Visualisation in Mathematics Aims

Visualisation in Mathematics
• To reflect on current practice in providing
opportunities for developing visualisation
• To engage in a number of activities that
involve visualisation and reflect on the key
skills and attitudes involved
• To explore ways that visualisation can be
incorporated into classroom practice
• To consider resources that might be useful
Warm up!
Describe a route from Calcot to
Birch End.
A Powerful Force
‘Imagery is a powerful force for perception
and understanding. Being able to “see”
something mentally is a common
metaphor for understanding it. An image
may be of some geometrical shape, or of a
graph or diagram, or it may be some set of
symbols or some procedure.’
Open University
Current Practice
• Consider the visualisation opportunities
you offer your children in your
mathematics lessons.
• Numbers –
Eight, five, four, nine, one, seven, six, ten,
three, two
• Months –
April, August, December, February, January,
July, June, March, May, November, October,
What shape does this net make?
Which face is opposite GHJK?
Which edge meets IL?
Which points meet at A?
Progression in
Practical experiences
Visual experiences
Abstract experiences
100 square
100 square
• A hundred square has been printed on
both sides of a piece of paper. One square
is directly behind the other.
• What is on the back of 100? 58? 23? 19?
• Can you see a pattern?
Time to Imagine....
• Imagine a clock with hands, on the wall
in front of you.
• The long hand is pointing to 4. The short
hand is pointing between 11 and 12.
• What time is it?
• Now imagine the clock is behind you
and you can see it in the mirror.
• The hands look as though they are
saying twenty-five to three.
• What time is it really?
• Now imagine a digital clock behind you.
In the mirror, it looks as though the time
is 10:11.
• What time is it really?
Points to consider
1. The ability to visualise representations,
pictures or images and then adapt/change
them is an important tool in learning
2. Children need extensive practical
experiences in all aspects of mathematics.
3. Visualisation is not about blue-sky thinking.
4. Visualisation activities in YR might look quite
different to visualisation activities in Y6.
Implications for Teaching and
Teach children
how to visualise
familiar 3-D
shapes in a
variety of
Level 4
Level 5
Level 4
Shape 1 –
View from the front
Shape 1 –
View from the left
Shape 1 –
View from the right
Top view
Front view
Shape 2 Two views
•NNS Shape and Space booklet
•nrich website
•Beam – ‘Eyes closed’
•Anita Straker – ‘Talking Points in Mathematics’
•Maths Trails - Visualisation
•Talk for maths – mind’s eye
•Open University – Learning Space – ‘Using
Visualisation in Mathematics Teaching’
Key Messages
• Visualising is a critically important skill in
developing mathematical understanding.
• Visualising does not tend to appear in
published schemes.
• As teachers we need to ensure that we are
very aware of all the processes of
mathematics and so we must always attempt
to know what our students are visualising.