Early Arithmetic Strategies 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 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.

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

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 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

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 = 23 121 (1176) (5898) (5873) (5354) (3070) (1750) 5% 26% 25% 23% 13% 8%

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 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