Visual images for single digit numbers and ten
by Steve Chinn
Definitions of dyscalculia focus on very early number. This includes ‘subitising’, the ability to look at a random cluster of up to 5 items (I use dots in this Blog) and know, without counting what quantity is there.
When we teach these early numbers, it will help our pupils if we use visual images. However, not all images are equal (in the way they present a quantity and in what can be inferred from those images). I am a great believer in asking myself, ‘What else am I teaching?’ For example, rote learning usually teaches just one thing, one fact, at a time and tends not to purposely interlink ‘facts’ or draw out other information. I show a sequence of images for the numbers 1 to 10 in this Blog:
Two other factors are worth mentioning here. The first experience of learning something new will be a dominant entry to the brain. That is fine if what is learned is correct, but not if it is wrong. We teachers must find a new way of teaching this ‘wrong’ information that is powerful enough to inhibit its dominance in the brain and replace it with correct information. I believe that if this information is now interlinked then those links also support the entries to the brain. And, if I can make that information pertinent to the developmental nature of maths, then I have a valuable bonus for future learning.
It seems that we humans appreciate consistency which means that inconsistencies can confuse, or even demotivate, us. Early numbers can do that.
SO, what I want you to do is to look at my sequence of images for the numbers from 1 to 10 and seek out any inconsistencies, any patterns and any consistencies, any links and any potential for developmental input. Those are unlikely to happen with just rote learning (even with cartoon images). AND students can discuss images. Much more difficult to do that in a meaningful way with just the digits.
The visual images can be discussed as stand-alones. For example, the 10 image can be seen as 5 + 5 or 2 x 5 or 9 + 1. The 7 image as 5 + 2 or 4 + 3 or 6 + 1. The 4 image as 2 + 2 or 2 x 2 (compare that link with 5 + 5 and 2 x 5). The 6 image as 5 + 1 (not shown).
They can be discussed as comparisons, for example 9 = 10 – 1 or 8 = 4 + 4 + 1 or 8 = 7 + 1 or 9 = 7 + 2 or 5 = 4 + 1, or links (number bonds) for 10 such as 8 + 2 = 10 or 7 + 3 = 10.
This comparing and decomposing could also be done with chunky two-colour counters (Amazon- https://amzn.to/3GnUK4Y), bringing in a tactile dimension.
This more varied approach addresses facts and develops a better sense of numbers and how they inter- relate, and of the operations.