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• Realizing the problem-solving phases of Pólya in classroom practice

  219-232

  András Ambrus

  Krisztina Barczi-Veres

  Views:

  124

  When teaching mathematical problem-solving is mentioned, the name of Pólya György inevitably comes to mind. Many problem-solving lessons are planned using Pólya's steps and helping questions, and teachers often rely on his heuristics even if their application happens unconsciously. In this article, we would like to examine how the two phases, Making a plan and Looking back, can be realized in a secondary school mathematics lesson. A case study was designed to observe and analyse a lesson delivered using cooperative work.

  Subject Classification: 97B10, 97C70, 97D40, 97D50

• Looking back on Pólya’s teaching of problem solving

  207-217

  Kaye Stacey

  Views:

  229

  This article is a personal reflection on Pólya's work on problem solving, supported by a re-reading of some of his books and viewing his film Let Us Teach Guessing. Pólya's work has had lasting impact on the goals of school mathematics, especially in establishing solving problems (including non-routine problems) as a major goal and in establishing the elements of how to teach for problem solving. His work demonstrated the importance of choosing rich problems for students to explore, equipping them with some heuristic strategies and metacognitive awareness of the problem solving process, and promoting 'looking back' as a way of learning from the problem solving experience. The ideas are all still influential. What has changed most is the nature of classrooms, with the subsequent appreciation of a supporting yet challenging classroom where students work collaboratively and play an active role in classroom discussion.

  Subject Classification: 97D50, 97A30

• Approximated Poncelet configurations

  163-176

  Örs Nagy

  Szilárd András

  Views:

  34

  In this short note we present the approximate construction of closed Poncelet configurations using the simulation of a mathematical pendulum. Although the idea goes back to the work of Jacobi ([17]), only the use of modern computer technologies assures the success of the construction. We present also some remarks on using such problems in project based university courses and we present a Matlab program able to produce animated Poncelet configurations with given period. In the same spirit we construct Steiner configurations and we give a few teaching oriented remarks on the Poncelet grid theorem.

• How to use our own program evaluation system to streamline teaching computer programming

  73-80

  Sándor Király

  Szilveszter Székely

  Views:

  35

  During computer programming contests the use of automatic evaluation systems is becoming more and more frequent. In said systems the contestants are allowed to submit their source code that will be evaluated with the results reported back to them. According to this report the contestant can realise for what test cases his program works properly and for what cases does it fail. This kind of on-line evaluation system is used for example in the International Olympiad in Informatics (IOI), in the final round of the Nemes Tihamér National Programming Competition, and in the Selection Competition for IOI in Hungary. A contest management system can be used for other purposes apart from this singular example. A well-developed evaluation system can foster not only the teaching of computer programming and the preparation of students for programming contests but the teacher's work as well.

• A mathematical and didactical analysis of the concept of orientation

  111-130

  Eszter Kónya

  Views:

  41

  The development of spatial ability, in particular the development of spatial orientation is one of the aims of mathematics education.
  In my work, I examine the concept of orientation, especially concepts of between, left, right, below, above, front, back, clockwise and anticlockwise. I analyze answers given for a simple orientation task prepared for elementary school pupils. I would like to call attention to the difficulties pupils have even in case of solving simple orientation problems.
  We have different ways to know more about the crucial points of a concept, especially of the concept of orientation. In this study I bring out one of them. I analyze and make some didactical conclusions about the origin and the axiomatic structure of orientation.

• Consequences of a virtual encounter with George Pólya

  173-182

  John Mason

  Views:

  107

  The consequences of a virtual encounter with George Pólya as a teacher are recorded. An instance of his influence on my mathematical thinking is recounted through work on one of the problems in one of his books.

  Subject Classification: 01A99, 11A05, 97-03, 97D50

• Dressed up problems - the danger of picking the inappropriate dress

  77-94

  Anna Muzsnay

  Csaba Szabó

  Views:

  15

  Modelling and dressed-up problems play an inevitably unavoidable role in mathematics education. In this study we would like to point out how dangerous is it to dress up mathematical problems. We go back to the principle of De Lange: The problem designer is not only dressing up the problem, but he is the solution designer, as well. We show three examples selected from Hungarian high school textbooks where the intended solution does not solve the problem, because the dressing changes the context and changes the problem itself.