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• The unity of mathematics: a casebook comprising practical geometry number theory and linear algebra

  1-34

  Peter Hilton

  Jean Pedersen

  Views:

  28

  We give a sustained example, drawn largely from earlier publications, of how we may freely pursue a line of mathematical enquiry if we are not constrained, unnaturally, to confine ourselves to a single mathematical subdiscipline; and we draw conclusions from the study of this example which are relevant at many levels of mathematical instruction.
  We also include the statement and proof of a new result (Theorem 4.1) in linear algebra which is obviously fundamental to the geometrical investigation which constitutes the leit-motif of the paper.

• Freudenthal fantasy on the bus, an American adaptation

  133-142

  Judit Kerekes

  Tünde Jakab

  Views:

  61

  In the 1960’s two mathematicians, Hans Freudenthal in the Netherlands and Tamás Varga in Hungary, had argued that people learn mathematics by being actively involved and investigating realistic mathematical problems. Their method lives on in today’s teaching and learning through the various components of cooperative and active learning, by taking ownership in learning, and learning through student dialogue. The goal is to create a welcoming classroom atmosphere in which play takes the front seat. One such scenario is visiting various (animal) stations at the zoo by bus (illustrated by pictures). Passengers are getting on and off the bus at each station (illustrated by arrows), which is modeled on the open number line. This adapted and modified action research was carried out with 5-yearl-old children in public schools of Staten Island, NY in 2019.

  Subject Classification: 97D40, 97F20, 97F30

• Gaussian iteration of mean values and the existence of 2^(1/2)

  35-42

  Zoltán Daróczy

  Views:

  33

  We propose a method for proving the existence of √2 and finding its approximate value in secondary education.