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.

The how of standardized tests

Yesterday over donuts and coffee, I had the beginnings of an interesting conversation with a colleague. Our juniors are scheduled to take the Smarter Balanced Assessments (SBAC) at the end of this week, and it has been the source of a great deal of controversy over the past few months. MANY of the students are opting out, our federal funding is still officially at stake, there is a flurry of legislation pending in the state legislature, and there are very strong opinions on all sides.

I say it was the beginnings of an interesting conversation, precisely because of those strong opinions.  Since our school is required to give the tests, and since the students not opting out of the test will invest significant energy in doing well, I feel strongly that we should do our best as a school to get real, usable data.  To do otherwise means our results are essentially useless to us, even as a baseline for future testing.

My colleague feels (just as strongly) that the SBAC assessments are (1) damaging to kids because they test things the kids have not been taught in our current curriculum, and (2) part of an unethical, profit-driven cycle that we should disrupt in every legal way possible, including by opting our own children out of the testing and encouraging others to do the same.

Strong opinions can lead to strong reactions.  But as my neighbor the Zen priest says, “Just because you see the bus going by, that doesn’t mean you have to jump on and ride it wherever it is going.” In other words, don’t react without thinking.  Listen first, then consider, and then respond. Both my colleague and I did a good job on the surface; we appeared to listen thoughtfully to each other and discuss our disagreements like grownups.  (At least my colleague did, and I hope I did, too.)

But on my side, the key phrase is “appeared to,” and I know that part of that appearance was an act. Granted, I wasn’t just responding by reflex. I was thinking carefully before I spoke, largely because I really respect my colleague and didn’t want to offend her.  But mostly I was thinking, “How can I express myself really clearly so it’s obvious that I am correct on this?”  I was granting the validity of her arguments, but not really trying to put myself in the position of understanding and supporting her opinions.  I know that it’s intellectually lazy of me to disagree with someones opinions unless I’ve made that effort.  It also deprives me of some really interesting ideas.

So, with apologies to my colleague for not doing this in the moment, here I go.

Argument one against SBAC testing: It damages children to test them on content they don’t know.

I do believe that many, maybe most of our students are upset when they face test questions they can’t immediately see how to answer. Some of them are demoralized; they see it as confirmation that they aren’t good at the subject. Others get angry that they are being unfairly assessed on content they haven’t been taught.  But whose fault is that?  I think it is something we as educators have brought on ourselves, by never presenting kids with test questions that they shouldn’t immediately know how to answer. We scaffold the heck out of everything.  We try  to teach each student in Vygotsky’s zone of proximal development, but we take great care never to test them there.  We train students that we hope for them to get every answer correct, and we are disappointed when they don’t. We make fixed grading scales that penalize the students when the teacher writes a question they can’t wrap their heads around yet.  As a result, neither the teachers nor the students ever really find out what they can do.

This is poor preparation both for college and for life.  Both places are chock-a-block full of questions we don’t know how to approach.  Often our half-formed answers and attempts at answers have really important consequences.  We should be preparing for our entire lives to climb all sorts of challenging cliffs, hoping to find a hand- or toe-hold that will let us get up to the next ledge.  It should be fun and invigorating to do this.  As teachers, we need to prepare our kids in such a way that the majority of them get the chance to respond to challenges in this way, rubbing their hands together in anticipation. So how do we go about it?

My colleague is right.  We don’t do it by throwing a test like this at them for the first time when they are juniors in high school.  We don’t do it by throwing it at them once a year at “standardized testing time.”  But I’m right, too.  We really need to do it somehow, and we need a measure that shows we aren’t doing it now.

Argument two against SBAC testing: it is part of an unethical, profit-driven cycle that we should disrupt in every legal way possible.

I definitely agree that standardized testing has become way too profit-driven, and that a whole exploitative industry has grown up around our quest for data about our students.  I’m not sure how we should respond as teachers. I think it is really important not only to assess our students on what we have taught them, but also to know how their learning (and our teaching) compares to that in the rest of the world.  Any attempt to measure such a broad question is going to be imperfect, but that doesn’t mean the measurement isn’t important.

A bigger question is how to keep profit and exploitation out of the equation.  Is it even possible in our system? In an education system where every state and sometimes every local school district has a different curriculum, whom can we trust to come up with standardized measurement tools? How can we all have input on what it should look like?  How can we both use the data as educators and keep the data from being mis-used by others?

