Transcript File

The
Early Arithmetic Strategies
Framework
and the K-10 Numeracy Continuum
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
The Stages of Early Arithmetical
Strategies (EAS)
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
Emergent
•Does not have one to one correspondence
•May know some number words
•Does not recognise numbers to 10
•Can not count to ten
Perceptual
•Counts collections that they can
see, hear or feel
•Counts by ones
•Names / identifies numbers to 10
•Concrete materials
Figurative
•Can count concealed items
•Understands that numbers are entities
•Still counts from one
•Can count beyond 20
•Understands before and after
Counting on & 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
•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
Overlapping Waves of
Strategies
60%
Perceptual
Counting on
Per cent
50%
40%
30%
Facile
Emergent
20%
Figurative
10%
0%
<5
<6
<7
Age
<8
<9
< 10
(1176)
(5898)
(5873)
(5354)
(3070)
(1750)
5%
26%
25%
23%
13%
8%
n = 23 121
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.
Linking EAS levels to the Syllabus
EAS Level
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-andback
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.
NS1.2
Facile
Uses a range of non-count-by-one strategies such as use of
doubles and near-doubles.
NS1.2
NS2.2