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• Metacognition – necessities and possibilities in teaching and learning mathematics

  69-87

  Johann Sjuts

  Views:

  287

  This article focuses on the design of mathematics lessons as well as on the research in mathematics didactics from the perspective that metacognition is necessary and possible.
  Humans are able to self-reflect on their thoughts and actions. They are able to make themselves the subject of their thoughts and reflections. In particular, it is possible to become aware of one’s own cognition, which means the way in which one thinks about something, and thus regulate and control it. This is what the term metacognition, thinking about one’s own thinking, stands for.
  Human thinking tends to biases and faults. Both are often caused by fast thinking. Certain biases occur in mathematical thinking. Overall, this makes it necessary to think slow and to reflect on one’s own thinking in a targeted manner.
  The cognitive processes of thinking, learning and understanding in mathematics become more effective and successful when they are supplemented and extended by metacognitive processes. However, it depends on a specific design of the mathematics lessons and the corresponding tasks in mathematics.

  Subject Classification: 97C30, 97C70, 97D40, 97D50, 97D70

• The influence of computer on examining trigonometric functions

  111-123

  Djurdjica Takači

  Radivoje Stojković

  Jasminka Radovanović

  Views:

  205

  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.

• Efficient language teaching software in a multimedia context

  361-374

  László T. Nagy

  Ágnes Stóka

  Views:

  198

  In this article I deal with the efficiency of multimedia teaching programs, analyzing possibilities for their improvement in the field of language teaching. This research has been carried out with the use of the latest technologies, language teaching software, internet based language teaching applications, digital dictionaries, online content, and the latest results from the field of computational linguistics. The goal of my research is to create a general model that serves and supports various kinds of approaches to improving efficiency; I cannot attempt to present a complete, detailed analytical review due to the complexity and size of this topic. However, my opinion is that by considering and understanding the theoretical aspects of the subject, and supported by certain important ideas, we will be able to achieve remarkable improvements in the field of learning efficiency and knowledge retention in the language teaching and learning process that might lead to outstanding results.

• Applications of methods of descriptive geometry in solving ordinary geometric problems

  103-115

  József Szabó

  Ildikó Molnár

  Views:

  123

  The importance of descriptive geometry is well-known in two fields. Spatial objects can be mapped bijectively onto a plane and then we can make constructions concerning the spatial objects. The other significance of descriptive geometry is that mathematical visual perception of objects in three-dimensional space can be improved by the aid of it. The topic of this paper is an unusual application of descriptive geometry. We may come across many geometric problems in mathematical competitions, in entrance examinations and in exercise books whose solution is expected in a classical way, however, the solution can be found more easily and many times more general than it is by the standard manner. We demonstrate some of these problems to encourage to use this geometric method. Understanding the solution requires very little knowledge of descriptive geometry, however, finding a solution needs to have some idea of descriptive geometry.

• Exploring the basic concepts of Calculus through a case study on motion in gravitational space

  111-132

  Miklós Tekeli

  János Karsai

  Katalin Kopasz

  Views:

  343

  In universities, the Calculus course presents significant challenges year after year. In this article, we will demonstrate how to use methods of Realistic Mathematics Education (RME) to introduce the concepts of limits, differentiation, and integration based on high school kinematics and dynamics knowledge. All mathematical concepts are coherently built upon experiences, experiments, and fundamental dynamics knowledge related to motion in a gravitational field. With the help of worksheets created using GeoGebra or Microsoft Excel, students can conduct digital experiments and later independently visualize and relate abstract concepts to practical applications, thereby facilitating their understanding.

  Subject Classification: 97D40, 97I40, 97M50