Monday, 1 February 2016

How many?

The pride of the young mother is tangible, "Jimmy can count to ten!" she declares!
Jimmy recites the numbers beautifully, perfectly in fact, in the adorable sing-song voice only a toddler can achieve.
"Wonderful!" you respond in justifiable congratulation.  "Jimmy, how many bricks am I holding?"
Jimmy obediently chants again; "One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten" and wanders off happily to continue bouncing Peppa Pig on the sofa, his new counting song interchanging with baa baa black sheep. Young Mum is left puzzled, staring at the three bricks you are holding.
It's the one to one correspondence, you see.  A missing link, if you will, for many children who can 'count' by rote and all too often, simply miss the bit where the number is associated with an object.
Later, many children find themselves caught out when they are adding and taking away, calculating using a number line and using concrete material in maths.  Their work is simply incorrect, they are not able to count accurately.  They do not understand the 'oneness' of one.
Maybe they were in the top group in pre-school and reception and moved on to using numbers to calculate BEFORE they were ready.  Heaven forfend.

Don't get me started about moving children on too quickly in order to meet targets!

To help: Count in number sequences from different starting points.  Count in every day life. Leave the counting in 2s, 5s and 10s for a bit and simply find out how many shoes there are on the shoe rack today.  Estimate first, is that reasonable?  Who has the biggest pile of coins, Let's find out by counting, How many more do I have? Can you give me 12 cake cases/18 screws for this project/24 red lego bricks?

Stages: 1. Label each object as you count (one-to-one correspondence); 2. Remember to stop at the last object (this can take a while!) and declare 'How many?' 3. Count accurately without missing numbers, recounting objects by moving objects as you count. 4. Count larger groups of objects by grouping. Here come the 2s, 5s and 10s beloved of the national curriculum.

Another common misconception is found when children begin to 'count on'. In addition, we say "Put the biggest number in your head and count on from there".  Lets say the calculation is 12+4 -not enough fingers to count the whole thing.  The child obediently chants "put 12 in my head" and counts on "12, 13, 14, 15" The answer is 15.
How confusing is that?!!!
To the child, the counting from 12 is the same as counting from 1.

Now, if these children had had enough time to get to know these early numbers, perhaps been able to recognise the link between 12+4 and 2+4, see that both numbers were even perhaps, they may have been able to know more reliably if their answer was reasonable.  But for now "count on from the next number" has to suffice as we try to make sure little Julie learns this process correctly.
My favourite: 

How many squares?

Playing with early number is absolutely vital to successful calculation later.  Recognise odds and evens by making rectangles with objects. Share play coins or counters between the teddies, who has the most? Are the piles the same? Is that fair? Count, count, and count again!

A wonderful website to introduce a fun, creative approach to maths at all levels is nrich. Teachers can use this to help them teach at the new desired 'mastery' level.  Home schoolers have the joy of being able to use this approach without restriction, deepening that understanding of number and the relationships within and throughout.


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