1. Lyne & Longcross
Concrete Pictorial Abstract Key Stage 1 Mathematics Maths Hub Conference 16th June 2017

2. Aims of the session
To understand how the CPA approach can enhance children’s learning
Introduction – just giving a flavour of the course today
New course trialling it this term

3. So what is CPA?
Children need to experience a mix of three different modes of learning:
Enactive, Iconic and Symbolic.
Jerome Bruner
real objects
pictures
symbols
5 = 3 + 2

4. There are 7 jelly beans and 5 fruit pastels, how many sweets altogether?
“Show me”
“Prove it!”
Have a go
Share ideas and representations
Actual sweets, counters, beadstrings, numicon, cuisenaire, numberlines, white boards and pens, tens frame, bar model, part, part whole model, tally
Represent your answer using concrete objects, pictures and number sentences.

5. This is how children in Year 1 and 2 approached the problem …

7. Zoltan Dienes said that children learn mathematics by means of direct interaction with their environment. He was also clear on the value of play. … and cautioned on the need for “variability”
“Once we have got children to play a number of mathematical games, there comes a moment when these games can be discussed, compared with each other. It is good to teach several games with very similar rule structures, but using different materials, so that it should become apparent that there is a common core to a number of different looking games,”
DIENES – variability principles
Perceptual Variability principle – a variety of embodiments eg. Dienes, money but the same concept
Eg my representations of numbers in different ways place value
The Perceptual Variability Principle. This principle suggests that conceptual learning is maximized when children are exposed to a concept through a variety of physical contexts or embodiments. The experiences provided should differ in outward appearance while retaining the same basic conceptual structure. The provision of multiple experiences (not the same experience many times), using a variety of materials, is designed to promote abstraction of the mathematical concept. When a child is given opportunities to see a concept in different ways and under different conditions, he or she is more likely to perceive that concept irrespective of its concrete embodiment.

8. Piaget’s work on Schemas underlined this need for variation to establish facts.
Piaget (or Benny Hill?)

9. The Connections Model

10. Build it
Draw it
Write it

11. Match the different representations
Find your partners with the other calculations eg all the ways of representing 3 x10
When you’ve found all the ways can you put the pictures in order of progression

12. What do they know? Both of these look the same from the surface.
Unless you ask the right question you wont know until they move on to something new. Lucy and Laylas video (photos)

13. Lucy and Layla place value
Lucy and Layla – Year 2 this year (Autumn term)
Lucy – Blonde hair
Both working below –
Have strengths in different areas
In SATS achieved age related but unsure where to plot them
Watch both children at the start and notice how they are ordering

14. What do they know? Unless you ask the right question you won’t know.
What questions could we ask?
The difference between a superficial understanding and mastery.
Depth of knowledge.