The
E arly A rithmetic S trategies
Framework and the K-10 Numeracy Continuum

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

 Emergent
 Perceptual
 Figurative
 Counting-on-and-back
 Facile

• 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

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

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

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

• 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
• Uses a range of non count by one strategies such as doubles and near doubles

60%
Perceptual
Counting on
50%
40%
30%
Emergent
20%
Figurative
10%
0%
< 5
(1176)
5%
< 6
(5898)
26%
< 7
(5873)
Age
< 8
(5354)
25% 23%
Facile
< 9
(3070)
13%
< 10
(1750)
8% n = 23 121

• 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.

EAS Level Description Syllabus link
Emergent
Perceptual
Figurative
Counting-on-andback
Facile
Cannot count visible items.
Does not know the number words or coordinate number words with items.
Working towards NES1.2
Able to count perceived items.
Builds numbers by using materials or fingers to find the total count.
Determines the total of two concealed groups but starts counting from “one” to do so.
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.
Uses a range of non-count-by-one strategies such as use of doubles and near-doubles.
NES1.2
NS1.2
NS1.2
NS1.2
NS2.2