Any thoughts? More questions? Please leave them in the comments!

Beginner’s mind in teaching

I’m not a beginner at math. I’ve used it for decades (yikes!) for a wide range of things, from modeling flow in the earth’s mantle, to calculating drilling-mud weights in an oil well, to building the roof for a bay window, to calculating how big a load of goat manure my truck’s suspension can handle. I have known and forgotten more math than most of my students will ever see in their lifetimes.

I am, however, a beginner at teaching. I have very little formal training in pedagogy and child development. My file of teaching tricks is still very slim.  I don’t know most of the jargon that gives entry into the teacher clubhouse, and I make newbie mistakes in the classroom every day.  I am constantly amazed when a group of students will blindly follow my directions—as if I were an expert or something—and I live in fear of the moments of student revolt that inevitably happen, when a planned lesson goes all pear-shaped in the blink of an eye.

I am also a beginner at meditation.  I am a haphazard student of Zen Buddhist philosophy, mainly because my neighbor is a Buddhist priest. (She also danced to the Rolling Stones in a miniskirt and stiletto boots at her 50th birthday party this year, so she’s probably not what you were picturing.) In the best Zen tradition, I take what is useful to me from the practice, and what has most transformed me so far is the idea of beginner’s mind.

Beginner’s mind, or Shoshin, is a concept from Zen Buddhism, also known as “don’t-know mind.” It isn’t the same as ignorance. It’s an idealized state of being without preconceptions, open to what is really happening, and eager to learn and understand. A teacher with beginner’s mind doesn’t assume she knows the answers to questions.  She doesn’t assume that she knows the causes of student errors, even when they appear to be the same errors students have made in previous years. The teacher with beginner’s mind constantly asks, “What is really happening here?”

I’m kind of cheating, but not really. In a way, it’s easy to achieve beginner’s mind when you are new to something. As a new teacher, literally not knowing what I’m doing, I’m more likely to question my own methods and assumptions, and to listen to advice from more experienced teachers. But this constant questioning can be exhausting, particularly if I let myself feel that I should know, that I ought to be better at this by now.   True inexperience can actually be an impediment to achieving beginner’s mind.  Fear, defensiveness, pretending confidence—these are all reactions I’ve had to my lack of experience, both in the classroom and in meetings with my colleagues. These reactions are enemies of the “attitude of openness, eagerness, and lack of preconceptions” that I want to maintain.*  They also tempt me to fall back on the areas where I have confidence: applied math and science research.  They tempt me be to be an insufferable know-it-all in those areas in fact.

Instead, I try to embrace what I don’t know, and learn about it. I try to notice, not assume. I try to think not “This is an angry student,” but “This student has acted angry in class every day so far.” Not “This student can’t learn this stuff,” but “This student doesn’t understand what I just said.” Not, “This student is lazy,” but “This student doesn’t appear to be making any effort.” or even better, “This student is sitting without picking up his pencil, and he’s not watching what I am writing on the board.”

There’s a balance to strike, though.  As teachers, we have to plan, try to anticipate the errors that students can make, so that we can have resources at hand to help them recognize and correct their misunderstandings. We have to predict what students will find interesting, or funny, or boring, and we have to plan how long activities may take.  However, being willing to be wrong can lead to a better lesson. When I explicitly try not to assume the causes behind what I see happening, I’m more likely to find a way to solve the problem at hand.  The intentional cultivation of beginner’s mind also pays other, unexpected dividends in my life: better personal and professional relationships, better parenting, and renewed delight in simple mathematics that I thought I thoroughly understood.

For as long as I can call myself a beginner, I will try to use my lack of experience as an asset.  As I get better at this teaching thing, I hope I will also get better at the practice of beginner’s mind, so I can continue to see each student, each problem, each colleague with fresh eyes.  So please help me here, in the comments.  How do you keep things fresh for yourself and your students?  What benefits have you seen?


*I lifted those words directly from the Wikipedia page on Shoshin or Beginner’s Mind.  The full sentence is as follows: “It refers to having an attitude of openness, eagerness, and lack of preconceptions when studying a subject, even when studying at an advanced level, just as a beginner in that subject would.” I smiled when I read it.