Year 2 was all algebra, all the time. Few things are as draining—or as revealing of the utter emptiness of our educational policy—as teaching algebra I in high school.
The epiphany moment: Realizing that kids could distribute and combine terms but lack the skills to work the steps in combination. I noted this in first year, and just the hint of its return in the fall led to the development of the Multi-Step Equation Drill Down and the mantra “Distribute-Combine-Isolate”.
Technically, this process is called a “reteach”, but another thing I learned that year is that done well, a reteach is much more than reviewing the same material. Once I realized, less than a month after covering equations, that most of the kids could solve 3(x+5)=18 but not 3x+2(x-7) + 6 = 6x – 2, I didn’t drop everything. I finished up with linear equations and considered the best way to move on this. The problem wasn’t the individual steps, but the confusion that resulted when using the processes in combination. So why reteach? Instead, I just explained to the kids where their confusion started, by using a problem set similar to the one above.
When done properly, the kids are totally on board. The minute I put the two problems up and demonstrated common mistakes, I had their attention because they were bothered by it, too. Which is a bit weird, because trust me, I can list a million things that kids don’t get about algebra. And yet, the kids know the difference between something they completely don’t understand and something they vaguely feel they should understand, but don’t. The confusion they felt during a complicated multistep equation fell firmly into the latter area.
I learned that even unmotivated students have this, dare I say, inchoate yearning to having confusing areas clarified. Spotting these areas and drilling down gives the students faith in their teacher. They can see the teacher is paying attention to mistakes, distinguishing between utter confusion and “man, I almost got this but sojmething’s wrong”.
And the performance pop from these clarifications is huge. The majority of mid-level ability kids never lost the DCI clarity. I attribute this to the time spent in the darkness, followed by the blazing light of knowledge. Or maybe I just pick my moments well.
Never fear, most of them still struggled with “is this slope negative or positive?” Alas, that confusion has nothing to do with procedural confusion.
Other things I learned:
- Data Collection and Analysis: as a long-time analyst, I knew how to evaluate the data, but this was the first year I had the opportunity to gather and compare the data.
- I always differentiate instruction, but in Year 2, I ran 4 different lesson plans at all times. This led me to realize that teachers can pick their discomfort. For me, watching kids be either lost or bored leads to far greater stress than the work involved in running four classes simultaneously.
- Low ability students: In algebra I, you often get kids who literally do no work, or who scribble frantically but clearly have no clue. At the end of the first semester, I put them on a contract. I would pass them if they demonstrated competency in five high-leverage areas: linear equations, quadratics, multistep equations, and simple systems.
I didn’t need to use it in Year 3, but I strongly recommend this approach. Motivation among my low ability kids increased dramatically. Even the kids who ultimately failed due to attendance issues saw a big bump in their ability to solve multi-step equations and factor quadratics.
Some earlier posts that expand on these issues: Teaching Algebra I and Teaching Algebra, or Banging Your Head with a Whiteboard
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