Hey, application! I started doing finger math with my kids after reading this post. We have learned finger counting 1 to 99 and the trick to multiply 6–10. They already knew the trick for multiples of 9. We're going to keep going!
I think just about every Egan post has got a mental thumbs up from me so far (somatic metaphors again!), but this one gets two thumbs up.
A lot of people say math is hard because it involves logical thinking. That can't be true - kindergarten kids can think logically if it's related to something they know and care about! No, the problem with math is that it is ABSTRACT, and people forget to ground it in reality when they teach it. ("New Math" failed, among other things, for that reason.)
On the question how finger math leads to mental math ... there's something I read in a book once but I can't for the life of me remember where. The setting was some Asian kid in a western class where they were trying to teach place-value the abstract way, and it was not going well for the rest of the class. I forget if it was the soroban or the Chinese suan pan, but this kid had been taught on the abacus at home and kept saying things like "Isn't it obvious? To add 8 you add 10 and subtract 2" while demonstrating how you "borrow" a bead from the next row over.
The longhand addition on paper does have to come at some point, but if you're teaching the right way then kids will just go "oh, it's like abacus, but on paper".
(The adult version of the abacus, by the way, is the slide rule. It would not be the worst thing in the world to still teach that.)
Speaking of somatic - there's a bunch of anecdotes about the famous physicist Feynman (https://vamsionnet.tripod.com/syjmf/adbt.htm) such as when a mathematician is describing some theorem and he is picturing it as a "hairy green ball thing".
Hazel, if you can point me to a slide rule you'd recommend on Amazon, I'd LOVE to learn to use it!
And something you said is key:
>> "The longhand addition on paper does have to come at some point, but if you're teaching the right way then kids will just go 'oh, it's like abacus, but on paper'."
Amazon doesn't bring up many slide rules - if you enter the term you get a lot of things that are not slide rules, though there are a few manuals that come up. Ebay is a much better place to look. If you can, get an "Accumath 400" as that's the standard one that was given out to high school students in the past - but most models have the same basic scales, and just differ in which extra ones they add on top of that.
Here's some pictures, and some examples of what precalculus was like back in the day. I presume, because you're doing a physical calculation on the rule rather than a purely mental one, it would have made for a very different classroom setting.
The very basic idea is that if you want to do 3+5, then you can take a 3 (cm) block and a 5 (cm) block out of your box of Cuisenaire rods, put them end to end, and then measure the result and see it's 8cm. Can we do the same for multiplication, square roots, logarithms etc.? We can, we just need more special blocks. And instead of carrying a box of them around, we just engrave their lengths on a ruler, and the slide rule is born.
I use ASL numbers to count reps when exercising or praying a rosary without beads! One hand takes you to ten (and usually I just count tens on my other hand). It’s (pardon me) handy.
ASL numbers aren’t designed so much to enable arithmetic, but they do let you differentiate eg three and four from greater distance.
Hey, application! I started doing finger math with my kids after reading this post. We have learned finger counting 1 to 99 and the trick to multiply 6–10. They already knew the trick for multiples of 9. We're going to keep going!
I think just about every Egan post has got a mental thumbs up from me so far (somatic metaphors again!), but this one gets two thumbs up.
A lot of people say math is hard because it involves logical thinking. That can't be true - kindergarten kids can think logically if it's related to something they know and care about! No, the problem with math is that it is ABSTRACT, and people forget to ground it in reality when they teach it. ("New Math" failed, among other things, for that reason.)
On the question how finger math leads to mental math ... there's something I read in a book once but I can't for the life of me remember where. The setting was some Asian kid in a western class where they were trying to teach place-value the abstract way, and it was not going well for the rest of the class. I forget if it was the soroban or the Chinese suan pan, but this kid had been taught on the abacus at home and kept saying things like "Isn't it obvious? To add 8 you add 10 and subtract 2" while demonstrating how you "borrow" a bead from the next row over.
The longhand addition on paper does have to come at some point, but if you're teaching the right way then kids will just go "oh, it's like abacus, but on paper".
(The adult version of the abacus, by the way, is the slide rule. It would not be the worst thing in the world to still teach that.)
Speaking of somatic - there's a bunch of anecdotes about the famous physicist Feynman (https://vamsionnet.tripod.com/syjmf/adbt.htm) such as when a mathematician is describing some theorem and he is picturing it as a "hairy green ball thing".
Hazel, if you can point me to a slide rule you'd recommend on Amazon, I'd LOVE to learn to use it!
And something you said is key:
>> "The longhand addition on paper does have to come at some point, but if you're teaching the right way then kids will just go 'oh, it's like abacus, but on paper'."
Yeah — this pattern doesn't replace written math; per MULTIPLE REPRESENTATIONS°, it strengthens it: https://losttools.substack.com/p/multiple-representations
Come to think of it, that's probably a large part of the strength of this...
Amazon doesn't bring up many slide rules - if you enter the term you get a lot of things that are not slide rules, though there are a few manuals that come up. Ebay is a much better place to look. If you can, get an "Accumath 400" as that's the standard one that was given out to high school students in the past - but most models have the same basic scales, and just differ in which extra ones they add on top of that.
Here's some pictures, and some examples of what precalculus was like back in the day. I presume, because you're doing a physical calculation on the rule rather than a purely mental one, it would have made for a very different classroom setting.
The very basic idea is that if you want to do 3+5, then you can take a 3 (cm) block and a 5 (cm) block out of your box of Cuisenaire rods, put them end to end, and then measure the result and see it's 8cm. Can we do the same for multiplication, square roots, logarithms etc.? We can, we just need more special blocks. And instead of carrying a box of them around, we just engrave their lengths on a ruler, and the slide rule is born.
I use ASL numbers to count reps when exercising or praying a rosary without beads! One hand takes you to ten (and usually I just count tens on my other hand). It’s (pardon me) handy.
ASL numbers aren’t designed so much to enable arithmetic, but they do let you differentiate eg three and four from greater distance.