7yo understands maths concepts but can't do mental arithmetic

[vvviola]

(Background: not in UK, have moved from one school system to another, including house/country/other side of world move.)

I've noticed over the past few weeks, since DD1 (7.5) started her new school, that while she understands maths concepts very well (addition of numbers in 100s, subtraction, fractions, time, measurement, 3D shapes), she seems to have no ability to remember basic addition/subtraction. She counts on her fingers all the time, even with sums that I know she must know (caught her doing it with 3+2 yesterday!)

Her previous school weren't big on drilling/rote learning (are any schools now, I don't know), and as she was in a mixed class it seems like any of that sort of stuff was done at the lower class level (I swear she spent 2 full years doing counting in 2s and 5s and counting backwards from 10!!)

Am I right to be concerned about this? Should I just let her new teacher deal with it or is it worth trying to do some work on basic facts myself with her?

It doesn't seem to be causing her much trouble at the minute and she's not struggling with maths, but I can see that it's going to cause a lot of issues as things get more complex.

For basic adding, we found board games with 2 dice very helpful.
Or playing 'shops' for both adding and subtracting.
Otherwise it took DD2 a while, but she's way better now at 10.5 than she was at 7.5.

I would work with her, rather than rely on the teacher. Fluency in maths facts is very important for proper understanding later, and not all schools emphasise it.

Ds1 is like that, he is 8. Dd gets it and makes leaps, connections and patterns in her head. Ds1 just doesn't.

Money is good, encouraging him to count his pocket money. Count it before we give it then ask how much he will have when we give this week's/how much he will have left after buying wanted toy/how much left to save. Playing board games, monopoly etc. Dh encouages him to move without counting each square so using the numbers on the board and doing the sum in his head or in monopoly using the principle that there are 10 spaces to a side. When doing homework we support him, allow him to explain how he was taught rather than using our ways (maths has changed since I was that age!) and if we help him with a sum we might think up a couple of extra examples to reinforce before moving on or if struggling with a sum use a simpler example with the same concept then tackle the one he was stuck on.

He is getting there. Times tables makes a big difference. If they can nail those and know them by rote it helps a lot. We got a CD for the car which has been handy and also as his confidence starts to grow and his understanding grows he is realising how his tables are useful and is more motivated to learn them.

Does she like to play on a tablet? We found Squeebles is a great package to train it, far more than mummy and daddy.

We also play lots of board games, letting her pay in the shops, even Smarties are great for subtraction games.

I agree with many others that playing 'shops' or playing with real money is the best way.

Asking a child to add 2 and 3 instantly sounds like work to them. But saying if I want to buy this for 2 pounds and this for 3 - how much do I need to take to the cash register is better. There are so many great online computer games for this, but being able to physically hold money really kicks starts this.

Number lines can help get rid of the finger counting as they help to visualize. I know at my DS's school they still did columns of 25 number facts to 20 they keep practising until they can do it under a minute. Even if they same sequence this helps eliminate the finger counting.

It's like a muscle the more you exercise it , the stronger it gets.

At a high level mental arithmetic is irrelevant.My DB is a Maths professor and cannot divi up a restaurant bill for toffee!

My younger DD was poor at mental maths. She managed a B at Maths GCSE though. I think it becomes of less importance as the child gets older, but obviously improves the speed of calculations if you can do sums mentally rather than writing everything down. I think the advcie above is excellent.

I'll give my standard Numeracy information, which may help:

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Practical things are best for grasping number concepts - bricks, Lego, beads, counters, money, shapes, weights, measuring, cooking.

Do adding, taking away, multiplication (repeated addition), division (sharing), using REAL OBJECTS as just 'numbers' can be too abstract for some children.

Number Bonds of Ten forms the basis of much maths, so try to learn them. Using Lego or something similar, use a LOT of bricks (of just TWO colours, if you have enough) lay them out so the pattern can be seen of one colour INCREASING while the other colour DECREASES. Lay them down, or build up like steps.

So:

ten of one colour none of other
nine of one colour one of other
eight of one colour two of other
seven of one colour three of other

etc,

then of course, the sides are equal at 5 and 5; after which the colours 'swap over' as to increasing/decreasing.

To learn TABLES, do them in groups that have a relationship, thus:

x2, x4, x8

x3, x6, x12

5 and 10 are easy

7 and 9 are rather harder.

Starting with TWO times TABLE, I always say: "Imagine the class is lining up in pairs; each child will have a partner, if there is an EVEN number in the class. If one child is left without a partner, then the number is ODD, because an odd one is left out."

