Can I Get Some Feedback With That Pie?

    My most popular post to date is a description of an activity Jeff and I did with the fourth graders about a year and a half ago, a revised version of the Everyday Math game Angle Race  we called the Pie Eating Contest.  So when it came time to revisit some of the same concepts last year with the fifth graders, I suggested to Rich we try the activity again.

Most of the kids remembered how to play, and they were excited to see the game.

We had the kids cut out their angle pieces and compose them into right angles and straight angles, and write the corresponding number models underneath.

While the kids were working, I thought of a comment that Annie Fetter had written in response to a post describing a game I had introduced to the second graders:

    Annie's comment was intriguing.  Asking the kids to respond to this prompt would be a great way to get them thinking about the inner mechanics of the game.  It would be an opportunity for them to form an opinion and provide justification, something that Kristin Gray had me considering.  I decided to have the kids write about it, but also wanted them to include some type of visual representation.  Using the pie itself seemed like a good idea:

After several false starts, here's what I came up with.  Most kids decided to use angle measures to describe the luck/skill relationship.  But others used percentages, and one student played out a demonstration game.  Most students agreed it was mostly luck.

     The prompt provoked some lively debate, and what happened next is what always happens: we were left with a pile of about 40 papers.  Now what?  How should we respond?  Many of their justifications were vague and unconvincing.  If we wanted the kids to get better at this, what type of feedback would be appropriate?
  Feedback is something that had been bothering me, mostly because I'm not very good at providing it.   Michael Pershan had been blogging about the topic, and inspired me to reflect on a part of my practice that is, quite frankly, lacking.  I decided to experiment with comments based on "noticing and wondering":

I decided that each paper would get one "notice" and one "wonder".   I asked them to revise their explanation, integrating the answer to my wondering question.

    My intention was to push the kids to justify some of their statements with more detail.  What is it about the cards that has to do with luck?  What are the particular skills involved?  The class came up with a list as we debriefed:

Rich noticed something very interesting.  It was the kids who struggled with using the protractor correctly who were best able to identify the component skills.

 After they completed their second drafts, I had another go:

I made a point of noticing what they had added, and chose to poke them on something different.

    Rich and I had a discussion with their writing teacher.  Guess what?  They were working on writing persuasive essays in writing class!  Could we use some of their writing language in math class?  We borrowed a poster of hers:

The kids were surprised to see this hanging in Rich's room.  We had them use it when working on their final drafts.

        As school starts up again, the experience reminds me of two things I want to work on this year:

• Collaborate with teachers to explore ways we can give better feedback.  I believe that couching the feedback in "I notice/I wonder" language has potential.  It  provides a model for kids to give feedback to each other, and is more specific than a star, a smiley face, or a check mark.  I realize that it is impossible to do this for every piece of work the kids hand in, but we can pick our spots.
• Make better connections with our ILA teachers.  We want kids to construct viable arguments. They do that in writing class!  We want kids to make sense of  problems. This is a familiar sight in all the reading classes in my school:

What would happen if we asked kids to use their active reading strategies and "post-it" their way through text-heavy problems in math class?

   Yes, the Pie Eating Contest has come a long way from its humble beginnings as the Angle Race game.  But it took a village to make it happen.  Thanks to Dan for popularizing it, to Annie, Michael, and Kristin for helping it along the way, to my amazing colleagues at school, who continue to let me use their classrooms as places where we can learn and grow, and of course to the kids, who greet all (OK, most) of our new endeavors with enthusiasm and good cheer.