
The Way You Learned Math Is So Old School - grellas
http://www.npr.org/2011/03/05/134277079/the-way-you-learned-math-is-so-old-school?ps=cprs
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mynegation
At risk to be downvoted to death, I have to say that the new way of
multiplication is actually _better_ than the old one, at least for kids
starting to learn how to multiply.

All the new multiplication algorithm does is makes implicit additions
explicit, so that you do not have to keep carry-over digit in memory. 144 is
120+24 and 720 is 600+120. Sure it trains your short memory, but we are
talking about 7yr olds here. Once kid feels comfortable s/he will naturally
move to the "old" way of multiplication.

And anyway... It is easy to nitpick on something we understand very well, but
how about the topic? What would you do to make math more enjoyable in the
classroom? I know what worked for me personally and that was not classroom
drilling of multiplication, divisions, and stupid problems with two pipes
filling the pool at different speeds.

What made me love math are Marin Gardner's books and other fun math books. It
was much more interesting to solve crimes with what I later came to know as
propositional logic, or cutting tori in different ways.

~~~
Splatchar
I think you've nailed it by considering the carry-overs.

With the new method there's less opportunity for error. The old way, there are
_two_ sets of carry digits: those arising in the initial multiplying, then
more in the final adding up (though not in the example given). Sometimes I
would try to remember them; sometimes I would write them down in various
places; frequently I forgot or muddled them up somehow.

Another benefit is: the new way gives you a sense of the magnitude of the
final answer more quickly. Approximations are useful. Contrast with the old
method which begins by multiplying the least significant digits.

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zwieback
Either way is fine, I think, if you the child understands the underlying
mechanism. I'm the father of a 3rd and 5th grader in US public schools and I
think the math curriculum is very good. However, sitting down and explaining
basic arithmetic is important. I also teach them to estimate and come up with
a quick upper and lower bound before they start the problem.

I went to school in Germany and our methods of multiplication and especially
that of long division were a little different. When I first looked at the way
long division is done in the US I thought it was confusing and my first
reaction was that my method was better. It took a little time to overcome my
cultural bias but I'm all better now.

Still waiting for the US to switch to Celsius and metric, though...

~~~
dhimes
I agree. For learning, the method shown is fine. Why? Because it teaches and
honors _place value_ , an extremely important concept in developing numeracy.
I'm fine with any method that uses that.

I am _not_ fine with something my kids call the "lattice method." The point of
this method is simply to get the correct answer for multiplying large numbers.
Is it clever? Yes. Does it work? Yes. But it does not teach _math_. If the
educators' goal is simply to give a technique that works and gives the correct
answer, teach them to use the calculator on their cell phones.

Lattice method for multiplication:

[http://www.coolmath4kids.com/times-tables/times-tables-
lesso...](http://www.coolmath4kids.com/times-tables/times-tables-lesson-
lattice-multiplication-1.html)

~~~
decklin
I'm not sure why you think this lattice method does not teach place value. The
page you linked to doesn't explain (at all) why it works, sure, but the method
is just a clever way of notating place. I would expect any good teacher to get
his or her students to understand that, and not just mindlessly fill in
numbers.

~~~
dhimes
_I would expect any good teacher to get his or her students to understand
that_

That's not how I've seen it used. I've seen it used as a procedure for getting
the answer. Compare that to the method shown in the npr link, first line: the
numerals are 2 and 3, but the numbers multiplied 20 and 30. That's what I mean
by teaching place value.

In the the old-school method I learned, we respected place-value by indenting
(from the right), optionally writing the zeros.

