SEAL (Stages of Early Arithmetical Learning)
Research in the 1990s showed there are significant differences in the numerical knowledge of children when they begin school.
These differences in number knowledge increase as children progress through schooling.
This is clear tendency for low attainers in the early years to continue to be low attainers through their primary years and develop negative attitudes towards mathematics.
There is an need therefore to give every child a positive understanding and success in early number work.
In 1992, Dr Robert Wright began developing the Maths Recovery Programme. This is a distinctive approach that clearly links research to classroom pedagogy.
This was based on his research with Dr Leslie Steffe on identifying the Stages of Early Arithmetical Learning.
The Stages of Early Arithmetical Learning is a model that we can use to understand the development of children’s numerical knowledge and is good introduction to this pedagogy.
Information below is a brief introduction to SEAL with video examples. This should be read in conjunction with the Maths Recovery books. Information about these books and Maths Recovery training can be found on the The Maths Recovery Website
Emergent Counter
An Emergent Counter:
Attempts to count
May not understand all counting tasks (social counter?)
The child may not know all the number words.
The child may not be able to coordinate number words with items.
The child may not have the organisational skills
CLIP 2 Emergent Counting (1).wmvEva is an example of an emergent counter.
When asked, "Give me 7 counters" she grabbed a collection of counters and handed them over without attempting to count them. When she was then asked to count the counters she attempted to count them in ones. She could coordinate the number words with the counters but missed out some counters. When this task was micro-adjusted to counting items in a row, Eva successfully counted the counters.
Perceptual Counter
Can count perceived items
May involve seeing, hearing or feeling items
May create perceptual replacements for abstract problems
CLIP 3 Perceptual counting unscreened.wmvWhen presented with 4 screened counters and 3 screened counters, the child could not calculate how many there were altogether. However, when the counters were unscreened the child quickly counted them together. This child needs to see all the counters to solve the task.
When presented with 4 screened counters and 3 screened counters the child replaces the counters with fingers and successfully counts them together.
When presented with 8 screened counters and 5 screened counters the child attempts to replace the counters with fingers but runs out of fingers.
When the counters were unscreened the child successfully counts them together.
CLIP 4 Perceptual counting screened.wmvFigurative Counter
Can count the total of two screened collections (and possibly solve abstract questions like what is 5+4).
Counts from one to solve the problem
E.g. If asked what is 13 add 3. The child would count 1 2 3 4 5 6 7 8 9 10 11 12 13 . . . 14 15 16
CLIP 5 Figurative Counting.wmvWhen presented with 11 screened counters and 5 screened counters the child counts how many there are altogether. She does this by counting from 1 to calculate the total. Although the child counts all of the items individually, she does not need perceptual replacements. She successfully uses her fingers to keep track of the five she adds on.
Initial Number Sequence
Child uses and understands counting-on rather than counting-from-one.
Uses counting on to solve additive tasks and counting up to solve missing addend tasks.
May use count-down-from strategies.
When presented with 8 screened counters and 5 screened counters the child successfully counts on from 8 to calculate the total.
When presented with 4 screened counters and then asked how many more to make 9, the child successfully counts on from 4 up to 9 to calculate the missing addend.
The child has secure knowledge of how use count-on and count-up-to strategies.
This child is not yet able to use a count back strategy to solve subtraction tasks. The child reverts back to perceptual replacements (fingers) to calculate subtraction tasks and is therefore limited to subtraction within 10.
CLIP 6 Initial Number Sequence Addition.wmvIntermediate Number Sequence
The child understands and effectively uses:
Count-on strategies
Count-up to strategies
Count-down-from strategies
Count-down-to strategies
The child can choose the most efficient of these strategies to solve the problem e.g:
If presented with 16-3, the child would count back 3– “16...15,14,13”
If presented with 16-14, the child would back from 16 to 14 (or vice versa) and count the difference– “16... 15, 14”
CLIP 8 Intermediate Number Sequence.wmvWhen asked 16-3 he counts back 3 from 16. However, when asked 16-14 he uses a count-back-to strategy and counts the difference. He chooses the most efficient strategy to get his answer.
At this stage he still counts in ones.
Facile Number (to 20)
The child uses a range of non-count by one strategies:
Compensation
Using known results
Adding to ten
Commutativity
Subtraction as the inverse of addition
Awareness of ten as a teen number
This child has facile number structures to 20.
He can recall a large number of number facts within 20. He uses this knowledge and his experience of structuring numbers to quickly calculate any number problem within 20.
CLIP 9 Facile Number Sequence.wmvFacile Number (to 100)
Can structure numbers to 100
Can combine and partition numbers in a variety of ways
Can solve higher decade addition and subtraction tasks using jump strategies (is not reliant on written algorithms)
Understands and is beginning to recall equal groups and shares (common multiplication and division facts)
CLIP 10 Addition and Subtraction within 20.mp4Cameron is now a facile counter. He can quickly work out addition and subtraction tasks using jump strategies.