Launching Hard-To-Figure-OUt Tasks

It was another strong week in my Thinking Classroom.  Having had to think and figure things out for themselves every single school day for a full six months now, my students are able tocover huge amounts of content in a short amount of time.  It was almost comical this week.  They learned how to simplify variable expressions via combining like terms, applying the distributive property, and factoring in a class and a half.  In my prior, mimicing classroom, that was a three or four day affair, and it still would have been shaky at the end.

Both of these skills - combining like terms and moving between standard and factored forms of expressions - were not ones I expected students to be able to figure out organically. In the past, I've written about "introducing the minimum, then thin-slicing to the maximum" for topics where this is the case.

That's what I ended up doing here, too, but not the same way I had before.  In my first video demonstrating introducing the minimum, I was in front of the class showing how to approach thinking about the topic.

This week, I tried showing them completed examples to think about during the task launch.  For combining like terms, they saw a few un-simplified expressions pair with the simplified version.  For  distributing and factoring - which remarkably they were able to figure out in the same, shorter-than-usual class period (!) - I showed examples of the the same expressions in factored and standard form.

It was remarkable, and it allowed them to dig right into the thin-slicing and run with it.

I've got videos of each to share below.  

The first is just the task launch for combining like terms.  This was the first of the two days I tried the task launch strategy.  One of the things that made me fall in love with the new tactic is that, by the third example, you can hear how excited the kids are that they already that they see what's going on, and they literally can't wait to get into the first unfinished example before I even send them off.

This second video is of the task launch for applying the distributive property and factoring.  Similar enthusiasm - once they see it, they can't wait to get going.  This video also includes a full recording of a single group working on the thinking task - mic-ed and all!  These two were right next to the camera when I moved it and were nice enough to let me record them.

This third one is the same as the second with a different class, but it also has our weekly rule review and some recall practice prior to the task launch.  Feel free to skip to 13:45 you want to see the task launch, or 18:00 if you want to see the thinking group in action.

All in all, I really liked the task launch tactic.  There are certain times when, rather than "figuring something out," we need students to learn a particular mathematical convention or process, and it has to be the way it has to be.  There are certain things that we can all solve our own way or have our own way of doing, but certain things have to be understood the way the broader mathematics community understands it.  Knowing the vocabulary, conventions, and customs of math is part of belonging to that community.  Here, I hope, is an approach to building that belonging but still maximizing thinking along the way.

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