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Visualisation in Mathematics

Visualisation in Mathematics. Aims. 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

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Visualisation in Mathematics

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  1. Visualisation in Mathematics

  2. Aims • 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

  3. Warm up! Describe a route from Calcot to Birch End.

  4. 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

  5. Current Practice • Consider the visualisation opportunities you offer your children in your mathematics lessons.

  6. Activity

  7. Answers • Numbers – Eight, five, four, nine, one, seven, six, ten, three, two • Months – April, August, December, February, January, July, June, March, May, November, October, September

  8. Sequencing Practical

  9. Nets What shape does this net make? Which face is opposite GHJK? Which edge meets IL? Which points meet at A?

  10. Progression in visualisation Practical experiences Visual experiences Abstract experiences

  11. 100 square

  12. 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?

  13. 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?

  14. Points to consider • The ability to visualise representations, pictures or images and then adapt/change them is an important tool in learning mathematics. • Children need extensive practical experiences in all aspects of mathematics. • Visualisation is not about blue-sky thinking. • Visualisation activities in YR might look quite different to visualisation activities in Y6.

  15. Implications for Teaching and Learning Teach children how to visualise familiar 3-D shapes in a variety of contexts. Level 4

  16. Shape 1 – View from the front ?

  17. Shape 1 – View from the left ?

  18. Shape 1 – View from the right ?

  19. Shape 2 - Two views

  20. Resources • 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’

  21. 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.

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