### Can You Teach Children Maths?

Ten year old Quinn has got her SATs coming up next week. One area of weakness I've picked up on is her maths. She's said she doesn't "like it" but that must be as much to do with how it's taught at her school as anything else. Maths can surely be fun? I know I love it and it's always been my favourite subject at school and then, later, university.

Can you teach maths to somebody who isn't mathematically-minded though? Surely, yes, to a degree (just not degree level maybe). I've been trying to help Quinn recently but Karen has said I'm over doing it and can't expect people to understand things just because they come easily to me. I know this and have tried to keep it as simple as possible. While we've had some success with fractions and negative numbers, we're not doing so well with equations.

One question from her test paper consisted of a table of numbers and formulas. For each value you had to work out "n" for each corresponding formula. One pairing was formula 5n-2 and the value 38.

The fact it was in tabular form maybe confused her. So I told it was just like the equations we'd been talking about a few days before. At that time I thought she'd got the idea of basic algebra, but she still looked confused when I wrote down the problem like this:

`5n-2=38`

I've tried equating (ha ha) equations to a balanced sea-saw. The bits on either side of the equals sign need to balance out and always be *equa*l. From there, I explained as simply as possible that, with the above equation, we have to simplify it down to the point where we have nothing but n on one side of the sea-saw. So we then know n=??. To do this we get rid of all the number. We get rid of the -2 by adding +2 to each side. I'll say to her: look what happens if we add two more to both sides. The sea-saw is still balanced and the equation becomes:

`5n -2 +2 = 38 +2`

She sees that things cancel out and that it can be re-wrtitten as:

`5n = 40`

Similarly, I'll tell her, we can get rid of the *5 by dividing both sides by 5. Like so:

`5n/5=40/5.`

The times by 5 and divide by 5 on the left cancel out to give:

`n = 40/5 = 8`

To me this *is* simple. Maybe not entirely intuitive but certainly easy to grasp. The kind of thing I do in my head without a second thought. I can see that it might be confusing though and try to assume nothing. Another approach I took was to say we could move things from one side to the other to try and get "n" alone on one side. When you move something to the other side it has the opposite effect. Move -2 over and it's a +2. Move *5 over and it's /5. You can demonstrate this with real numbers - explaining that 5-2=3 is still true when we write it as 5=3+2.

Half the problem is getting her to start using scrap paper and a pen to "visualise" the problems. Instead she will struggle to do it in her head. The other half of the problem is that she take the defeatist's approach of assuming it must be hard and so not even worth trying to work out. As she keeps reminding me, I'm thirty and she's ten. What I showed her yesterday was this equation from my university maths course-work, from when I was twenty. This, I told her, is "adult maths". What she's trying to do is **not**.

Luckily she didn't ask what it meant as I have no idea whatsoever. It's amazing what you forget you once knew. One day in the future I will have no idea what half of this Domino stuff was all about. Hopefully.

I am going through exactly the same thing with my neice and her maths. I have found that one of the easiest ways to demonstate things is to start off by showing it in reverse. Show n = 8 then say if I multiply both sides by 5 you get 5n = 40 etc, this hopefully shows them how you can generate a complex looking equation from simple steps and therefore can convert the complex equation back again.

One of the biggest stumbling blocks was getting her to comprehend the order in which you need to process the elements of the equation, brackets first etc. However I think(or at least hope) that we have finally got that one covered.

From one Notes Developer/Part-Time Maths Tutor to another wish her luck from me!!

Jake

Had (and still have) exactly the same problem with mine - he's 13 now. Have you pointed Quinn to the BBC education site where some of this stuff is made a bit more fun? {Link}

Thanks guys. I've just noticed another source of possible confusion. How's she to know that 5n is 5*n and not simply that n is a missing number - so it could be 51, 52 or whatever. Maybe she needs to know that 5n mean 5 times n. I'd overlooked that.

I'll show her the "Numeracy" section on the BBC site when she gets in tonight.

Jake,

Good stuff! We homeschool our children and I teach the Math and Science to them. I have to say a lot of what never made sense in school makes sense now as I do it with them. Whenever possible, I try and equate the practical aspect of the mathematical truth I am trying to teach them.

Would you know I just took the GRE to get into a Masters program and all the Math I've been teaching my 15 yr old paid off :) So you never know when the stuff you're teaching is going to pay off.

Still enjoying your site as always. Keep up the good work.

