Building A Thinking Classroom - Into the Weeds

Monday marked another big day in the process of building a thinking mathematics classroom - the first curricular thinking task that would cover a topic that students would not have prior exposure to (or so I thought, at least).

The topic was situations that involve taking a fractional part of another fraction. The sample situations my district provided (which they took from a lesson my state provided) imagined a person named Deja attending a potluck.  So I started their thinking task with the examples provided:

This thinking task really got us into the weeds.  There were a lot of situations to manage, and I struggled to manage them all effectively.
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• Several thinking groups thought about these situations exactly as I'd hoped they would.  They productively struggled to make sense of the situations first, then worked toward figuring out a way to represent them that would lead them to a solution.  I was able to listen, offer a hint to point them in the right direction, and let them sort it out from there.
• Several groups had one member of the group who had learned that multiplication would lead to a correct solution in these situations, and that member of the group told the rest of the group "you just multiply, trust me," and then the group just did that without thinking.  These groups were remarkably resistant to my nudging them to think, even when two members of the group didn't know what to do or why it would work.
• Several of the groups just guessed (correctly) that multiplication would solve these.  Their logic was basically, "there are two numbers, we've already covered addition and subtraction, I'll bet you just multiply.  Again, zero thinking, and very little willingness to respond to my encouragement to try and make sense of the situation rather than guessing.

Several groups thought about the situations exactly as I'd hoped they would.

• Several of the groups read these as subtraction situations (which they very closely resemble, and which is always a tough part of teaching this), and then I had a very good basis to start them thinking differently about them since they'd applied thinking already.  I helped them identify the difference between, say "eating 1/3 of the remaining part of the lasagna" (today's task) versus "eating 1/3 of the entire lasagna" (a subtraction situation), and then their thinking was very good.​

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I wrapped up the day in a very uncomfortable place for a teacher used to teaching through mimicking - I had students with very different understandings and very different approaches at the end of the day:

• I had students who had a thorough understanding of how to organically think about, make sense of, represent, and find a solution to these situations.
• I had students who had worked with students in the category above, but had not attempted to understand for themselves - they let the lead members of the group do all the thinking, and they themselves came away with nothing.
• I had students who knew (from prior classes) that multiplication was the correct way to solve these though calculation
• I had students who worked with students in the category above, but who had no idea why that calculation would work, nor, in some cases, how to do that calculation.

​​I tried handling "check your understanding" time a bit differently today.  I went right into it after thinking.  My hope was that this time would point out to those who coasted on the understanding of others or who just let the group list out some answers without personally following the thinking that how they handled the day's thinking was not productive for them.  A bit of accountability for the thinking work, you might say.

I think this went well, impromptu as it may have been.  A lot of the students settled right in and felt good about the fruits of the thinking.  Others sat down with an "oh crap" look on their faces and literally couldn't do anything.  At least we had something to reflect on, if not any learning to celebrate.

So here I sit, with a weekend to sort it out, deep in the weeds of a thinking classroom.  Here, I think, are my takeaways from this first attempt:

1. I'm probably going to have to get comfortable with the idea that "thinking" for many students will involve organic problem solving, while "thinking" for many others will involve primarily working through calculation.  I think this is probably ok, but I'm going to have to adjust to people understanding the same content differently rather than everyone understanding it the way I've taught them to understand it.
2. Students are going to need some guidance that the group "having a list of right answers" to the thinking questions is not the goal.  I didn't think I had presented the work that way, but there were definitely groups where one member either knew or figured out what to do, and the rest of the group tried to just let them do it.  Even when I saw this happening, it was hard to put a stop to.
3. I'm going to have to teach the kids that calculating is not necessarily thinking (though sometimes it is)

I'll probably devote Monday entirely to consolidating - which I'm admittedly not at allcomfortable with yet - so that I get certain baselines of understanding in place.

Image taken from https://buildingthinkingclassrooms.com/14-practices/

I'm in an decidedly agonizing place for someone who is accustomed to leaving most days assured that I've taught every single student to mimic a new skill with evidence to show for it.  I'm able to teach through mimicking at a really, really high level, and I've grown used to the end-of-the-day glow of a well-executed mimicking lesson where the students are confident and I'm confident and I have proof that everybody learned.

Part of what makes this so hard is that I'm not used to this.  Is this always how it goes?  Did it go this way because I'm still a work in progress as a thinking teacher?  Did I screw up?  Did I nail it?  Which unexpected decisions did I handle correctly, and which ones did I botch?  

We'll see if I can get out of the weeds on Monday.

​Or if the weeds are the place to be, after all.

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