Saturday, April 24, 2010

Transparent Algebra: My Concept List

Let's review:
Now we'll take a short break from the long and meaty posts and take a look at my draft concept list for Algebra. The idea behind the concept list is to not only identify the core concepts that students need to master in my course (not the nice to have ones, but the must have ones), but to identify the ones I'm going to assess and shoot for mastery on.

Like most teachers, I struggle with this because I want to include too many things. I'm pretty sure I have too many concepts on this list, yet I'm not sure I want to pare it down any more because I want my assessments to be frequent and targeted. If I whittle my list down too much, then that stretches the interval between assessments and invites the possibility of assessing on too big a skill range. I'm still pondering, though, which is why I'm hoping you'll take a look and give me some feedback. (And, again, this is just the skill part of my class, more in future posts about what else we will be doing during class.)

Some caveats to keep in mind:
  • I do have a curriculum I have to follow, and some students switch at semester, so the breakdown between the two semesters isn't negotiable.

  • The Algebra team I'm joining gives common final exams each semester, which means my end-of-semester summative exam is pre-determined.

  • We have our state-mandated testing (CSAP) in March, and the ninth grade CSAP includes some items that typically wouldn't be covered in Algebra (or at least not before March). So we teach Probability earlier in second semester than might be typical, and most teachers take at least a week or two to do some Geometry stuff before CSAPs.

  • All education is global, but it's also local. My class will meet four days a week for 59 minutes each class. I'll see them about 60 times first semester (with 5 of those shortened periods due to our PLC's), and about 65 times second semester (again, with 5 of those shortened). Compare that with David, who sees his classes five days a week for 94 minutes at a time and has them all year. Or with Matt, who sees his classes five days a week for 84 minutes a day. So we all have to adapt based on our specific circumstances, and that not only impacts instruction and assessment strategies, but also concept lists (mine is likely to be a little shorter than some other people's - well, at least when I get it narrowed down it will be).
So, I'd appreciate any feedback you have on the list (which is a published Google Doc that does change as I make changes, so you may see differences as I react to comments/suggestions).


  1. I don't really have any suggestions for you. Looks like a good list to me. It seems like your skills are specific enough so that your assessments will tell you exactly what needs work and yet not too specific so as to create an unreasonable number of assessments.

    The thing that is interesting to me is how algebra is different depending on the region. I didn't notice anything on your list pertaining to work, rate or mixture problems. Is that not covered in Algebra 1?

  2. Your list is similar to many of the ideas in our Algebra I. We usually break up the semesters into a linear semester and a non-linear semester so the systems usually falls in the first semester. That is probably dependent on your teaching team though.

    Your list is topic/concept based. It is a great start but what is it about each topic that you plan to assess? What is it about proportion and percent problems that you want students to be able to do or understand? I'm sure you know these things from your experiences but as an outsider it is difficult to know if your idea of mastery would be the same as mine. Do you have particular assessment questions in mind that if a student could do them that would indicate master?

    These are the questions we are discussing right now in our district trying to have teachers align their expectations.

    We address many of the typical algebra word problems in the unit with systems (mixture, rate). We usually don't go too far with Rational Expressions. Much depends on student success before that point.

  3. David, I'm still diving into this, but my sense is that we don't do much with work, rate and mixture. My gut feeling is that's at least partially due to the time factor. We see our students for fewer days/minutes than many Algebra teachers do, and we devote a couple of weeks to Geometry concepts because of our state testing. But, to be clear, I'm still trying to figure this out, so I could be wrong about that.

    brattsYeah, the concept list is the start. Once I'm fairly settled on that, then developing the assessments is one of my summer goals (in addition to the videos, and all the in-class stuff, and, oh yeah, my current full-time job).

  4. I don't teach algebra, but love it. However, my comments may not be valid. I'm just thinking of literacy connections and wondering how you will assess for algebra vocabulary which I see as critical to communicating about algebra concepts. Also, have you thought of using a discussion forum for students to discuss the various solutions they used to solve a given algebra problem giving credibility to the process as well as the final product?

  5. Just a thought...You have 'lines of best fit' in your skills list. What is the skill you want them to take away from your class? Consider activities that get students to understand modeling linear relations. Most, if not all, of these activities can require the student to represent linear relations in tables, graphs, equations, and words. Inherent to these multiple representations, students are also learning about rates of change, solving equations, forms of equations, and a deeper understanding of functions. Along the way, simple skills, such as order of ops, are being reinforced though not directly.

  6. thurj - Jon, thanks for chiming in. Yeah, I’m with you on the modeling, but the inclusion of line of best fit (and most of the others) was from working backwards from the common final exam the Algebra team has developed. I’m struggling with separating the bigger picture concept (like modeling) that I would like them to understand, from the very specific, very targeted skill (like finding a line of best fit) that I want to use for my assessments (and, of course, the final exam they’re going to see that’s not “mine.”)

    Do you have suggestions of a way to structure this that meets both those needs?

  7. ...also, what thoughts (if any) do you have on integrating graphing calculators (student accessible technology).

  8. In the way of structure...should we let the test govern the teaching, the teaching govern the test, or just teach. I understand what we are held accountable to, but there has to be a better way.

    I offer no solutions! Incapability, thy name is Thurmond.

    Being new to blog posts, how do I have a conversation? Should I keep posting comments?

  9. Jon, my thoughts on graphing calculator technology are incomplete at the moment because it’s been too long since I’ve been in the classroom and I don’t know the current capabilities, the current norms, and the current availability. My preference would be to use netbooks, geogebra (which I don’t know how to use yet), and web apps, as I suspect that I’ll find graphing calculators too limiting. (But I also suspect I’ll find freely available apps too limiting as well, and, of course, I don’t have access to a class set of netbooks/laptops.) Wanna help me learn more about this? (Specifically, the capabilities of Nspire re: Algebra and what we have available at AHS - particularly first hour MWRF next year?)

    I agree there’s a better way (have you read my blog before?). But I’m also sensitive to the fact that I’m joining a team and a process and that I only have one section of Algebra. I’m hesitant to suggest any kind of major change before I’ve even spent one day in an Algebra classroom this century. So I’m looking to try to bridge the skill-driven, curriculum-mandated, semester-divided existing framework with the concept-thinking-lifelong-learning-based class I’d like to teach. I want both, and I’m looking for help in how to do it.

    You’re doing just fine with the comments, keep it up. The other option, of course, would be to start your own blog to continue the conversation there. We could also start a rogue PLC of interested math folks in our building if you want . . . (serious suggestion)