Use Lego bricks again, lay them out in a column of 2 wide to learn 2x table. Go half way down the column, and move half the bricks up, so that now the column is 4 bricks wide. That gives the start of 4x table.

Then do similar things with 3x and 6x.

With 5x, try and count in 'fives', and notice the relationship with 'ten' - they will alternate, ending in 5 then 10.

It is important to try and UNDERSTAND the relationships between numbers, and not just learn them 'by rote'.

An inexpensive solar powered calculator (no battery to run out!) can help learn tables by 'repeated addition'. So: enter 2+2 and press = to give 4. KEEP PRESSING = and it should add on 2 each time, giving 2 times table.

There are good web sites, which can be fun to use :

www.ictgames.com/

www.woodlands-junior.kent.sch.uk/page/default.asp?title=Woodlands%20Junior%20School&pid=1

On Woodlands school site, go to 'Woodlands Resources' and select from there.

(Things seem to have changed on that site recently, so I don't guarantee you can get it, but it's worth trying. Otherwise Google woodlands-junior.kent)

Hi vviola:

Just to say that agree with a lot above & agree Woodland Junior School Maths Zone is very useful (see especially games under place value/ hundred square/ addition & subtraction) - and Ferguson's comprehensive suggestions but would add that sometimes maths makes more sense when phsycially manipulating things - often this can be done through games:

With borrowing/ carrying concept:
we found working with food/ objects really helped - we used different but similar things to distinguish tens from units - so grapes for tens and raisins for units or duplo blocks for tens and lego blocks for units. We reviewed that you can only have one digit in each column: 0 - 9 in units column (right most place in whole numbers) and tens column also just 0 - 9.

So adding 9 + 6 - two plates of raisins - you can see that you have 15 in total by counting them all up but also get that you can't write 1-5 in the units column. On paper you're going to have to put the 5 in the units column and carry the ten - but that step isn't always obvious at 7 years of age. So say Wow! We have way more than 9 raisins we're going to have to trade some in for a grape. One grape = 10 raisins - count out 10 raisins exchange for a grape. You then have 1 grape and 5 raisins which then can be scored down on paper (I tend to draw two columns) under tens (show grape)/ Units (show raisin) column - as 1 ten (make a 1 in teh left column) and 5 units (mark a 5 in the right column) - which we read as '15'.

Works well with subtraction as well. So say you wanted to take 9 from 13 using duplo and lego. Duplo block = ten and unit block = one (units).

So on one plate you'd have 1 duplo block and 3 lego blocks. You want to take away 9 (which would be 9 lego blocks) - but you don't have 9 lego blocks on the plate. Solution - cash in your duplo block for ten lego blocks - take away the 9 from that - you have one left - put it with the 3 other lego blocks - and you have 4 lego blocks left - which is the solution to 13 - 9 = 4.

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Subtraction is ideal at the dinner table. Have your DC count out his chips/ peas/ mange tout/ broccoli/ baked beans/ carrot sticks/ etc... and suggest he takes away 3 (have him eat them up) - then ask how many are left. He may have to count them up - but it's a really nice visual way of reinforcing the maths concept of subtraction. DH was very helpful with this - applying the principle to fractions in relations to desserts - i.e. what happens if I eat 1/3rd of your slice of cake? What fraction is left?

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The card game 21 (or blackjack) is also very helpful working all these number bonds to 20. (and I do mean every possible combination to make the numbers between 1 - 20 - often schools make it sound like you just need to know combinations for 10 or 20 and not all the ones between.). In fact to get really fluid with calculations you need to understand all the ways to make 8 as much as 10, for example.

Play it open handed at first - so your child can learn the game/ see the decision making process (i.e. I have 17, there are lots of high number cards out on the table - do I risk asking for another card?).

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You can also play snakes and ladders with more than one dice (so 2 dice would be numbers up to 12/ 3 dice numbers up to 18/ 4 dice numbers up to 24) - we find you have to play the board more than once with such big rolls - but it really helps work those additions.

For subtraction just play the board backwards.

We started out with DDs counting on - then encouraged counting in jumps - so with a roll of 16 - maybe adding 10 to your place (say it was 23) - so getting 33 and then trying to add 6 or counting on 6. Ultimately moving to just adding it all in your head.

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Finally we played number bond snap:

So set a target number - say 9. Use an ordinary deck - Ace = 1/ 2 -9 as marked/ face cards all = 10. Shuffle. Place deck face down and we tend to write our target on a post-it and put it next to the pile of cards. Flip the card. Say it's 7. First to shout out 16 wins the card. The overall winner is the one with most cards at the end of the game.

