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Division Frustration redux

Ron picked up my division frustration post and ran with it.

The issue with learning something like long division is that a child who knows how to multiply, compare and subtract can follow the mechanical process of long division without learning a thing other than they have to do more of stuff they already know how to do.

I believe that is the reason most kids who start having problems with math at ages 8-12 have problems. It isn’t that they aren’t capable of it, but that they see no reason for it. They are just doing the same things in different ways to different numbers. And it’s boring….

…What we did was use real problems. Packages of items that contain X items costs Y. How much did each X cost? This package contains 18 items. That one contains 24. Which one is less expensive per item? Opportunities for real math are all around us

I agree with him, to a point. When we were doing early math, real life problems were a mainstay of what we did. Even early division was pertinent as we divided pizza and apples. As we’ve reached the process of long division we’ve slipped away from doing real life problems in lieu of practice problems (hot dog buns simply don’t come in packages of 1,876!). I’m going to make a concerted effort to again incorporate real math into our schedule – thanks for the reminder, Ron.

But, here’s the problem. Sometimes math is boring. Even so, we need to know the process. Even if we use real life problems, the fact is kids need to understand and remember the method, the steps they must take to get to the answer. With long division, there are no shortcuts – miss just one step and the whole answer is off. No matter how relevant we make math, kids still need to understand each function and how to solve a problem whether it’s real or hypothetical.

With E, the boy in question, he simply has a hard time absorbing the process. He has consistently had problems with retaining the functions of math on paper. And yet, he does this amazingly complex math in his head. Because he can do mental math with small numbers, he has a tendency to try and do part of a division problem in his head, forgetting to write down a key figure, only to end up in a quandary because his answer isn’t coming out correctly. He may, as Faith said in the comments of Ron’s post, just not be ready. And that’s why we are stepping away for awhile - I’m thankful that we can. I don’t worry about his math skills – he’s very quick with those and has a great understanding of numbers and how they work. But at some point he will need to learn – and grasp – the process of long division, complete with all of the boring steps. I just don’t think it’s going to be right now.

throwingmarshmallows said,

August 4, 2006 @ 4:06 pm

If it helps, when I first started homeschooling, a friend posted on a local email list a story about her son learning long division. Basically he could not figure it out. She tried all sorts of different ways to get him to understand and finally put it aside for a little while. When they came back to it, he still did not get it. So they put it aside again. This time for a year or so. Still did not get it. At this point she decided that he could probably get through life without being able to do long division so she decided to drop it. A little while later, he came and asked her to explain it again and in 15 minutes he totally got it and to this day has no problem. He just needed time. And she also thinks that moving forward in math to other related concepts probably helped him figure it out as well.

This is one of those stories that has totally stuck with me and I try to keep in mind any time that we get stuck.

Aren’t we so incredibly lucky that we have this freedom to put things aside when we need to?

~Steph

Miranda said,

August 5, 2006 @ 10:58 am

A couple of alternate suggestions for the long division algorithm:

First… don’t learn it! It’s of little to no practical use.
http://globofthoughts.blogspot.com/2005/10/long-division-ugh.html

Second… learn the “Partial Quotient” procedure instead. It is so much more intuitive!
http://www.millburn.org/MATH/Everyday/algorithms/division.htm#A2

Miranda

Ron said,

August 5, 2006 @ 4:58 pm

In your earlier post, I think you mentioned testing. For anyone whose kids have to take state tests, they have a problem that we didn’t. Once my kids understood the principle of dividing and were able to divide in their head, long division on paper was easy. On average I spent maybe 1/2 to 1 hour each for my second and third child to teach them long division on paper (they spent more time on it than that :) ).

Steph’s last paragraph makes a great point in the flexibility we have. And IMO you have made the best choice possible by taking a break.

JoVE said,

August 18, 2006 @ 8:32 am

Steph’s comment makes me think of any number of stories my parents told me about folks they knew who didn’t think they were good at math and then having a very short lesson as an adult where it clicked. One of these stories was about a school vice-principal who was going to have to sub for a math teacher and admitted to the math teacher that he could do it because he didn’t understand math and couldn’t teach it. the Math teacher gave him a short lesson and the guy got it. My parents always told these stories to illustrate the importance of good teachers. But maybe it is also about timing and being ready to learn.

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