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Counting

Why is it, at one extreme, some three years can do abstract maths in their heads, while at the other extreme, some five years olds can't reliably count to five.

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What makes the difference is:

• Exposure to real life mathematical experiences using concrete (real) materials

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• Having an awareness of mathematical concepts e.g size, shape, colour, patterns, counting, etc

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• Having an understanding of mathematical terminology e.g. add, take away, lots of, divide, more, less, larger, smaller, etc

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• Having positive mathematical experiences while young. e.g. while driving in the car, cooking, gardening, building with parents

Early positive exposure to maths makes children's independent maths abilities higher. For example:

I'll retell a conversation as best I remember it, just so you realize what's possible... because it stunned me.

One day I was driving down the road and I had my three year old in the back of my car. His older brother had been learning his first lot of multiplication tables, that being x 2.

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'Two lots of two... that's four isn't it Mum?  He held two fingers up on each hand.

'Yes,' I replied.

'And two lots of four, that's eight isn't it.'

'Yes.' I again replied and caught a glimpse of him with four fingers on each hand, moving each consecutive finger as he counted them. I was impressed by his early understanding, as I hadn't ever see him do it before.

'And two lots of eight, that's ...'

I smiled as I thought... he's run out of fingers. But I caught a glimpse of his face in the rear view mirror. He was initially perplexed but then his eyes rolled up to the left and he imagined.

'... And that's sixteen isn't it Mum,' he said. And he smiled because he knew what he'd done was hard.

So how did this happen?

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When I analysed how he could do this I realized it was because he'd been exposed to maths concepts incidentally from a very young age and had lots of practice with real maths examples.

Size: "Look how much taller it's grown. It's the same height as your brother. Will it get as tall as me? Who can find the biggest tomato?"

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Number & Comparison: "I wonder which plant will have the most? Let's count and see."

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Subtraction: "If Grandma wants three tomatoes from this plant how many will be left for us?"

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1 (a.) Then progress real counting to five.

â€‹My son could just 'see' the answer in his head in abstract form.

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To begin; I'll divide maths concepts into basic areas to help you understand how you can expose your children to maths as part of everyday activities.

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BASIC COUNTING SKILLS:

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Some of this may seem obvious but I've learnt over years never to assume any knowledge and to begin at the beginning, particularly with mathematics because it's sequential.

Below I'm suggesting an order of the introduction of difficulty as your child learns to count. For activities you will need to go to the link page at the end of this page.

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Rote counting is the sequence.

Real counting is the number of items.

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1. Begin with rote counting to three

and reinforce with real counting. Include simple songs, chants, rhymes to reinforce three.

How many yellow blocks are there?                       How many yellow flowers?                       Let's put five blueberries on each dessert.

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N.B. Children will initially have to move items as they count them.

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Later they'll be able just to touch them or point to them.

Finally they'll be able to count with their eyes.

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Some will be able to recognise collections of dots such as on dice.

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2. â€‹â€‹Progress rote counting to six, then eight then ten.

Find real examples of counting up to ten.

Important Considerations

• Consideringing that 'th' is one of the last sounds for a child to be able to say, listen to how, many four or five year olds, actually count.

'firdeen, fourdeen, fivdeen, sixdeen, sevendeen...'

• But if they're younger or still can't accurately produce even the sounds above, counting often sounds more like this:

'birdeen, bordeen, bideen, dideen, dendeen...'

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• The similarities between birdeen (thirteeen,) and bordeen (fourteen) are obvious and children often omit one of them.

• Also  fifteen and sixteen have the same middle sound so again one of these is frequently omitted.

• And then having sixteen and seventeen both beginning with 's' adds yet one more confusing factor.

3. Progress rote counting to twenty.

â€‹N.B: There are often Counting Pitfalls

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The most common pitfall people make is thinking if their child can do it faster it must be better; but that's rarely the case.

For example. Children may parrot 2 + 2 = 4  with no concept of addition at all.

If your child has the chance to understand real or concrete maths before moving them onto visual representations of maths, or abstract maths, they'll have a lot better chance of understanding how maths works and feel more positive about it over the long term... because they'll be good at it.

Many children have difficulty keeping the counting sequence correct between 13 and 17 inclusive.

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â€‹â€‹What I did to overcome this problem, was to enunciate my sounds very clearly and see if the child could hear which sound each number started with. I also raised my pitch as I counted through fourteen, fifteen and sixteen  emphasizing each number differently.

I also reinforced the progression with numerals once they were reasonably reliable with their counting. Useful phraseology: "Thirteen is a bit like three teen, fourteen is obvious, fifteen is like five teen, six teen and seventeen are also obvious and that helped some children who understood the concept but had a speech delay.

â€‹4. Progress rote counting to thirty.

• Another pitfall is twenty nine to thirty, which trips a lot of children up and it often needs to be treated specifically. Many children will go 'Twenty ten, twenty eleven, twenty twelve, etc'

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Considering we're looking at learning to count over years guided by the child's ability I've included the next two areas as well. But I strongly suggest looking at the Web page The Importance of Proximal Development to help guide you.

â€‹5. Progress rote counting to one hundred.

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Another Counting Pitfall:

Yet another pitfall while counting to one hundred is omitting the fifties, the sixties or the seventies completely. This can be overcome by introducing a numerals chart and explaining how our system is based on lots of tens.

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6. Progress rote counting to one thousand.

Something to be aware of: Going from one hundred and nine to one hundred and ten to one hundred and eleven also seems to trip children up and may need to be taught specifically while most others in the sequence through to one hundred and ninety nine progress naturally.

Include numerals incidentally at first so children realise numerals represent a value. Numerals particularly useful once you get over thirty.

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There are a multitude of simple counting songs and activities on

For more Maths Ideas go to the links below:

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