It's the university at the door - they want me to give my degree back

[brixtonbrood]

The list of Things Which I Have Trouble Explaining To Small continues to expand, and she's on a bit of a roll at the moment.

Does anyone have any good links to resources (or, at a pinch, actual paper books) that would enable me to begin explain infinity (just aleph null will do for now I think) and higher dimensions to a four year old who is very keen to have them explained convincingly?

He (who is my normal resource for technical explanations) is excused maths, and in particular, as an engineer, is excused higher dimensions as he thinks they're a mathematician's con trick.

Yes I know I *should* be able to explain them, but I've previously had serious trouble with explaing why one and one does not (or does) make eleven, so my track record is not good.

I would have breathed a huge sigh of relief that tonight's question was "What's a quarter in maths language?" because I know that one, but you try and explain that in thirty seconds post lullabies with the lights out. She's been promised that if she gets dressed really quickly tomorrow morning Mummy will explain it then, because even I should be able to explain fractions if I have a pen and paper to do it with, or, better, a piece of toast and a knife.

Comments

[juggzy.livejournal.com]

Cuisenaire RRods

You can also buy them at Amazaon.

This is mainly for the place value thing, for which an abacus would also help

Unless Small is a genius (I'm not disputing it) play a game with 'larger number'. Take turns to see who can say the largest number. Let her deduce that nobody can win that one.

[brixtonbrood.livejournal.com]

Oh those look good - they've probably got something similar at school somewhere, but given that her teacher was firmly informed that it was school policy that reception children were not allowed to borrow library books regardless of whether they could read them, my faith in them has been rather shaken.
The place value thing seems to have come and gone, but I'll dig the abacus out. The higher dimensions thing isn't going away though - school is doing one-d two-d and three-d shapes with them, and she's not taking no for an answer about what comes after that.

[juggzy.livejournal.com]

I think you'll probably have to talk about the dimensions as a way of finding something. Get some newspaper and put it on the floor and have fun locating toys at different coordinates (or use chalk on tarmac). Then (can you get one of those three dimension noughts and crosses boards?) find a way to extend that to locating an object in space using three numbers. At this point, she should take the fact that there are only three (or four if you want to include 'when' something is) as self evident. I very much suspect (although I could be wrong) that what she's doing when she wants to know about more is a number game (pattern sensing and extending child) rather than any naturally deep insight into the structure of the Universe, although she is laying excellent foundations for the abstractions that will be involved in higher mathematics and particle physics later on. Even if they're very clever, the likelihood is that they're operating at the concrete stage when they're four years old. So, she's going 'why do the numbers of dimensions stop' rather than something deeper, which is very very clever in itself for a four year old. By the coordinates game, she should be able to figure out for herself why the numbers of dimensions stop at three.

You might want to divert her by showing her the nine times table and seeing if she can spot a pattern (and then extend that to the three times table).

[juggzy.livejournal.com]

Mmm, (just thought of this) - a book with squared pages. She can find an object on any page by counting the along and up, and she can find how deep down into the book an object is by giving the number of the page that the object is on. That might work - try that.

[juggzy.livejournal.com]

(and she might come up with the idea that the books have to have numbers so you know what book something is in, and then the idea that shelves have numbers, and that is probably as concrete as you are going to get over 'higher' dimensions.

[juggzy.livejournal.com]

Sorry for the multi post mentalism. The upshot is that we only need three dimensions to say where anything is in our world (sideways, along, and up), but we could have different 'location' systems where we would need more than three numbers to say where anything is.

[brixtonbrood.livejournal.com]

That all sounds fantastic, thank you - v. exciting to see your fabled teaching fu in action. At the very least a starter course in Cartesian goemetry will allow us to play Battleships (I cannot bring myself to play noughts and crosses, it strikes me as dishonest).
I've got a great times tables Ladybird book with the numbers laid out in grids coloured in to show patterns in the tables - must dig that out....

[juggzy.livejournal.com]

heh. thanks, but I don't think I have much fu at the moment.

I'm just interested in the nine times table as a pattern discovering thing for them. If she hasn't met tables yet, the cuisinaire rods should demonstrate in a concrete way that muliplying is a short hand for adding a lot of times.

Then look at the nine times sequence in particular. The numbers go: 9, 18, 27, 36, 45, 54, 63, 72, 81 etc. Ask her what she sees. See if she can pick out any patterns in that. Nine times table is particularly good for this sort of stretching (seeing if she can pick out the patterns is also a test. Don't give her help).

[bugshaw.livejournal.com]

Then teach her base 8, get her to work out the 7 times table in that, and see if she can spot a pattern ;-)

Re: higher dimensions. Is she up to Flatland? Identifying with the intrusion of a sphere into 2D space, and trying to get a brain around what a 4D object in 3D space might look like?

[brixtonbrood.livejournal.com]

As noted elsewhere I'd be very tempted to try her out on Flatland, but the social and gender political stuff makes it out of the question.

[celestialweasel.livejournal.com]

I recommend White Light by Rudy Rucker as a bedtime story :-)

[brixtonbrood.livejournal.com]

I would be very tempted to try Flatland, but the lurch into Marxist/feminist social and gender politics would just be too tricky, and of course once they can read it's more difficult to skip the boring/problematic bits of books.

[celestialweasel.livejournal.com]

There is the Planiverse by A.K.Dewdney to consider, then. The creatures are on the surface of a circular planet rather than moving over a plane which seems more natural to me somehow. IIRC correctly there is not much in the way of tricky material.

[juggzy.livejournal.com]

slaps the weasel

[celestialweasel.livejournal.com]

I thought this looked quite good
http://mathforum.org/library/drmath/view/60400.html
(there is more on that site)

Or this, which has Cantor's hotel but less sex and therefore is probably better than White Light (which was a joke :-)) http://www.c3.lanl.gov/mega-math/workbk/infinity/inhotel.html

[tinyjo.livejournal.com]

My major memory of infinity as a proper concept was reading the phantom tolbooth, which is a fantastic book all round.

[undyingking.livejournal.com]

Mm, "What's the biggest / longest number there is?" I read that when I was about 7 I think, but it might be OK for reading-to at 4...

[brixtonbrood.livejournal.com]

Ooh, good point. I'd forgotten it had infinity stuff in there - unfortunately I think some of the other stuff is just a shade too tricky, but I'll certainly bear it in mind for next year (obviously we do have a copy).