Many students who are able to recite the number naming sequence (ie, count orally) to 20 and beyond; recognise, read, and write number words and numerals to 10; and count and model small collections (less than 20), will guess when asked ‘how many’ in a particular collection or to identify which of two single digit numbers presented orally or in written form is the larger/smaller, and/or experience difficulty when counting larger collections (40 or more) accurately.
This could be due to/associated with:
- a failure to understand that counting is a strategy to determine ‘how many’ and/or that the last number counted says how many;
- a mismatch between the oral words and the objects counted (eg, matches objects to syllables, omits certain number names);
- a failure to organise the count to avoid counting objects already counted; and/or
- a superficial understanding of numbers 0 to 10 (ie, limited to simple counts and recognising, reading and writing number names and numerals).
By the end of Level 1 students need a deep understanding of the numbers to 10 both in terms of what they represent and how they might be reconfigured or viewed in relation to other numbers. In particular, they need to have developed flexible mental objects for each of the numbers that go beyond the recognition of number names and numerals to include rich part-part-whole knowledge based on visual imagery. This supports trusting the count in the sense that when students read, write or hear ‘seven’, they can imagine what that collection might look like and how it relates to other numbers. For example, they can see
a seven in their mind’s eye as
1 more than 6,
1 less than 8,
3 and 4, or
5 and 2. This is not about addition or subtraction. It is about deeply understanding what each number means.
A key indicator of the extent to which students have developed mental objects for the numbers 0 to 10 is the extent to which they can recognise collections of these numbers without counting, that is, they can subitise.