Friday, August 24, 2012

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.


  1. I love the idea of finding unfinished answers interesting. Too often I get hung up trying to find wrong answers interesting, and don't give enough attention to those who struggled through a certain path that led to a dead-end...especially if that dead-end could have been salvaged. Thanks for bringing that to my attention.
    In terms of building a team mentality, we actually *always* work through problems in groups (2-4) first. (That's not entirely true: sometimes we'll start a problem individually, then create the groups based on the path that learners are taking to solve it). We don't actually do things individually until after we've struggled through it together...then they'll get a new problem to work on by themselves (sometimes very related, sometimes novel but using the same concepts). This takes a lot of team-building and a focus on collaboration on the front end, but I think it pays off at the back.

  2. This was a great, timely read for me. I've been battling the student frustration problem myself these first two weeks as my pre-calc and calculus students are adjusting to having a new math teacher (for them). Getting them to be OK with struggle is proving to be my problem thus far. I look forward to reading your continuing perspective. It's already been a help and encouragement.

  3. I'm better at problem solving when I stand at a whiteboard than sit down with paper. And when I play with a koosh ball. Moving around gets the blood flowing and the whole brain involved. When I get stuck I can stand back and look at the big picture. Taking breaks is also important. I would give each group a piece of real estate on the whiteboards, give them all koosh balls or puffer balls, and allow them to take water breaks at will. (or some other quick break activities) At the very least, release them from the prison of desk+chair.

    Presumably you're using SBG. Take the pressure off by reminding them that a right or wrong answer on any given day isn't going to affect their grade. Make some kind of poster or have a phrase you repeat or do something to set the tone of the class accordingly.

    How often should you do problem solving? As much as humanly possible! In the long run, you want students to become more comfortable with frustration -- to be able to work on a problem for hours like we sometimes do. I'm not sure how to get there, other than keep doing tougher problems.

  4. I love your idea of interrupting more regularly. I think too often I have a chunk of student work time followed by a chunk of lets talk about your work. In order to decrease the frustration I should pause more regularly and have shorter chunks of each (working/discussing).

    I also think the importance of recognizing unfinished problems is underrated. Just today (the first day of school!) I had a student offer up his work to display on the document camera who is a great example of this. He thought he did the problem wrong, but the class convinced him that if he kept going on the path he started he would come up with a correct solution that was solved a way none of them had thought of.

  5. The dilemma you first highlight regarding the backlash of students, parents, and the school system itself in response to presenting students with difficult problems is, in my experience, only somewhat true. I am a major proponent of a more foreign style classroom and that is how my classes tend to function. True, there is a lot of push back from students for the first 12 weeks to a year and a lot of criticism initially from parents; however, once the logic behind the strategy is explained and backed by research, the number of critics decreases sharply.

    I think you did a nice job of pointing this out by stating that you plan to explain this to your students in the first week. This will help but it will not fix the problem, only time and familiarity with the new model can do that (if my research is correct). I believe it was in an article written by Mary Stein that she pointed out her belief that in order for the new model to be successful, it must be district wide. While I don't agree entirely (at least I hope it isn't true as it would invalidate all of my current efforts), I do believe that the premise of student familiarity with the model is the key!

    In addition to familiarity, I find collaboration among students while struggling is extremely important. Thankfully this is also backed by research not just my experience as it is one of the components of the gradual release model (even though I order that model extremely differently than the traditional American model.

    By the way, it is refreshing to read about someone having similar struggles to my own, so thanks so much for making me feel a little less isolated!

  6. It's possible you've seen this before (it's now buried back a bit in my archives) but I highly recommend hint tokens if you know the students are going to be peppering you with too many questions.

  7. I teach supplemental courses in advanced mathematics through a local nonprofit organization, and based on my experience, I have found it helpful to be explicit that the point of the program is to serve up hard problems. Hard problems make people feel stupid, but they can overcome their feeling of stupidity being demoralizing if they know that everyone who tackles hard problems feels the same way. I have a FAQ about that, "The Explorer is the Person who is Lost, or Courage in the Face of Stupidity," posted on the Epsilon Camp website.

  8. Richard Rusczyk at also has some interesting things to say on this topic.