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Web Papers

Over decades Douglas Williams has written several papers and articles and given many addresses on issues and ideas in mathematics education. Some are listed here in date order. The list will be added to from time to time.

Feel free to quote from these sources or print and distribute to stimulate educational debate. We ask only that you acknowledge the source.

Many other teachers have also written for our site. You will find John Gough's Poly Plug Review on this page and contributions from many others in Research & Stories.

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Red Square  Aha! Teaching Maths is Simple (PDF file)
  • Spring 2010
  • First published in Primary Mathematics, Mathematical Association, UK, Spring 2010, Volume 14 Issue 1.
  • The article opens with the proposition that 'Teaching maths is simple ... but subtle.'; moves through examples leading to the statement 'Let the kids do it. The subtlety is in being the teacher who can facilitate this.'; and draws near to conclusion with 'This is the simple but subtle description ...(of the Working Mathematically Process)... that has brought success to hundreds of classrooms from K to 12.'. The examples are drawn from Calculating Changes and as the article unfolds the reader develops a deeper understanding of the philosophy and practice of this Mathematics Centre network.


    • The article is laid out as in Primary Mathematics.
    • In the references at the end of the article substitute for to find the intended reference.
Red Square  Menu Maths & Other Models for Making Mathematicians (PDF file)
  • November 2013
  • First published in Mathematics Teaching, Association of Teachers of Mathematics, UK, November 2013, Issue 237.
  • School mathematics is about learning to work like a mathematician in best practice classrooms. In this article the concept of giving learners a choice - because mathematicians have a choice about the problems they will investigate - is explored through various menu-based models. In the same sense as a menu offers a diner a choice of what to savour, so Menu Maths offers students a choice of how to 'get stuck into' their mathematics. But this is not a free-for-all. The teachers control the menu - in fact work particularly hard to provide the best menu items they can find. Usually there is a common content thread within the menu which allows teachers to enrich the learning with related whole class investigations - perhaps even with text-based material!
Red Square  Review: Poly Plug Game Pack (PDF file)
  • June 1996
  • John Gough writes an extensive and insightful review of Poly Plug Game Pack for Vinculum, published by the Mathematical Association of Victoria.

Red Square  Assessment, Recording and Reporting in Mathematics (PDF file)

  • April 1997
  • Explore the concept of planning assessment when planning a lesson or unit of work rather than it being added on as an after thought. Alternative assessment techniques in mathematics education are explored.
  • This paper has contributed to the PD from MC workshop day of the same name and is provided as a reference in that session.

Red Square  Curriculum 2000

  • October 1999
  • What would a curriculum for the 21st century look like? A paper to stimulate debate.

Red Square  Learning to Work Like a Mathematician

  • December 5th 2002
  • Text of an address to the Annual Conference, Mathematical Association of Victoria.
  • A development of the philosophy of Curriculum 2000 that builds the mathematics curriculum around the ways of knowing of a mathematician.

Red Square  Maths Not At The Movies (PDF file)

  • June 2006
  • First published in Vinculum, Mathematical Association of Victoria, Volume 43, Number 2, June 2006
  • As working like a mathematician becomes the focus of your teaching, even textbook problems are approached differently. In this article a classic 'stupid' textbook problem is examined in the cold grey light of dawn. Elements of the Working Mathematically Process become critical to its solution.

Red Square  How Can Solving the World's Hardest Problem Inform Mathematics Teaching? (PDF file)

  • November 30th 2009
  • Text of an address to the Secondary Convention, Mathematical Association of Western Australia.
  • Revision of Learning to Work Like a Mathematician (2002) enhanced by DVD and slide show and additional photo show. Slide show and photo show display in Acrobat Reader - use arrow keys to move through the slides.
  • Video of the BBC Horizon Program Fermat's Last Theorem can be found on the web. Search Fermat's Last Theorem BBC. For the purpose of this address only the first seven minutes is necessary. Finish at Andrew's words "Mathematician's just love a problem..."

Red Square  An Ocean of Possibilities (Video & PDF file stored on Cube Tube)

  • March 2010
  • First published in Mathematics Teaching, Association of Teachers of Mathematics, UK, March 2010, Issue 217.
  • The Working Mathematically Process is exposed through Task 216, Square Pairs, a problem that has been researched by two modern mathematicians. It becomes clear that the reason for mathematics education is simply to develop and expand that process. Elements of best practice teaching craft likely to captivate, fascinate and absorb students in this process are also explored. It is proposed that there is a broad ocean of possibilities similar to Square Pairs available when the decision is made to approach learning this way.

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