Paradise Found asked the following question in her blog:

How is it possible that a child can understand and complete the process of long division one day, and have forgotten how to do it by the next day?

I immediately opened the post from bloglines and started writing an answer. Then I thought that others might be interested in reading it:

The problem most kids have with math is they learn the mechanics of it but don’t understand why the mechanics of it solve the problem (in this case division). Long division is a repetitive process of the repetitive process of multiply-compare until the right number is found and then subtract.

If I haven’t pointed it out yet, after a certain point in math, almost everything reuses the simple math that was learned in the early years. So, it is by nature *repetitive*. 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.

I did a homeschool workshop a little over a year ago. During the workshop we got onto the subject of math and a one mother mentioned her child having problems with math. I responded, “He’s what, 9 or 10?” She was speechless. Because I was able to see all the faces in the audience, there were a few other mothers there who had had the same issue at the same age at some point.

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 ๐

I personally think long division is like reading. With reading, some kids get it at 4 and other don’t until 10. It’s developmental. Long division is the same way. It requires understanding place value, knowing your math facts very well, and keeping track of a complex, multi-step process. My kids were okay with the place value stuff but the latter two, easy recall of math facts and keeping oneself organized through a complex process were things they had to work on. Fourth grade is when math books usually introduce long division. I think for a significant portion of children this is just plain too early. They might have mastered basics of arithmetic, but that does not mean they are ready for long division. The kids struggle and struggle through this painfully, never quite getting it. They have to wade through this for years and, of course, lose confidence in their abilities. I think if they don’t get it in fourth, move on, try again in 5th, move on, etc. At some point it usually clicks. My oldest got it in 6th, the second one was the same way, except he still needed organizational help in 7th. Though he did seem to conquer that aspect pretty well (by using graph paper! Something so simple!) My third child had no problem with it in fourth grade. It just varies according to the student.

Blessings,

Faith

I remember reading in one of my homeschooling books somewhere that then entire primary grades math curriculum–all of it–can be taught to a sixth grader (or up, really) in a matter of weeks. It really is so repetitive, which makes it easier for me not to stress too much about it.

We’re working on fractions this year, which means going back and making sure we’re cool with times tables, multiples and factors. I mean really, that’s all fractions are!