Algebra for All

January in Portland pretty much sucks from my point of view. It’s very dark and generally rainy, and everyone sort of holes up in their burrows. Students feel overwhelmed with the end of second quarter and the long stretch ahead before spring break. A lot of us get depressed, and everything seems dreary.

That’s why I made sure the Algebra unit fell in January for sixth grade math. I’ve always loved teaching algebra, I like this algebra unit a lot, and it tends to be a student favorite. It’s a great leveler and renewing math experience, because unlike with fractions or decimals or LCM/GCF, the sixth graders are starting fresh with something fairly new instead of building on years of elementary school material that some are shaky on.

But to one person in my classroom, learning algebra wasn’t new or fresh: it represented the return of repeated frustration and self-perceived failure. The paraeducator who comes to my first period class every day and helps kids after school was audibly and visibly anxious about the algebra unit. She told me she had been taught algebra over and over, for years, by at least four different (good) teachers, and said, “I just can’t get it.” It was pretty clear she truly didn’t understand algebra very well before we started the unit. But I knew she is one of the hardest workers I have ever met and is determined to do right by our kids, so I told her sincerely that I was sure she could do it and I hoped she would like algebra better by the end of the unit.

Portland Public Schools’ sixth grade Algebra unit is a weird little hodgepodge curriculum chunk put together by the district and using some old material from the Lane County Mathematics Project (that’s Lane County, OR, down by U of O). Some of the formatting issues are exasperating, but every year I love the basic curriculum ideas more. It combines ideas of algebra “pieces” (basically hand-drawn tiles), number tricks, and visual patterns with an equation-solving method they call backtracking, which you can get the gist of at (my notes from when I eventually wanted to help kids make the connection to more conventional equation-solving). The whole unit is just very hands-on: n is a variable that things are happening to which you can see, and you do lots of reasoning forwards and backwards and finding algebraic connections between things. It’s limited in that backtracking doesn’t work until you’ve got an equation with only one term with variables, but it is absolutely fantastic for learning about inverse operations in algebra and understanding how order of operations affects equation-solving. Most kids can do four-step equations with no problem before long.

All through the unit, my paraeducator co-worker pushed herself. At first, she wanted to check her work with me a lot, and she was frowning and anxious. Then she started relaxing and enjoying it when the students would sometimes help her see mistakes. Eventually she started showing actual pleasure in getting problems right, which was happening more and more, with much less guidance from me. Toward the end of the unit, when we studied simplification and the Distributive Property, we had a setback when she was sick for days, and came back in a panic over what she had missed, but she caught up fast.

Today I gave the students their unit test, and the paraeducator took it and asked me to grade hers. Except for one tiny you-forgot-to-say error (-1 point), it was PERFECT. She analyzed a tile pattern and found its equation, graph, and table, and she solved equations like 4(x+1) + 3(2x+5) – 10 = 29 and (10n – 7)/2 = 9. I am certain those problems are way beyond what was her usual comfort and competence level before this unit. I was so proud of her!

Even before I graded it, she reminded me of all the times she had been through algebra units, and all the teachers, and she said this was the best experience by far. “I finally get it!” She was giving me a lot of the credit, and I was passing off the credit to her previous experience (which probably paid off more than she thinks), but mostly to backtracking and the other curriculum features.

But you know what? It still makes me feel really great. This curriculum is a little quirky to teach with, and I have worked hard at making it work, including, of course, MTBoS conversations. I’ve always had fun with it, but it is just terrific to hear from someone who has had terrible associations with algebra that it worked for her, too.

I’m still glad January’s gone, but I’m also happy it wasn’t a total waste!


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