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Chapter 4 – Option 1 (Reflection)

02/08/2020 9:12 PM | Karen Campe

Reflect on the list of teachers’ comments on page 57. What language do you currently use when students make mistakes? What language might you use going forward?


  • 02/09/2020 11:59 AM | Rene Chin
    I think I do ask a lot for agreement or disagreement with responses to questions, but I don't stick long enough in the mistaken thinking that might be occurring. I want to feel more comfortable staying in that place and encouraging further discussion and thinking. I want to make sure my face matches my verbal behavior. Often I remain neutral but my face may say otherwise. I will be aiming for more inviting facial expressions this week and leaning into those mistakes for longer periods of time.
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    • 02/09/2020 3:49 PM | Alison Foley
      Hi Rene - I feel the exact same way you do. I try to celebrate mistakes as they are a necessary part of learning and agree that it is important "to teach students to take mistakes in stride" (p. 57). Like you though, I feel I don't stick with the mistaken thinking long enough. Sometimes it is the pressure of meeting curriculum goals in a specific amount of time and sometimes I think I just want to help students "fix" their thinking too quickly. My goal is the same as yours moving forward - remaining more neutral and allowing more time to grapple with those mistakes by encouraging more discussion and thinking.
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      • 02/14/2020 6:31 PM | Karen Campe
        Rene & Alison, I agree with both of you -- time pressures can prevent us from really examining mistaken thinking or looking at a variety of mistakes to tease out what can go wrong while solving a problem.
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  • 02/09/2020 12:42 PM | Peggy Bell
    I celebrate mistakes in my third grade classroom. I like children to see that I make mistakes and they in turn feel more confident when they make mistakes.
    We take some of those mistakes and turn them into a math forum sharing thinking and analyzing them to see what the student is thinking and where he or she is coming from. I resonate with Shawn's comment "I know we've got a really good mistake we can talk about." I feel energized as Justin did "I see where they're thinking. I see where that's coming from!" I like to think I am supporting a growth mind set in my classroom where mistakes allow children to critically look at their work and grow in their perseverance until they understand where their thinking was erroneous. Through this process they are able to develop improved reasoning.
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  • 02/10/2020 11:51 AM | Alisha Signore
    We've been working on error analysis the past couple of years and process vs. mastery goals.I love the idea of the best error of the day to analyze and develop better reasoning. The emphasis is on solving efficiently and sharing/using models not getting to the right answer. We have a poster in our room- "Mistakes grow your brain!" Many times students make computation errors and we may set a goal for that like checking work for accuracy but still praise the process. We read the book Your fantastic, elastic brain which shows the science behind mistakes are necessary to learn and how we can grow and shape our brains.
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    • 02/14/2020 9:01 PM | Karen Campe
      Alisha (& this also relates to Peggy's comment above), have you seen "My Favorite No"? It is a technique where the teacher does a quick warm-up problem, then chooses one of the wrong responses as the best error to discuss as a whole class. It will be discussed thoroughly in chapter 5, up next, but here's a preview:

      This is a video from the Teaching Channel showing the technique in middle school math:
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      • 02/27/2020 8:04 PM | Nicole Gilson
        This is a great idea! I am going to look into this...I have a student who is paralyzed in math for fear of making a mistake. Never thought to try this...
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  • 02/11/2020 9:36 PM | Luke
    When a student makes a mistake in a whole-class discussion, I may say something like (among other things)...
    ~"let's look at this"... then I will start breaking it down and ask for further explanation from the student who shared or others. Or I might refer back to the problem and ask for connections to it.

    When grading papers I may write...
    ~How did you get this?
    ~I see what you are trying to do but...
    ~I may underline, write a ?, underline keywords from the problem

    Overall, I try to keep it simple and direct. When a kid is sharing in class and clearly struggling I lead them on, make some (any) connection or highlight one point to create some value in their response. At times others are so eager to share or correct a "wrong" statement that it can be intimidating for a kid who is unsure and feels they are saying the wrong thing.
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    • 02/14/2020 6:35 PM | Karen Campe
      Luke, you've identified one of the problems with discussing mistakes in class: how do we make them productive and not intimidating to the student who has made the mistake? It takes practice, careful choice of our language, and an environment with mutual trust among the students & teacher. Challenging!!
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  • 02/14/2020 6:30 PM | Karen Campe
    The phrase from Justin, that “there’s some kernel of truth to it” (the mistake) really resonates with me. I work hard to figure out what is correct about my student’s thinking so that I can build from there. Sometimes it is a correct concept that is applied in the wrong context (like creating common denominators to multiply fractions… which isn’t actually wrong, just adds more complexity) and other times part of the student’s work is correct and other parts are missing (like with exponents such as (2*x*y^3)^5 becoming 10*x^5*y^8 which has two different mistakes).

    One of my strategies to get students to (safely) discuss mistakes is to frequently do “find the error” type problems; the Algebra 1 and Algebra 2 textbooks we use have them in most sets of exercises. Students need to identify the error, explain why it’s wrong and how to do it correctly. Another technique is "Two Truths and a Lie" where students create 3 math examples in which one contains a mistake.

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  • 02/28/2020 2:22 PM | Jennifer Rianhard
    When a student makes a mistake, I will usually say we'll let's look at this or tell me more about your thinking. Sometimes the student will pick up on their own mistake, but sometimes it takes a back and forth discussion between the student and teacher. Mistakes are a part of learning. That's how people learn, by taking risks and trying and then fixing their thinking.
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