We learn a lot from each other. When I was leading an EMIC (Exploring Mathematics In Classrooms) course a few years ago, This Works For Me really worked for me.

One of the participants demonstrated how she used a polythene sheet about 2m x 2m which was marked in squares to do sorting and graphing exercises with her infants. For example, jumpers which were taken off after running around at recess could be sorted into colours. A column was labelled with a colour card and one jumper was neatly folded into each cell. This was an instant graph and encouraged counting and difference activities.

In my own training as an EMIC leader I had become hooked on kinaesthetic learning through involving the whole body in the mathematics activity.

Sometimes the juxtaposition of two ideas results in a brainwave (rather than a headache) and that's what developed from these two experiences. Thought - what about making a mat with cells large enough for the children (not neatly folded) to sit in the cells and become part of the graph?

THE MATHS

I introduced teachers to these initial ideas through an article and workshop at the 1993 December Conference of the MAV. The article, (See Williams, [1993] below) begins:

Have you ever considered just how much mathematics involves the use of grids?

• data is represented by assigning value to cells of a grid.
• graphs are drawn using the co-ordinates which label the intersections of a grid.
• the concept of multiplication (and its inverse) can be modelled as a rectangular array which can be represented on a grid.
• the place value aspect of number can be modelled as an abacus and this can be represented on a grid with 9 (or 10) rows in each column. Once numbers are represented by this model, operations on those numbers can also be represented.
• geometric shapes can be represented on a geoboard which is a grid where the line intersections are the focus.
• grids provide the playing board for many games and puzzles. Chess is obvious and the grains of rice on the chess board problem (1 on the first cell, 2 on the second, 4 on the third, ...) is well known.
• a spreadsheet/database depends on a grid for its existence.
• we ask children to learn multiplication tables which are arranged as a grid.
• the area of a rectangle is measured by a grid of squares.

THE MAT

The article goes on to describe the mat:

The dimensions shown here make a mat large enough to fit comfortably into a school's multi-purpose room.

Shade cloth (Sarlon Polyshade) is extremely durable and is purchased in 180cm widths. For a cost of $80-100 (which is a tiny component of a school's maths budget) two widths 7.2m long can be bought and taped together with gaffer tape. Then, two hours work with a ruler, a spirit based permanent marker, a long plank and a colleague (knee pads help too!) produces one of the most useful teaching aids a school can possess.

THE MATT

Matt Skoss, head of mathematics at Alice Springs High School, read my 1993 article and immediately began exploring possibilities. He has since presented with his mat at the National Council of Teachers of Mathematics meeting in San Diego in 1996 and at an OECD conference in Canberra in 1997.

MATT'S MATHS MAT ... ... March 2004

REFERENCE

Williams, D. [1993], Maths On A Plastic Mat, Mathematics: Of Prime Importance, edited by Mousley, J. & Rice, M., Mathematical Association of Victoria, Melbourne

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