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The Stages of Learning Early Numeracy Concepts

The stages of learning early numeracy concepts are: emergent, perceptual, figurative, counting on and facile. An overview of expected understandings in each stage is included below, and examples of assessment tasks for some stages are available as well. Classroom programs are best developed by referring to the stages of learning that individuals are working within.

Students who are working at the Emergent Stage of Learning in Numeracy:

• May be able to say some number words

• May relate some counting words to the process of counting

• Cannot consistently reproduce the correct forward number sequence or backward number word sequence between 0 and 10

• Are unable to correctly count collections of up to 10 objects

• Do not know all the number words

• Cannot co-ordinate the number words they know with items when asked to count a collection

• May be able to identify and name some numerals (not consistently identify or name 0-10 or beyond)

Learners in the Emergent Stage are working towards:

• Counting collections

• Identifying numerals

• Labelling collections

Students who are working at the Perceptual Stage of Learning in Numeracy:

• Are able to count collections of objects they can see, touch or feel (rely on concrete representations of numbers)

• Consistently apply the 1-1 principle of matching one number word to each object

• Demonstrate their understanding of the numerical value of a collection by counting and labelling collections from 1-10 and beyond

• Can say the numerical sequence to more than 10 (The size of the collection they are able to count will be dependent upon their knowledge of the forward number sequence)

• Rely on the strategy of counting by ones and always begin at one when they count

• Typically, count from one when determining the number before or after a nominated number

• Confidently produce the forward or backward number sequence in the range 0-10 (always begin at one when counting forward)

• Identify and name numerals 0-10 or beyond

• Are developing the ability to recognise number patterns

• Know that numbers can be represented in a variety of ways (eg. different visual representations of 5)

Learners in the Perceptual Stage are working towards:

• Adding 2 collections of items

• Counting without relying on concrete representations of numbers

• Usually recognising standard patterns for a collection of up to 10 items without counting them

• Consistently saying the forward and backward number word sequences correctly (to 10)

The Stages of Learning Numeracy: Assessment Task (Perceptual Stage)

Students who are working at the Figurative Stage of Learning Numeracy:

• Are able to count collections which are totally or partially concealed

• Often rely on counting by 1s, starting from 1, to find a total

• Have an understanding of numbers as entities (eg. when asked to show 6, can instantly raise 6 fingers without needing to count)

• Demonstrate understanding of conservation of number

• Can represent a number in a variety of ways through such strategies as separating (partitioning) and combining

• Consistently produce the correct forward and backward number word sequences from 0-20 (many children can go beyond)

• Are able to use their knowledge of forward and backward number word sequences to produce the number before and the number after a nominated number

• Demonstrate their understanding of the numerical value of numbers by naming numerals and labelling collections of up to 20 items

Learners in the Figurative Stage are working towards:

• Using counting on to solve addition tasks

• Using counting down to solve subtraction tasks

• Developing base 10 knowledge

• Forming equal groups and finding their total

The Stages of Learning Numeracy: Assessment Task for the Figurative Stage

Students who are working at the Counting On Stage of Learning Numeracy:

• Use their knowledge of both the forward and backward sequences of number words to solve addition and subtraction questions

• Uses strategies of counting on from a given number and counting down from a given number confidently

Typically, use the strategies: • Count forward from the larger number when finding the total of two numbers

• Sometimes use the strategy of “counting up to" in an effort to find the difference between two numbers (often combined with holding up fingers eg. 6+?=9 - “7,8,9”

• Count down from the larger number to find the difference between two numbers 9-3= “8,7,6”

• When counting down to the smaller number to solve subtraction problems, students count backwards from the larger number 9+?=6 - “8,7,6” often using fingers to assist

• Are developing automatic recall of basic addition and subtraction facts

• Are able to produce forward and backward number word sequences up to and beyond 100

• Can use their understanding of the base 10 number system to solve number tasks, using concrete materials to visually represent the numbers involved

Children at the Counting on Stage are working towards:

• Applying a variety of strategies other than counting by ones to solve arithmetical tasks

• Forming equal groups and finding the total, using skip counting

• Developing a concept of 10 as a unit

Assessment Task for the Counting On Stage

**Further Stages of Learning: Markers for students who are at the Facile Stage are being developed.

Stages Of Learning: Facile coming soon

Count Me In Too Website (NSW Australia) This site offers online activities to support students who are working within each stage, as well as teacher support.


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