Mathemagica - Mathematica Player completes the magic square

I have, in the past, seen the effective use by contributor AbsentCat of magic squares in a remarkable spread of contexts. From the moment they learn to add three single digit numbers together for a two digit answer (the row/column/diagonal sum of a 3×3 magic square is 15), children are fascinated. The intellectual appeal can still be triggered at any age above that - I have seen it enthuse a mixed truancy group with ages from 10-16, a hospital education group containing a very sick 18 year old cancer patient, and a pensioners’ Third Age study group. Only the management and presentation needs to change.

And the magic square is not just an entry point to mathematics: it has ramifications for almost every other curriculum (and wider) context.

Having seen this success I have, naturally, copied it in my own teaching and staff development work. But always on paper. For very small children, a paper sheet is the only approach that works (mark each correctly entered number with a brightly coloured counter or, if appropriate in the context, a sweet or piece of dried fruit). For older pupils, however, hands on ICT approaches offer tremendous potential - and Allmath.com’s interactive “sheet of paper equivalent” (see below) is wonderful. The missing element has, until now, been an instant, hands on generator and explorer of any n×n magic square or squares on demand.

For the teacher, Matlab and many compatible systems (including the free version of Sysquake and its Palm implementation Lyme) offer a very useful command to generate magic squares: “magic(n)” where n is the size of the square. (My thanks to AbsentCat, who pointed me to these resources.) For some older pupils, these are also useful.

There are a lot of useful materials on the web for building an ICT based “magic square portal” in the classroom. All that is needed is an interactive square calculator. For older secondary ages (Y8 for some pupils, Y13 or beyond for others), Sysquake Remote web implementation is a possibility, but not for the primary years. The Wolfram Demonstrations Project and free player, however, offer just the thing: a magic square generator with “dragable” column/row/locus cursor.

This Mathematica demonstration allows a magic square of any (odd number) size from 1 to 13 to be generated instantly using a slider at the top of the frame. A cursor can then be dragged around the square, highlighting the row and column containing a particular selected cell. Computation is left to the pupil, which is valuable arithmetic practice, but the cells involved are clearly isolated which minimises mistakes. A perfect fit for the missing piece in the ICT magic squares session.

Starting points for other material which has served me well are:

• Allan Adler’s Mathforum pages on magic squares
• Allmath.com’s interactive equivalent of a paper magic square sheet

[contributed by Chandra]