Dan

Stonybrook, NY

Regarding the sea-saw, remember that a real picture involves things. So on the left you may have 5 eggs (hedgehogs, tortoises, whatever) and something like a weight representing the number -2. On the other side you have a weight of number 38. 38 could also be 19 x 2weights. Not sure how you handle a -2 weight though! Perhaps keep positive numbers for a while until the concept is grasped. Maybe an understanding of "minus 2 on the left is the same as plus 2 on the right" is important first so you can redraw the scales with 5 hedgehogs on the left and 40 weights on the right. If you represent 40 weights as 5 x 8weights, the weight of the hedgehog may be clearer?

Sort of how I did it at school, and I went on to confuse the hell out of myself by degree maths. Relating things to reality is important for all ages - even when I tried to help my dyslexic husband do the maths for degree level engineering (now there's a challenge).

And whatever you do it must somehow be fun.

Good luck,

CAroline

Try explaining it in other terms with containers that can be variable.

5n-2=38

or...

5 equally loaded IPods - 2 mp3 files = 38 Total Mp3s files

How many Mp3s (songs) are in each Ipod?

C'mon... don't you want to raise an Apple junkie and keep that company going? :)

>don't you want to raise an Apple junkie

No. Not really. In the same way I wouldn't want to raise a Windows junkie or a Linux junkie. She can make her own mind up. Macs will probably win though as they're more bling than PCs.

As a girl who almost failed math, I can say that conceptual problems are difficult to deal with. It's much easier for me to learn with actual *things*. I used toothpicks or marbles or whatever for basic equations like the one you're showing above.

Sort of along those lines, Stan Rogers has an interesting blog entry about differing learning styles:

{Link}

Maybe a better idea would be to present maths as a set of rules for a game. Simple rules - complicated game. If they don't like the complicated game they can still learn only the simple rules and pass exams ;-) Don't try to connect mathematical entities to reality. Complex numbers, n dimensions, calculus etc will give your young friend a lot of trouble if she tries to visualise them later in high school. Arghh, I'm just babbling. BTW, maths used to my fav subject too. Not anymore. I decided to study applied maths and things got %$"#$%&# complicated. I hope I'll have my b.sc. by the end of October. It's gonna be a long summer as I will be writing my final thesis.

P.S. You don't want to raise a junkie ;-)

One thing she's good at is complicated rules. If you play a game with her half the time is spent explaining the overly-complex rules. Kids!

Yeah, I know what you mean about not having to think about something, and then describe it in detail to someone alien to it.

Writing it down helps for sure. Then basically doing what we can to get n on its own is the next step. Add 2, the divide by 5. The way you did it seems the simplest to me.

Calculus was a lot harder for me. I did those maths courses @ UMIST too, without the Maths A level beforehand. I got by, but it was a lot harder for me to identify what I should be doing next to whittle the sides of the equations down. 5n-2=39 cries "Add 2" whereas your hieroglyphics cry "Your move!" to me.

Some people just have a knack for seeing how the unknows are cloaked. This is what the really good maths people on my course seemed to have. I don't think you can teach that, although it might be possible to *learn* it by watching how they did it.

I didn't beat myself up, it's just a natural mental gift they have - there's no point beating yourself up that people are taller than you (a physical merit) so why worry about the mental ones too?

I found this an interesting read:

"Daniel Tammet is an autistic savant. He can perform mind-boggling mathematical calculations at breakneck speeds. But unlike other savants, who can perform similar feats, Tammet can describe how he does it. He speaks seven languages and is even devising his own language. Now scientists are asking whether his exceptional abilities are the key to unlock the secrets of autism. Interview by Richard Johnson"

{Link}

Various people have touched on the issue here. I think being "mathematically minded" comes down to being able to think conceptually. Writing things down can help, but everyday maths (comparing prices, estimating fuel consumption, etc) is mostly done on-the-fly ie. with nothing to write on.

My eldest son really struggles with maths. I've had a hard time teaching him all the tricks I use to make calculations in my head. Relating to practical examples does help, but when you get to complex equations there is often no real world example (well, not at his age).

His brother on the other hand just gets it instantly. I can remember many times at the dinner table asking the school boy some mathematical question and his pre-school brother providing the answer!

My approach: I have always loved maths, and I know it is important in everyday life. So, for the son who just doesn't get it, I focus on everyday applications (including some programming - he's interested in computers), but mostly focus on the other things he is good at. It's important that kids know that failure at one thing (eg. maths) doesn't make them a failure at everything.

Just another tip:

Teach equations as a way to keep an account of exact justice.

(What YOU have got on one side ... compared to someone else ... and manipulating it in a real world game. An unknown may be what's hidden in a box, wallet ...)

Childeren do understand and care about justice. (And there are some recent evidence that even monkeys do ;-)

I like your

So what is the answer ???????

because all it has at the end is n=1,2 ....