
Parents Rise Up Against A New Approach to Math - kradic
http://www.washingtonpost.com/wp-dyn/content/article/2008/02/18/AR2008021802244.html?hpid=topnews
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randrews
I can see what the textbook authors intended here, I think. There's not a
whole lot of point to memorizing multiplication tables, it's much more useful
to be able to work out arithmetic in your head. The way described here (going
to multiples of ten and adding) is pretty close to the way I do it (going to
prime factors and then multiplying back). Probably the authors wanted to teach
what my grade school teachers called "mental math", which sounds like a worthy
goal to me.

What's impossible to tell without looking at the textbook is, are the parents
resisting because they equate math with memorization, or because the textbook
fails to teach "mental math"? The article is slanted a bit toward the latter,
and I was looking forward to reading it and laughing at the dumb textbook
writers along with it, but I'm not so sure.

I love the picture on the article, also. The kid, sort of dopey and puzzled-
looking, and the father, with the sad look on his face, far in the background,
out of focus, powerless to help... It's perfect.

~~~
bokonist
I mostly agree. I never did math the traditional paper and pencil way; I
always used various short cuts to do mental math. Schools are leading kids
down the wrong path teaching the traditional carrying-the-one approach. Nobody
does that in real life. I do think though, that having command of the
multiplication tables is extremely important, because it makes all future math
so much easier.

~~~
randrews
There's probably some minimum that you need, like maybe multiplication up to
10x10, and squares up to 20 or 30.

I like the idea (though not the name) of mental math. I think that if all you
teach someone is multiplication tables and long division/multiplication, then
they'll be as lost without a pencil and paper as someone who doesn't know the
tables is without a calculator.

I can see a case for learning mental math to solve small-number problems
quickly, but really, anything I would want to do longhand, I (and most anyone
else) would just use a calculator.

Really why I think long multiplication/division became popular? It's easier to
grade homework. If a student hands in just the answers, who can say whether
they did it in their heads or with a calculator?

~~~
rkts
> why I think long multiplication/division became popular? It's easier to
> grade homework.

No, it became popular because it used to be necessary. Math education (at all
levels) is designed to teach 'how' rather than 'what' and this made sense when
computation was something you had to do on paper. As to why it hasn't adapted,
my guess is politics. There are too many people who lack any capacity for
abstract reasoning but squeak through math classes by memorizing rules and
procedures. These people naturally make a fuss when the rules and procedures
are taken away and they start doing poorly.

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boredguy8
While there are many problems with the education system, this is why I don't
get opposition to vouchers. There are lots of ways to teach. School districts
don't adapt to their customers - they use homogeneous systems with at best 1
or 2 levels of differentiation. Wouldn't competition be good?

~~~
yummyfajitas
Most people form their political opinions based on their self image, not on
rational thought. I.e.

"I'm an artistic creative person" -> "I'm a Democrat" -> "I support abortion."

Or

"I'm a good Christian" -> "I'm a Republican" -> "I support lower taxes."

How does this relate to vouchers?

1\. The beneficiaries of the current monopoly oppose vouchers due to simple
greed.

2\. Their political allies try to protect them, to keep votes/campaign
contributions coming.

3\. "People like me (e.g. political allies of the teachers union) oppose
vouchers. Therefore, I oppose vouchers. Only bad people on the other side of
the fence support them."

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Alex3917
Summary: School system alters math curriculum for students. Parents, being
naturally curious, read up on the relevant academic research into math
pedagogy using ERIC and JSTOR. The parents listed the pros and cons of each
curriculum, carefully comparing the two options. Then, just to be sure, they
cross-validated their findings with the latest research in cognitive
development and educational theory.

While realizing that science is an ongoing and imperfect process, they were
sufficiently convinced of their correctness to proceed with creating an
informative and emotionally compelling website to spread their newfound
knowledge.

~~~
gscott
Schools do not teach everything in the classroom. They send the kids home with
2 hours of homework and the school expects that the parents to know how to do
it.

It would be alright whatever they tought, if they could teach it in school
first before sending it home but they can't because they have so much
information to cover that is on the state test they often send the excess home
without teaching it or without teaching it fully.

I have two kids one in 5th and the other in 6th grade. With school, homework,
and activities (scouting, guitar, drums, karate, church youth group, after
school activities, etc) our kids are often pulling 10 hour days.

~~~
abstractbill
Homework often gets sent home because parents expect it, not because teachers
think it's useful. My wife has tried not assigning any homework at all, or
assigning open-ended homework (e.g. read any book you like for at least half
an hour). The complaints from parents were overwhelming, and now she's back to
assigning busy-work that she feels is useless for anything but keeping parents
happy.

