Tuesday, July 17, 2012

Lotsa Links: Tanton, Busking, Cat in Numberland, Spot It, ...

While I was on vacation I kept seeing fabulous stuff online. No time to write about it all, but I want to both share and store my many finds here.

Shecky reminded me of this set of 4 videos that James Tanton did.  I'm not sure what #2 means (watched the video a while back, forgot the details), but the rest sounds great to me.

This might be a good place to direct my students in the first week. Maybe I'll give them some choices, and ask them to tell me what they think of at least one website.

Mary O'Keeffe wrote earlier this summer about doing Guerrilla Math Circles at a local park. She did a Pascal's Triangle question, making a big triangle with sidewalk chalk. I like the idea of grabbing the attention of random people in public. This video on Maths Busking* looks like something similar.

Malke wrote a great post about her daughter's take on The Cat in Numberland, pointing to a fabulous review of it [pdf] I hadn't seen before. It goes into great depth on the pedagogical issues involved.

While I was at the Math Circle Teacher Training Institute (just last week? is that possible?!), I ran a math circle for the top level kids, mostly 12-16. I had them analyze Spot It. (Posts here, here, and here; can you see any progression?) There were 9 kids, in 3 groups of 3. Each group approached it differently, and one young man (call him Trevor) became absolutely obsessed with the problem. It was a delight to get to work with this group. Our institute participants were there to observe me, and I seduced them into thinking about the problem too. A few of them were able to multi-task well enough to give me some good feedback. One noticed that Trevor and I got into a conversation that excluded the other kids (oops!). But the other kids watched us for a few moments and then decided to get back to work on their own ideas! (Invisibility achieved, though indirectly.)

The adults, who were working on the floor in the back of the room, made a bigger dent into the problem, and spurred me to think more about whether cards with 5 or 7 pictures per card can be made with the process I came up with in January. (5's, yes. 7's, I'm not sure yet. This question has connections to something called finite field planes, which I intend to explore soon.) Bowman Dickson was in that group and wrote a great post about their thinking. He also wrote about the origami he learned to make.  (I meant to make some origami, but never found the time - dang it!)

[Note added on 11/30/12: Perhaps 5's cannot be made. The procedure Bowman's group used, which I had also used, does not work for 5. A student apparently made a deck using trial and error. I wonder if I can replicate that.]

Dan McKinnon seems to be thinking about number theory on his blog, mathrecreation:
[For] these kinds of sequences (generated by polynomials with Integer coefficients) - their terms are either always even, always odd, or alternate between even and odd values (e.g. you won't get a sequence that goes "even, even, odd, .." or some combination other than the three possibilities mentioned). Can you see how you can show that this is true using similar arguments to the ones used here for last-digits?

More:

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* Busking is a British term meaning performing for donations.

5 comments:

1. One meaning of #2 is to not plunge into calculations without thinking: if memory serves, he uses the sorts of examples where if you look at what appears to be a bunch of grunt/grunge arithmetic, there's a zero hidden somewhere in the mess that will make everything a gigantic number or algebraic expression. . . times zero. So if you see that, no need to do all that other work.

2. Oh yeah! I think I'm remembering that, 5*479*2, or (x-a)*(x-b)*(x-c)*(x-x)*(x-y)*(x-z). Good call. I don't guess I'd have made that #2 myself. I wonder if there's a broader principle he could have thrown that in with...

3. Thank you so much, Sue, for sharing your great reads! After last math circle workshop, I must have spent two solid evenings watching Tanton's videos; trying to save up now to get a couple of his books. (Do you have a particular recommendation?) I have to spend some time with Spot It; someone else had written about it too, referencing you, but I can't recall.

4. Math Without Words is great for playful problems.

I think his stuff on Egyptian fractions is in Arithmetic: Gateway to all. I think it's great for my diverse students to see the Egyptian history.

Did someone beside Bowman mention Spot It?

5. Hmmm, I thought it was a female who'd mentioned Spot It. I did Egyptian fractions with my students 2 years ago with my geometry kids, will do it again because starting next year I get the geometry kids for DOUBLE periods! So excited, more Sketchpad too. Ok, will check out Math Without Words, thanks, Sue!