Lessons from Bowen and Darryl Thursday, Jan 28 2016 

At the JMM this year, I had the pleasure of attending a minicourse on “Designing and Implementing a Problem-Based Mathematics Course” taught by Bowen Kerins and Darryl Yong, the masterminds behind the legendary PCMI teachers’ program Developing Mathematics course, with a significant assist from Mary Pilgrim of Colorado State University.

I’ve been wanting to get a live taste of Bowen and Darryl’s work since at least 2010, when Jesse Johnson, Sam Shah, and Kate Nowak all came back from PCMI saying things like “that was the best math learning experience I’ve ever had,” and I started to have a look at those gorgeous problem sets. It was clear to me that they had done a lot of deep thinking about many of the central concerns of my own teaching. How to empower learners to get somewhere powerful and prespecified without cognitive theft. How to construct a learning experience that encourages learners to savor, to delectate. That simultaneously attends lovingly to the most and least empowered students in the room. &c.

I want to record here some new ideas I learned from Bowen and Darryl’s workshop. This is not exhaustive but I wanted to record them both for my own benefit and in the hopes that they’ll be useful to others. In the interest of keeping it short, I won’t talk about things I already knew about (such as their Important Stuff / Interesting Stuff / Tough Stuff distinction) even though they are awesome, and I’ll keep my own thoughts to a minimum. Here’s what I’ve got for you today:

1) The biggest takeaway for me was how exceedingly careful they are with people talking to the whole room. First of all, in classes that are 2 hours a day, full group discussions are always 10 minutes or less. Secondly, when students are talking to the room it is always students that Bowen and Darryl have preselected to present a specific idea they have already thought about. They never ask for hands, and they never cold-call. This means they already know more or less what the students are going to say. Thirdly, they have a distinction between students who try to burn through the work (“speed demons”) and students who work slowly enough to receive the gifts each question has to offer (“katamari,” because they pick things up as they roll along) – and the students who are asked to present an idea to the class are only katamari! Fourthly, a group discussion is only ever about a problem that everybody has already had a chance to think about – and even then, never about a problem for which everybody has come to the same conclusion the same way. Fifthly, in terms of selecting which ideas to have students present to the class, they concentrate on ideas that are nonstandard, or particularly visual, or both (rather than standard and/or algebraic).

This is for a number of reasons. First of all, the PCMI Developing Mathematics course has something like 70 participants. So part of it is the logistics of teaching such a large course. You lose control of the direction of ideas in the class very quickly if you let people start talking and don’t already know what they’re going to say. (Bowen: “you let them start just saying what’s on their mind, you die.”) But there are several other reasons as well, stemming (as I understood it anyway) from two fundamental questions: (a) for the people in the room who are listening, what purpose is being served / how well are their time and attention being used? and (b) what will the effect of listening to [whoever is addressing the room] be on participants’ sense of inclusion vs. exclusion, empowerment vs. disempowerment? Bowen and Darryl want somebody listening to a presentation to be able to engage it fluently (so it has to be about something they’ve already thought about) and to get something worthwhile out of it (so it can’t be about a problem everybody did the same way). And they want everybody listening to feel part of it, invited in, not excluded – which means that you can’t give anybody an opportunity to be too high-powered in front of everybody. (Bowen: “The students who want to share their super-powerful ideas need a place in the course to do that. We’ve found it’s best to have them do that individually, to you, when no one else can hear.”)

2) Closely related. Bowen talked at great length about the danger of people hearing somebody else say something they don’t understand or haven’t heard of and thinking, “I guess I can’t fully participate because I don’t know that idea or can’t follow that person.” It was clear that every aspect of the class was designed with this in mind. The control they exercise over what gets said to the whole room is one aspect of this. Another is the norm-setting they do. (Have a look at page 1 of this problem set for a sense of these norms.) Another is the way they structure the groups. (Never have a group that’s predominantly speed-demons with one or two katamari. If you have more speed-demons than katamari, you need some groups to be 100% speed demon.)

While this concern resonates with me (and I’m sure everybody who’s ever taught, esp. a highly heterogeneous group), I had not named it before, and I think I want to follow Bowen and Darryl’s lead in incorporating it more essentially into planning. In the past, I think my inclination has been to intervene after the fact when somebody says something that I think will make other people feel shut out of the knowledge. (“So-and-so is talking about such-and-such but you don’t need to know what they’re talking about in order to think about this.”) But then I’m only addressing the most obvious / loud instances of this dynamic, and even then, only once much of the damage has already been done. The point is that the damage is usually exceedingly quiet – only in the mind of somebody disempowering him or herself. You can’t count on yourself to spot this, you have to plan prophylactically.

