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?

I used mixture of resources with my ds, some posters, some second hand educational toys from cousin(fraction sets, peg board, tangram, 3d shape puzzles, etc), and some I bought from charity shops(teaching clock, abacus, number magnets, etc).
I think posters are good if the child is interested(my ds demanded me to buy all available at the library), they can see it all the time and learn without an effort.

My DS6 was doing that in reception perhaps even end of nursery, his maths has always been really good and the teacher has told us he is ahead in this area. he did it mentally however he struggles understanding the concept behind it eg number bonds etc. To be honest I was the same, I could never get my head around the way the teacher explained it but always figured it out my own way if that makes sense? Nothing has been mentioned this year of him being particularly ahead with his maths ( to be fair I think the teacher is struggling with him as he is easily distracted) I ti k perhaps because he can get the answer but not explain the method of how he got to the answer.

crazymum, that's what my ds's reception teacher focused on. For him to explain how he got the answer. Luckily my ds's reception teacher was a maths specialist, and able to see what his problem was.
If your ds's teacher is not doing it, I suggest you do make him able to explain how he got the answer.
From what I heard, the way my ds works out things are different from normal, but it still gets the same answer and he understand the concepts, and teacher said it was fine.

I think it's really hard to teach something that you're good at. Much better coming from someone who is either a trained teacher or who has just learnt it so can relate to the learning process.
I note also that a leading Harvard professor whose lecture I listened to noted that once he quit explaining stuff to students and instead asked them a question and left them to figure it out, recorded that as a turning point in his career. Student achievement rocketed.

In my view, what they are doing in schools now is a good thing. I was born in 1979 and schooled in the 1980s-1990s (obviously - good at maths, see? ). I was good at maths. Seriously good. I had been doing maths questions on a computer that my dad had programmed, in an age where most people didn't have home computers, before I started school. By the time I was year 3, I wasn't allowed to do the times tables tests, because there was no point, as I got 100% and finished them in 3 minutes, so I did maths investigations instead. We worked from maths textbooks, and I was so ahead, that I had to either do the art project (we were building Noah's ark in the corner of the classroom) or help the other kids who were struggling. I'm not saying that to boast, just for context.

I just saw numbers, and maths was beautiful to me. This continued in secondary school, except that when I asked for harder work, I just got more work at the same level. I found some areas tricky, where they involved visualisation of rotation, etc., because I'm not good with that, but anything involving numbers, I aced.

However, I came unstuck at A-level. Because I was amazing at maths, and just knew the answers to questions, in part because I had secure knowledge of my times tables to 13×13 and square numbers, cube numbers, etc., I had never got in to the habit of writing the method for my answers. In A-level, with more complex problems, writing each step of your method is vital. It took a lot of frustration to learn that lesson.

The new way of teaching children is completely frustrating to me, as a 'numbers girl', but I can see that it is teaching my children what the numbers actually are before learning the more efficient methods for solving the problems. They aren't being taught a 'sausage factory' method for problem solving. They are being taught how to manipulate numbers.

Also, Numicon is worth its weight in gold. I have a set at home to use with my girls.

Great post, lougle, thank you for sharing an experience. Very encouraging.

Hi OP and PPs

first off, thanks for an interesting thread :)

OP I do get your 'method' and agree that if you properly understand place value and how numbers work, then you should be able to 'see' that 20-8 is the same as 10-8 just with an extra '10' underneath. Not a technique, an 'understanding'.

I think that your mistake was in thinking 'I've explained place value/how numbers work, now she gets it and can apply it'.

'Getting it' can be different depending on the child, but not many 5yos would 'get it' simply from having it had explained to them.

Perhaps before you start challenging her to apply it again, give her more opportunities to work on really 'getting it' - e.g. Dienes cubes, Numicon, those number arrows where you stick the units into the tens arrows... You have basically identified an aspect that she doesn't quite get yet, so you know what to work on! Sometimes it also helps to let the child work it out for themselves, e.g. give them lots of questions such as 10+6, 10+8, 20+3, etc and 26+4, 13+7, 54+6, ... and they'll work out the 'pattern' themselves.

FWIW, I have a great example from a friend that illustrates a child who really 'got' the fact that e.g. 12 is like a 2 with a 10 alongside:

Mum and daughter (just turned 9) were a bit bored on a long train journey. DD suddenly said: 'Mum, I know what all numbers from 1 to 5 added up results in. It's 15'. DM: 'That's right. I know what you get when you add up all numbers from 1 to 10; can you work it out?' DD, after a few seconds (in which she added them up mentally): 'That's 55'. DM: 'That's right. Hmm, how about all numbers from 1 to 20?' DD, takes about 20 seconds: 'That's 210'. DM: 'Oh, that was quick, how did you work that out?' DD: 'Well, it's 2x55 +100'.
It took my friend (DM) a moment to figure out what her DD had just done. Basically, she had recognised that each number 11 to 20 is the same as each number 1 to 10, just with a 10 added to it. There are 10 numbers 11 to 20, so that is 10 times you have an extra 10, i.e. 100. So you have all number 1 to 10 (=55), twice (once for 1-10 and once for 11-20) -> 2x55, plus 10x10. Pretty clever, that!

