Maths on a Mat with Matt
Matt Skoss
The Maths Mat is one teaching strategy that allows:
• children to construct their own mathematical concepts
• kinesthetic learning styles to be catered for
• multiple representations of ideas
• cooperative learning in a risk-taking atmosphere
What is the mat? It is a large piece of shade cloth (7.2 m x 3.6 m) with a 10 x 5 grid painted on it. The squares are
approximately 70 cm x 70 cm. All the activities involve ‘doing maths’ with your body – kinesthetic learning. These
ideas were inspired by Doug Williams’ paper in the 1993 MAV conference proceedings – Maths on a Plastic Mat. The
mat helps students to develop their own understanding of a concept, rather than just being ‘told’ something. Activities
have been devised from early childhood to Year 12, in the areas of coordinate geometry, measurement, algebra,
transformational geometry and chance and data.
I attended my first MAV Conference in 1994. Just as I left for the airport, a colleague said: “I don’t know
why you bother going to conferences. Research shows that if you don’t use an idea after 12 days, you never
will.” With that ‘vote of confidence’ I resolved to bring back one ‘big idea,’ and develop it further in
professional development settings in the Northern Territory. Since then, numerous classroom teachers have
contributed ideas, and ‘tweaked’ existing ideas further.
Development of tasks and activities for the maths mat have been guided by two principles:
Good mathematics curriculum starts with rich mathematical tasks.
Doug Williams – Curriculum Corporation
Geometry that can be told is not geometry.
Dick Tahta – Open University, UK (source unknown)
One activity (Figure 1) that challenges adults and children alike is:
“Using the elastic, make a triangle that has an area of 6 square units.”
Figure 1
This ‘simple’ task challenges the concepts a learner has constructed for themselves about area and triangles.
Both students and teachers are often ‘not sure if they are right’ when first faced with this challenge. Tweaking
the question to “make a triangle with an area of 7.5 square units” causes students to move outside their previous
understanding of how to calculate area of triangle. Cooperation is vital, but the deliberate choice of not
specifying how a group is to work together creates some valuable ‘tension’ in the learning activity.
When a group of learners share a rich common experience (often a kinesthetic experience), they retain an
image of the experience in their mind for a long time. Their teacher only has to say “Remember when we...” and
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the students conjure up the image, which allows them to reenter the experience. Referring to a previous shared
experience supports further learning, creating an active culture of learning.
For student learners, the maths mat contributes to building a richer classroom environment. Students
construct their own rich images and metaphors, which helps them engage with the mathematics in different
settings. For example, bilateral symmetry can be represented:
• on the maths mat
• on a geoboard
• using dotty paper
• using Cabri Geometre/Geometer’s Sketchpad
• using concrete manipulatives
Figure 2
Figure 2 represents a challenge to students on the maths mat. Four students (GHIJ) are invited to use
elastic to creat e a quadrilateral that they find interesting. (The teacher is able to draw attention to various
features of the quadrilateral ‘on the fly’.) The only constraint offered to the students is that their quadrilateral
should be in one half of the maths mat. Two more students use elastic to act as the line of reflection (AB). Four
more students are then invited to use elastic to reflect the shape GHIJ about AB, to form the transformation
G’H’I’J’. Experience in trialling this activity in a variety of settings has drawn the author’s attentiont o the
importance of involving the rest of the class in the activity. Challeng e them to give instructions to the students
creating the transformation. Invariably, at least one student will be in the wrong place. By creating a climate of
‘doing maths as a community,’ students are able to engage in the mathematics.
A teacher can create ‘leverage’ from this community, by inviting students AB to move one square to the
left or right, and then invite the audience to give instructions to students G’H’I’J’ to move, to ensure that their
quadrilateral is a reflection of the original. Moving the line of reflection AB diagonally offers a challenge that
creates some conflict, which needs to be resolved. Figure 3 is an example of such a challenge, where students
G’H’I’J’ may have to work off the maths mat. They are not sure if they are in the right place. This dissonance is
a useful tool for a teacher to intervene with some strategically placed questions.
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are needed to see thi s pi ctur e.
Used with permission from Matt Skoss
A
G
G’
H
I
H’
I’
J
B
J’
Figure 3
Each setting offers different opportunities for teachers to intervene in the learning process. In a physical
setting such as ‘on the mat,’ reciprocal obligations of teachers and students as fellow learners is brought to the
forefront, with an invitation to learn, participate, conjecture and verify their mathematical experiences. Students
still have to choose to engage in the mathematical discourse.
The skill of the teacher is critical, requiring:
• thorough knowledge of suitable open-ended tasks and potential ideas and concepts
• engaging students in the mathematical challenge
• strategic intervention coupled with critical questioning
• a capacity to monitor multiple events, reflect-in-the-moment while maintaining the pace
Bibliography
Williams, D. (1993) Maths on a Plastic Mat, in Mathematics: Of Primary
Importance, Mousley, J. & Rice, M. (Ed), Mathematical Association of
Victoria, p.249
Matt Skoss
Email: matt@skoss.org
Phone: 0418-624631
QuickTi me™ and a
decompressor
are needed to see thi s pi ctur e.
Used with permission from Matt Skoss