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Saturday, July 2, 2011

Virtual Conference on Core Values: Mistakes are Made

To sum up the center of my classroom in a phrase: We Make Mistakes. Sometimes deliberately and sometimes not, but we celebrate both kinds.

Non-educators are maybe puzzled at this statement, but all the teachers in the audience have already started nodding along with me.

See, lots of people think that learning happens like this:
and that that sparkly rainbow is the maaaagical majesty that separates good teachers from bad.

But those who have spent some time, you know, actually responsible for other people's learning know that it really happens more like this:
We could just call it "Piaget for Dummies." Other authors have likened the confusion to the conflict in a story. That little star is a place a teacher's skill is really important, because that's the point where kids might feel stupid and check out and also probably hate you for making them feel that way.

So, I'm very deliberate about centering lessons around mistake-making in non-threatening ways. If all my lessons have one thing in common, that would be it. Here are two specific strategies.


The first one became a staple in all my classes late last year and is really just Cornell University's GoodQuestions project, by way of Helen Doerr at Syracuse University, who sums it up this way: "A good question is divisive."

Pose your question. Here is one I plan to use next year in Calculus:
Compel the students to register a choice. You could use clickers, poor-man clickers, or polleverywhere. But it is important that they commit to a choice. And it's best if they can't see what other people selected until everyone's vote is registered. Ideally the responses will be more-or-less evenly distributed, or at least there will be no clear winner. Which is awesome! Because even if it ends up that you're wrong, you can't feel too bad about it if a third of the class agreed with you.

The point is to instigate an argument that can be settled with mathematical justification. If you're not sure how to get the justification ball rolling, try "Would anyone care to defend choice A?" If you're desperate, pass out slips they can write their name on and hand in for participation credit whenever they present an argument. Whatever you do, for goodness sake, don't tell them the right answer. (Like, ever. Let them come to consensus. Learn how to ask helpful questions without giving away the store.) Unless for some reason you want to completely shut down discussion. And thinking. You know you've got a really good question when you don't have to pull teeth to get kids to talk because they are so compelled to explain their reasoning that it overcomes their fear of everybody looking at them.

The Tyranny of Randomness

My second strategy is, I imagine, common in most math classrooms, and that's getting kids to the board to present their work. When I get them at the beginning of the year, they are freaked out by this. Of course. Standing in front of a room of your peers, potentially exposing your ignorance, is super intimidating until you do it a few times and everybody is doing it and you realize it's not such a big deal.

"Will you check it first?"
   "We'll all check it together!" (This is not optional!)
"What if it's wrong?"
   "That would be awesome! I'm kind of hoping it's wrong actually!" (If anyone points and laughs, I'll kill them!)
"I didn't get an answer..."
   "We'd still like to see the progress you made!" (Get up there, kid!)

I've always done this but sometimes have used volunteers, and sometimes have played with ways to randomize selecting students. For example, use the random integer function on the TI and match it to a numbered list of names. I also tried the popsicle sticks, but I am not that organized and kept losing them. Neither of these methods was very satisfying, because they couldn't see the process and had to take my word for it being random. But random selection really helps, here - when any of them could be selected at any time, they become more likely to give a problem some honest effort. Also, if they see a machine pick, they don't blame/hate me for picking on them.

Then last year I found the best thing - SMART Notebook has a flash random word chooser in the gallery (if you can't find it you might need to update the Lesson Activity Toolkit) - so I just have a file saved with a different page for every class with the students' names. When it's time to select a student, I just fire it up and we can all see it ping around before it settles on a name. It's very suspenseful.

Whatever you do, you can't let them off the hook. When selected, they're going to stand in the front of the room and pick up a marker and write something. (Alternatively, going to put their work under the document camera, or whatever process you've worked out.) Or you might as well go back to asking for volunteers, and it will be the same three kids who are the only ones doing work and going to the board.  You'll probably have to be annoyingly insistent for a little while until they become convinced of the inevitability of the situation.

There is a free random word chooser here that seems to work pretty well, but I have not tried it in a class. (And you'll want to turn the sound down/off because, ugh.)

The moral of the story: confusion and mistakes are necessary for learning. So much so, in my opinion, that I center my classes around them! Thanks for attending! Check out the other presentations!


  1. Great post.

    Small tip (? you probably already know it): After you put the names in the Name Picker in SMART Notebook, just drag the completed Name Picker to the "My Content" folder, and you can access that section of students anytime you want without having to open a Name Picker Notebook. Its hard to explain, but you'd have several completed Name Pickers in My Content, one for each section.

  2. Good tip, Dan, thanks. When we first got the smartboards, I kept losing all the stuff in My Content because of they way they had the files organized on the network. Something about roaming profiles? I don't know, but I kind of gave up on using My Content. I should give it another go.

  3. I've used the random name picker you linked to. The sound amuses the students.

    I like the Mythbusters credo: FAILURE IS ALWAYS AN OPTION.

  4. For random selection, I have a Probability Kit: a lunchbox containing a deck of playing cards, some whiteboard markers, and a ten-sided die. Depending on the application, you can use the kit for totally transparent selection by having one of the kids select. (If they don't trust the kid, have him do it under the ELMO, for all to see.) I have teams of four, so usually the card suit selects the team member and the die selects the team.

  5. So many goodies in this one. Name Pickers! Awesome graphics! (How did you do those?!)

    And (but you knew this, I bet) star examples of one of Doug Lemov's 49 Techniques of champion teachers: Normalizing Error.

    "Error" is not as big a deal in English as it is elsewhere; so much of what we do is defined by individual creative license and/or worked on via individual conference that it's fairly easy to downplay/deflate/defuse. That being said, our adolescents are arguably more sensitive to it than the average bear, and handling it at any point requires TLC. Surprisingly, I use my ELMO often as successfully with "stuck" work as I do with model examples.("Are you feeling stuck?...Do you want to put this under the ELMO to get some suggestions from other people?")

  6. Hi Kate,

    I believe it is Ted Mahavier who has a grading policy where 1% of the student's grade is based on making his or her first mistake at the board. He says that this is a great ice breaker early in the semester: a student will make a mistake at the board, and a classmate will comment that the presenter's grade for the semester just went up.

    I have mixed feelings about grading like this (and grading in general), but it could make students feel a little better about making a mistake during a presentation.

  7. Dina I don't think I got that far in Lemovs book. I gave up when he was poo-poo-ing grappling with unfamiliar problems in math class. I guess he doesn't know that part is necessary to learn math. Anyway, I will go back and read what he says about normalizing error. Thanks for the tip. My view is more - if you picked an answer that turned out to be wrong, there's a reason you picked it - a good reason possibly, that makes perfect sense to you. Let's hear about it so we can all learn something. It's a hard trick but works great when I pull it off.


Hi! I will have to approve this before it shows up. Cuz yo those spammers are crafty like ice is cold.