1. Early Arithmetic Strategies
The
Early Arithmetic Strategies
Framework
and the K-10 Numeracy Continuum

2. The Learning Framework
The learning framework in number was initially developed for the Count Me In Too project in 1996
It outlines how students move from using naive strategies to increasingly sophisticated strategies in order to solve number problems
The transition from simplistic strategies to more sophisticated strategies underpins the structure of the framework

3. The Stages of Early Arithmetical Strategies (EAS)
Emergent
Perceptual
Figurative
Counting-on-and-back
Facile
One of the difficulties with inefficient strategies is that, although they are slower, they still work. This means that inefficient strategies can be very persistent.

4. Meanings Emergent - coming into existence
Perceptual – relating to the ability to interpret or become aware of something through the senses
Figurative – Represented by a figure or resemblance; symbolic or emblematic.
Counting on & Back – this needs no explanation
Facile – easily accomplished or attained

5. Emergent Does not have one to one correspondence
May know some number words
Does not recognise numbers to 10
Can not count to ten

6. Perceptual Counts collections that they can see, hear or feel
Counts by ones
Names / identifies numbers to 10
Concrete materials

7. Figurative Can count concealed items
Understands that numbers are entities
Still counts from one
Can count beyond 20
Understands before and after

8. Counting on & Back Facile (Flexible)
Counts on (or back) from a number rather
than counting from one to solve addition and subtraction tasks
Has a sense that the count of one of the numbers has already occurred
Counts beyond 100
Has automatic recall of some facts
Facile (Flexible)
Uses a range of non count by one strategies such as doubles and near doubles

9. Overlapping Waves of Strategies
60%
Perceptual
Counting on
50%
Data from 2000
Emergent
40%
Facile
Per cent
30%
Figurative
20%
10% 0%
< 5
< 6
< 7
< 8
< 9
< 10
Age
n =
(1176)
(5898)
(5873)
(5354)
(3070)
(1750) 5%
26%
25%
23%
13% 8%

10. Why is the Framework Important?
It is considered more “user friendly” than the syllabus.
It provides more “detail” about specific strategies.
Broadens teacher’s knowledge of how children learn mathematics by focusing on strategies which students apply when solving arithmetic and counting tasks.
Teachers use their knowledge of the EAS to plan appropriate instruction.

11. Linking EAS levels to the Syllabus
Description
Syllabus link
Emergent
Cannot count visible items.
Does not know the number words or coordinate number words with items.
Working towards NES1.2
Perceptual
Able to count perceived items.
Builds numbers by using materials or fingers to find the total count.
NES1.2
Figurative
Determines the total of two concealed groups but starts counting from “one” to do so.
NS1.2
Counting-on-and-back
Counts-on (or back) from a number rather than counting from “one” to solve addition and subtraction tasks. Has a sense that the count of one of the numbers has already occurred.
Facile
Uses a range of non-count-by-one strategies such as use of doubles and near-doubles.
NS2.2