3) Designing the problem sets specifically with groupwork in mind, Bowen and Darryl look for problems that encourage productive collaboration. For example, problems that are arduous to do by yourself but interesting to collaborate on. Or, problems that literally require collaboration in order to complete (such as the classic one of having students attempt to create fake coin-flip data, then generate real data, trade, and try to guess other students’ real vs. fake data).

4) And maybe my single favorite idea from the presentation was this: “If a student has a cool idea that you would like to have them present, consider instead incorporating that idea into the next day’s problem set.” I asked for an example, and Bowen mentioned the classic about summing the numbers from 1 to n. Many students solved the problem using the Gauss trick, but some students solved the problem with a more visual approach. Bowen and Darryl wanted everybody to see this and to have an opportunity to connect it to their own solution, but rather than have anybody present, they put a problem on the next day’s problem set asking for the area of a staircase diagram, using some of the same numbers that had been asked about the day before in the more traditional 1 + … + n form.

I hope some of these ideas are useful to you. I’d love to muse on how I might make use of them but I’m making myself stop. Discussion more than welcome in the comments though.

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Talking Openly about How to Do It Better Friday, Jul 30 2010 

The Hardest Questions Aren't on the Test: Lessons from an Innovative Urban SchoolLast week I somewhat impulsively picked up and read cover-to-cover the new book of an important mentor of mine.

The Hardest Questions Aren’t On the Test: Lessons from an Innovative Urban School, by Linda Nathan

Linda is the principal of the Boston Arts Academy, where I did my student teaching a decade ago, in what I believe was the school’s 3rd year of existence. The book is largely a collection of vignettes from the BAA’s 12-year history. The vignettes have a theme:

Education involves facing difficult dilemmas. The thing that needs to be done is to bring together the people involved, open up the lines of communication, and try to figure out jointly what to do.

Some of these dilemmas are pedagogical, some pragmatic, some political, and some interpersonal. Some are a combination. The community of people involved may be administration, teachers, students, parents, or a combination. But however configured, Nathan is saying this process is at the heart of education: put the hard choice to the community, and keep everyone engaged with each other as you undertake to work it out.

This book was a very refreshing read for me. We are deep in the days of Arne Duncan, Michelle Rhee, Race to the Top, the Common Core Standards, and the tendency among journalists1 to regard the KIPP schools as the greatest thing that have ever happened anywhere in the universe because they have high test scores. Now I have some nice things to say about some of these things. The Common Core Standards in 6th to 8th grade math are an order of magnitude better (i.e. shorter and less concerned with trivia) than the New York State standards have been, and while I have no firsthand knowledge of KIPP schools, I’ve been curious about them in a good way since my student teaching year at BAA, when a fellow student teacher came back from a visit to a KIPP school very excited about SLANT. But what this list is meant to capture is that I can’t escape the feeling that the highest-profile conversations about education in this country, in their frenzy regarding accountability and competition, have totally lost sight of the following facts:

a) Students are people and they have cares and values.
b) Teachers are people and they have cares and values.
c) Everybody involved has cares and values.
d) Education takes place in a community. (Corollary: improving education involves improving community.)

Reading The Hardest Questions… felt like walking into a room full of people who had never lost touch with any of this. Nathan is talking about thinking through educational dilemmas with her staff and students and being guided by what all the people involved value. Stating and working for what matters to her, and asking her teachers and her students what matters to them. It’s absurd that this should feel like a refreshing notion, but to me right now, it does. The Race to the Top funding criteria include a lot about assessments and data that will be used to measure teacher and principal effectiveness, and no encouragement whatsoever for students, teachers, principals or even state superintendents to reflect on what they value.

