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We learn a lot from each other. When I was leading
an EMIC (Exploring Mathematics In Classrooms) course decades ago,
This Works For Me really worked for me.
One of the participants demonstrated how she used
a polythene sheet about 2mx2m, 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.
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In my own training as an EMIC leader I had become
hooked on kinaesthetic learning through involving the whole body in 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.
Williams, D. [1993], Maths On A Plastic Mat,
Mathematics: Of Prime Importance
edited by Mousley, J. & Rice,
M., Mathematical
Association of Victoria, Melbourne
The article 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.
In 2004 Matt began making mats for other teachers. A slide show of his activities, as presented at BCME 6, 2005, and details about his Mat can be found here.
In 2006 Matt presented his workshop again at the December Conference of the MAV. Two Swedish teachers, Per Berggren and Maria Lindroth were present and they were so impressed they made their own mat when they returned to Sweden. An article about a mat activities workshop they led in Stockholm can be found at the same link.
Perhaps it will be you who is inspired next.
Doug. Williams
2010
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