Visibly random grouping. Every single day.

Yesterday I finished the first week of my third year teaching.  I feel like I ran a marathon. (Not that I’ve ever actually run a marathon, but you know what I mean.) Each year I’ve been surprised how tired I felt at the end of the first day. Each time I have felt like I was losing my voice, but it recovers by the second day, and by the end of the week my tiredness has hit a plateau.  I seem to remember that the second week will be easier, and that I will hit my stride fairly quickly.

This year, I’m teaching two new curricula (for Algebra and Honors Geometry), and it’s only my second time teaching AP Statistics.  Add to that a switch to proficiency-based diplomas and common-core standards, and I feel like a brand new teacher. Beginner’s mind, indeed!

Given all the new challenges, maybe it wasn’t wise to throw an additional twist into the mix, but I’ve done it anyway. Each day, I’ve changed the seating in each of my classrooms, randomly assigning each student to sit at one of the six tables in my classroom.  I was afraid it would be awkward, that the students would resist, and that I wouldn’t be able to make my naturally disorganized self stick to the system. But I’m doing it, and I want to share how it’s going.

Last spring I read a paper by Peter Liljedahl called The Affordances of Using Visibly Random Groups in a Mathematics Classroom.  The upshot of the paper is that randomly grouping students every day improved group work and student interaction in a variety of ways.  The paper is worth reading.  Go ahead and click through, really!

With the exception of the AP stats class,  I let students sit where they chose on the first day. Then I explained to each class that I would move them randomly every day, and summarized the benefits suggested by the Liljedahl paper.  Each day I would deal out shuffled playing cards (aces through sixes) to the students, and students would sit at the correspondingly numbered tables.  There would be three or four students at each table, with a different arrangement every day.

Here are my impressions after the first four days.

  1. PLUS: Student seem to kind of like it.  When I described it the first day, they looked skeptical.  When I passed out cards the second day, they looked surprised that I was following through with it, but they took their cards, compared them, and took their seats.  By the end of the week, the early arrivals would ask for their cards so they could sit in the right place and not have to move later.  I was worried they would try to switch cards with each other, but no one seems to have thought  of that yet.  Or maybe they aren’t concerned enough to bother with it.  All of the students, ranging from freshmen in Algebra 1 Part 1 to seniors in AP stats, seem curious about the method, and compliant.  Maybe it’s more interesting to them than the typical seating arrangement.
  2. PLUS: So far, the classes seem more interactive than in previous years, and I’ve had few behavior problems.  There are a few “live wires” in each class, as usual, but so far they haven’t been able to settle into any particularly disruptive behavior patterns.  It may be that they are just slower to get comfortable, and that I’ll be dealing with more issues as they get to know all the other students better.  But in this first week, the classes seem much more receptive to my expectations, and they seem to be listening to each other more closely when they ask questions or volunteer answers.  They turn to look when students speak from other tables, and they direct their comments to the class as a whole, rather than just to me or to the students at their own table.
  3. PLUS: I am much less stressed about where I stand, which boards I write at, and which table I hand papers to first.  I have always worried about favoring one part of the room, so that certain students were always far from the point of instruction.  I still try to move around and use all of the whiteboards and chalkboards, but when everyone is sitting in a different place each day, it matters less. By the same token, when students go to the board to work on problems together, they don’t end up at the same board every time.  I don’t know if that really matters, but I like the idea of them getting a different perspective each day.
  4. MINUS: It’s hard to learn their names when they move every day.  I’m not very good at learning names as it is. Or faces.  I think I must have some slight disability in this area, because often I can’t remember people’s faces, even when I’ve met them a few times. It’s embarrassing introducing yourself to adults and having them say, “Yes, we’ve met before at so-and-so’s house.”  It’s also embarrassing sitting down next to a student in the lunch room who was just in your first geometry class and saying, “What math class are you taking this year?”  Anyway, it’s harder to learn names when they aren’t sitting in the same seat each day, but I think I’m learning their faces better, and I am recognizing them in the hall more quickly than I have in previous years.

I’m curious to see how this plays out throughout the year. I have up to 24 students and 6 tables, so it works well for groups of three or four. (I had 25 on my list on the first day, and I was planning to throw in a joker and make it wild, since I didn’t have room for another table.  But a student dropped, so I didn’t get to see how that would have worked.)

Have any of you tried random grouping? What is your procedure? Do you like it? Do you have any advice or things I should watch for?

Half-similar papers update, or I’m not as awesome as I thought.

OK, I came up with an investigation in my class that I thought was really awesome. (See previous post.) It was simple, engaging, and collaborative, and the students actually argued about it and then rolled up their figurative sleeves and worked it out with only occasional intervention from me.  In addition, there were multiple ways to solve it, and there was room for extension at the end.

But I felt slightly less cool when I realized that the next section of the textbook had a homework problem that was almost exactly like it. (It was couched in more pseudo-context about a greeting card manufacturer who for some unfathomable reason cared whether their card, when folded, was similar to the unfolded state….)  So I’m not as blindingly original as I felt in the moment.

Nevertheless, I assigned the problem as part of the next night’s homework assignment.  That’s when the real ego smack-down happened.

They had no idea how to solve it.  I don’t think a single student could do it. (At least, no one would admit to solving it, which is another problem in classroom culture I need to deal with.)  This was almost EXACTLY the problem they did as groups THE DAY BEFORE.

Here’s me.

So what is the deal?  Does group work feel good to us as teachers, while not really teaching the students anything?  Does it make us think they are learning individually, when really they are just leveraging each other’s partial understanding?

What can I do as part of group work to help each student to consolidate the whole process?  (I am thinking journalling about the problem, but that’s something for next year, because there’s not time in the schedule to establish that as a classroom habit at this point.)  Is there something not as time consuming I can do (or have them do) as a wrap-up?

Help me, math twitter blogosphere. You are my only hope.