Last week I posted Myths About Math. This is the second installment in my series of posts busting those myths. Mind Over Math's 7th myth was "It's bad to count on your fingers."
When I'm teaching I often think out loud. Talking about powers, I often count on my fingers: 2 (first finger) times 2 (second finger) is 4, times 2 (third finger) is 8, (fourth finger) 16, (fifth finger) 32. I know my students haven't memorized powers of 2, so the quickest way to figure them is to multiply repeatedly by 2 and keep track on our fingers.
Of course, students who haven't memorized their times tables, but who add well, can do the same. Fives are the easiest: 7 times 5 is... 5, 10, 15, 20, 25, 30, 35 (and we stop when our 7th finger pops up).
So counting on our fingers is useful any time we're trying to figure something that needs a repeated step. Perhaps the thing I want to figure can be memorized. But if I haven't memorized it yet myself, the most efficient way to figure it will likely involve fingers.
Learning math is a process. Young children can add 2 blocks and 3 blocks by touching each one and finding the total. At some point, they learn that they can imagine the blocks and count them by touching a different finger for each one. And those fingers are one of the first steps towards the power math has to generalize.
What happens when a person becomes embarrassed about counting on their fingers? If they still want to think, they'll hide it. That's the better option. A worse option happens to way too many students: This may be the point where discomfort with not living up to someone else's expectations makes them give up on math, and then they just guess.
What do you think?
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i think it's worthwhile having
ReplyDeletea few tricks for calculating
with your fingers *beyond*
"counting on"...
there's a passage in
_stand_and_deliver_,
for example, where
escalante shows a student
a trick for finding multiples
of nine (spread both hands
so 1-10 appear right to left;
lower the n-th finger;
9n = 10L + R
where L="fingers to the left"
(of the lowered nth finger)
and R="fingers to the right".
(of course he doesn't put it
just like that).
the point for us right now is
"not only is finger counting
*not* a bad idea... *some*
people find it useful to
develop *advanced*
finger counting techniques"
(and math-teacher legends
have been known to exploit 'em).
i compute powers of two
on my fingers for the crowd
every chance i get
(two to the fifth is... let's see...
2 [thumb] 4 [thumb-and-index]
8 [three fingers; you get it], 16, 32).
or did when i was a math teacher.
of course, one has *heard* of
such as "chisenbop"... which has
no appeal for me personally
but which to which i owe
a professional's respect:
somebody's getting paid
for this stuff which is more
than i can do.
Ah yes, the nines trick. I personally don't care for it, because it doesn't have any relation to understanding. (If I had trouble with a nine-times fact, I'd do the ten-times-x fact minus x.) I also have trouble remembering how things like that go.
ReplyDeleteBut I'm a big fan of whatever works, and that is probably one of the better finger 'tricks'. It might even be possible to talk about why it works. (Our decimal system is historically based on us having ten fingers. Here's our ten fingers. Each nine we addd in adds a ten, and takes away a one, so...) That would make it fun for me.
When I do multiplication [623x94 ] , I find it more efficient to do the multiplication facts in my head and the carried digits on my fingers. My brain does only multiplication. My fingers do only addition.
ReplyDeleteage 57
I know how to use a calculator but there's no need to neglect using my head.
When I saw anon's reply, I re-read this thread. I see that I wrote:
ReplyDelete>I personally don't care for it [nine times finger trick], because it doesn't have any relation to understanding.
I take it back. I have some cute pictures for all the 'times' facts, like a 6-pack of soda for 2x3=6 or a carton of eggs for 2x6=12. All the nines show the finger positions for the trick vlorbik described above. I showed it to the kids, and we all thought it worked like magic! If any of them want to use it, I'll ask them later why it works. (It's very connected to meaning. I was wrong.)