So today seemed to go really well until right until the end, but then it seemed like maybe they weren’t getting it after all. Of course, it was the Friday before a three-day weekend, plus we don’t meet on Tuesday so I won’t see them until Wednesday, but still.
We started with our usual opener (pdf), but I tried something different today. As I’ve mentioned before, I’ve been surprised about how long the students are taking to do what I consider to be pretty routine stuff. So, each day on the openers I’ve been saying things like “I think these should take you about five minutes” or whatever, but then they take ten minutes and I’m not quite sure what happened.
So today I decided to make it a little more explicit, I put suggested completion times after each opener. Now, I want to be clear that I don’t believe that speed is the most important thing here. I don’t want to rush my students. Yet I also believe that students must have a comfort level and facility with the mathematics to do things at a reasonably good pace if they’re ever going to be able to move forward and work on more interesting – and complex – mathematics.
So at the beginning I told the students what I was doing, and that they shouldn’t panic if it took them longer – or shorter – to do each problem. I told them that those times were the times that were the target for them, where I would like to see them get. I also told them that the total time on the timer was slightly more than the sum of the times, so that I didn’t push them too much (I think I had four minutes on the timer in the upper right corner, even though the suggested times totaled three minutes). When the timer went off, I then said that if they were finished, or working on #3, they were in pretty good shape. But if they weren’t even on #3 yet, then perhaps there was some concern there and they might want to come in and get some help. They then had several minutes to talk over the openers in their groups before we worked them on the smart board.
I’m not sure how I feel about this, as part of me really hates doing this. But they did seem a little more focused today, and I’m going to try it for a few weeks and see what happens.
We then moved on to the lesson (pdf), where we approached solving two-step equations via the idea of working “magic” with numbers. So, here’s the scenario. I told them to pick a number between 1 and 25 and write it down. I then gave them one operation at a time (“Add 8” or “multiply by 4”). After each operation, they then wrote down their result. After about five operations – and keep in mind they have calculators for this – I then revealed the magic and told them what the last number they wrote down was (“5”, or “Your original number”).
Now, I knew this was going to happen, yet it still was somehow a surprise. A fair number of students didn’t get “5” or “their original number.” So, here’s my question to you, is it unreasonable to expect that students, using a calculator and taking one basic operation at a time, couldn’t complete five operations in a row successfully? I’m really struggling with this, because I think (perhaps naively) that they should be able to and that, if they can’t, they are going to struggle mightily in Algebra. Given the fact that clearly some of them are struggling with this, I’m not sure what to do to help them. Ideas?
After translating the “magic” to the algebra to show them why the tricks worked, we approached solving two-step equations by “undoing” operations. As we were working through this I was feeling pretty good, they really seemed to be getting it and understanding the concept, even if they were still a little shaky with the fourth column (“The Algebra”). But then I turned them loose (in their groups) on the last page of the lesson, and suddenly a whole bunch of them didn’t know what to do. Not just with the fourth column, but with the other columns. I had anticipated they would struggle with the last one (writing their own given just a result), but not that they would struggle so much with the first two.
Their homework for next week (again, I won’t see them until Wednesday), is to watch the video on solving two-step equations (in addition to completing their reflection/goals assignment from Wednesday), so hopefully that will help solidify the concept of undoing and what to write for each step.
So, overall, week three felt better, but still nowhere near where I want it to be. I did much better on my timing each day, and I think I’ve scaffolded things better for my students, but I still worry that I’m doing too much of the thinking. As always (at least until the end of the year), next week is another opportunity to do better. Let’s hope I do.