When learning about number, one of the most important things, initially, is to be able to ‘visualise’ the number. i don’t mean the shape of the number, I mean the number of objects that fit with that number. As an adult, if I was to say “Can you picture the number 5 as a group?” The odds would be that this is what you would see in your head. This is a very distinctive number and when we see this orientation of dots we automatically see 5.
When children start to use numbers, especially in calculating, it is so important that they see the number they are working with. This is a part in the steps to becoming independent in number skills.
If children need their fingers, counters or blocks to ‘see’ the number that is the stage they are at and it should be encouraged.
When teaching 6 year olds, I found it sad to see children hiding their fingers under their legs while they counted them. A calculation such as 4 + 3 = would have half a class of children scrambling to hide their fingers so I couldn’t see them using their fingers as a method of adding. This isn’t fair to the children. I would always make a point of saying ‘well done’ to a child who was looking at the class number line or using their fingers in view of everybody.
Once a child can visualise the numbers, the use of fingers or counters gradually diminishes. This is where mental maths shows its worth. The more practice a child has of hearing calculations e.g. What is seven add eight, the more ingrained the numbers become and eventually they don’t need to count on their fingers.
This concept of ‘visualising’ goes across the board in mathematics. Close your eyes and see a triangle. Now can you draw a triangle? This sounds so easy but if you can’t picture a triangle, you cannot draw one. In the early stages children will need to see a triangle to be able to draw one. The more practice a child has of using the mind to picture a number, shape or pattern, the less they need concrete objects to help them find the answers to problems.
Children who are used to this ‘imagery’ are able to solve complex, multi-step problems mentally and with relative ease. In a classroom it is rare to see a child who can use imagery effectively but when one does come along it is amazing to watch. I have come across one 7 year old who could add three 3 digit numbers in the blink of an eye. This young man has a wonderful talent that can be transferred to real life easily.
My worry is that there aren’t enough children who have the opportunity to gain this skill because they aren’t allowed to use their fingers! How quickly could you complete this calculation in your head? 145 + 287 + 323 = ?
There are adults who have difficulties with numberwork and need visual clues. This is due to missing steps in the learning process including ‘seeing the number’
Can you remember using fingers or counters to understand number?
Do you think you have missed some crucial steps in your learning?