Joy with numbers

Initially children might start to recognise some number words such as “I am three,” “one, two, go!” Counting may begin with rote counting (just reciting the sequence of number words), or by using number words to count objects in front of them.  In either case, it’s exciting to hear how their sequence develops. 

Usually, both types of counting initially consist of:

• a conventional portion, for example, “1, 2, 3”
• a stable non-conventional portion “5, 8, 6”
• a nonstable portion (sometimes called a ‘number salad’ where numbers are tossed in in any order) producing any sequence of number words, which varies each time.

For example, you might hear a child counting, “1, 2, 3, 5, 8, 6, 9, 4,” then “1, 2, 3, 5, 8, 6, 4, 10, 12”. In this case, 1, 2, 3 are in the conventional order; 5, 8, 6 is a stable non-conventional order; and both 9, 4 and 4, 10, 12 are nonstable sequences – that will vary each time. Sometimes non-traditional number words are included in the sequence, like “eleventy.”

There are some important steps in the complex task of learning to use the number words to count objects.  These include:

• memorising the chain of number words.  As noted above, this might initially be incorrect (for example, “1, 2, 3, 5, 8, 9”) but provides an important language base for counting.
• matching number names to objects, although they may skip or double count (1:1 not yet established) or may have 1:1 correspondence but an incorrect sequence of number words.
• rational counting where there is a 1:1 matching of number words to objects.  Usually, this involves the child maintaining a physical link between the number word and object – moving, touching, pointing, or nodding at items as they count them.

When objects are arranged in recognisable patterns (based on visual structure), such as the patterns on dice or dominoes, then mokopuna can start to recognize the smaller numbers without having to count each dot. This is known as ‘subitising.’ For example, over time familiarity with dice patterns help mokopuna to recognise the patterns for the first six numbers, without needing to count.

As children’s counting develops you might notice that children learning to count in English may experience difficulties with the ‘teens’ words and the decade numbers (20, 30, etc.).  This is because in English, as in many European languages, the spoken numerals do not always reflect the elements of tens and ones that are contained in them. For example, the fact that 11 is composed of a single tens value and a single unit’s value is not evident in the English number word eleven (Geary et al, 1997), whereas in te reo Māori it is clear: “tekau ma tahi.”

Another challenge is that numbers like fourteen and forty sound very similar in English, even though they represent very different amounts. In te reo Māori and in many Asian languages the spoken numeral corresponds exactly to the implied quantity, which creates a more ‘transparent’ number grammar. 

Although counting words vary from culture to culture, Peters (2001:12) highlights the following five principles, which are involved in learning to count in any language:

1. One-to-one: each object is counted exactly once. This involves keeping track of items that have been counted and those that have not, while producing distinct number words one at a time. For example, a child might point to or touch each object, or gather each object while saying the number name, ensuring a systematic process that accounts for each object.
2. Stable order: the sequence of number words must be produced in a consistent, stable order.
3. Cardinality: the last number word in the count represents the total number of objects. For example, if five objects are counted as “1, 2, 3, 4, 5,” the last number, “5,” describes the entire set.
4. No limit: there is no limit to the number or type of items that can be counted.
5. Irrelevant order: the order in which objects are counted does not affect the final count.

Mokopuna discover the joy of numbers when the adults around them provide intentional resources, show shared enjoyment of maths and use counting language. Over time, mokopuna can come to recognise that numbers can amuse, delight, comfort, illuminate, inform, and excite. Kaiako have an important role in providing a joyful number-rich environment and foundation of lifelong learning and love of maths.