our article, we are seeking a more emphatic use of methodology belonging to digital teaching materials, drawing on the experiences of three implemented projects. Our aim is to draw the attention to the anomalies we found in the implementation of the projects, which must be taken into consideration in new developments already at the planning stage.

• The hyperbola and Geogebra in high-school instruction

  277-285

  Eugen Ljajko

  Milan Mihajlović

  Zlatka Pavličić

  Views:

  35

  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.

• Some Pythagorean type equations concerning arithmetic functions

  157-179

  Ildikó Kézér

  Views:

  59

  We investigate some equations involving the number of divisors d(n); the sum of divisors σ(n); Euler's totient function ϕ(n); the number of distinct prime factors ω(n); and the number of all prime factors (counted with multiplicity) Ω(n). The first part deals with equation f(xy) + f(xz) = f(yz). In the second part, as an analogy to x² + y² = z², we study equation f(x²) + f(y²) = f(z²) and its generalization to higher degrees and more terms. We use just elementary methods and basic facts about the above functions and indicate why and how to discuss this topic in group study sessions or special maths classes of secondary schools in the framework of inquiry based learning.

  Subject Classification: 97F60, 11A25

• The influence of computer on examining trigonometric functions

  111-123

  Djurdjica Takači

  Radivoje Stojković

  Jasminka Radovanović

  Views:

  23

  In this paper the influence of computer on examining trigonometric functions was analyzed throughout the results questionnaire. The students, as usual, had to examine two trigonometric functions, both were given with the appropriate instructions. Three groups were tested. Two of those three groups were prepared with the help of computer and the third one was taught without computer. From the analysis of the questionnaire it follows that the computer has a great influence on understanding of the connections between the graph and very complex calculations.