Parents Rise Up Against A New Approach to Math | Hacker News Reader

Parents Rise Up Against A New Approach to Math

washingtonpost.com

17 pointskradic27 comments

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.

>There's not a whole lot of point to memorizing multiplication tables

I disagree. Knowing the answer to a simple multiplication problem instantly will help when solving a more complex, multi-step algebra problem -- your concentration flows better.

For example, imagine teaching a child to factor a second-degree polynomial. You probably wouldn't get very far if s/he was constantly having to enter numbers into a calculator.

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.

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?

> 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.

I think it's odd that most people aren't required to memorize simple sums. I still find myself adding some numbers by picturing dice and counting the dots. I have them memorized now, but old habits...

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?

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."

"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."

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.

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.

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.

/Apparently no one has my sense of humor.

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.

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

"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,

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

I feel the same way about "Good Times".

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.

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).

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.

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.

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...

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).

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.

Amusingly, the methods she described are almost exactly how I do arithmetic. And when I can't solve a problem mentally I do just grab a calculator. I don't recall using long multiplication or long division since I was in elementary school.

I do long multiplication all the time... In the Emacs "multiplication puzzle" mode.

I love the magic seven technique for division. It's essentially "given x / y, keep subtracting y from x until x is 0, then count how many times you did it!"

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