Today I had the non-pleasure of walking several students through long division. Hey, it’s In The Curriculum.

I do, absolutely, think there’s value in knowing how to do long division, and learning what the pieces of the process mean.

However, when a student doesn’t know single digit multiplication, much less division, and doesn’t know how to subtract if there’s borrowing, then that student is not learning how to do long division and that student is not learning what the pieces of the process mean.

I did have some success asking whether 8 cars would fit into five parking spaces, and other concrete connectors… but there’s got to be a better way.

The students had multiplication charts — when I provided them with charts that go up to 30, it made the task a bit easier. I wish I could be sure that they were processing the regular changes in number sizes…

However, I have happiness. My little ID works to get me into the quiet, quiet room upstairs, and I have the exercise files for the rather dated actionscript game that I’m playing with. Lynda.com sent them my way in less than 24 hours, and I’m not a premium member; it’s an “aged” tutorial. (I think I will let ’em know when I’m done with it ;))

*flash animation, math, rant*

ashanam

September 27, 2012

Oh, they aren’t internalizing the regular changes in number sizes. They are just memorizing numbers, which usually doesn’t completely work and they come up with things like 5×7 is 36. I don’t know what it takes to get that sense that 64 is an “eight-y” kind of number, but multiplication charts don’t do it. We had these cool manipulative thingies that worked on a principle of area, so that you could make, say, an 8 by 8 square and then count it to see that there are 64 squares when you are done. That’s what did it for me. And lots of bean counting when it came to division. In the press to get kids to learn more faster, there is no longer enough bean counting. (I think.) But the process of long division is worth teaching even if they are struggling with the pieces. Just learning a complicated process (that’s useful) has a value for developing the executive function.

xiousgeonz

September 27, 2012

Welp, I don’t even think they’re memorizing numbers. They’re using the times tables chart and copying them. Bluntly thinking, the numbers could be wingdings.

Learning a complicated process that’s useful has value — so, just how useful is long division? They’re not going to learn it well enough for it to go into long term memory, and the only place they’d see it again is if they get to factoring, which always start with an equally painful application of long division to polynomials. I must suggest that the odds of ’em getting to factoring without knowing how to borrow in subtraction are a tad low, too.

That brings to mind, though, that folks sometimes seem to really master stuff … when they *have* to incorporate it into the next level. It’s paradoxical… and it’s only sometimes… tho’ I have a hypothesis about it. When students are being “taught” things like the order of operation and adding like terms, it’s in isolation *and* it includes all the weird looking stuff. When it’s applied, things tend to stay simpler. When students have to do all those inane “order of operations” exercises, it’s dizzifying. When they have to apply it, the “trick questions” aren’t there.

Rachel Baron

September 27, 2012

I’ve found that some students learn long division better if they write down the multiplication facts they’re using. For example, if a student figures out that 5 goes into 37 7 times, then I have them write 5 x 7 = 35 on the left side of the problem next to where the – 35 goes. This helps students see the multiplication involved, practice those times tables, and helps them decide what number goes “on top.” I’ve had a handful of students just take off once they started writing down that extra step.

Conceptually, I’m very much in favor of bean counting or drawing dots and circling them, etc. The main problem is that most of the time, the books and worksheets skip too quickly into huge numbers. I did have a student who would make 76 dots on his paper in order to circle groups of eight, but that kind of patience is rare!

xiousgeonz

September 28, 2012

Think I’ll test that out. I imagine a “bean counting” transferred to computer and set up as sort of “bejeweled blitz” …