My oldest daughter is working on long division in her math class. This is their new method they’re learning to do it (sorry about the poor quality — it was a crappy phone cam image and then I tried to make it more readable in Photoshop).
Now how does this new method made things easier? It involves several more steps, and gets a helluva lot more complicated as you had more digits to the dividend. And this is followed several pages of pretty pictures that is supposed to make this make more sense. As an old math geek, this personally makes less sense to do it this way, as it involves more steps in the long run. There are then pages of pretty pictures that try to make it easier, but it just confuses me even further. My daughter’s smart enough to understand the old-school method, and prefers it to the new-fangled method.
Am I missing something here, or does the attempt to make all math into pretty pictures just make folks understand it less?
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Actually, I can see the elegance in what they’re trying to teach… it’s just that the explanation is wordy. Basically, it’s trying to add up easy-to-find sums instead of doing the division in the precise fashion that we learned as kids.
I know you’re a math geek, too, Burton: Did you do long division like this in the 5th grade? Do you think if you did long division like this as a kid you would have been into math?
I was confused at first, then i saw how it worked. Something to focus on: is it making our kids smarter? One may need to test that…
I understand how it works, but I still hate new math. My kids’ math homework takes forever, because a problem that could be solved in 2 seconds in the old way takes 10 minutes in the new way. Plus, my boys do most math in their head, so having to write out the extra 57 steps makes them (and me) cranky.
We have this conversation every time we do math homework. If kids can learn all these superfluous steps, why not just teach them the simpler old style?
Parents are part of the learning process as evidenced by all of us helping our kids with their homework. It seems to me that unless a new way is proven to be better for a majority of kids we shouldn’t change the way we teach these types of things because it messes up the home learning. The cynical side of me says they keep changing things like this to sell textbooks and require teacher training.
How are kids graded? Are they graded on the their mastery of the technique, or their ability to get the right answers?
For example, if your daughter prefers the old way, and gets the right answers on her homework using it, will she get full credit?
Probably not, Robert. The fact that they’re asking her to draw accompanying pictures speaks to that. She’s doing it, as she understands she has to go through the motions sometimes (she’s always been one of the smarter kids in her class), but my wife and I always certainly have our influence on things at home.
But I agree with what somebody said above, and would say even more: I think that because parents aren’t getting involved with their kids schoolwork enough that they’re doing this kind of thing.
I had a terrible time with the “familiar” method. I just couldn’t do it at all, because it requires that you must precisely find a multiple. The “new” method lets you choose any multiple at all. This method is not at all new; I learned it in fifth grade back in 1968. It was my first real success with math. I went on to get my degree in mathematics and then to graduate school at OSU. I think you should learn it both ways (I use the first method now). Remember division is repeated subtraction (as multiplication is repeated addition); the “new” method is a little more faithful to this definition. Anyway, the “new” method ignited a lifelong interest in math for me.
The original method assumed that you would be able to figure out/know that 13 would “fit” three times in 48. If you were wrong, you would have to go back and start again. This way, you can guess your way to a solution and not waste time. I see the use of showing this method to the students, but would hate to force them to a method and show the work for an unnecessary method.
I guess that’s my gripe, Homersolo: Forcing them into the method when they’re full comfortable with the other method.
Without a calculator, do these two problems: One your way one the “new” way. See which you get done faster with.
1) 43257232102 % 2735214
2) 72341879822 % 3105221
I don’t need a calculator. I use Google 😉
Under the answer: “More about Calculator”. Cheater.
What I can’t believe is that came out to an interger without a remainder. I just made up really long numbers. The odds of randomly creating a division problem where you divide an 11 digit number by a 7 digit number and having the result be an interger has got to be a long shot.
That is quite impressive actually. I didn’t even realize that when I plugged the numbers in there. Most impressive. I think you missed your calling.
Seems to me that by letting children ‘chose’ what they will divide by, they are no longer required to actually do any difficult multiplication (meaning, always multiplying 13 by 2 since it’s easier than figuring out how to multiply 13 by 3) and can actually cause kids to have MORE difficulty with math, later.
You know what, I find I have to come to the defense of the “new” way. My first reaction was that it was kind of stupid, but I’ve been mulling this over, and I have to say I kinda like it. For starters, it’s not all that different. The essence of both is in repeating a two step process: 1. Make a guess as to what number will best divide into the numerator, then subtract the product of guess x divisor. Rinse and repeat.
The difference is that the old way requires each guess to be the “best” guess – I remember having that drilled into me when I was taught this, and I remember _really_ struggling with that aspect it. It was annoying how much eraser I used up redoing guesses. The way the old way is drawn out it just doesn’t deal well with imperfect guesses. This makes the initial learning curve harder; students can’t learn the process without also having to learn to make perfect guesses.
I don’t know about others here, but when I do division in my head, I gravitate toward imperfect shortcuts. For example, if I want to do 7382 / 23, it would go something like this:
– “Let’s start by subtracting 23*200(4600), leaving 2782.”
– “Hmm, guess I could have done 300, so take off another 23*100 (2300) leaving 482”
– “Now take off 23*20 (460) leaving 22”
– “Okay, let’s add that up 200+100+20 = 320, and remainder of 22. Done.”
The _real_ trick to learning this is the ability to keep two running sums in your head at the same time, and the new way seems more adaptable in that regard. It teaches the process while allowing for imperfect guessing skills. And students will develop those skills in time because making better guesses makes the process shorter and easier.
The only change I’d suggest to the current curriculum would be to show the Old way as an optimization once students are comfortable with the New way.
“Okay, class, now that we all know how to do division, let me show you a really bitchin’ little trick…”
I remember hating the “familiar” version way back in elementary school. What’s the largest multiple of 47 that can fit into 392? Back in the 7th grade, I used to waste TONS of time and scratch paper just doing trial-and-error to figure it out. Furthermore, I think it’s harder for kids to understand why the “familiar” version works compared to the new one. It was always just an algorithm I memorized that happens to get the right answer. It wasn’t until college, in fact, that it clicked for me as to why it worked. I think the “new” method, although potentially having more steps, is conceptually simpler. In your example, all you do is add up easy multiples of “13” until you get to 481.