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• Metacognition – necessities and possibilities in teaching and learning mathematics

  69-87

  Johann Sjuts

  Views:

  167

  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

• Analysis of fixations while solving a test question related to computer networks

  111-129

  Tibor Ujbányi

  József Katona

  Attila Kővári

  Views:

  93

  Examination of human eye move is useful because by eye tracking and definition of visual attention, may making conclusions about hidden cognitive processes which are harder to examine. With human eye tracking, visual attention can be defined, therefore hidden cognitive processes may be revealed and examined. The goal of the research, presented in this article, to analyze the so called fixation eye movement parameter recorded during a test question related to computer networks. The paper present what significant differences detected between pre-knowledge and the number of fixations using statistical analysis. The results show a moderately relationship between previous knowledge and fixation counts.

• Bemerkungen zur Prototypentheorie – Begriffs - und Konzeptbildung

  365-389

  Éva Vásárhelyi

  Views:

  85

  Psychological theories of prototypes are put forward by mathematical modelling. Some didactical consequences are discussed on the background of this analysis. By the help of an example (classification of convex quadrangles) hints are given for didactical interpretations of actual models of cognitive psychology dealing with problems of constructing prototypes.

• Why some children fail? Analyzing a test and the possible signs of learning disorders in an answer sheet: dedicated to the memory of Julianna Szendrei

  251-268

  Katalin Fried

  Views:

  156

  Teachers and educators in mathematics try to uncover the background of the mistakes their students make for their own and their students' benefit. Doing this they can improve their teaching qualities, and help the cognitive development of their pupils. However, this improvement does not always support their students with learning disorders, since their problem is not caused by wrong attitude or lack of diligence. Therefore, it is the interest of a conscientious teacher to recognize whether the weaker performance of a student is caused by learning disorders, so the helping teacher can give useful advices. Although the teacher is not entirely responsible for the diagnosis, but (s)he should be be familiar with the possible symptoms in order to make suggestions whether or not to take the necessary test of the learning disorders.
  In this article, through examining a test and the answer sheet of a single student, I show some signs that might be caused by learning disorders.