I retweet Scott's video talking about multiplication with his daughter. (He has lots of nice videos along these lines.)

Martin responds with a connection.

Brad shares the video.

I respond, prompting a (as usually, intriguing) Dan tweet. Which will double as the moral of this blogpost.

**/Explaining/ a trick is good math!**

Which Marilyn responds to... (talk about fanboy). And we will be looking into this trick.

Cool stuff in Nicholas' trick shared by Ms. Burns.

Links: Scott's post with his video, Brad's video, Marilyn's blog with her trick.

Since this wound up here, I thought I'd share how I subtract.

When I was in 2nd grade, Mrs. Schultz told us you can check subtraction by adding the result back. 6 year old mathchico thinks that if this is always correct, why don't we do that in the first place?

132 - 49? 3 plus 9 is 12 so 1+4 (now I'd say ten + forty) is 5, and 8 plus 5 is 13. Done, 83.

Over the years I've gotten in a lot of trouble for not borrowing.

One more:

6+5=11.

8+(6+1)=15

7+(4+1)=12

2+1=3.

Solved and checked, Mrs. Schultz!

Peace be to any teacher who had me in class, up to and including my advisor, Nigel Higson.

And Dan writes my signoff:

Reacting to your tweet "I'm more of a #nixthetricks guy"

ReplyDeleteI think there the word "trick" encompasses two separate phenomenon:

(1) rote memorization that (tries to) substitute for mathematical understanding

(2) patterns that can be discovered by doing mathematics around arithmetic calculations

By "doing mathematics," I mean practicing the mathematical habits of mind, particularly observing, forming conjectures, testing those conjectures, developing explanations or proofs.

Often, the way the "trick" is presented makes it fall into one or the other bucket. Certainly all of the ones in this post (and the linked posts) could go either way. For teachers, the safety valve to remember is "will it always work? why or why not?"