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Thoughts on Pólya’s legacy
157-160Views:83There 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. -
Prime building blocks in the mathematics classroom
217-228Views:81This theoretical paper is devoted to the presentation of the manifold opportunities in using a little-known but powerful mathematical manipulative, the so-called prime building blocks, originally invented by two close followers of Tamás Varga, to support discovery of various concepts in arithmetic in middle school, including the Fundamental Theorem of Arithmetic or as it is widely taught, prime factorization. The study focuses on a teaching proposal to show how students can learn about greatest common divisor (GCD) and least common multiple (LCM) with understanding, and meanwhile addresses internal connections and levels of abstractness within elementary number theory. The mathematical and methodological background to understanding different aspects of the concept prime property are discussed and the benefits of using prime building blocks to scaffold students’ discovery are highlighted. Although the proposal was designed to be suitable for Hungarian sixth graders, mathematical context and indications for the use of the manipulative in both primary and high school are given.
Subject Classification: F60, C30, E40, U60