White Paper on Problem Solving: Struggle without frustration

I’m pretty confident that if I just give my kids a bunch of really hard problems to solve, the following will happen:

• First, the class erupts with demands for help.
• Then, the class collectively gives up. Two kids keep on working, because they’re those kids.
• Students complain to their parents, who complain to the school, who pass it on to me. (“They say you’re not teaching them anything.”)
• I fax (fax!) everybody in school a long memo detailing where our profession has gone wrong and how to steer it right.
• I get fired and lose all my clients save for one hot-headed wide receiver.
• Together we teach each other the importance of trust, love and commitment in both personal and professional relationships.

And I certainly don’t want that to happen.

In the previous post I explained how, last year, I responded to the pressure of keeping my kids un-frustrated by making my problem sets easier. In the first post, I explained why I shouldn't have done that. In this installment I want to come up with some strategies for helping my kids feel comfortable with struggle. I’ll keep my eye on the comments; if you’ve got something good, I’ll toss it into the post.

But first, yet another picture of a cat with a Rubik's cube. Seriously, how many of these are there on the internet?

Never mind. Stupid question.

How to keep kids from getting frustrated* by difficult problems:

* Frustration is sometimes OK, but is just as often unproductive for a student. For the rest of this post, you can assume I'm talking about the unproductive stuff.

Let's start with a distinction. When a kid gets frustrated in an unproductive way while working on math, her frustration comes in two flavors:

• social
• intrinsic

Social frustration comes from feeling as if she's inadequate relative to her peers or relative to the expectations of others. It's real, but it comes from her understanding of other people's views of her. Intrinsic frustration is everything else. It's the stuff that would cause a person to walk away from a problem even in a closed room, with nobody watching. (I don't really know where "privately feeling stupid" fits. But whatever.)

Here are ideas for minimizing the social pressures:

• Be explicit: One day last year, during a quiz, a kid pointed at me and said, "Mr. P, you put a problem on this that we've never seen before!" And I was, like, yeah that's what I was trying to do. But that was actually a really good moment, when the class came to understand what I was about. I should've talked about that in the first week: "Yo, kids, I know this class is different. But it works and you'll still have support, and it'll be OK." That sort of thing.
• Find unfinished answers interesting: Last year we never had conversations about the kids' work with the whole group. This year I'll bring to the fore not just correct answers, not just finished answers, but approaches and ideas from unfinished problems. I'll intentionally spread the wealth, so that we're talking about everybody's work, eventually. And we won't do the embarrassing "So where did he go wrong?" questions, at least not at first. Instead we'll celebrate the process by asking, "How could we finish it off using his approach?" We won't force everyone to go through the ringer, at least not at first.
• Try to build team mentality: This is a bigger classroom management puzzle for me, but I'm going to start by throwing in questions to the problem set that say "Look around. Does anybody need help? Take five and see if you can be of service." 

And here are some ideas for minimizing the intrinsic pressures:

• Mix up easy (but cool) and hard problems: When things are going well, when you're in the zone, you're in a state of flow. Flow is what keeps most of us coming back for more, even when the going gets rough. By mixing up the satisfying questions with the knotty ones, I'm betting that I can get more kids working for longer. (Also, a really good problem has easy, cool and hard aspects all wrapped up in one neat package. Keep an eye out for those.)
• Be more interesting: Whenever a kid gives up on a problem, part of the problem is motivation. If the problem was SUPER interesting, he would probably keep chugging away. So I need to do a better job finding more interesting problems and more interesting hooks into those problems. 
• Interrupt more often: There were times last year when kids would be working on problem sets (i.e. worksheets) for 20-30 minutes without serious interruption. That's great, but one way to release the pressure of frustrated students is to pause and take a deep breath. I'll interrupt them more often when I sense that people are struggling. We'll talk about the problems, get some approaches and strategies up on the board, discuss next steps and then send them off for another 5-10 minutes.
• Refer to common problem solving strategies: I'm betting that if we have a repertoire of habits of mind/strategies that we can all talk about, things will go down easier. I think we'll probably have a poster up in the classroom (like Daniel Schneider's) that has a list of things to try when you're stuck. We'll start with three: Guess/Check/Generalize, Tinker and Find an Easier Problem.

I fully expect the comments to be awesome on this post. 

Coming up next I'll agonize over whether this sort of problem solving should be an everyday part of my class or whether it belongs alongside other ways of doing things. I'll also post a sample problem set for the first week of class.