Transparent Algebra: In-Class Part 1 of TBD (Openers)

Now that I’ve discussed my return to the classroom and talked a little bit about assessment, homework, and my fledgling concept list, I want to move on to what we’ll actually be doing in class. As you can tell from the title, this will be broken down into multiple posts, with the total number still to be determined. First up is openers.

(Note: I used to call these warm-ups, but - and this is probably just semantics – I don’t really like the connotation of that. That somehow we’re “warming up” for the real work that’s to come, and that this isn’t that important. I like “opener” better because it feels like it begins the learning for the day, not just prepares you to begin. I’m probably over-thinking that.)

I have a love/hate (well, okay, like/dislike) relationship with openers. I like them because they get kids thinking about mathematics as soon as they walk into the room (even before the bell rings), they provide a way for students to get more practice with Algebra and mathematical thinking, and because they are a nice companion piece to my (still evolving) assessment plan. I also like them because some students really like and respond to routine – they know when they walk into my class what to expect (at least in the beginning).

But that’s also part of what I dislike about them – the routine. Some students also really dislike the routine of a typical math classroom, where they know they’re going to start with the same ‘ole openers each day. And while I like getting them thinking about mathematics right away, I dislike the way it interferes with the more personal interaction/relationship building that I would like to take place as I greet and talk with students each day. While that can still happen with openers, I think there is at least an implied pressure to get started on them, and it makes it a little harder (at least for me) to be spontaneous.

Despite my misgivings, my current thinking is to go with openers because I feel they’ll help me maximize the learning time with my students. I don’t want to waste even a minute of the limited time I have with them, so this helps me approach that unattainable goal.

What’s on the Openers?

Glad you asked. Here’s a proof-of-concept (yes, saying proof-of-concept makes me feel important) PDF of a fictional opener that might theoretically occur the day after viewing the video in my homework post. Please note this opener has more questions on it than I would normally include, but I wanted to include one of each type of question I’m considering using for openers. So a typical opener might only have four of these types of questions, or might have two of one type and one of another, and often will combine several types in one problem, but this gives you an idea of the scope.

Here’s the key to those opener questions:

(R) = Review. This is just what it sounds like – review of a skill that they’ve theoretically already mastered. Designed to be short and quick.

(N) = New. This would be a concept that’s fairly new to them and that they probably have not mastered yet. In this example, it’s a problem of the type they saw in the video the night before.

(C) = CSAP. CSAP is our state-mandated testing that occurs in March each year. Since the 9th grade CSAP (most of my students will be 9th, a few might be 10th) covers some topics that are not in our Algebra curriculum, this is one way of addressing that.

(W) = Writing. Still thinking about how best to do writing (coming in a future post), but I’m thinking my openers will include some of these. This will often not be a separate category, but will be combined with others.

(V) = Vocabulary. I think vocabulary is important, but I’m not sure how to teach it well (especially with my limited class time with students). This is one attempt to address this.

(E ) = Estimating. I think this is a skill that we underestimate (pun intended) the importance of. I’m not sure how often I can fit this in, but I’m going to try.

(M) = Measurement. This is helpful not only in the obvious ways of actually being able to measure stuff, preparing them for Geometry in the following year, and preparing them for CSAP, but also because I think it’s critical in terms of their number sense and their ability to judge the reasonableness of real world answers.

(TFTD) = Thought for the Day. Just because I like it.

If you move past the first page of the PDF you’ll notice that each opener then gets its own page. My plan is that students will work the openers individually (in their notebooks), then will discuss them in their groups (modifying what they have in their notebooks if it needs revising after the discussion). Then I’ll ask a student to come up (representing their group) and work/explain the problem on the Smart Board (and students will modify their notebooks again if necessary). You’ll notice there’s a place on each opener for them to “sign” it – going for some ownership there (too hokey?). After different students have worked through all the openers for that day, I’ll PDF it and post it to our class website. (I thought about recording the students as well, but thought that was too much, too fast, and also added some technical complications that perhaps weren’t worth it.)

So, as with all of these posts, I’d love some feedback, ideas to make the openers better, or links to your already created openers that I can just “acquire.”