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light3
Surely that method of multiplication is not suited for larger numbers, to get
246 * 369 u do 200 * 300 200 * 60 200 * 9 40 * 300 40 * 60 40 * 9 6 * 300 6 *
60 6 * 9 So for x-digit multiplied by y-digit u need to write down x*y
products and then sum it up, where as for the old method you need to only
write down min(x,y) products and sum it up.

~~~
hackerblues
This is somewhat misleading. Yes, it's true if

    
    
        3 * 123456789
    

counts as one multiplication.

But if you're doing the 'old' version you implement it as 9 single digit
multiplications:

    
    
        3*9, 3*8,....,3*1
    

all written down with appropriate carrying.

If you do it with the new method you again get 9 'single' digit
multiplications:

    
    
        3*9, 3*80, ..., 3*100000000
    

which you then add up.

\---

The old methods efficiency comes from writing the steps out in a compact
notation, not from reducing the number of multiplications or additions.

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JoelMcCracken
Geez, there are so many things wrong with this article, all I could do was
scream "shut up" in my head.

The only thing worse than math education in the US is the pop culture-media
surrounding it.

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madcaptenor
To be honest, I just _know_ 36 times 24. I've spent enough time dealing with
numbers with all their prime factors small that I can just see it's 864. It
might also help that I know there are 24 hours in a day, 3600 seconds in an
hour, and 86,400 seconds in a day -- and I probably have a lot of random facts
like this somewhere in my head that I at least occasionally pin mental
arithmetic problems on.

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Jach
I don't really think the methods are important, what's important is whether
students decide to learn more advanced math later (say at least up to
Calculus), and more importantly whether they like doing so. Too many people
say "I hate math", learning multiplication one way or another shouldn't affect
that strongly.

The article has a few nice quotes I like: "Computers do arithmetic for us,
Devlin says, but making computers do the things we want them to do requires
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.'

While I can do multi-digit multiplications just fine and have a high
confidence in my answer, I'd much rather a calculator do it for me, allowing
me a higher confidence in the answer and just being done faster to use the
result for some other purpose.

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Newky
I hope that I am not straying off topic, but certainly where I was schooled
(Ireland), the main issue in the poor math performance falls on the "uncool"
reputation which Maths has received in the past few years.

If you make it so that a child likes maths and feel's no peer pressure to just
give up, the way in which one multiplies may become less significant.

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darthvivi
Changing the way the multiplication algorithm is taught isn't going to fix
anything.

There needs to be a fundamental change in the way mathematics is taught. Right
now what most schools teach in math class resembles trivia more than
mathematics. There is no appeal to intuition or understanding, because
clueless symbol manipulation and memorization of formulas is apparently what
really matters. It is not necessary that the student really understands what
he is doing. Why is the product of two negative numbers a positive number?
"That's just the rule." Why is dividing by a fraction the same as multiplying
by the reciprocal? "That's just the rule." These are very simple concepts that
can be both logically and intuitively presented to students, yet growing up
those were the answers I received. Even high school geometry, which used to be
taught decently, has now been replaced by curriculum that does not emphasize
proofs or any kind of true understanding/intuition.

Unless students discover the beauty of mathematics independent of math class,
or enjoy following arbitrary rules, it is no wonder they develop a dislike for
mathematics.

Although the author's writing style is a little bit annoying at parts, this is
a good read: www.maa.org/devlin/LockhartsLament.pdf

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Mz
I'm pretty math-challenged these days without a calculator (gone are the days
I could run the numbers in my head faster than you could punch them into your
calculator), but I tend to do weird things like break stuff down into primes
and then multiply it out from there.

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baddspellar
I have an 11 year old daughter who I help with math homework every week. Some
of the new methods work for her, and some are terribly confusing to her. I
think it's good to expose kids to a variety of methods in math. I am
concerned, however, and the near-complete lack of emphasis on memorizing the
basic math tables and doing calculations in your head. Doing that at a young
age really helped me to understand numbers. Many of the techniques they teach
in school are techniques I figured out on my own by exposing myself to large
numbers of calculations.

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kaeluka
This is the way I do multiplications mentally since being a child, but I never
quite thought about that fact, that this is "new". How do you guys execute
multiplications in mental math?

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hencq
Aside from the 'new' way of multiplication (which doesn't strike me as too
bad), I think asking kids to make a stem-and-leaf plot of the birthdays in
their class is actually really cool. It shows them how the things they learn
can be applied to real things and it could open the way for interesting
discussions as well (though the birthday paradox might be a bit much for 5th
graders perhaps).

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ern
After watching a video on Khan Academy on Lattice Multiplication, I assumed
that it was the "new way" of doing multiplication by hand.

I certainly would use lattice multiplication in preference to traditional long
multiplication methods if I ever had to multiply large numbers by hand. I
wouldn't be able to say which method is better for a 7 year old learning the
concepts though.

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icegreentea
...Does anyone actually teach their kids with that retarded method? All it
does it take up more space, and shift the burden from screwing up carries
while multiplying to screwing up carries while adding.

And since it's so brain dead to implement, I can't see any significant amount
of kids even reflecting on how 'the numbers work' based on that.

~~~
hackerblues
As far as I know every child in England is currently being taught this method.

I'm not sure that I would leap to calling it retarded. I agree that it takes
up more paper but paper isn't the most expensive thing in the world.

What it does do is make explicit why the old school method works. Look at the
explanation given by the article for the old method:

'Answer = 720, Because: 2x36 = 72, with a 0 added in the ones place.'

No, the reason you get 720 isn't because you 'added' a 0 in the ones place
(72+0 = 72). It's because you are multiplying by 20 and not by 2. The old
method hides this fact and corrects for it by a mechanical process: first
write down a zero and then shift the other entries to the left.

Your criticism is analogous to calling Assembly retarded because Haskell
exists. They serve different purposes.

~~~
Groxx
I still encounter people who try to teach long multiplication to kids by
saying "add a zero in the ones place". And college students who fail to
describe _why_ they add those zeros (typically liberal arts majors (no
offense. They just rarely minor in math, and many quit doing math entirely
after they get the minimum to graduate)).

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randrews
The way the article shows is essentially calculating:

(30 + 6) * (20 + 4)

Which is great and all, but I think it would make more sense to do this:

(24 * 6) * 1 + (24 * 3) * 10

This is a lot closer to how machines actually do multiplication, so if the
goal is to conceptually understand multiplication so you can have a computer
do it, that makes more sense to me.

Plus it's easier to do in your head that way.

~~~
flogic
My inclination would be to be much less computer like about it. First start
with some observations about the numbers. 24 is one less than 25. 4 * 25 is
100. 36 is 9 * 4. Therefor the answer is (9 * 100)-36=864. Numbers have
properties. You can use these properties to do less mental work or at least
take up less mental temp space. Not sure how you teach people to do that.

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JSig
I wish to hell I had learned the Soroban growing up. Now it's on my unending
todo list. I'll probably make a go at it when my kid is ready for it. We can
learn together :)

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YooLi
In my head I would do:

30 * 24 (which is just 3 * 24 * 10) = 720 6 * 24 (which is the same as 12 *
12) = 144 720 + 144 = 864

