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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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Matt Skoss exploring the mat with Andy Martin and family at BCME 6, 2005, England. See slide show reference below.
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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 relatively small cost 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, at the time head of mathematics at Alice Springs
High School, read my 1993 article and immediately began exploring
possibilities. Early on he 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. He has continued to run Maths on the Mat with Matt workshops well into the following century and, as a mathematics education consultant, has used it time and again in schools.
The Dates
1993
Mathematics On A Plastic Mat, my 'lesson notes' from a workshop in September. Not the first workshop I led using this resource, but the earliest record I can find.
Maths on a Plastic Mat, the original article.
1995
Matt's Math Mat Matters, an article in The Classroom Connection recognising some of the work Matt and his team had been developing based on the original article. Information above is drawn from the first two pages of this article.
2004
Matt began making mats for other teachers.
2005
Matt presented his workshop at BCME 6 in the UK and later enjoyed replaying the experience for Andy Martin and his family. Photos from that extra session are recorded here as a slide show. They reveal many possibilities for learning mathematics through whole body involvement.
Andy bought Matt's kit on the spot. A win for his school, and a win for Matt who didn't have to freight it back to Australia.
2006 / 2007
Matt presented his workshop again at the December Conference of the MAV. Two Swedish teachers, Per Berggren and Maria Lindroth were present and were so impressed they made their own mat when they returned to Sweden.
This article, Maths on a Mat (Swedish style), Matte på en Matta reports on a mat activities workshop they led in Stockholm.
2021
Matt was captured by The Coonamble Times presenting a mat workshop in regional NSW as a part of a project of the Mathematical Association of NSW (MANSW) to support rural, regional and remote teachers to build local, self-driving, professional development networks.
- Click the image to reveal the article.
- Click the article to toggle zoom in / zoom out.
Article used with permission of
The Coonamble Times:
https://www.coonambletimes.com.au/
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2023 & 2024
| For the 2023 December Conference of the Mathematical Association of Victoria Matt added a sorting network with a musical outcome.
- Click the image to play a short video from the conference.
- Also learn from a video of extracts from a workshop at the 2024 conference which was jointly presented by Eleni Pilafas, Matt Skoss and Doug Williams
... Maths on a Mat: 3 Generations.
- Perhaps it will be you who is inspired next.
- Perhaps you will
Make Your Own Maths Mat like Eleni and Matt did for Croydon Hills Primary School. This link includes a video of Eleni and Matt making a mat from start to finish.
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Eleni was a participant in this workshop. She organised her school's mat early in 2024.
Doug. Williams, 2010
(extended 2012, 2021, 2023, 2024)
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