Today was . . . confusing. I’m pretty sure it was confusing for my students, but it was also confusing for me. We started with the usual opener (pdf) and they seemed pretty stumped again. At this point I’m expecting them to be able to do a straightforward order of operations problem, particularly because they have calculators. That wasn’t the case, as some of them struggled with 1a.

I knew they would struggle some with 1b, as I could tell when they did the openers on Friday that they weren’t very comfortable with distributive property. (Note to self: I need to find out for sure what they’ve had in middle school. I know in the past that distributive property was something they had been exposed too, but now I’m wondering if perhaps that’s not the case anymore). I wasn’t that concerned that they struggled with 1b, as this was another opportunity for them to see how to do it, and because I know tomorrow I’m going to give them more practice with it.

Question 2, however, was a little bit depressing. While I knew some students would struggle with it, I wasn’t prepared for the number of students who apparently had no idea where to start. I referred back to what we did on Friday (suggesting they look back at our work from Friday if they didn’t remember), and referred to the video they watched on solving two-step equations. I was anticipating that they would be able to do column 3, “undo the steps,” and struggle a bit with column 4, “The Algebra,” yet many were unable to even start the undo the steps column. I think this confirms my supposition that at the end of the day Friday they didn’t get it quite as well as I had hoped, but I’m also frustrated since I thought the video they watched should’ve helped solidify the idea of simply doing the inverse (opposite) operation. When I ask how to “undo” something they all seem to know, yet they can’t come up with what to ask on their own. I’m hopeful that when we do some more practice problems tomorrow (no new stuff) it will begin to click for more students.

Then the lesson (pdf) today was equally frustrating. (Note: image from Discovering Algebra from Key Curriculum Press). We did what I thought was going to be a quick and straightforward experiment, using their textbooks as a ramp and rolling pencils off of them, and then measuring how far they rolled. Then we were going to plot the points and see if there was a relationship (greater the height of the ramp, the farther the pencil rolled). I’m not sure if it’s just too early in the morning, or if I did a really bad job explaining this, but they moved through this so lethargically that it felt like by the end they had no idea why we did it. Again, I’m feeling conflicted about how much scaffolding I need to give them to be successful, versus my philosophy that they need to be problem solvers themselves.

Then we moved on to a data set from the U.S. Department of Transportation, showing the average fuel efficiency of U.S. passenger cars by year since 1980. I pulled the chart from the web and then started a table for them. I then asked them to copy the year and the mileage from the chart into the appropriate columns in the table, and then in a third column they had to calculate the years since 1980. I demonstrated with the first three points to make sure they knew what I was asking them to do, then asked them to complete the rest of the table (they did not have to copy the actual chart itself). That proved really difficult for some of them, so once again I’m questioning my assumptions about what is reasonable to expect 14 and 15 year olds to do. Should transferring information from the chart to a table, when I setup the table and help them with the first three data points, be pretty straightforward as I think it is, or is that unreasonable?

Either way, that took much longer than I anticipated (yeah, back to my poor timing issues that I thought I had resolved). As some students had finished their tables and others were still working, I revealed step 2 so that the students who had finished could start on their graphs. Again, I worried that I was scaffolding too much by telling them to scale both axes by 1’s. It turns out that that wasn’t enough scaffolding for many, as they labeled their x-axis 0, 5, 10, 11, 12, . . . Once again, my assumption was that they have done some graphing previously and that this wasn’t completely new for them. So, again, I need to find out for sure (in my own defense, I did ask the students if they have graphed previously and they say they have).

I then talked through steps 3 through 5 to make sure they knew what I was asking for, and then gave those to them for homework (as well as a few will need to finish the graph as they did not finish in class). I’ve been working really hard at not trying to play “gotcha” with checking their homework, but I think I may be wavering a little bit on that. Every day I talk about the importance of doing whatever I’m asking them to do outside of class, and the importance of coming in for help when they don’t understand, but the blank looks are starting to wear on me a bit. My philosophy of continuing to trust them and share with them the reasons I’m asking them to do things, and then giving them time to figure it out and start stepping up will eventually have to end if they don’t step up. As I said to someone I was talking about this with today, eventually if it’s not working for my students, then I’ll have to change something as I do have a limited amount of time with them (even if I think that’s detrimental to them in the long run).

Today felt like I stepped back about two weeks.

Hi Karl, I've read each post now and if you wouldn't mind I'm going to offer some constructive criticism here since today was a frustrating day. Please keep in mind that I'm a totally mediocre teacher so 2 cents plus at least another dime for this.

ReplyDeletePerhaps this is a problem with the blog medium itself, but I think there's a certain lack of flow to your day to day. That is, I don't get the sense that each day is leading and building on the next. Instead, it looks like one really interesting problem/activity, followed by a tangentially related, but also really interesting problem/activity.

I've got 8th graders, so it's not too different from your age. We really need to develop an idea over time. IIRC, yesterday you did two step equations, today was graphing. For graphing, there were a few different skills they were working on (creating graphs, linear relationships, extrapolating, best fit).

So if I was your student I think I'm missing two things. 1. I don't get a sense that we're building towards something. 2. I don't get a chance to play with one idea/concept/skill. We're jumping from one thing to the next and I'm not sure what I should be focusing on.

