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By Gillespie L. J.

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It is significant in the context of this work that the language of judgement around the concept of proof is very largely aesthetic. In this range of approaches there is a category known as proof by existence. We know that it is possible to have objects of a certain type because an instance has been produced. In a fundamental sense what we have with Rena and Eileen’s work is a ‘proof by existence’ of the possibility of a different and powerful way of approaching elementary school mathematics. Their methods have many features in common with the more widely known contemporary approaches to reform in mathematics education, especially those outlined in the ‘Standards’ documents for Curriculum and Evalutaion, for Professional Practice, and for Assessment generated by the American National Council of Teachers of Mathematics (NCTM, 1989, 1991, 1995).

There are also many illustrations of Escher paintings, and methods for creating ‘Escher-like’ tessellations are outlined. The children were fascinated by a tessellation of dogs, because they could see how a simple square was transformed into a dog, which could then be tessellated over the page. Another feature of the book is that a series of dot-grid pages is provided, all of which can be photocopied so that people can make their own tessellating patterns on paper. Having spent a considerable amount of time manipulating objects and searching for tessellations inside and outside the classroom, I was sure that giving the children a couple of different kinds of dot-grids would yield some interesting results.

Many of the children were somewhat dismayed as the rinsing caused some of the paint to run off as well; they were assured that paint ran off my card as well as Eileen’s, and that all would be well. 12 Removing silk from cardboard backing 40 Chapter 2 The completed silk painting was then glued to the rectangular piece of card; the resulting ‘insert’ was glued to the window, and the children had two cards each to their credit. The first was the silk card, the second was the card ‘left over’ after the silk piece had been removed.

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An Equation for the Haber Equilibrium by Gillespie L. J.

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