I bet most of you have seen the silly thing that was going around Facebook. It was a poll which asked: 6 ÷ 2(1+2) = ? It didn't seem worth even commenting on, because it dealt with such a silly issue. But it adds to math's bad reputation, and I loved Vi Hart's response, which is at the end of this video. (She saw a different problem floating around, 48÷ 2(9+3), which addresses exactly the same issue.)
The first part of her video is fun too. I bet she's lying about not knowing what 6x7 is, but that's ok by me. Maybe she can help the hopelessly honest among us (like me) learn to lie a little bit more. It seems pretty important to develop a culture of questioning instead of answering among math teachers and students, and that might just help.
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That was fun!! Sometimes I miss the challenge of high school maths (even though I'm 35 and most of it is now foreign to me through neglect) ... it's always exciting to have those neural pathways opened again.
ReplyDeleteI'm not on Facebook so haven't seen this before. Thanks.
I'm a working mathematician and a college teacher, and I don't know 6 times 7 by heart. I have to do 3 times 7 (which I do know by heart) and double it.
ReplyDeleteIn school, once I realized how to do things like this, I stopped memorizing times tables, so they are only in my head up to about 6 times 6.
So, I wouldn't be at all surprised if Vi is being sincere about 6 times 7.
Thanks, Andrew!
ReplyDeleteI used to have trouble with 7x8, and have found that particular fact is troublesome for more students than any other. (Unless my own trouble has biased my perception.)
I have a terrible memory, and was only missing this one. So I guessed she was teasing, so that she could show some cool relationships.
But your story makes me realize that it's perfectly likely that she is being sincere. Now, instead of just referring to my own bad memory, I will tell students that many mathematicians have worse memories than mine for this sort of memorization. The relationships are key.
Hmm, I want to try to do more mental math at the beginning of each class. It's a small change I've meant to make for a long time. I wonder if writing a blog post about it would help me make the commitment and really do it.
I wanted to mention even when people think they have a particular arithmetic fact memorized "cold" and not derived from other facts, we know from cognitive science experiments they sometimes derive them anyway (but it is internalized enough they don't realize it).
ReplyDeleteFascinating! Any good reading on that?
ReplyDeleteI have no data but my personal observation is that when I learn a concept, it really sticks whereas a fact my not. It is interesting to think about facts having an internal non-conscious understanding.
ReplyDeleteI do thank my 4th grade teacher who "forced" me to learn my times tables. That has been extraordinarily useful.
Isn't this vedic mathematics? Saw some of these in blogs dedicated to vedic maths
ReplyDeleteI hadn't thought about that connection. I'd love a pointer to those vedic math blogs.
ReplyDeleteThe video doesn't appear to be working..or just won't work on my computer. :(
ReplyDeleteWhen you think about how we tend to teach multiplication facts, you'll see why most people have a hard time with facts with combinations of 6s, 7s, and 8s. We start by teaching the "easy" facts of 0, 1, 2, 5, 9, and 10. Then we go back and teach 3s and 4s. Students struggle, but can often still count by 3s or 4s.
This covers all of the facts except those with only 6s, 7s, and 8s. It's hard to count on by these numbers, or to keep the composition of these facts in our heads. So these facts are the ones people tend to find most challenging.
It works from here, but here's the youtube link: http://www.youtube.com/watch?v=a-e8fzqv3CE
ReplyDeleteI think this is
ReplyDeleteVedic Maths