5 year old maths/number understanding

[nordicwannabe]

My academic IQ is probably around top 0.5 - 1% of the population. So I'm not a genius by any means, but I'm used to understanding academic things easily.

I have a 5 year old DD (in Reception). A few people have told me she's clever, but sometimes I find myself really doubting it So I wanted to run this by you guys. She's obviously not gifted the way kids are when described on here - but given my own IQ I'd expect her to be reasonably far to the right of the bell-curve, and I'm looking for reassurance from people (who hopefully won't judge me for the question) that this behaviour doesn't rule that out!

Today, I was trying to show her what the digits 'mean' in written numbers. We have one of these posters with all the numbers up to 100 in lines of 10. I explained that the first digit shows how many groups of 10 there are (showed her on the poster) and that the second digit shows how many 'extra' there are. So far, so good. She seemed to get that, and was able to express a few numbers that way.

But then I was tried to show her how you can use that in sums (this was all in the context of a pocket money calculation!) And it all went wrong. She was struggling to subtract 8 from 20, so I showed her on the poster how you can just subtract it from 10 (which she can do) and then add the result back on to the other 10. And I tried to show her that you can do the same thing when subtracting from 40 or 50 or 60.. But she didn't get it, and just started saying random numbers!

This seems to me a fairly fundamental concept - what a number means, and how you can manipulate it.

Please don't blast me - of course I don't mind how clever she is. But I do recognise that her life will be easier if she's clever 'enough' and tbh I also find it strange when she doesn't understand things. Is it just that my expectations are out of whack, or is she actually not that great at maths?

What noble says is correct. Before understanding the number system in an abstract form, children need experience of it in concrete ways. Some children move on very quickly from this to apply their knowledge in the abstract, others don't. I would expect children in Year 2 to have a very solid understanding of place value and calculations with two digit numbers.

The new emphasis on mastery in the primary maths curriculum means we continue using concrete and visual representations, alongside the abstract, up to the end of KS2.

My husband is like this. His expectations of our son's ability to grasp things were, and probably still are, totally unrealistic. He's 8 now. His teachers say his maths skills are extremely good but he has expected him to understand things that are probably much later in the curriculum. At 5 just let them relax and enjoy it x

I'm year 3 teacher. You are expecting your child to work out subtraction involving exchanging. This is something that my class have spent weeks learning. We started by using base 10 to make the numbers and exchange and then subtract, before moving on to column subtraction. About half of my class is secure in the concept and the others still need to make the numbers with the base 10.

Absolutely no way would I expect this sort of maths to be performed by a child the age of yours. If she can count out an amount of objects and then physically subtract an amount, then she is doing great and is exactly where we would expect her to be!

Don't push her too hard OP. You could put her off completely. Stick to concrete examples, don't try abstract too soon. As PP said, we use concrete manipulatives throughout primary now.

Leave the kid be. At her age the mist important thing is to be confident with numbers and what they represent. Count forwards and backward to 20. Good number formation.

For the future,some kids don't "see" numbers, that doesn't mean they're not clever just that they are using a different method to get the result. There's nothing wrong with that.

bear - it was clearer with the visual aid, honestly!

noblegiraffe - really interesting to hear how this is taught by the experts. I can appreciate that hops right/left might help a child to visualise addition/subtraction as inverse operations. I do worry that using a number line too early would encourage her to learn it as a technique, rather than visualise what addition and subtraction actually is. I guess that's where continuing to use concrete counters comes in!

Daffydil - that's good to know that showing her that wasn't completely crazy! So it looks like I just tried too early, and probably didn't explain it very well.

To those saying I shouldn't teach her abstract concepts since I'll confuse her/put her off - and also that if she's bright she'll figure it out herself - I respectfully disagree. We don't question that taking our kids to the park often will help them develop a natural ease of movement which will benefit them all their lives (even if they don't become athletes). I think that holds for most things - including numbers and maths.

But I'll definitely take the comments on board: reduce my expectations, keep it very light and occasional, and make sure I only take it as far as she wants to go.

It's really useful to hear what other children this age are doing. Thanks!

We don't question that taking our kids to the park often will help them develop a natural ease of movement which will benefit them all their lives

Yes but you don't push the park on them if they don't enjoy it. Or put a 6 month old on the monkey bars and let them figure it out themselves . Or put a toddler that can't reach the ground in a swing and expect them to move by themselves. Even the park has skill levels that kids grow and develop into.

Play lots of games with her, snakes and ladders, junior monopoly, shops, that sort of thing. Let her learn through handling numbers in every day life.

That's true, RebelRogue - and the purpose of this post was to figure out whether my expectations were wrong. Turns out they were.

But the tricky thing with maths is that you can't see it like you can playground equipment, so kids won't give it a go unless you show them. I won't apologise for putting DD up on the monkey bars to see how she would get on! I've already said that I'll make sure I don't push it or make her feel like she's failed.

@nordicwannabe actually some kids do end up "seeing" numbers,once they have mastered the basics. They can manipulate them and work them and solve a lot of problems in their heads. It's amazing to watch. I also work in a school and it's fascinating how in the same year you get so many methods of solving the same basic question from the quickest mental maths to a slow but steady working it out. It's also interesting to see that top sets can struggle with a method because they know the answer already,but the lowers will get it straight away because it makes sense to them or it's more visual.

I don't want you to apologise and I'm sorry if I've been harsh. Just trying to say that your DD not knowing 20-8=12,especially by that particular method is not a sign of anything yet.

But remember maths is taught very differently nowadays and the methods we have are not the same ones as a school. It’s built up gradually adding concepts along the way. Introducing a different method that can be at odds with this can cause a lot of confusion

DS is a similar age (about to turn 5). He is by a long long way the best at maths in his class he's pretty average at lots of other stuff there's no particular reason for this, it's just a quirk.

