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Problemorientierung im Mathematikunterricht – ein Gesichtspunkt der Qualitätssteigerung
251-291Views:7The aim of this article is to give a synopsis of problem orientation in mathematics education and to stimulate the discussion of the development and research about problem-orientated mathematics teaching. At the beginning we present historical viewpoints of problem orientation and their connection with recent theories of cognition (constructivism). Secondly we give characterizations of concepts that stand in the context of problem-orientation and discuss different forms of working with open problems in mathematics teaching. Arguments for more problem orientation in mathematics education will be discussed afterwards. Since experience shows that the implementation of open problems in classroom produces barriers, we then discuss mathematical beliefs and their role in mathematical learning and teaching. A list of literature at the end is not only for references but also can be used to further research.
Zusammenfassung. Ziel des Beitrags ist es, eine Synopsis in Bezug auf Problemorientierung im Mathematikunterricht zu geben und die Diskussion bezüglich Entwicklung und Forschung eines problemorientierten Mathematikunterrichts zu stimulieren. Als Erstes werden historische Gesichtspunkte von Problemorientierung und deren Verkn üpfung mit neueren Erkenntnistheorien (Konstruktivismus) vorgestellt. Zweitens werden Erläuterungen zu Begriffen, die im Kontext von Problemorientierung stehen, gegeben und verschiedene Ausprägungen der Behandlung offener Probleme im Mathematikunterricht diskutiert. Argumente für eine stärkere Berücksichtigung von Problemorientierung im Mathematikunterricht werden danach erörtert. Auf Barrieren bei der Implementierung von offenen Problemen im Unterricht, die durch mathematische Beliefs (Vorstellungen, Überzeugungen) geprägt sind, wird zum Schluss eingegangen. Die abschließend aufgeführte Literaturliste dient nicht nur dem Beleg der Zitate, sondern kann auch zu weiterer Vertiefung genutzt werden. -
Zbigniew Michalewicz - Matthew Michalewicz: Puzzle Based Learning: An introduction to critical thinking, mathematics, and problem solving. Hybrid Publishers Melbourne 2008 (Book review)
415-420Views:40Based 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. -
Solution of an open reality based word-problem in two secondary schools
143-156Views:106This survey through an open reality based word problem is intended to assess - in two secondary schools in Komárom (Hungary) and in Komarno (Slovakia, Hungarian name: Révkomárom) in grade 10 - the ability of students to realize openness of a task. The comparison is justified by the fact that the language of teaching is Hungarian in both secondary schools, but with different curricula. This survey is related to the Content Pedagogy Research Program by the Hungarian Academy of Sciences. It is preceded by several surveys with a word problem (Pocket Money) of the third author and led by her between 2012 and 2015, and within that project in 2017 within a large sample test, among about 1500 students and university students in Hungary (?, ?) (?, ?). In our research we wanted first to assess how openly work students in two schools of the two cities mentioned in solving the same task. The answer to this question was similar to the large sample test results, so most of the students worked in a closed way, when solving this word problem. So we went on and tried to explore how students thought about their own solution given to this task, through mixed-type interviews.
Subject Classification: 97D70, 97F90, 97D50, 97M10
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Is it possible to develop some elements of metacognition in a Mathematics classroom environment?
123-132Views:89In an earlier exploratory survey, we investigated the metacognitive activities of 9th grade students, and found that they have only limited experience in the “looking back” phase of the problem solving process. This paper presents the results of a teaching experiment focusing on ninth-grade students’ metacognitive activities in the process of solving several open-ended geometry problems. We conclude that promoting students’ metacognitive abilities makes their problem solving process more effective.
Subject Classification: 97D50, 97G40
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Teaching of old historical mathematics problems with ICT tools
13-24Views:20The aim of this study is to examine how teachers can use ICT (information and communications technology) tools and the method of blended learning to teach mathematical problem solving. The new Hungarian mathematics curriculum (NAT) emphasizes the role of history of science, therefore we chose a topic from the history of mathematics, from the geometry of triangles: Viviani's Theorem and its problem field. We carried out our teaching experiments at a secondary school with 14-year-old students. Students investigated open geometrical problems with the help of a dynamic geometric software (GeoGebra). Their research work was similar to the historical way. -
Decomposition of triangles into isosceles triangles II: complete solution of the problem by using a computer
275-300Views:29We solve an open decomposition problem in elementary geometry using pure mathematics and a computer programme, utilizing a computer algebra system. -
Decomposition of triangles into isosceles triangles I: let the students ask bravely
163-184Views:26We report about working up an open geometric problem as a mathematical research with pupils of a mathematics camp. This paper shows the didactic aims and the methods we worked with, the didactic results. The second part of this paper gives a general solution of the problem, using pure mathematics and a computer programme. -
The Project Method and investigation in school mathematics
241-255Views:39The Project Method (PM) is becoming more common in the teaching of mathematics. Most of the time, Project Method means solving open and relatively wide formulated problems for the application of particular mathematical topics and the solving of everyday life problems.
At present many experts in the theory of teaching mathematics advocate teaching activities as the characteristic for most mathematical work in the classroom. Thus, there is a question: whether it is possible or eventual desirable to use the PM for solving genuine mathematical problems. This paper deals with this question and discusses the connection between the PM and investigation of new mathematical knowledge for students. Our experience has shown that the PM in connection with investigations can be a useful and effective approach to teaching mathematics. -
Consequences of a virtual encounter with George Pólya
173-182Views:106The 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