You can play this for subtraction as well. So again chose a target number - let's say 9. Use all cards up to 9 in an ordinary deck. Values as before. Flip the card - say it's 8. 9 - 8 = ? first to shout out 1 wins. The overall winner is again the one with most cards at the end of the game.

HTH

Just wondering as you say you have moved. Is the school language different to before?
I grew up bilingually but my schooling was all in the same language. For the longest time I was not able to do mental arithmetics in the other language. Even now, I find myself translating the problem to my school language, solving it, then translating the answer back.

I think that is because I remember the 'addition facts' in words rather than in abstraction. So when I used to see 4+2= I would kind of read it out loud in my head - in my school language - four plus two equals .. And my brain would provide 'six' and then I'd translate the word six into the abstract 6.

So if you have indeed moved to a different language school, the issue may simply be that she has to re-learn the number facts in the other language.

I think that is because I remember the 'addition facts' in words rather than in abstraction.

This is exactly why maths facts are not that helpful. They are just rote learning and add very little to real understanding of mathematical concepts.

If your DD understands the concepts, OP, I would back off and let her solve it herself. It will come in time. Not understanding the ideas at this age would be a big problem. Being a little slower to work without props like fingers really isn't.

I'm the other way round - great mental arithmetic, struggle with the facts, rules and reasoning. I'd much rather be like your daughter TBH. She will be able to progress with maths as it gets more complex and abstract. For adding up you can always use a calculator /spreadsheet.

If you just want her to get better at mental arithmetic I second the mantra of practising. She will get better soon. Numbers are all around us, there is so much you can do! Add up figures on numberplates, add up the shopping as you go, find out which item is cheaper out of two on offer when the cost unit is different, double up or half baking recipes, convert metric to imperial etc. God I must be a geek

HTH

I also agree with those saying the adding small numbers will come with time. If you did want to do arithmetic with her, it would be better to do number bonds to 10 or times tables. If she is getting the concepts, it sounds as though she has a natural flair for maths. It would be much better to encourage this than to make it tedious by insisting her rote learning small sums.

I think this is ok and not a huge worry.
My dd was doing this at 7. She is now 8, nearly 9, and has finally kicked the counting on fingers habit. However, we did do lots of maths at home to get to this stage.

I posted on here a while ago, as my DD really struggles with maths and arithmetic. We were recommended a book called Power of 2. It's expensive - about 20 - but we've been working through it and I would say it's beginning to help. It's a series of basic arithmetic questions that you work through WITH your child, starting from a very basic point and building from there. We try to do 10 mins or so most days, and I would say DD's confidence with basic sums is beginning to increase. You won't find it in the shops, and it doesn't seem to be widely known - not sure why. I'm impressed with it.

Thanks everyone for all the advice and suggestions.

There was no language change - both English speaking countries, just a large difference in style/teaching methods.

DH got totally exasperated with her at the weekend when she seemed completely unable to add 5 and 4 together (I have no idea of the context, I just came in at the end of the conversation). He felt very guilty afterwards so we've stepped back a bit and will have a think about how to work on this with her.

It's a relief to hear of others who were similar and grasped it eventually.

Last week I think I discovered part of the reasons behind it. Being part of the "top" maths group in her mixed-year class in her previous school seems to have meant that it was assumed she was doing the calculations in her head, and they didn't notice her using her fingers all the time. And when new concepts were taught she was able to pick them up relatively fast, so as far as everyone else was concerned, she was where she should be.

DH often takes her and DD2 out to a cafe after school when he picks them up - perhaps I'll suggest that as a starting point he lets her calculate the bill and hand over the money.

My DD is similar. We are doing a few minutes in the car on the way to school every morning and the regular practise is helping, plus just a few minutes and no pressure, keeping it all well within DD's abilities. Started with adding 1 to a number, then adding 2, then adding 10, lots of additions up to 20, doubling numbers, adding on 9 ( by adding 10 and taking off 1) now moving onto tables as school insists. But getting the concepts and methods is more important in my view, so I wouldn't be too worried.

Second the recommendation for squeebles or similar. There's no substitute for practice for getting these things smooth and quick, and games are brilliant for getting that practice in without them noticing.

While I agree that getting the concepts is the main thing, as they get higher not tripping or taking time on the basic arithmetic helps a lot, so they can concentrate on the concepts. When I was doing A-level and even higher maths I used to practice on one of those Little Professor toys to get my speed and accuracy up at exam time - anyone remember those?