Yes renaming is the same as borrowing, back in the day.

Borrowing is the word that made me cry in math for first and second grade. I was glad to find out it had acquired a new name when DD started school.

(Because - "neither a borrower nor a lender be," taken literally.)

Renaming also makes more sense, I think. The number hasn't changed; you're just renaming what's there.

In Leping Ma's book on teaching Mathematics and comparing China to the US, she uses the term "decomposing" as in "decomposing a 10" when you don't have enough ones to subtract.

Ha, I like "decomposing" - as in "decomposing into its constituent parts." I just wish I didn't get a picture of roadkill in my brain.

Yes, DS and I laugh when the EPGY lecture talks about decomposing. We think about dinner for vultures...

Here's something cool (and free )!

http://nlvm.usu.edu/

When I explain "borrowing" to kids I say that we take a 10 and break it apart into 1's or we take a 100 and break it apart into 10's, etc. Legos are a great way to demonstrate this.

When I teach subtraction I say things like, "You can make a 10 out of a 3 and a 7. If I take away the 7 part the 3 part is left." So many kids get stuck in counting backwards mode or drawing ten dots and crossing out 7 one at a time mode. They don't think of numbers as chunks. They are only thinking of them in terms of counting.

Kriston, sorry if I freaked you out with the wikipedia stuff. And remember, it's just notation! There are beautiful books about fractals and the Mandelbrot set. Kids love to study the pictures and look for patterns. And, guess what--that's what mathematicians do, too!

Today, with my math class I had them do some experiments on Mobius strips, cutting them in different ways. We also generated a distribution graph by rolling two dice and graphing the results. I try to use math vocabulary when I talk about these things. I say things like "surface" and "topology" and "distribution" and "probability". And I read to them from Penrose the Mathematical Cat.

You know, I don't want people to think that I'm against teaching the standard algorithms for doing calculations. It is important for kids to know how to do those things. The standard algorithms are an important tool because they always work, even on problems that don't have quick, elegant solutions. The standard algorithms should be part of every kid's arsenal of knowledge. But these algorithms are calculation tools; they are not the essence of mathematics.

We like poetry because it shows us unexpected and beautiful connections between words, images and emotions. Mathematics can show us unexpected and beautiful connections between numbers, objects and abstractions. I know it sounds corny, but I have always loved that Disney film "Donald in Mathmagic Land." It's from the 50's or 60's I think, and some parts seem a little dated, but it does a good job of communicating the poetry in math and the presence of math in our daily lives.

Right on, sister! That's what I want DS6 to get from my teaching. I know he'll get the usual algorithms along-and-along. That doesn't worry me. But I worry a lot that the poetry of math will escape him.

I loved that movie, too. How funny! I hadn't thought about that in years...

I have strong vivid memories of HATING that movie...said the friend with dyscalculia!!!!!!!!!!!!!!!!
hee hee hee
seriously , I think that movie evoked strong reactions of anger when I was about 7. Maybe in school? I can't remember now.
We were made to watch it and I was crying on the inside.