I’ve decided to reflect on the interleaved algebra 2 course that I’ve designed and taught over the last couple of years. My hope is that by taking a more outward-facing approach to the curriculum, it will help me make it better. This is the 0th post in the series.
Two years ago I decided to turn my algebra 2 curriculum upside down. I did away with the thematic units that I used for my entire career and instead structured the course around interleaving topics. This was quite a shift for me, and I’ve written several posts about it, including a recent one about the mess of it all and why I love it.
Up to this point, I’ve never felt the need to formalize the curriculum. In year one, I didn’t know what the hell I was doing and developed all of it on the fly. It was an experiment. Last year, I heavily adapted much of what I did during the first year and reached a place where I could actually talk about what was happening in my classroom. This year I’m refining it. I’m even trying to integrate a book study. Since my head is now above water, and things haven’t been a complete disaster thus far, I’m feeling the need to take a more critical and reflective look at the sequencing and structure that I’ve developed for the course. To thoroughly think through my clutter of concepts and numbers and spreadsheets, to piece together a narrative from this tangled mess of a curriculum, is what I need to do to help improve it. For me, this means that I have to write about it. (It also wouldn’t hurt to have a coherent representation of the curriculum that someone else could understand.)
For fear of going mad, I’m breaking up how I reflect on the course by marking period. At the end of each marking period, I’ll write a narrative detailing the units that we studied during that time, my thoughts about them, and how they fit together.
Since this is the initial post, I’ll attempt to write an overview that I know is rushed and incomplete.
The course is based on the algebra 2 Common Core standards and taught through many non-thematic units. This means that, instead of being topic-centered, with concepts being taught in blocks of related content, concepts are problem-centered. This places emphasis on problem-solving, yes, but it also means that concepts throughout the course are interleaved. Instead of being introduced consecutively, related concepts are spaced out and learned over long periods of time.
To accomplish this lofty goal, each day we explore problems in class. Some days, there’s a singular focus, where all of the problems are related to one another, but most days we discuss multiple concepts that may or may not be directly connected. Disclosure: This doesn’t mean the problems are especially good, interesting, or challenging. On the contrary, because I teach a Regents course, the problems are quite boring.
What the course does well, I think, is challenge the notion that math needs to be taught linearly (like it is with traditional, thematic units). The cumulative nature of a course’s sequencing is overrated and less important than I think most math teachers realize. For example, early in the year, students in this course learn about factoring, graph analysis, and trigonometry concurrently. While these concepts are not completely distinct from one another, they probably wouldn’t be taught at the same time in a standard algebra 2 class.
As the year goes on, topics are revisited many times. We take bite-size chunks of content, digest them, wait a little while, and then go for seconds, and thirds, and fourths as the year progresses. Trigonometry is the best example of this. As I mentioned, we kick off the first unit studying trigonometry and we’re still learning (not reviewing) new trigonometric concepts in April. By design, it takes a while, sometimes months, for big ideas to mature in the course. Naturally, this development occurs a lot in the spring as we approach the backstretch of the school year. We’ve been studying certain topics for a long time, and it slowly starts to come together through the dozens of problems we have solved. As topics are woven toegther and learned little by little, finding connections between problems a foundational aspect of the course.