5 Practices

Blog 10--a third of the way through!  #MTBoS30

I just had the first teacher evaluation I have ever had where I felt perfectly natural and confident.  It was wonderful. I didn't feel as if I was trotting out some dog and pony show just for my boss.  I didn't spend hours writing up lesson plans to ensure perfection and absolute control over every moment of the class. I just thought--there we were in the middle of a task we started last week and needed to finish--so let's finish it. I had fun! The kids had fun! I'm pretty sure they might have even learned something!

Contrast this with my evaluations during the period of NCLB.  Those evaluations were always about keeping the students "on task." From what I could tell, "on task" meant that students were working intensively on a math problem as if their life depended on it.  Students were expected to walk in the door, become immediately "on task," and remain there until the bell rang.  Needless to say, my students were "off task" too much because I had the temerity to let them talk to me and listen to what they were saying.  I had this theory (call me crazy) that they were probably stressed enough by all of the expectations being heaped upon them and that sometimes, they needed to blow steam here or there.  I also have this crazy theory that these "blow off steam" moments generally lead to interesting mathematical discussions about life.  Personally, I treasure those moments when I can help my students see that math is all around us and not just on a standardized test somewhere.

But no one ever mentioned evidence of learning or understanding of deep mathematical concepts.  No one bothered to do anything but make check marks on a paper.  In one instance, two particular students were deemed "off task" because one of them was helping the other.  It would be better, I was told, if they were to understand these procedures on their own--independently--talk about unproductive struggle!

So aside from the obvious differences between NCLB and CCSS, what else has changed in my teaching to enable me to be so much more confident about what I am doing?  Simple--The 5 Practices.  I first encountered this book at the NCTM regional conference in Las Vegas in 2013.  Somebody whose knowledge I respected recommended it in a session and so I bought and read it.

And didn't make a lot of changes.

Sometimes these things take time.

At some point, I picked the book up again and got to thinking about the biggest roadblocks to implementation.  I realized that the lack of good questions/problems to discuss was holding me up.  I teach 6 different math classes and it's really hard to come up with problems that work for all six classes all the time.  I started experimenting with modifying tasks from our current textbooks to make them more open ended.  I tried some out.  Some worked well.  Some failed miserably.

Upon reflection, I realized that some of my tasks had become too involved and challenging.  I was having to help my students too much because the task was too much, and it was taking several class periods to get through the task in any meaningful way.  I think the students begin to "lose the thread" of the task if there are too many steps and calculations.  I found that if I could shoot for one class period for the task plus discussion, this was better.

I also found that I really have to work on the low floor/high ceiling concept.  My classes encompass every level from struggling/resource to very advanced student.  I was having to help too much because the floor wasn't accessible to the lowest students.  It's got to be something they can dig into and find some success at or they will just give up.  I was also losing some of the higher end students because the ceiling was too low.  I had to prepare the task so that everyone could access it and experience some success, so that there was somewhere to go for those who finished it early and so that I had a clear stopping point that could be reached by most or all students.  I found that taking time to help the struggling students but expecting everybody to "finish" the task completely dragged the time way out.

In re-reading the book, I found the Task Analysis Guide (Smith and Stein 1998) on page 16 to be instructive.  I evaluated some of the tasks I had used in terms of the demands I was making on my students' thinking and found that I hadn't done too badly in terms of lower-level vs. higher level demands.  I had just made too many demands for one problem.  I realize now that I was trying to model my problems after the Performance Assessment problems that they see on the SBAC.  While those tasks are a good starting point, they generally do have 4-6 different parts.  They aren't intended as teaching vehicles.  You could probably get 4-6 different appropriate tasks out of one SBAC style performance task, but they would need to be sprinkled in at the right places in the curriculum as each full task covers a broad spectrum of standards.

So I've scaled down my idea of what a task encompasses.  I still struggle with the floor/ceiling problem but I'm getting better.  I've learned that students are more productive if I type up a set of instructions and questions and project those while they are working.  I can refer them back to the instructions to help keep them on task or say "so do you think you could answer that question in a way that makes sense?" to help clarify their thinking.  I have been adding my ceiling in the form of some extra steps to follow and extra conjectures to think about.

There are also far more examples of authentic tasks available now.  I love using Fawn Nguyen's visual patterns.  Open middle has been a good source.  Illustrative mathematics and NCTM's Illuminations also have good collections of problems to use. We are transitioning to EngageNY next year and I am hopeful that the tasks they provide are authentic or can be adapted to use with the 5 practices.  Interestingly, I am now less concerned with how good/bad/appropriate that any given curriculum is because of the 5 practices.  I know I have the tools to transition to the You-We-I model.