Counting:

key ideas and important concept knowledge

Key ideas

The overarching key ideas of estimation, benchmarks, visualisation, equality and equivalence, language and strategies need to be considered when developing units of work in counting. The specific key ideas in counting are: quantity, abstraction principle, one-to-one principle, stable-order principle, cardinality principle, order- irrelevance principle, ordinal principle, conservation of number and subitising.

Quantity

A quantity is an amount of something which is determined using a number and a unit.

The term ‘manyness’ applies to discreet quantities. When a set of discrete items is counted, the result assumes that the unit is one collection.

The term ‘muchness’ applies to continuous quantities.

Abstraction principle

In the abstraction principle, different sized or unrelated objects can be counted and treated the same numerically. Items that cannot be seen can also be counted – for example ideas, characters in a story, sounds, etc.

One-to-one principle

In the one-to-one principle, words in the forward or backward counting sequence are mapped onto the objects being counted; that is, there is one word to one object.

Stable-order principle

In the stable-order principle, there is a fixed order of words in the sequence when objects are counted.

Cardinality principle

In the cardinality principle, the last number indicates the total number of items; that is, it is a cumulative count.

Order-irrelevance principle

In the order-irrelevance principle, the order in which objects are counted does not change the quantity.

The above five principles are from the work of

Gelman and Gallistel (1978).

Ordinal principle

In the ordinal principle, numbers are used to indicate the position of an object in a numerical sequence or order.

Conservation of number

In conservation of number, the number of objects in a collection does not change as the spatial arrangement of the collection changes.

Subitising

Subitising is an instant recognition of a small quantity without counting.

Important concept knowledge

Number patterns

A number pattern is a regularity in a sequence of numbers. Number patterns are a type of growing pattern.

Number word sequence

The number word sequence, forwards or backwards, is the fixed order of number names.

There is a difference between reciting and counting a number word sequence.

Reciting a sequence of number words is by rote, whereas counting is the allocation of each spoken number word with an item.

Students begin to learn the number word sequence and then use this sequence to count collections.

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