He 'gets' numbers and understands place value but I tried to explain your method to him and he just looked at me very puzzled (and told me he could take 8 from 20 by taking away 4 and another 4). I wonder if they just need to find a method that works for them? Or my explanation was terrible

I know his classes' aim for the year is to teach counting to 20 and working on one more and one less than. So I think your DD is ahead of the game if she can manage more than that.

As an aside- I don't think maths progress is linear, or that early ability is much of an indicator at all. My dd struggled with maths in primary school now she's in the top set at secondary. I was top at primary, average at gcse and top at A level (& I have a 1st class degree in pure mathematics). No way would I expect a 5yr old to be able to do 20-8 without counting objects.

Think back to when you were 5. Did anyone try to teach numbers to you using the methods you've tried? I'm willing to bet they didn't. But obviously it hasn't hampered you, has it?

My son is g&t for maths. I’ve never really tried pushing him at home unless he asks. I have bought the fun workbook things in the past which he wanted and enjoyed but I’ve always been if the opinion that the teacher is the professional and knows much better than I do on how to get him to understand. He has asked about things in the past and of course we explained things to him then.

I see nothing wrong with teaching a child, if that is what you want to do and she enjoys learning.

I have a theory that maths education does help a child to get better at maths. Doing this 1-2-1 is a lot quicker than in a class of 30. I never used to wonder what IQ my dd was at, but just looked at where she was now and what was the next thing she could learn.

There are several things I have leant about teaching 1-2-1:
Keep it light, make it fun, make it visual, (ie, use drawings or objects as much as possible) and children learn by doing rather than being told. Teaching is as much about listening to what children understand as telling them about maths. When I introduced new topics, I would tell dd I did not expect her to understand it, I was just telling her it was there. Each time we returned to it, she understood it more.

Do not be put off teaching her. Of course children do get better at maths by being taught. Mathematics has been developed by humanity over thousands of years. No child is going to work it all out by themselves by 4 or by any other age. They all need to be taught maths. It does not matter what IQ they are, just that they are improving and still enjoying learning. Comparison with others or expectations of what their capabilities should be are pointless.

My 7 year old is very good at Maths and I have a high IQ, did Maths to a high level etc. I don't think she could do this at 5, maybe at 6. What she could do was add and subtract 1 digit numbers very quickly (quicker than her older sister who is bright but better at other subjects). She also understood sharing and multiplication and place value. Still, we have one daughter who is obviously going to be a strong mathematician and one who probably isn't, despite both parents being strong and achieving highly. Genetically speaking it's not a given.

I have a theory that maths education does help a child to get better at maths.

Of course it does! Otherwise my job would be a bit pointless

@noblegiraffe

Good. The more we can do to get children away from the idea that there is a maths gene which you either have or do not have, the better.

Asked DD (6 y1) to do 20-13. Tried to show her and explained your method. She looked at me like i was mad,told me to go away then proudly came with the answer 7. She drew her own number line and did it that way.

At that age we used to play with the old Cuisinaire rods and also numicons, just to play, talk about which one was bigger and smaller, honestly Numicons are brilliant. You can get them on amazon. They are just good fun to play with, build structures, repeating patterns, etc. And excellent at explaining some concepts such as adding and taking away, doubling. later on they are great at explaining multiplications.

I just think that it's often the method used that can make it difficult for little ones to understand. I would start with using things in your environment - DS learned to count in twos whilst walking down the street and guessing the next house number. He learned odd and even numbers that way to. And counting backwards/taking away.

Another tip is to get a 10-sided die (yes they exist!) and when you roll a 2 for example the child h as to shout what it takes to make it up to 10. This is great to learn number bonds.

I used to play a 'game' with DD at this kind of age where we started with a set number of counters/dried beans/beads/whatever and then she closed her eyes and I took some away and she had to 'guess' how many I had in my hand. She absolutely loved it and had no idea she was learning maths. You can start small, with five or ten, and build up.

mongoose and rebel - I can imagine the look, since DD did the same

But to everyone saying that the technique was confusing, or techniques have changed: I really I wasn't trying to teach her a technique! I was trying to expand her understanding of numbers, which I think is something fundamentally different.

gnu - you would lose that bet! I have a very vivid memory of my Dad doing exactly that for me when I was about DD's age. I was skipping along the road, holding his hand, and he was giving me easy multiplication sums to do. I was finding one tricky, and he explained an easier way to do it - and suddenly I understood how you could manipulate the numbers to make the sum easier (pretty much what I was trying to show DD).

But maybe you only get that through exposure to many techniques. And either way, I clearly explained it badly to her!

I've realised writing this that my own family experience is part of the reason I feel so strongly about talking with DD about numbers. Growing up, I often talked about science and maths with both my Dad and my older brother. I also find it intrinsically cool and interesting, and want to share it with DD!

This thread has given me some very good pointers to make that more likely to work:

• reduce my expectations hugely! Simple and concrete for now
• ‎tell DD I don't expect her to understand it straight away I actually think this will help hugely!
• ‎cuisinaire rods, numicons, 10-sided dice, and guessing games with sets of beans. Sound fab! Can't wait.

Thankyou everyone.

Buy a numicon set on Amazon and look on the New Zealand website in how to use them - very visual for kids

No, that’s hard for a five year old. My son who is gifted in maths could subtract since and double digit numbers into the thousands at that age but he isn’t normal! My 8 year old daughter who is very good at maths has probably just about started to do it.

When my daughter was in year one school gave me the new national curriculum for maths. It’s quite challenging for the majority of kids but is a good indication of level of understanding at that age. I wouldn’t try to go beyond it unless your daughter is doing so off her own back.