Sunday, September 27, 2015

Meatball Surgery

     This summer our district renewed its commitment to Everyday Mathematics, purchasing the 2015 EDM4 for all grade levels K-6.  Theresa and I have spent the past weeks helping teachers navigate their way through many of its improved features, which include: a different online platform, a revised order of units, and new manuals, assessments, games, differentiation options, and manipulatives.  So far so good.
      One morning last week I stopped by to check in on one of our grade 4 math teachers. She was busy at her back table, writing out a bunch of posters:

         She explained that she was copying over problems from the student journal:

Read these problems.  When your eyes glaze over, raise your hand.

And you thought you were done!
    It was her intention to put the kids in groups and have them spread out all over the classroom floor, an idea I supported fully.  But I had seen these problems over the summer, and didn't like them.  Wordy, dense, unengaging, and contrived were four adjectives that came to mind.  Time for some meatball surgery.

I suggested separating the question from the scenario.  Put out some post-its and ask the kids what they notice and what they wonder.  Or tell them it's a number story with the question removed and see if they can guess the question.  Just give them time to process all that information without the anxiety of having something to figure out.  
      For an opening math message, I suggested she find a picture of one of the tall buildings and do a simple notice and wonder.  Perhaps a visual and a small discussion might help set the table for some of the comprehension work that would follow.
     When I got to class later that morning, I saw this up on the SMARTBoard:

Trump Tower.  The kids had some interesting observations about its shape and composition, and were very curious about its height.
     She divided them into groups and gave them the surgically altered problems:

They noticed and wondered...
...and came up with their own questions.

When they finally received the actual assignment, most of them were ready to give it a go.

Each student in the group got a different colored pencil.  A way to make sure everyone participates.
     We stopped the kids several minutes before the end of class and gathered everyone together to take a look at some of their addition strategies under the document camera.
     Later, I went back to take a look at the manual.  This was Lesson 1-6: Guide to Solving Number Stories.  The heart of the lesson, which was slated to take 30-40 minutes, was composed of three parts...

1.  Math Message.  Instead of the Trump Tower notice and wonder, here's what the kids were asked to do:

   Read the Math Message problem on journal page 13.  Be ready to explain what you already know from the problem and what the problem wants you to find out.

(I've voiced my criticism about math messages like this.  I'll just say that many kids in the class would not even make it past the first few sentences before completely shutting down.)  After an unspecified amount of time, the teacher is instructed to move on.

2.  Using the Guide to Solving Number Stories.  Instead of giving the kids the scenarios with the questions removed and asking them to notice, wonder, and/or come up with their own questions, the teacher was to refer the students to this guide...

     ...and use these questions...

  • What do you know from reading the story?  
  • What do you want to find out?  
  • How can you find the number of stories Terrell needs to climb?  
  • What will you do first?  
  • What strategy or tool can you use?  
  • What is the unknown quantity?  
  • What number model might we write, using a letter to stand for the unknown, to represent what we want to find out?  
  • Are you finished?  Why or why not? guide a whole class discussion on the problem solving process.
     After helping the class come to a consensus regarding the correct solution to this problem, and reviewing some of the different addition strategies employed by students, the teacher is to move on to the next step.

3. Solving Multistep Number Stories.  The teacher is instructed to put the students in partnerships to complete journal pages 13 and 14.  Remember them?

page 13

page 14

     Back together as a whole class, the teacher is instructed to ask volunteers to share solutions to the problems.
     This is pretty standard stuff.  And kids need strategies to solve number stories. But it's unimaginative.  There's too much whole class, teacher-directed discussion, which means more opportunity for kids to tune out. My quick meatball surgery was intended to lower the barrier to entry to these difficult-to-access word problems, and to get the kids more involved in their own learning. It's nothing amazing or revolutionary, only the best I could do given the time that I had. The classroom teacher had good instincts.  It's only her second year teaching, and I'm confident that given a little time and some good PD she will be able to make those changes and decisions on her own.
     But it's really not a sustainable model.  Teachers, especially elementary school teachers who are responsible for teaching multiple subjects, do not always have the time to perform the kind of surgery lessons like this require.  They may not even be aware that other types of strategies, activities, and instructional practices exist.  A lesson from a curriculum interested in making math meaningful, accessible, and engaging should deliver them right to their classroom door.  Is that an unrealistic expectation?

Thursday, September 10, 2015

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.