Articles

• Thoughts on Pólya’s legacy

  157-160

  Alan Schoenfeld

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  134

  There is a saying, "the older I get, the smarter my parents become." What it means, of course, is that the more we learn, the more we appreciate the wisdom of our forebears. For me, that is certainly the case with regard to George Pólya.

  There is no need to elaborate on Pólya's contributions to mathematics – he was one of the greats. See, for example, Gerald Alexanderson's (2000) edited volume The Random Walks of George Pólya, or Pólya's extended obituary (really, a
  53-page homage) in the November 1987 Bulletin of the London Mathematical Society (Chung et al., 1987). Pólya was one of the most important classical analysts of the 20th century, with his influence extending into number theory, geometry, probability and combinatorics.

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• Pólya’s influence on (my) research

  161-171

  Benjamin Rott

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  113

  In this article, I outline the influence of George Pólya's work on research in different areas and especially on mathematics education, namely heuristics and models of the problem-solving process. On a more personal note, I will go into some details regarding Pólya's influence on my own work in mathematical problem solving with a focus on the research project for my PhD thesis.

  Subject Classification: 97xxx

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  146

• Consequences of a virtual encounter with George Pólya

  173-182

  John Mason

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  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

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  113

• Teaching undergraduate mathematics - a problem solving course for first year

  183-206

  Eng Guan Tay

  Kok Ming Teo

  Tin Lam Toh

  Pee Choon Toh

  Weng Kin Ho

  Khiok Seng Quek

  Yew Hoong Leong

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  103

  In this paper we describe a problem solving course for first year undergraduate mathematics students who would be future school teachers.

  Subject Classification: 97B50, 97B70, 97D50, 97D60, 97F60, 97U30

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  142

• Looking back on Pólya’s teaching of problem solving

  207-217

  Kaye Stacey

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  231

  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

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  250

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

  219-232

  András Ambrus

  Krisztina Barczi-Veres

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  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

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  152

• The tradition of problem-posing in Hungarian mathematics teaching

  233-254

  Zoltán Kovács

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  182

  Based on the literature, Pólya was influential in problem-posing research. The present paper draws attention to a book written with Pólya's collaboration, which has not yet received sufficient emphasis in the problem-posing literature. On the other hand, Pólya's impact on mathematics education in Hungary has been significant, including the problem-posing paradigm. Two works, published only in Hungarian, that rely heavily on problem-posing are highlighted. Furthermore, it is presented how problem-posing appeared in the Hungarian Complex Mathematics Teaching Experiment (1962-78) led by Tamás Varga.

  Subject Classification: 97D50

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  195