conuly

Many Hands Make Fractals Tactile

http://nyti.ms/XWkCac

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How High Could the Tide Go?

http://nyti.ms/10zYreh

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Generation LGBTQIA

http://nyti.ms/RGv4TA

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For Space Station, a Pod That Folds Like a Shirt and Inflates Like a Balloon

http://nyti.ms/UusiiZ

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Casting out nines

It's a different way to check your math work than "doing it backwards". It's not perfect (you have a 1 in 9 chance of getting a false positive, and it seems that if you transpose two numbers it won't make a difference to the end result), but if you're mostly competent at basic arithmetic or just need a quick check, it's a lot of fun.

I taught it to Ana, but because "casting out" isn't a term in her vocabulary and because it's unlikely she'll ever learn it in school (so she doesn't really need to know the correct term) I called it "throwing away" the nines instead.

For multiplication, I stumbled across something called "Indian hand multiplication" (which is exactly what it sounds like, and even the "Indian" part seems to be accurate, not like "French" toast or "German" measles!) which is much niftier than the nines trick everybody knows. (That'd be the nines trick with your fingers, not the nines trick where you add up the digits. Fun fact, that second trick works with ANY base system. If you're working in base N, multiples of n-1 will always add up to n-1. So in base 12, multiples of 11 will always add up to 11, and in base 16 multiples of 15 will add up to 15 and so on.)

I can't describe it, I've yet to master it, but when I do you can bet I'm going to show the nieces!

http://www.murderousmaths.co.uk/books/BKMM3xft.htm
http://jollymaths.com/?page_id=7

SERIOUSLY. CLICK THE LINKS. It is absolutely worth it, especially if multiplication is your vexation.

Let's say you had to do some math in your head. No calculator or pen and paper, though you could also use your fingers and toes (or other body parts as appropriate. As a kid, I'd count to twelve by closing my eyes!)

There's a lot of ways to do this, and they don't all rely on what you do when writing with pen and paper.

Like, take 8 + 5. Working with Ana, I've found that I usually add 5 + 5 and then 3 more. I could also add 8 + 2 and then 3 more, but even though that's the same equation I would not do that. I don't know why. It's just easier to break apart the numbers that aren't fives.

Ana starts with 8 and starts counting upward. Evangeline... well, that's a bit big for her, but with smaller numbers she counts with her fingers, even if she's not using her fingers. So she would go "One, two, three, four, five. One, two, three, four, five, six, seven, eight" before counting straight up to 13.

But I have no idea what other people do. I'm sure there's a huge range of things. (I'm sure plenty of people have, for the sake of convenience, all their single digit combinations memorized, for example.) What do you do?

One on why calculus

A page with a link to a PDF about teaching math. I've had the same thought about how I was taught science in school, and I could probably write a whole post on that myself. DEFINITELY read it... I may have posted it before? Read it again!

One on teaching math later. Some of the comments are worth reading, so check those out as well.
I got this link from the comments mentioned above, in fact.

I was the only one who made it - the other grown-ups I saw were taking their kids out of school because of the snow. When Ana gets home, I'll have her change fast and send her out to play, or maybe we'll even go to Silver Lake. It's great packing snow.

They're going over in Ana's class "fact families", which is basically a run-down of the commutative property of addition plus the related subtraction equations. (So if they get the problem 3 + 8 = ? they're supposed to work out 3 + 8 = 11, and then write down three more problems: 8 + 3 = 11, 11 - 8 = 3, 11 - 3 = 8. Easy peasy for some of them.)

So they do group work together, and then they go into their separate leveled groups to do practice work on their own. (Ana is in the "Red" group, but I don't know what group that is. I can guess based upon the fact that these were the kids saying that their work was "easy". I have to talk to Ana about that, and maybe the teacher as well. If they're saying the work is easy, what is the effect on the kids for whom it's not easy? It's not much better than saying, if somebody gets it wrong, "Oh, that's so stupid". Ana wasn't one of the ones commenting on how easy it all was (she was the one saying you're not supposed to talk while working...), but just in case I want to make sure she knows that's Not Acceptable.)

I was also a little concerned, the kids were fidgeting a bit. That's normal - they're six and seven, after all! - but the teacher didn't seem to have much of a way to deal with it other than to tell them to stop and to make threats she obviously didn't want to carry out (you never want to have to carry out a threat, really, because once you do, what do you do NEXT?) about taking away a gumball from the chart that, when it's full of gumballs, will get the class a small treat. At the end of the group work a lot of kids were suddenly getting up with an urgent need for the bathroom (in the classroom) or a tissue, presumably because that doesn't constitute fidgeting. But if they're moving in their seats, it's not because they want to annoy the teacher or disrupt the class, it's because they need to move, right? If you don't want them to fidget, surely it's better to deal with the problem at the source (whatever it is that's making them move around, probably just the effect of sitting still too long) than to try to fix it at the end? Heck, there's probably a way to do that without even pausing the math lesson. But I didn't think that this was the right time or place to bring this up, honestly. There might not be a right time or place for this one.

One on the packing of tetrahedrons

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And one on basic math, using rocks to demonstrate. He makes a very clever comparison at one point between "calculate" (from "calcula", pebble) and "Einstein" ("one stone").