Again, this might be a problem with the medium, but from an outside observer, that's what it's coming across as. But that's why we blog right? Send me a tweet if you've got any questions/disagreements. I'd love to hear from you about this.

ReplyDeleteJason- No, I think you’re right on, flow is a huge concern for me and something I’m looking at every day. Some days I think I’m doing okay with it, others days not so much. I think the blog is giving you a pretty good idea of what’s going on, but there are two things it probably isn’t giving you.First, it doesn’t tell you where I’m going. Now, admittedly, that’s also a problem for my students, but without you being able to see the big picture of my semester plan, I think it might be hard to see how it fits together (or perhaps doesn’t fit together).

I’m structuring my class around the big essential learning for our first semester: understanding and applying linear functions. So, instead of teaching solving equations in isolation, I’m trying to connect them as quickly as possible to graphing and linear relationships. For me, teaching things like solving equations out of context is one of the major problems we have in math instruction. The unifying factor in first semester algebra is linear functions, yet we often teach solving equations as if there’s no connection. I’m trying to make that connection clear and explicit, although obviously I’m not doing that very well at the moment. My hope is that as we continue to explore graphing, equations and linear relationships over the next couple of weeks, those “tangentially related” activities will turn out to not be so tangential.

The second thing the blog doesn’t tell you is about the structure and schedule of my school. If you have already read this (in previous comments last summer on The Fischbowl when talking about sbg), then you can stop reading this now.

(comment is too long for Blogger, so I'll split it here - see next comment for continuation).

ReplyDeleteJason- continuation of previous comment.My school has a variable schedule, which means I see my students four days a week for 59 minute class periods. By the time you factor in class meetings, MAP testing, holidays and a furlough day, I’ll only see my students 61 times this semester. Of those 61 times, at least six of them will be shortened classes (about 40 minutes) due to late start PLC days or assemblies. I don’t know your schedule, but after conversations with lots of other folks, I suspect that my contact minutes with students is much less than most folks trying to teach Algebra. (As part of the sbg discussion, I discovered that David and Matt each saw their students for 80 or 85 minutes a day, five days a week. That works out to almost double the number of minutes I’ll see my students.)

Yet I still have the same curriculum to cover. In first semester Algebra I’m supposed to “cover” Chapters 1-7 in the textbook that I’m not really using. That’s (chapter titles) Expressions, Equations and Functions; Properties of Real Numbers; Solving Linear Equations; Graphing Linear Equations and Functions; Writing Linear Equations, Solving and Graphing Linear Inequalities; and Systems of Equations and Inequalities.

So what I struggle with is that I don’t have time to let students “play with ideas” for very long. That was the genesis of creating the videos to watch outside of class. Watch the “lecture” on the specific skills outside of class so that we can have more time in class to play with the ideas. But, obviously, that only works if the students actually watch the videos and work on some of those skills outside of class, and if I do a good job of connecting the concepts in class so that they feel it is building toward something. With mostly ninth graders, who are both adjusting to high school and to the expectations of variable scheduling (doing a lot of stuff outside of class and coming in for help), that’s a tough transition. And, even if that’s working perfectly, we still have a limited number of minutes to play. Which is a big part of my frustration with Algebra right now, but it’s still a reality I can’t change.

So, I’m trying to connect all the concepts of first semester to understanding and applying linear functions, I’m trying to shift some of the instruction to outside of class with the videos, I’m trying to constantly spiral back (and forward, for that matter) to keep everything fresh in their minds and hopefully connected, and I’m trying to make it flow in some reasonable fashion. And, oh yeah, I'm trying to get them to be self-directed, independent yet still collaborative, curious and passionate learners. Right now, I don’t think I’m doing any of that very well.

I love that you are trying to do this: "And, oh yeah, I'm trying to get them to be self-directed, independent yet still collaborative, curious and passionate learners."

ReplyDeleteI think it will eventually happen, don't give up. It does sound like you are jumping around a bit, but I see what your long term goal is. And in my experience in teaching math (junior high level) you just have to slow down and give them time to play with the concepts, maybe discuss the concepts in groups (Kagan's jigsaw model maybe? I've seen great results with it in math classes.)

I clump concepts, which it sounds like what you're doing, so that I can cover the chapter topics with a lot more time to work on each concept.

I agree with 100% of everything you said. I figured it was a blog as medium problem. I probably used the term constructive criticism inappropriately. I meant more like I'm offering a reminder. Math teachers in particular are guilty of feeling the pressure to cover each standard. We all know that's impossible to do in any meaningful way. The "rush to cover" is something we all fight every day. Our total instructional minutes are similar to yours (50 min x 5 days) and every year I find myself paring back the curriculum. But every year I'm also more satisfied with the learning that's happening. Like Suzy said, we all have to remind ourselves to give them time to play with the concepts.

ReplyDelete

ReplyDeleteJason- Again, I don't think it is the blog as medium, I think you pretty much nailed it. I'm just struggling to do what I think is best, balanced with what I have to do, balanced with, oh yeah, what is actually working for my students.

ReplyDeletesuzysouth- Yeah, trying to figure out how to do that well. I can see what I want, I'm just not getting there. Yet.