Monday, July 30, 2012

"When a student asks for help on a problem, I..."

[Click here for the bigger version of the pic.]

What's missing from this chart? What do you do to keep kids working on a difficult problem?

Two caveats to my chart:
  1. I'm not saying that "promotes/eliminates struggle" are the only relevant factors when deciding how to intervene with a student. But one of the things I'm worrying about is how to make my kids more comfortable struggling with tricky problems. I'm interested in what I can say to a kid that will make him/her more likely to keep on trying something difficult.
  2. There are obviously things that need to happen beyond the student-teacher interactions in order to promote the kind of environment that I'm looking for. Some of the stress my students experience when they get frustrated is intrinsic to the math problem. But some of the stress is social, a result of kids feeling like they're dumb for having to work so hard. We need to do things in class that normalize struggle and effort. (I think public presentation of interesting dead-end approaches and whiteboarding might be part of the solution.) So good interactions in the heat of the moment is just one aspect of what has to go on.


  1. Have you seen "My Favorite No"? That's one of the ways I hope to celebrate mistakes. (Let's go beyond normalizing them!)

    Also, talking out your thinking often helps clarify it, so up near the top I'd add "Ask them to explain their thinking so far."

    1. Interesting. I think that celebrating errors is important, and I think "My Favorite No" is a great activity. But that's all about normalizing (or celebrating) errors. I'm more interested in normalizing struggle.

      I think they are separate things. I've had students who quickly come up with an answer that they know is wrong, but they're OK with that. They're comfortable with error, but they're not comfortable with struggle. (To complement that: I have students who are comfortable working really hard on a problem, until they realize that their hard work lead them to a mistake.)

      Do you think that normalizing error and normalizing struggle are deeply connected, Sue? Will making my kids more comfortable with mistakes cause them to be more comfortable with difficult problems?

    2. I'll have to think about that.

      My second suggestion felt like more of an addition to your thinking. I've been reading The Psychology of Leaning Mathematics, in which the author writes about the importance of talking through your ideas. I want to think about all these ideas while I'm teaching next semester, and see which resonate with me and my students.

  2. Not math specific, but teaching about perseverance...
    Our school recently embraced Carol Dweck's idea of mindset, and several of us spent time in class discussing how to help students (and teachers) change from a fixed to a growth mindset. My students even started encouraging each other by saying things like, "Come on, growth can do it!"

    Several of my students blogged about changing their mindsets, and it made me happy to hear they less often "throw down their pencils in frustration..." (Although they kept reminding me that they would still throw pencils when I gave them the "Norman window" type problems.)

    Several of our teachers also created "Failure Walls," and they made bulletin boards with quotes about the importance of learning from mistakes. Teachers even encouraged people to contribute (on post-its) examples where they have learned from mistakes. We now use the phrase "glorious struggle" to help remind each other of a growth mindset.

    Just a few thoughts for Monday...

  3. when it comes to their thinking I am always asking them question like you have diagramed in your LOVELY drawing but I also made up these math metacognition steps that are similar to a problem solving process...They are not so much steps as much as questions that I want students to ask themselves as they are trying to solve a problem. it is kind of what we ask ourselves when we try to solve a problem but we probably do it without knowing it. I haven't been able to be consistent in using it but it is on my list of things to really push this year. Beside vocabulary.

  4. Sometimes I just tell'm - well, it's ok. That's what you are here for.

    But whenever a student struggles, I try to figure why that struggle is happening. And in my world of education of special needs students, that struggle can be all over the place. Sometimes, I didn't put up enough road signs, sometimes there is an unexpected developmental delay, sometimes it is a deep-seated aversion to looking incompetent.

    Last year I had a student who (still) struggles with long division. Not really because he can't mentally understand task but because long division is a multi-step process and his working memory can only handle about two-step problems. Give him a calculator...he's gone! The result was a number of inner discussions about struggle versus result.

  5. "normalizing struggle" - one way is to point out that "hey, you're struggling but not giving up - good work!" but that's cheap-o, ain't it?
    I'm also thinking that celebrating multiple competencies in mathematics is one way to encourage students to continue struggling. I got this idea from reading about Complex Instruction, which mentions mathematics competencies such as procedural solving, asking questions, using different representations such as graphs, formulas, tables, text, thinking logically, seeing connections to other ideas, extending the problem further, etc.
    So if the student is not achieving the correct answer, the teacher could still say "great questions you're asking!" or "that's cool how you used both a table and a graph to understand the problem more clearly." In this way we avoid that the student loses the motivation to continue the struggle because of labeling the work as failure.
    I also sometimes just laugh and tell them "you worked on this, what, ten minutes? I've been working on a problem for ten days now, but you know I think I'm getting somewhere!" The more math you know, the longer it takes to solve mathematical problems. Kids should get to know that.

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  7. Interesting post. I'd love to have some better strategies to promote struggle, particularly for the jaded, bottom-set pupil.

    I can't remember whose blog it was, but I remember reading about somebody's technique to teach some generic problem solving strategies early in the year (write down just the important numbers/variables/unknowns, draw a diagram, try some basic cases, write the problem as an equation, etc.), then whenever a pupil was stuck they would just ask, "Which strategies have you tried so far?" and get them to try another one.