My Favorite Mistake Remix

Caveat: much of my work this year involves … first making sure that classrooms are safe and productive learning environments and then second helping classrooms that are mostly on the traditional spectrum become more awesome (aka student-thinking-centered).

One “tool” I’m thinking about today is this “favorite mistake” activity.  I first heard it as a Do Now review where the teacher quickly looks through student answers to the Do Now and then posts his/her “favorite mistake” for everyone to discuss.

In many of the classrooms I’m in, students are much more focused for the first 2/3 or so of class, and become less focused/productive near the end.  One idea I’m toying with is a remix of My Favorite Mistake …

With about 15 mins left in class, post one (high leverage) problem and two solutions.  Every time, there is EITHER one accurate/one mistake or two mistake.  Students think/write/decide in partners and then vote and discuss (this, tailored to the context and teacher, and more fleshed out).  Followed by some sort of exit ticket/reflection about the entire class.

I hope this idea will help give more focus/thinking/interest to the end of class.


Eric the Sheep


This week, the last week of instruction, my classes are completing portfolio and working on the Eric the Sheep problem.


I’m really enjoying another opportunity to run my class how I want to run it next year (all the time!). We started by brainstorming problem-solving methods. Then I asked if anyone knew anything about sheep shearing and showed an illustrative youtube video. I’m not sure how legit a use of technology that was, but it definitely helped hook students into the problem. We are 3 days away from the last day of classes and while a few students complained about doing work, zero (zero!) asked why they had to do this problem/what it had to do with real life. I think because it’s such a rich task (not because 100% of my students will one day be shearers/barbers). Here’s what students WERE saying …

“Ms. Langer, I need a way to figure out the answer without using chips!”
“We tried that rule too, like that exact rule, but it didn’t work for the first question, and any rule you make for a pattern has to work all the time.”
“She can’t watch this video; she’s vegetarian!”
“Why do you guys like goats and sheep so much!?”
“It’s not 18; it’s 16. Look!” (Actually, “it” was 17 … ;))
“You take all the time you need …” (A student who accurately answered the last step, which we had sloppily answered. Whoops/great!)
“I don’t want to draw 50 circles!”
“Wait, I didn’t understand what you just said about why I am wrong; can you say it again?”

AND I get to practice better discussions. Awesome. I tried to follow some of my discussion checklist for the discussion.  I had two goals: comparing representations of the pattern and generalizing. I had looked at the students’ work and had a trajectory/few ideas I wanted to surface (Why do you round up after dividing? What’s the connection between the groups who divided by 3 and the group that subtracted 3 repeatedly?). I didn’t choose a student to lead the discussion because that’s not a practice in my class this year, but I did have students present and they ended up taking over the conversation from me whenever I tried to direct things too much (sweetness).  Some questions I was left with included …

– How to deal with everyone writing up their math work but not everyone presenting. It seems much more authentic to write up your work neatly so that you are prepared to share your thinking with others (as opposed to writing it up b/c the teacher told you). And indeed, we did some really good talking and looking at each others’ work. But, I had everyone write up their thinking, and only some of the groups presented (some groups’ ideas overlapped/were incredibly similar). How did the students feel who wrote up their work but didn’t present, only participated in the discussion? (I guess I should ask them!) Would it work to have a norm of everyone writes up their math work so they’re ready to present/participate in discussion; not everyone will always “present,” but everyone will always participate?

– I HAVE TO worry less about content. I think worry less philosophically, but in the moment of class, I keep wanting to steer the discussion towards the generalized rule. I wanted to interrupt students who were inaccurately explaining why you round up. But really, the students were handling the discussion fine (and asking genuine questions), and I just needed to chill out!

Overall, super excited for next year, lots of problem-based learning, more discussions, more time on rich tasks, and less worry about content.


Discussion Checklist

I started to get my thoughts down for the aforementioned rubric. It came out as a checklist.  Here’s what I have so far.

Before the discussion, the teacher/students should:


During/After the discussion, the teachers/students should …


What do you think?

