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0 Emergent Counting Cannot count visible items. The child either does not know the number words or cannot coordinate the number words with items. Is unable to coordinate number words with items.

1 Perceptual Counting Can count perceived items but not those in screened (that is, concealed) collections. This may involve seeing, hearing, or feeling items. Each number word is accompanied by the production of a perceptual unit item.

2 Figurative Counting Can count the items in a screened collection but counting typically includes what adults might regard as redundant activity. For example, when presented with two screened collections, told how many in each collection and asked how many counters in all, the child will count from ‘one’ instead of counting on. The student can generate their own sensory input to make countable items when counting and is able to use counting in problem oriented contexts where some or all of the items to be counted are hidden.

Stage Stage Name Description Your notes Examples

3 Initial Number Sequence Child uses counting-on rather than counting from ‘one’, to solve addition missing addend tasks (for example, 6 + = 9). The child may use a count-down-from strategy to solve removed items tasks (for example, 17-3 as 16, 15, 14 – the answer is 3). First stage to where the student has awareness of the sequence of numbers in an abstract sense. Severs the dependence of their number concepts on sensory experience that characterizes stage 1 and 2.

4 Intermediate Number Sequence The child counts-down-to solve tasks such as 17-14 = . Reaching the answer of 3 by counting-down-to 14, i.e. 16, 15, 14 – the answer is 3 rather than doing the 14 counts-down-from 17, i.e. 16, 15, 14, 13, 12, 11, . . . 5, 4, 3. The child can choose the more efficient of count-down-from and count-down-to strategies. The student has an awareness of the number sequence from one to 14 but this awareness has limitations.

5 Facile Number Sequence The child uses a range of what are referred to as a non-count-by-ones strategies. These strategies involve procedures other than counting-by-ones but may also involve some counting-by-ones. Thus in additive and subtractive situations, the child uses strategies such as compensation using a known result, adding to ten, commutativity, subtraction as the inverse of addition, awareness of the ‘ten’ in a teen number. Students at stage 5 have an explicit awareness of subtraction as the inverse of addition and typically will use addition to work out subtraction.