Tuesday, June 6, 2017

My Favorite Mistake


When I was in my second year of teaching, a learning coach at my school forwarded me a link to an activity created by Leah Alcala called "My Favorite No".  The videos shows Leah using student's mistakes as part of the lesson; and the students in the class seem like they are really into the activity. I decided to give it a try!

Disclaimer: When my coach shared the link with me, I was super burnt out on "warm-ups" and, after several years of math class warm-up routines, my students seemed to be burnt out on traditional warm-ups as well. In fact, warm-ups seem to be the time for students to try ANYTHING to get out of doing work...to me, a sure sign of boredom and non-engagement: "I don't have a pencil" or "do I have to put the date?" or ""is this graded?" or "how many points is this worth?" or "will this be on the test?". Yes, I was ready to move on to something new and so were the students!

Three years later, My Favorite Mistake (I renamed the activity) has become my go-to warm-up routine and a cornerstone of my teaching practice. Thanks, Leah!

When I do it correctly, which doesn't always happen, My Favorite Mistake allows me to:
  • formatively assess my students. They don't write their name on their work, but they hand their work directly to me and I keep a list in my head of which students can/cannot do it.
  • facilitate a rich discussion about a common error. You know they type of error...when you are grading quizzes and EVERY kid makes that mistake with the negative. It's awesome to have a targeted, structured discussion about that error. 
  • use a classroom routine, on a near daily basis, that emphasizes how learning math requires a growth mindset. For My Favorite Mistake, I'm neither excited about nor interested in the correct answer. I think the kids love seeing me get excited about the errors. And the feedback I get from students is that they love this activity because they feel like they can make mistakes and it is not punitive.

How I use My Favorite Mistake

Update about normalizing errors in the classroom at the bottom of this post. 

When I plan a My Favorite Mistake, there are three components I consider. First, I need to choose the correct problem. Then, before I actually do it with the students, I need to think about the type of errors I expect to see. Finally, as I'm collecting student work during the activity, I need to sequence the errors so I present them to students in a way that makes sense. Note: this is an anonymous activity. The students DO NOT put their names on the paper. If you'd like to know who did what work, you can have them put their name on the back of the paper.


Choosing the Correct Problem

For My Favorite Mistake (MFM) I present students with one problem. I give each student a quarter sheet of paper (recycled from paper in the copy room). I tell them they cannot get help. 

I choose a problem:
  • related to the learning goal for the day. For example, in the systems of equations unit, before we start solving by substitution, I do a MFM on solving a linear equation with variables on both sides. In the exponentials unit, I do MFM on evaluating expressions with negative exponents
  • that is doable in 3-4 minutes. When I've done MFM and it doesn't work, it is because I choose a problem that has too many steps--if there are too many errors it gets overwhelming for me and for students.
  • that is mistake friendly. I don't want to give a problem that everyone will get correct--that's not the point. I need to find the goldilocks of problems...not too easy and not too difficult. 
  • that allows me to do the entire MFM activity in about 10 minutes

Anticipating Errors

This becomes easier with more time in the classroom and practice, but it helps me facilitate the classroom discussion if I think about the errors before I actually do the MFM.

Thinking about the errors also helps me select the correct problem to give. If I can't think of any "conversation worthy" errors or if there are too many potential errors, then it isn't the right problem to use.

Sequencing the Errors

Similar to the teacher in the My Favorite No video, I post a problem using my projector, I give the students quarter sheets of paper, they do the problem on the quarter sheet (no name) and I circulate to collect their work as they finish. It does take awhile to build the routine, so be patient with yourself and your students!

I sequence the work as I collect it. First I separate correct and errors, and then I sequence the errors in a way that, I hope, will build a rich classroom discussion.

For this MFM this is the first error I would show. Student forgot to "undo" squaring. 
This is the second error I would show. Student remembered to undo squaring, but forget the positive/negative.

