Content and Goals

Everyone plans differently, and I don't think there's one right way to do it. Over the years I've developed a process that seems to work well for me, so I thought I'd share the process I've gone through so far (and will continue to go through as I flesh out the specific lesson plans).

For me, I have to start with the big and then work my way to the small. By that I mean I need to have an overall plan for the entire year first before I start breaking down individual units, then individual topics within those units, and then individual lessons within those topics. I know this is very different from how some folks do this, but I find that I have to do it this way if I want to make sure my students learn the most essential concepts (as I determine them). If I don't look at the entire year first, I'll end up not getting to some concepts I feel are crucial in Algebra 1. (As always, this is a fine line between spending enough time on each topic that they understand it, but not spending too much time so that I don't get to topics that future math classes will assume they've had.)

As I mentioned in a previous post, our district's Algebra 1 course is aligned with the Colorado State Math Standards which, in turn, are aligned with the Common Core State Standards for Math. As I also mentioned in that post, our district has chosen Agile Mind as our online "textbook" resource for Algebra 1 (also for Geometry and Algebra 2). Agile Mind has a nice document (pdf) that maps their scope and sequence to the CCSS-M, and also some instructional notes for teachers that I went through and pulled out the goals and objectives for each unit.

At the top of that document you'll notice a note that says, "Topic order in 15-16: 1-7, 9, 11, 12, 14, 16-20, 8, 10, 13, 15". As mentioned in that previous post, with our Algebra classes only meeting four days a week, we can't possibly "cover" all the topics. So the Algebra folks went through and identified the order they would attempt the topics and see how far they could get. Their goal was at least to get to topic 20 (quadratic formula) and hopefully also come back to 8 (descriptive statistics). I think they had mixed success at achieving that, but that's sort of the "starting place" for my thinking.

I then went through all 20 of the topics (and associated standards) and tried to identify what I thought were the most important concepts in Algebra 1. (Obviously, this is very subjective, so I'd love any feedback you have on my choices.) Looking at my list, and comparing it to the order that the other Algebra teachers followed, my goal is to get at least through Polynomial Operations on my list. If I can touch on Rational Expressions and Special Functions, that will be a bonus.

So that gives me the basic outline for my year. I'm still waiting on some feedback I've asked for from an incoming freshmen about the topics they covered in 8th grade math this year. As I mentioned in that previous post, we have two main feeder middle schools in my district, but perhaps only 70% of my students will come from them because of open enrollment, with the other 30% coming from as many as 25-30 other middle schools (school-wide, obviously not that many just in my one class). But I figure if I can get some good feedback from this incoming student from one of our middle schools, I will at least have a better understanding of what students actually understand coming in (as opposed to what they theoretically have had based on the district curriculum).

My next step (in terms of content) will be to start planning those units, in order, and see where my semester break falls and try to make that a reasonably good breaking point. This can be complicated by the possibility of a common final exam but, in the past, we've had common parts of the final exam but then have been able to tailor it somewhat based on what we've covered, so I'm counting on that.

While students mastering the content is obviously a big part of Algebra 1, content is not my only goal. I also have other goals that, in my opinion, are even more important than the content (I know not everyone will agree). I'm still working on the specifics of this for this year, but I'll start with what I used in Algebra the last time I taught it (2013-14):

Course Goals:

• Content Goal: Learn the Algebra skills.
• Habits of Mind Goal: Become better problem solvers by getting better at asking good questions, thinking mathematically and reasoning mathematically.
• Collaborative Goal: Become better at working together to achieve a common objective.
• Metacognitive Goal: Learn more about yourself as a learner and use that to become a better learner.

One thing I know I'm going to add in (which I also had in 2013-14, but separate from the goals) is a Mindset goal. Here's the still-very-much-in-progress website for this coming year in Algebra. You'll notice a tab labeled Mindset which has a series of 3 sessions (plus a bonus session) that parents and students can choose to complete if they wish. This is something I will send to them before school starts and recommend that they take the time to complete. Especially for the incoming freshmen (the vast majority of my class), I think this is a great way to set the tone not only for my Algebra class, but also hopefully for their high school career. When I did this back in 2013-14, about 25% of the parents and students self-reported that they completed at least some of the sessions (and really liked them), which I figure is not bad (although I hope perhaps to improve on that this year given my school's emphasis on Mindset this past year). While the sessions will still be optional, I will create a Mindset goal to add to the course goals.

I've also toyed with delineating the 8 Standards for Mathematical Practice as course goals, but I feel that just becomes overwhelming. As you probably saw, I have a tab on the website devoted to those, and I will have posters in the rooms to refer to frequently, so I'm hoping that will allow me to make those an essential part of the course without making my "goals" list too long. Would love feedback on this as well.

I know there are many other goals I could include, but I think this gets to the heart of what I want my students to experience in my Algebra class. I'm still thinking about them, and I will probably at least tweak them (or perhaps even add or substitute) as I work through the more detailed planning this summer, but I think it's a good set of goals to have in mind as I start the planning process.

As always, I would appreciate your feedback to help me make this better.