“Long” multiplication

Today I’m teaching on-call, and just finished up a morning lesson reviewing multiplying three-digit by two-digit numbers with some grade 6’s.

This was a weird experience. I’ll be seeing a lot of grade 6’s this year, as I got a three-days-a-week contract teaching digital media arts to grade 6’s and 7’s.  However I’ve rarely taught math for kids this young, and never done a straight-up arithmetic lesson with them.  It raises all kinds of questions for me.

My plan was to review the answers for a handful of questions, and then assign the rest of them. But I didn’t spot an answer key anywhere so I started working them out on the Smartboard.  I had also glanced at the textbook and seen that the notes on the previous page found there mention multiple methods of solving – an area model, a long-form method of breaking apart hundreds, tens, and ones and pairing them up separately, and then usual “short” method of multiplying by hand.

So, I mention to the kids that there’s more than one way to do it, but I’ll start by reviewing the way I usually do it (the “usual”).  We get one question in, and a kid offers to show us a method his teacher last year showed him for 2-digit-by-2-digit multiplication.  He draws a box that breaks apart tens and ones for each number and pairs them up to multiply in a grid.

 

 

(Drawing with a trackpad here, sorry.)

So at this point I am nerding out and rather happy about this! The kid only sees this as something that works with numbers under 100, though.  On a later question, I drew out a 3-by-2 grid and suggested they could see if it works for these numbers too. I think I heard some out-loud “aha!” moments there, woo yay.

However, only kids who’d seen this last year seemed to be following, and afterwards I had a number of them asking me what to do when a textbook question wanted them to describe why they picked a particular method. “I’ve only been taught one way to do it.”

On top of this, I also simply stumbled with writing out too many of these problems myself and spending a bit too much time on it. Add a laggy SmartBoard to the mix and it quickly became a distraction. I finally pulled out my iPod calculator to quickly give them the last few solutions.

So, why? What do we get by having kids sit for half an hour working on these problems quietly, without exploring what the numbers mean or other ways of seeing it? Part of me wants to believe that this is a useful skill, that at some odd points in my life I need to work out a few calculations by hand. But honestly, I rarely if ever am without a calculator now.

Without the extra layer of meaning in seeing the problem multiple ways, I don’t know what the value is to it. But the number of problems, while not overwhelming, was still enough that you’d be hard-pressed to make time for having kids work things out more than one way. (You obviously could cut questions to make time – but not all teachers are comfortable with that.)

Is this going to shift for the better? We already have these changes mandated in the curriculum. But how many people are okay with this? How many generalists (because everyone at this level is, to some extent, a generalist here) have the experience to be able to go beyond what they were taught when they were kids?  (Frankly if there were shifts in teaching Social Studies over the last twenty years I’d have no idea what they are.)

I’m glad I had the chance to stumble through that lesson.  I’ve got no idea how to wrap this post up coherently though as it, like me right now, is kind of a jumble of questions, hopes, and concerns.

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