This isn't an error, but I would show it and ask for warm and cool feedback on this student's work (warm, checked their work. cool, didn't show all steps). 
Always the last step: show the exemplar student work--never my work!


The Power of Routine

I have 100% participation for MFM. EVERYONE tries the problem. All students indulge my request not help each other. 80% of the time, we have a fantastic class discussion during MFM. And none of that happens overnight.

Classroom culture takes weeks or months to build. I truly believe thoughtfully implementing routines in my classroom can create a pathway to my vision for classroom culture. But those routines needs to be consistent and there needs to be a lot of teacher to student feedback on the PROCESS of the routine. And this is the case with MFM.

After several weeks (months), things start to fall into place with MFM. But it takes a lot of patience on my end and it means I give a lot of feedback on the routine. I teach 9th grade students. For the first several weeks of school, students will constantly ask me, "do I need to put my name on the paper?" for MFM. They don't. For the first couple weeks, students will ask "is this is graded?" It's not--plus your name's not on it...how would I grade it?!! You get the idea. This doesn't become a perfect routine in one day.

Participation Structure

Last, I want to explain how I structure the class discussion. At this point, students have done the MFM problem. I've collected and sequenced their work. I post the first error and I say, "talk to your partner. What is the mistake in this student's work. BE PREPARED TO SHARE. It is ok to be wrong; it is ok to share a point of confusion. But I will not accept 'I don't know' or 'I didn't do it' as responses." I say that same every time we do MFM. For weeks. And it takes that long to build the no-opt out culture around this activity. After I say my part about sharing, I give students 30-ish seconds to talk and then I use a random number generator to call students.

Something new this year: when i called on a student, they would say, "that's my error, so I can't explain the mistake." Very clever!! This response actually threw me off the first few times I heard it. And, of course, being 9th graders, they could smell my confusion and they ran with it. "That's my error" quickly became their go-to response. Now I add the disclaimer, "even if this is your work, I expect you to share your thinking about the error. Talk to your partner and make sure you have an idea or point of confusion to share with the class."

So remember, be patient. The math students you have now probably have been drilled with the message that math is about being correct and being fast. It is possible to change that culture and My Favorite Mistake is one way to do that. But changing culture takes weeks or months, not days. Good luck!

UPDATE 8/1/2017: Normalizing Mistakes in the Math Classroom

I recently gave a workshop at a math conference about using routines to promote a growth mindset so of course I talked about using My Favorite Mistake as a warmup routine.

Several teachers had questions about my use of MFM. Their questions fell into two categories:
  1. Do I worry if students can recognize someone else's handwriting? (I don't, but can acknowledge this concern)
  2. What if a student is extremely uncomfortable sharing their errors?  Like, the student knows their work is wrong and they feel threatened that I might show their wrong work to the class. ( I would never make a student do something that makes them uncomfortable).
However, I want to shoutout a colleague for challenging these concerns. My colleague argued that if we as math teachers avoid showing student errors because of these types of concerns, we run the risk of perpetuating the fixed mindset culture in mathematics.

My colleague reminded me of the importance of body language and teacher tone when doing an activity like MFM. If I wince when I see a student's incorrect work, or if I say something like "this should be easy for you", I am feeding into the fixed mindset idea of math. But my colleague helped me realize the power of MFM in my classroom, and the reason I can make an activity centered around students' errors feel safe, is that I don't exhibit these kind of behaviors. For MFM, I get super excited about the mistakes. I don't wince, I genuinely smile. I don't say "this should be easy" I say "wow! what a great mistake to make! I love it!" With tone, demeanor, and body language, I am normalizing errors in my classroom. I am communicating my vision for classroom culture through my deliberate actions that say "I honor errors as part of your learning process". 

Thanks to the participants that raised some great questions. And huge thanks to my colleague for connecting the dots between not reinforcing a fixed mindset, normalizing errors, and using routines for growth mindset. 

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