I’m most excited about the planning stages, where the teacher has to really explicitly decide the purpose of the discussion. This could change based on what the students do, but having a clear purpose and recognizing the nuances between generalizing, versus comparing, versus giving feedback, etc. will help me make the discussions more focused and therefore (hopefully) more accessible and engaging.


Orchestrating a Class Discussion around Mathematical Goals

I keep detailed notebooks of thoughts gathered from PD, readings, and meetings, ideas for future problems, lessons, and units, and reflections of small victories, detours, or interactions.   I’ve used this system since before I’ve taught and it works well for me to process in the moment or look back on my thoughts.

I am in the process of rewriting/rethinking my course standards for next year and I reviewed my pie-in-the-sky thinking and goal setting.  And I stumbled upon my hopes and dreams of class discussions from July 10, 2009. Here’s what I came up with back in the day.

My non-linear notes:


And the more traditional notes:

Use sentence starters – How can I scaffold students to being good mathematical conversations?  How can we talk about the process and not just the solution?

  • Our approach was like ______’s work in that we both ______.
  • Our approach builds on _______’s work in that we _______.
  • Our approach was different from ______’s approach because ______.
  • I know this works because ______.
  • When I see ____, I infer ____.
  • I think this was _____ when I saw/heard <evidence> because <explanation>.
  • This work is similar to what we did before because …

Leading Questions (always connect to the objectives AND think about is the question to orient, assess, or advance student thinking – questions don’t always need to come from the “teacher”):

  • How were you thinking about it?
  • What stayed the same?
  • What changed?
  • Where did you start?
  • What seems significant?
  • How does this representation show your thinking?
  • Where are we able to generalize?
  • What is different between these two problems?
  • How do we capture that thinking onto paper?
  • What does you agree/disagree with from this group?
  • Think and digest this thought and rephrase their thinking.
  • Are you able to come up and explain/walk through your thinking?
  • What’s s/he doing?
  • What is the story of your work?
  • How could you show it another way?
  • How could you explain this in context?

I think this flash back is a bit exciting.  I know SL has been thinking about this a bit deeper than I have more recently, but my beginning thoughts from four years ago may persuade me to think a bit more about how to incorporate more sustainable discussion routines into classes.

Other awesome things I should think about/remind myself about for math discussions?


Since I wrote the post about Graph Theory, I’ve been toying with discussion in my head. So here’s what I’m thinking about one week later.

1) Create a rubric for pre-, during-, (and maybe post-) discussion for teachers.  This would include some of the 5 Practices explained here (thanks productivestruggle) and generally require that before discussion, the teacher knows what thinking from which students is most going to shape the discussion.  So yes, these rubrics will exist (soon? somewhat?).

2) Allow for different whole-class discussion modes. And practice/debrief them with students. There are lots of different types of discussions. I’m imagining places where the loudest voice wins and discussions are freeform versus places where people take intentional turns sharing ideas. Why shouldn’t the classroom have similarly varied discussion modes? I’m imagining that we could name whatever discussion modes we come up with and choose our mode based on the discussion or what the presenter/discussion-leader wants. (What other categories besides loudest-voice-wins and raising-hands should I be thinking about?)

3) Making norms with students, regardless of the discussion. Many teachers have students rephrase what the last person said before adding to the discussion; that is going to be one norm for sure. Other norms: How do students/how can we unobtrusively show agreement/appreciation for the speaker without re-stating? What language should we use for agreement/disagreement/building? How do we disagree respectfully? How do we react if we feel attacked?

Next year (maybe this year – team NV?), I want to start by having a “dual circles” discussion where, having established some norms, we have a discussion with half the class actually talking and the other half taking notes on what’s happening during the discussion, all followed by a debrief.

Also, JK and I have plans for making some pretty awesome exemplar (and non-exemplar) videos this summer — for turn-and-talks, small group, and whole-class discussions. Anyone want to star in them with us? You’d be FAMOUS.