September 9, 2017

Start of Year: Algebra 2

The last time I taught Algebra 2 was in 2010-2011. It was my first year at this school and I had a class of kids who were not excited about math - some had only managed to get credit for Algebra 1 by attending 3 weeks of summer school that everyone passes. I wrote at the end of my post on student reflections on the course: Thank goodness I'm not teaching Algebra 2 again! And I managed to avoid it for many years. The thing I hated about teaching Algebra 2 was it felt like Algebra 1 all over again, so when administration asked if I would move to Algebra 2 this year I said yes on one condition - that I could skip the review units. Because if kids have been learning about lines since 7th grade, why would I teach them yet another unit on lines? You say they don't get it? Who cares! There is so much math in the world, I would hate math too if all we ever did was repeat a mantra of y=mx+b, rise over run for five years in a row (linear review has infiltrated geometry too since kids take a state test on algebra and geometry that year). One, I don't particularly care if they can write the equation of a line from memory. Two, they're more likely to realize why lines are special if we do some stuff other than lines and then compare. But really, there's so much cool math we never get to, let's just move on! So I talked to a coworker who has taught Algebra 2 for the last several years and then my co-teacher (who also co-taught with that same coworker) and I sat down and made a plan together. We have a timeline for units that we will eventually add standards to as we get ready for the transition to standards based grading next year (this is the reason I got moved - they took two of us from the Algebra 1 SBG planning team and moved us onto other teams to repeat the process).

Aside from the essential content of Algebra 2 I have a few goals:

1) Expand students' idea of what math and mathematicians are by doing the Explore Math project. Instead of waiting until the end of the year I plan to have students complete one column per quarter which means frequent short presentations throughout the year.

2) Provide space for talking about big ideas, current events and equity issues. I'm not planning to do weekly homework the same way I did last year (I don't have lessons I like for this course, I can't be writing lessons and deep weekly assignments) but I hope to incorporate the same ideas in my class assignments. In fact, already started on day one! (below)

3) Push students to do more writing. I've always asked students to reflect at the end of class but with younger kids and a large number of them ELL or students with disabilities I asked for two sentences. I provided a third of a page per day this year, I'm curious if that will be enough or if I'll need to specify my expectations (and possibly modify for the smaller number of ELLs and students with disabilities). Inspired by Jonathan I'll be asking for longer explanations on assessments as well. Last year's weekly homework meant students regularly wrote persuasive paragraphs. This year I hope to continue to encourage debate while including some more expository writing.

4) Employ the strategies of visibly random grouping and vertical nonpermanent surfaces to improve students' confidence sharing their ideas with others. Marian recently tweeted about helping students find their inner rebel, that's definitely a factor in my goal of confidence boosting!

First lesson:

We are starting the year with piecewise functions (a tiny bit of linear review with a big focus on domain, range and fluency interpreting graphs). I told them the story of the weather caused by Hurricane Harvey in one location and asked them to graph stream elevation at that location. Then we talked about how data is more complex than the over simplification of our graphs - it could be raining at the same time the stream is draining and every time one of those rates changes the graph reflects it. Reality is way more bumpy than my grossly over simplified story. Next I showed them a graph of stream elevation at a different location and asked them to tell me the story of the weather there. Of course a verbal description isn't enough, so we also described numerically (domain/range) and with equations. After discussing two graphs in depth I projected them with two more, in a WODB format. Kids decided which one didn't belong, I emphasized the multiple right answers and they wrote their reasons on sticky notes to add to my display in the hallway. I was interested to find that some students asked for vocabulary "what's it called again when it goes over the red line?" to put their explanation in context. Throughout this conversation I shared stories (here's a timelapse my friend took, he didn't get flooded. See how this stream still wasn't drained on the 31st? The highways weren't drained until yesterday!) and invited questions. Yes, I picked this context on purpose, I want to talk about big things happening in the world in this class. We didn't specifically get into ideas of equity but I would like to think about how I could include something like this cost analysis soon (maybe it will fit in systems, that's our next unit). Slides here.

Since we had almost a full block on the very first day there was still some time left for students to get started on a problem set. I sent them to the boards to analyze other piecewise situations (for three problems I gave them the context and for one I gave them the graph).* You may notice I haven't mentioned the syllabus yet, I gave it out at the very end of class and told the kids to read it for homework but we would go over each aspect of class as it came up rather than me explaining it that day just for them to forget. And then I explained the journaling aspect of class and had them reflect on day one!

Second class plan:
Most students didn't finish their first problem of the problem set so we'll need to spend a bunch more time on that. Unsurprisingly they didn't all remember how to write the equation of a line so I'll do a very mini review of the various forms available to them and then send them back to their boards and groups to finish. I think I'll have them do Sara's 100 numbers activity to talk about how to be good group members first. If groups finish the problem set with time to spare then they can play on waterline. I'm saving function carnival for the next class - we'll complete it, do the follow up activity and then they'll have to write the piecewise equation for bumper cars and explain it for homework.

*Amazingly my evaluating administrator stopped by while one class was working on these problems. Teachers with tenure (like me) are supposed to be on a two year evaluation cycle but at the end of last year I got placed on a one year cycle. The concern was my classroom management and my evaluator asked why I didn't have my algebra 1 students up working at the boards the same way I used to with my geometry students. The reasons are complicated (as most aspects of teaching are!) but the point is that he wanted kids up at the boards at the end of last year and he saw my kids up at the boards the very first week this year. He was excited and I feel significantly less dread about the evaluation cycle this year!


  1. I like it! Whenever Algebra 2 starts with a lot of review of Algebra 1, it becomes deadly. I taught Algebra 2 for 19 out of the past 20 years, and I'm finally not doing so, which is something of a relief. At the public school where I teach (in Massachusetts) we've done something to alleviate some of the issues of Algebra 2 by incorporating statistics, probability, and abstract algebra (all at the honors level only), as well as linear programming and a full quarter of the year on cryptography and number theory (at both levels). I would like to say that my students' favorite unit is exponential and logarithmic functions... but if I said that, I would be lying.

  2. What a cool set of units to add in. Maybe we can find ways to fit those ideas in as well.

  3. How long do you send students to white boards for? I started using VNPS. I'm trying to balance giving problems worksheet style (pros: individual students are accountable. They have a record of their thinking) with VNPS (pros: it's fun and engaging, students are discussing, I can easily see their thinking. cons: some students let their group do everything). I haven't struck the right ratio yet.

  4. I'm still figuring this out too. I'm wondering if pairs is better for board work than groups? I definitely had one trio letting/making the lone sophomore do everything today. Tomorrow I'm going to ask them to record the most challenging problem in their notebook so they have some notes for reference.

  5. I don't have enough vertical white board space for pairs so I do groups of 3. I like the idea of having them go back to their seats and record their solution in their notebooks at the end. That might help my classroom management b/c some of those fast finishers fool around more when they're up and about versus at their seats.