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yummyfajitas
I just thought of a way to make sure the kids never get stumped. The kid in
the article was stuck breaking up 674 into easier numbers. Perhaps there is a
method of "breaking the problem into easier-to-digest numbers" that _always
works_.

Hmm, we could break up 674 as 600+70+4, and 249 as 200+40+9. I think this
method just might work for _all numbers_!

Now I just need a catchy name to market this. How about "Child-friendly
Mathematics: a -4'th century approach"? It's even diversity friendly (crucial
in the education market), since it was invented by a non-western culture.

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lvecsey
The new approach may be okay so long as the book is accurate. All too often
school boards default to a more error prone book, due to a connection to a
specific marketer.

Feynman on school books: <http://www.textbookleague.org/103feyn.htm>

~~~
boredguy8
"Later on, when the children know something about how the toy actually works,
they can discuss the more general principles of energy."

So true, and this is why the parents are frustrated. It seems much learning is
a process of successive approximations. Not only with adding -> algebra, but
more advanced things, like algebra -> number theory or geometry -> calculus.
You get to _doing_ some stuff because it _works_, then you realize (or rather,
someone brilliant like Leibniz realizes) there's something the same in all of
these cases,

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tptacek
It's hard for me to get too wound up about an issue for which there is
literally an episode of the Cosby Show.

~~~
mynameishere
I feel the same way about "Good Times".

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hobbs
The article didn't really make clear what the point is of the new new math. Is
it to provide a deeper understanding of number theory? Or is it to provide
different algorithms that don't require memorization of the multiplication
table?

Not that I know anything about math education, but how hard is it, really, to
understand that 3 x 7 means that you add 3 together 7 times? Once you
understand that, you understand the fundamental "meaning" of multiplication.

Granted, adding 3 together 7 times is the long and tedious way to do it and
there are handy shortcuts, but do we really need to understand how the
shortcuts work in order to use them effectively? Besides, based on the
[biased] reports given in the article, it would seem that the kids don't
really understand the mechanism behind the new methods either.

It would, however, be nice to do away with memorizing the multiplication
table. And maybe it really can be done with only a slight increase in
algorithmic complexity. If that's the case, then I imagine this is just the
age-old gripe of parents not knowing how to help their kids with their
homework.

~~~
sbr
i don't think anyone wants to throw away the multiplication tables, they're
written in our brains and can be accessed without much effort.

rather, it would be cool if kids could grasp, sooner than later, that "3 x 7"
is (the bulk of) the answer, no matter if the question is 21 x 49 or 1 x
(7/3).

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aneesh
Conceptual learning is fine, but you have to memorize some base cases. I don't
think about 9 x 9. I just know it's 81. If you have to think about that every
time, you'll be so slow at doing anything. At the same time, learn
multiplication too. You should know how to do 637 x 59 if you have to.

~~~
Retric
IMO the way you learn how to do 637 * 59 is also important. I don't think this
is faster but someone who does this:

637 x 59 = 637 * 60 - 637 = 637 * 60 - 637 = 36000 + 37 * 60 - 637 = 36000 +
40 * 60 - 637 - 3 * 60 = (36000 + 2400) - ( 637 + 180) = 38,400 - 817 = 38,000
- 420 + 3 = 37,000 + 580 + 3 = 37,583

IMO they are a lot closer to algebra than someone who does: 637 * 5 * 10 + 637
* 9 = (3000 + 150 + 35) * 10 + (5400 + 270 + 63) = 31850 + 5733 = 57,583

They also know it's around 38k at the second step.

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nickb
Take a look at this video. You will see why parents think this new textbook is
just not good enough. It discusses the 'new math' and textbook mentioned in
the video:

<http://news.ycombinator.com/item?id=119317>

No wonder kids from other countries are excelling at math...

~~~
abstractbill
That video totally backfires. I think many of the techniques she's bashing are
better than what they are replacing - I'll certainly use some of these when I
have kids. (Semi-relevant I guess: my PhD is in mathematics).

~~~
menloparkbum
the video does indeed backfire. the 'standard algorithm' is less efficient
than most of the other mental calculation tricks. in the trivial case of
multiplying two 2-digit numbers it looks easy, but it becomes cumbersome when
you're multiplying a column of three 4-digit numbers. it is even worse for
division. the reason why old school math teachers like it is because it is
easy to teach and grade.

regarding other countries: the countries where people are stereotypically good
at arithmetic don't teach the 'standard algorithm' as primary.

on the other hand, i've seen those books (math teachers in the family) and
they aren't very good. text books are a scam. students would do better with a
good teacher and cheapo dover paperbacks. there are a couple great ones on
speed arithmetic.