I second the previous poster, thanks for a very interesting thread OP. I totally get your method, that's the way I manipulate numbers in my mind when I need to work out something like what you said (20-8).

When my first son was that age, I had not point of reference on what he should be able to do, so my expectations were based on what the curriculum or the teacher said he should be doing at reception. When I saw they were learning doubles at school, I played lots of cards and dice games with him at home and soon enough he knew them all beyond the level expected at reception. When they were learning halves, the same thing, we practised halving all the numbers from 2 to 24, but soon he could apply the same principle to other two digit or three digit numbers in his mind. When we played card games and had add up or subtract several numbers he would quickly give me the answer and when I realised he was right, I would ask him to explain how he did it and it turned out he could "see" ways and manipulate numbers in his mind in the same way I was used to doing. Like in your example, he would tell me I know 20 is the same as 10 plus 10, and I know 10 minus 8 is 2, so 20 minus 8 has to be 12. Then in Year 1, his teacher said how unusual and talented he was in maths, and I just thought she was being nice or exaggerating in her compliments to him. But all his teachers ever since kept commenting the same. It was only when I started helping at a primary school years later that I realised that other children couldn't do what DS1 used to so easily in KS1, and that I got a real perspective on what is actually normal or a real expectation for that age group.

Now DS2 is at the same age DS1 was then, and in reception, and I can see that even though he is also clever, learns quickly and can already do things that other children in Year 1 and Year 2 are struggling to master, he has not reached the stage of being able to "see" and manipulate numbers in his mind like DS1 could, yet. I'm sure it will come to him eventually, and once it clicks in place he will be able to do it as many other children eventually do as well. But it just shows that every child is different, and we need to keep it all in perspective to make sure we have realistic expectations.

Lots of useful suggestions here for things and resources you can use with your DD! Some of my favourites are sum swamp game, snakes&ladders using two or three dice to practice adding up, and if your DD likes games like Top Trumps, I use them to practise lots of things like saying my number of double of this, or half of this, or this number minus this, etc, so DS has to work out first what my number is and then compare it to his to see if he's won or not.

I get you OP. I assumed my DD would share my interests and talents. But it's funny how things turn out. She doesn't share my interest in philosophy, drama, psychology, love of words and literature, feminist principles, interest in politics...... I will confess to being disappointed at first. But she's so musically talented that she is about to graduate from a conservatoire. I'm a bit musical, but she's so amazingly musical I'm in total awe of her. And yet the thing that makes me most proud is that she is a lovely, kind person. Honestly.

Who knows what lovely qualities and skills your DD will develop. Enjoy watching her develop.

Don't want to cause offence but everyone has different methods and yours sounds confusing! Have you tried doing it verbally? My son is good at maths and we work out a lot of it through conversation, he's not yet 5 but if I ask him what half a cake with 8 pieces would be he knows that's 4, or 50%. I find through him asking questions or me asking questions we work out what he's interested in or a good way of explaining it together, you can tell by their face if they're lost! A lot of it we do in the car which I think takes the pressure off, and if he can't do sometime we just move on. I suppose I am pretty confident he's good at maths though, he has a maths professor for a grandad and my husband and I both have maths a levels. I don't really know what he does at school maths wise, just go with interests and what they find fun. My son is really into infinity, such a geek in the making.

My DS1 is very good at maths, and I never had to teach him place value. DS2 didn't grasp it so quickly - I remember being concerned in Year 1 that he still seemed to be struggling with it. Now in Year 4 he is exceeding expectations - he's just so intuitive as his brother.

I would have done your problem with counting on - so +2 to get to 10 and then +10 to get to 20. (With or without a number line.) That's how they did it at school, and also roughly how I do it in my head. Obv the same as you were trying to convey, but slightly more explicit.

Hello, it is important to have high expectations for yourself and your children. The best approach to education should be the stage and not age, it is not impossible for a 5-year-old to subtract from 20. My 4-year-old can subtract and then compare varies subtractions within 100. The issue might just be the method and when a student does not understand an explanation, you just need to change your approach to teaching the topic. Try using Numicons, Mathelink cubes and even Nrich and various wonderful resources available to help teach your child. I hope this helps and if you have any further questions feel free to message me. Please do not be dissuaded by negative inputs.