Can you help a child with math homework ?
The old way:
The new way:
From
NPR:
If you're a parent of a certain age, your kids' homework can be confounding. Blame it on changes in the way children are taught math nowadays — which can make you feel like you're not very good with numbers...
That's largely to reflect the different needs of society," he says. "No one ever in their real life anymore needs to — and in most cases never does — do the calculations themselves."
Computers do arithmetic for us, Devlin says, but making computers do the things we want them to do requires algebraic thinking. For instance, take a computer spreadsheet. The computer does all the calculations for you automatically. But you have to write the macros that tell it what calculations to do — and that is algebraic thinking.
"You cannot become good at algebra without a mastery of arithmetic," Devlin says, "but arithmetic itself is no longer the ultimate goal." Thus the emphasis in teaching mathematics today is on getting people to be sophisticated, algebraic thinkers...
"Teachers have a very difficult task, and the task they have now is even more difficult, because in previous generations they could assume that in many cases the parents could help."
This must be a fairly new introduction into the teaching of arithmetic. I am still in my twenties and the old way is how I was taught to work through problems.
ReplyDeleteInteresting neither example is how I do "long" multiplication.
ReplyDeleteMy kids have been taught a method mostly like the second one but I do believe there is a difference in how they do it as well. Moving from significant digits to least significant really isn't a bad method.
It should really take about 10 minutes to get anyone up to speed on that second method.
My daughter forwarded this interesting article to me:
ReplyDeletehttp://www.maa.org/devlin/LockhartsLament.pdf
I was taught the "new way" in the '70s. :/
ReplyDeleteI'm 53 and an Australian and the new way is how I was taught (perhaps that's the Old Old Way?? LOL), but starting at the units end (ie 4 X 6, 4 X 3, add a zero etc).
ReplyDeleteO just asked my teen son to do a multiplication problem "the long way" and he used a different way called "the lattice method"
ReplyDeletehere's what that looks like:
http://www.coolmath4kids.com/times-tables/times-tables-lesson-lattice-multiplication-3.html
This was true with the "new math" approach in the 60's. It's certainly not a new problem. A nice clip of Tom Leher's New Math: http://www.youtube.com/watch?v=DfCJgC2zezw
ReplyDeleteLockwood you got to it before I could! I only came onto the comments so I could post the Tom Lehrer song
ReplyDeleteI feel the article is incomplete without dates and places!
ReplyDeleteIf there's a "new" way to multiply, when was it introduced and how widespread is it geographically?
Anybody who can do one method but not the other has been badly taught. And any teacher who will accept one and not the other is to blame.
ReplyDelete(a+b)*(c+d)
ReplyDelete= (a+b)*c + (a+b)*d [old way]
= a*c + b*c + a*d + b*d [new way]
six, meet half-dozen
For double digits, the new way is probably slightly easier for young kids to learn to do. For higher numbers of digits, the number or terms is going to make a big mess.
If they had written the sum terms in a different order, it would be more clearly isomorphic to the old way.
36
x24
---
24 [4*6] [carry the 2]
120 [4*30]
120 [20*3] [carry the 1]
600 [20*30]
This is basically just a more verbose way of notating the carry. The real difference is that in the old way, you're performing the 24+120 and 120+600 calculations partially in your head.
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ReplyDeleteThat's how I've always done math. I used to get reprimanded for it in school. Amusing.
ReplyDeleteInteresting...u learn something everyday eh :)
ReplyDeleteI've used both ways for solving a problem. Technically speaking to the question posed by the title, I've never really needed my mom to help me on homework. I usually had to do it by myself.
ReplyDeleteWhen I have paper and pencil (and no calculator or computer), I use the first method. When I have to do math in my head, I use the second.
ReplyDeleteI find my 8 year old son can do stuff easier in bites so I would teach this as round to the 25 ... 6 x 6 x 25 it is just a dollar fifty x 6 less the extra of 6 x 6 ... I like the new method breaks the math into bites rather than pencil strokes - I was taught the old way and hated it when I got half marks for the correct answer
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDeleteI use to teach Math to 6th graders and there are like 6 different ways to multiply now.
ReplyDelete