April 28, 2015

Algebra Review

We're just starting fourth quarter. The third quarter benchmark test results are in. The kids didn't do well. Now what?

For once, we're going to take some drastic action to remedy the situation rather than try to patch over gaping holes in the foundation. Scratch quadratics and statistics. We're spending the rest of this course really building a solid foundation. Our focus will be:

Solving equations and inequalities
Linear functions

It's not that we haven't taught these topics (and more!). It's that we haven't taught them to the point of recognition and retention. When I say "graph this linear function" kids can dutifully flip to that note card and with some guidance complete the task. They can do a couple more with minimal assistance. Then they can do the same process forever independently. Unless there's a pause. Say, 24 hours between class periods. Then they go back to needing some guidance. By the end of the week they're pretty good. They take the test on linear functions. They do okay. We move one. When I mix linear functions in with the exponential ones I'm shocked to discover they're already rusty. When we get to the benchmark test, all the topics are mixed together. There's no guidance. There's not a lot of success. Now, I could complain about how awful the benchmark test is all, day but the test isn't the point. I already knew this was an issue when I mixed linear and exponential functions. So what do we do?

On the one hand, they just need more practice. Lots of practice to make the thought "I need to graph an equation, I'm not sure what it looks like, I should make a table!" automatic. Part of what's preventing them from getting lots of practice with that thought is how loooooooong it takes them to make a table. They need practice evaluating functions (basic facts are weak). But the way to practice that is by doing it, and making a table is a great way to have repetitive practice with a purpose.

But, kids are only willing to do random practice for so long. And I don't blame them. It's boring and it's not helping them to build connections. So we need something more. And that's where you come in - I got a few (great!) suggestions from Twitter but I have a whole quarter to fill and I've already used my best stuff the first time through. Equations and lines. I'd happily take data based stuff so we can mix some stats in with our linear modeling, or exponentials/polynomials if they reinforce something more foundational. I'm considering factoring numbers - radicals - factoring expressions as an arc. I'm open to ideas, what've you got?


  1. Hi Tina,

    Thanks for this post and for all of your work. I admire your decision to privilege retention and depth over flowing forward. I bet that this was not an easy decision to make. It is a brave thing to do - good for you. I share your experience (and your angst) with students who seem to demonstrate mastery, but act like they have never seen the material before if a few weeks pass. It is painful as their teacher, and for me it was heartening to read that a clearly wonderful teacher experiences this as well.

    I have a few activities related to linear equations that worked well for me this year, and I wanted to share them here in case they might be useful for you. I put the related files in a Dropbox folder, which you can find here: http://bit.ly/1EiGC30

    1. I created some Geogebra files to imitate the Green Globs game. (kids played in groups, and were highly motivated)
    2. I used a version of a Launch Code Activity based on a 2013 article by Teo J. Paoletti from Mathematics Teacher
    3. Whenever possible, I asked kids to me between the four representations (Graphic, Algebraic, Verbal, Tabular). I would give them one, and ask them to create the other three.
    3. Dan Meyer's Pixel Pattern was a really good 3-Act for Linear Equations. Andrew Stadel's Cup stacking is a good one as well. These were both motivating and effective practice.

    Shoot me a tweet (@nhighstein) if I can share anything else.

    1. Thanks so much for your detailed reply! We've done stacking cups and what we call Rule of Four (the different representations) but the others are new. I'll definitely check them out.