How to Keep a BIG PROBLEM Going

Doing BIG problems with LITTLE kids involves a really beautiful set of challenges. Beautiful, I say, because though the obstacles are great, The Little Ones are capable of getting on board in endlessly satisfying ways.

One of the biggest challenges we face is trying to keep them engaged and pushing their thinking forward over a series of work sessions. Inside of that challenge is the fact that there are so many ways to be wrong, it can be hard to pick the most important issues to tackle or to pick the trajectory of skills and behaviors that will lead to the greatest growth in content. You've got attitude AND aptitude that you have to address, and it can feel a little bit like putting clothes on cats....maximum hustle in random directions while somebody is trying to scratch your eyes out. Too dramatic? 

I wanted to share a few things I think about when I'm planning for future lessons to push us on a Big Problem. First of all, I consider every work session to be an adventure in formative assessment. I'm constantly looking for strategies or behaviors that I want to promote. It's helpful here if you let go of "the right answer". There's time for getting right answers. I always say I'm not the kind of hippie who says "It doesn't matter if you're wrong, as long as you can explain yourself!" Actually, it does matter. It's math. There are answers in math, and I want my students to be good at getting them. However, having said that, if all I'm focusing on is that right answer, I'm missing opportunities to build their capacity to be mathematical in really challenging situations. I'm diminishing their long term ability to get right answers in powerful ways if I stop every half-baked thought or idea because it's not RIGHT. When I'm teaching the way I aspire to teach, we have to identify, exam, and discard a whole lot of "wrong" before I can say they totally own "right". That takes time, and letting go of nitpicking their answers can create space for the bigger work we are trying to do.

Second of all, I think about the Standards for Mathematical Practices (SMPs). There are 8, and they all focus on the behaviors of mathematically proficient students. If I know that I want to see students doing these things, I look for students who are doing them, and we name them and invite their classmates to do them. 

Finally, I look at misconceptions my students are nursing along. Misconceptions can manifest in very sneaky ways, and it's important to get practiced at ferreting them out...a misconception that isn't addressed will be cleaved to in really unattractive ways.

SO:  

1. Strategies I want to promote

2. SMPs students are doing

3. Misconceptions to address

Each Problem Solving Workshop follows the same structure....a mini lesson, a work session, and a closing lesson.  I wrote about introducing the problem here, Part 1. The next day, I did a mini lesson on what the word "each" means, here Part 2.  That same day, but written about separately here Part 3, I set the kids to working. I chose the following trays from that work session to share with the kids as a mini lesson to start the next work session the following day.

Focus of our Mini Lesson:

SMPs students are doing -SMP #1 

This tray just shows that a student started by making a train of 17 cubes to match the problem, which I always have posted.

This is what SMP #1 (make sense and persevere in solving problems) looks like with The Littles. During that first work session, some students couldn't really get started. They fumbled around a bit. Good job, Littles! You stuck with it! But we aren't just cheerleaders, we need to help them develop real strategies for getting on it. I showed them the tray and said, "How does this tray match the problem? Why did this person do this?" After some private think time, a little bit of partner sharing, and some questions for clarity, they told me that this makes sense because the problem says 17 acorns and these are 17 cubes, which are the acorns from the problem. I pressed on them until they articulated that if you weren't sure what to do, you could go back and look at the problem and see how it starts, and try to make your tray match the way the story starts.

And here we go! During the work session that day, they quickly got busy building their 17 acorns. Are you surprised that we are doing the exact same problem we already did? Pro tip:  don't introduce new problems every day. I like to share with them my favorite George Polya quote, "A problem isn't a problem if you can solve it in 24 hours". We are doing this problem again because that's what mathematicians do, they stick with their problem until they have learned everything there is to learn about it and from it. It's a good thing!

Strategies I want to promote

I followed the same process for the next two trays, just placing one in the middle of the learning circle and giving them some prompts to think about and partner talk about. Mostly, I just asked "What did this person do? How do you know it matches what is happening in the problem?"

And then this one, with the same prompts:

This one is different because it shows the squirrels. In Level B of this Problem of the Month, there are different kinds of squirrels and each type of squirrel can carry a different number of acorns back to their homes. Students will need to figure out how many trips the different types of squirrels will take to get the acorns back to their homes. In any case, managing the tools to represent both acorns and squirrels, in addition to the clever color coding to keep track of the different groups of squirrels, is a really helpful and powerful strategy for doing Level B, which we will be doing soon, so I wanted to make sure we put it out into our universe so we can call upon it.

And during the work session, after this quick inquiry mini lesson on these two different strategies for keeping track of feeding the squirrels in our problem, I saw the students experimenting.

 Various stages of making sense..... This little group had a hard time finding their error (they started with 16 acorns instead of 17 and thus ended with 3 acorns instead of 4) because they all made the same mistake and easily convinced each other that they were killing it. I made the executive decision to not address this wrong answer in real time, and instead held space for them to practice the strategy and practice their recordings.

 Another error....since this child was working alone and hadn't worked himself into a lather about how right he was, I found it easier to do the "match making"... This student was paired up with another student who used the same strategy, but who made 8 squirrels and 5 squirrels instead of 5 and 5. The dream is that when they talked it out, the other child would be convincing enough that this child will see how to fix their error without me being involved at all.

 I love this one, where he uses the tiles to be squirrels instead of the counters. I think little details like this show that he is really making sense of the strategy and making it his own, as opposed to just "mimicking" the strategy of using counters but not really understanding what he is representing. Kids have that kind of magical thinking sometimes, as though the math is in the chip instead of in the chip as representation. Recognizing that he can use any tool to show his squirrels is a little thing that feels very big in a primary classroom.

You nailed it, kid.

Now go find somebody to talk to!

Misconceptions to address

I saw wrong answers, but no real misconceptions. You can do everything "right" and still make mistakes. In life and in math, it turns out.

That was it for this session! Imperfectly perfect, in my eyes. So much movement in just this one attempt, and so many places still to go. That's how you know it's a good problem :) My "closing lesson" was on how we put away our trays and bags. Not life changing in terms of content, but lookit, these conversations have to happen. For my sanity.