Games For Writing Mathematics
In contrast to the articles indicating the ways we have introduced, into schools to affect teachers by showing them that there are different and much more effective approaches to mathematics teaching, the following notes are concerned with mathematical games leading to “mathematical essays.� I call limited domain a set of elements and operation chosen so as to determine what is to be taken as given. I give below some examples of selected choices that cover considerable ground at various grade levels and can be played in almost any classroom. 1 We put in a box a particular choice of elements and operations forming a limited domain and exemplify some of the steps, leaving to students the invention of what could follow. 2, 3, 5, x, - This means that in the equivalent expressions we make for 1, 2, 3, . . . only these signs appear (any number of times) e.g. 1~3-2, 2~5-3, 3~3x3-2x3, 4~2x2. . . . . . . If exponents, parentheses, negative numbers are allowed, then we can 2 have expressions like 5~32-22 , 6~22 -2x2x3-(3-2), 7~2x2 - (-3). Too many signs in the box will make the game too easy; too few may make it impossible to generate certain integers. A study of the following limited domains may teach readers how to exploit the idea:
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