Do you want to try this yourself? A real life class of students helped refine the theory below into an actual product. Assessments, practice, and a calendar are available in my Algebra II resources.

Algebra II is a pretty gnarly subject. Not being in a Common Core state, I haven't looked at the expectations there, but in Texas, the list is long. Oh so long. Given the number of topics and the length of a school year, it's like touring the entire Smithsonian collection in about 5 minutes. At the end you know you saw some things, but couldn't distinguish the Hope Diamond from the Spirit of St. Louis. 

Algebra II has eleven  major functions. Each is addressed one by one in isolation. You'll spend a few weeks at the beginning doing linear equations. A few months later you're knee deep in logarithmic equation solving. The problem I think, is that students view these as isolated activities. The linear parent function has certain things I can do to it. The logarithmic parent function has completely different things I can do to it. And yet, that's not true. The task in both cases is to find a solution to an equation, each parent function offering new ways to isolate a variable. A log is just a new layer on an old skill.

Why do I think these skills are viewed in isolation? Well, here's a portion of the fall final. 

alg2final.png

The results were not great. They weren't horrible, but they weren't great. Now, historically, I never have students do well on finals. But the point was when given the task of "solve the equation" they stumbled when multiple types were mixed together. I think rather than teaching them equation solving, it seemed like we were just doing a bunch of special cases during the year. Case A had nothing to do with Case B. Case A and B could not be identified in a suspect line up.

Some can point the finger at SBG. And in truth, I have subdivided Algebra II standards with such names as "Absolute Value Equations" implying that "these are special, nothing you do here can be re-used." I don't think this is the fault of SBG. The standards I used are based on the way our Algebra II textbook is organized. And if you give more traditional chapter tests in Algebra II, you are doing just as much isolation. You just happen to be calling it "Test: Section 2.5."

How could this be fixed? Well, here's a graphical representation of how we present Algebra II: 

original.png

It's a progression through the major parent functions. We tackle certain ideas about each one as we go along. Graphing translates pretty well between all of them, but equations and inequalities, the pillars of Algebra Skills™ are constantly coming and going. Each time they appear, the players have changed. And by isolating the parent functions in this way, we kind of say "ok, that concludes linear functions, let's pretend that never happened."

My proposal: turn this table

pivot.png

What does this accomplish? It changes the main ideas of Algebra II. Instead of being centered around a long list of parent functions, it now centers on seven Algebra Skills™. Rather than spend two weeks on linear equations, you spend three on the concept of Equations and Inequalities. Later on spend three weeks at a higher complexity level. What would a quadratic term do to our solving process? What about an absolute value term? What about an expression that has both quadratic and linear terms?

You address Equations and Inequalities using a series of the major parent functions simultaneously. Assess it via SBG, culminate it with some sort of Level 1 Equations assessment. Spend some time on Graphs and Transformations using that same simultaneous set of parent functions. 

I think it does a better job of showing the universal nature of Algebra Skills™ and getting a student to not freak out when you put a linear equation next to a quadratic. 

Part Two

Posted
AuthorJonathan Claydon