Where I teach, Algebra 2 is where differentiation gets kinda extreme. There are two sections in the school – I teach both – and each is a mix of kids. The reason there’s no Honors/Regular distinction is that, in a school this size, a split like that tracks out the whole schedule; you end up with a “high” and a “low” class in English, History, and science. So in each Algebra 2 class there are kids who totally love math and are excited for Calculus and science/math university studies, and kids who hate/fear math, barely passed Algebra 1 and Geometry, and are only taking the course because they’re hoping for a spot at a four-year college. And, of course, lots of kids in between.

Other courses are like this too, I know. But something about the advanced algebra content of A2, and its reliance on prior high school level math couses, makes it stand out. Here’s an example: We’ve been studying arithmetic and geometric sequences, recursive and closed-form versions. Modelling growth and decay, and some financy loan/investment type stuff. We’re headed for linear models of data and linear systems. I give a short pre-assessment to see what kids know and remember from Algebra 1 (and junior high); they have to find some slopes and solve a couple easy systems.

I get the pre-assessments back and look them over. In each class, four students have completely aced it. A couple of them even solved the systems by both substitution and elimination, and demonstrated (unasked) which name went with which solution method. Aside from these eight, everyone else pretty much bombed. But, within the bomb group there are several kids who I suspect have just forgotten how to do these problems, and some who probably never really got it the first time.

We do a one-week intensive unit on lines, slope, and solving systems, with a lot of skill practice. Kids really liked the “Arithmetic Simultaneous Linear Equations” activity found here. During this time, the students who killed on the pre-assessment work as a small group learning about matrices and operations on them. At the end of the week, I give a test (to everyone). Now I have all students meeting standard on solving basic systems (albeit with some algebra errors) except two kids in each class, whose algebra skills are seriously sketchy. I mean, they are consistently making some wild and shocking algebra blunders.

That brings us to today. After looking over the tests, we break into groups. At this point three different things are happening in class:

- The fast group is moving forward with matrices. They know that there’s a way to use the calculator to solve any linear system, but not exactly how. They are still looking for inverse matrices by hand, and I think their overall understanding is getting to where I will feel good about handing them the tech option soon.
- The bulk of the class is working in small groups on linear systems application problems, with each group presenting their solutions to the other groups. Sometimes I throw in the mistake game to keep things interesting. I am seeing signs of increasing confidence and facility from almost all of them.
- The kids who really struggled are working directly with me. We are hitting the basic algebra moves and trying to build understanding, and doing a ton of practice. Because everyone else was sort of cruising, I could work with these kids one-on-two for most of the class today (with some quick circulation to the other groups). The kids responded to this attention; I just hope they follow up with my advice to keep practicing outside class.

By Friday I’m hoping to see everyone meet standard on basic systems, so we can move on with confidence to more complex material.