Another refreshing aspect of The Hardest Questions… is that it doesn’t uniformly make Linda or the BAA look good. (Often – and from firsthand experience they are good – but not uniformly.) The book narrates some play-by-play encounters with some difficult conundrums that don’t have clear resolutions, so it airs some missteps. (Different readers will probably count different moves as missteps.) One of the most pernicious elements of the accountability-and-results orientation in the national conversation about education is that it gives everybody (states, schools, teachers and students) a great reason to hide every mistake. You can’t learn math while you’re trying to hide your mistakes and you can’t learn to teach that way and you can’t learn to run a school that way. You can’t learn that way, period.2

Some specific themes and highlights:

* Schools need to develop a “unifying framework” – what the school stands for educationally. This is not a mission statement that collects dust in an administrative folder but a vision articulated frequently to students of the most important themes in their education. The faculty needs to be involved in developing it. The administration needs to be willing to commit to it in a long-term way. The school community needs to periodically revisit whether and how the school is implementing this shared educational vision. At the BAA, the unifying framework the faculty eventually came to, after 2 years of discussion and debate, is a list of four “habits of the graduate” – refine, invent, connect, own. The idea is that these words are the faculty’s answer to the question, “what we are committed to cultivating in every student?” and that this goal defines the school. Nathan makes a point that she initially tried to have faculty sign on to other lists of words (that to an outsider now don’t look so different), but it turned out to be necessary for the faculty to go through the intense and time-expensive process of answering this question for themselves.

I am suspicious of statements that begin with “All schools should…” But this is one I truly stand behind: all schools should develop and use a unifying framework. The “new initiative every year” model doesn’t work. Teachers need to be involved in articulating the framework, and a school must be willing to commit to the implementation of the framework over the long haul. Finally, I would argue that schools without a unifying framework still have an unspoken one – a de facto assumption of what this school is about. If it were expressed in posters on the wall, these frameworks might be “We Are Failing: Who Should We Blame?” or “High Scores and College Admissions – Everything Else Be Damned!” To honestly answer the question “What does your school stand for?” takes a willingness to ask again and again how your practices are improving, what students know and can do, and how day-to-day realities in the classroom match the ideals you have articulated. pp. 30-1

* Developing a school’s commitment to social and moral values also takes a community-wide process, and this one has to go beyond the faculty to the students. And it needs to be continually recreated, because new kids come every year. Chapter 2 of Nathan’s book describes how the BAA faculty first articulated a group of “Shared Values” in response to a community crisis (a “white power” graffito in the bathroom), and then slowly learned more and more, over the course of a series of other community crises (involving theft, homophobia, alcohol…), about what it would take to make these shared values a part of student culture. Some highlights:

As Shared Values became a way to talk about what was important in our community, and even the way to address some of our rules, a few students suggested that we change our quarterly honor-roll assemblies to be called Honor Roll/Shared Values assemblies. They wanted the school to recognize students when they were “Caught in the Act of Shared Values,” a phrase they coined. Students or faculty could nominate students who had done something to exemplify a shared value. The action wouldn’t have to be a big deal, but it had to be something that everyone could applaud. We have, for instance, acknowledged students “caught in the act” of putting up posters that someone had ripped down, staying behind to help clean up a classroom, bringing in doughnuts for everyone in the class after a strenuous day of testing… pp. 38-9

In the spring of 2005, some BAA music students performed at a local music club… It was a wonderful concert; the house was packed… However, the next day the owner of the club called to report that alcohol had been stolen from her establishment.

Ms. Torres [the assistant principal] gathered all the musicians together, and initially had an awful time getting any of the students to say they had seen anything. Finally, one of the young musicians, Martin, a leader in the band, said to the whole group, “Hey, listen, someone saw something. It will be terrible for our school and our reputation if we don’t figure out who did it and make sure it doesn’t happen again….” Martin spoke fervently, but still nobody talked, not for another few days. During these days, the entire school was buzzing with talk about expulsions and rumors that the music department would never be able to perform outside of the school again. In the meantime, Ms. Torres and security personnel managed to uncover the truth: which students had actually stolen the alcohol, which had looked away but knew what was going on… They were all suspended and the ringleader… was expelled…

Even though this incident only directly involved one group of students, so many students were talking about it that Ms. Torres decided to hold another whole school assembly. She also decided to have students talk to students rather than… expect administrators to chastise everyone. Ms. Torres asked Martin if he would address the student body and explain why this was such a big deal… Ms. Torres explained, “I need you to talk about the larger issues, Martin…” He agreed.

At the assembly, Martin got out of his seat, twirling his drumsticks in one hand. “We all know this school is pretty amazing,” he began. “Sure, we’ve got beefs and there are things that we all think are stupid and try to change. Sometimes we do. I know all you freshmen want to have lunch off campus, for example. Well, maybe you can change that. But, you know, one thing that keeps us together is that we have these Shared Values. Sure, some of us might laugh when Ms. Torres gets on the intercom every morning and tells us to live one of the Shared Values, but it’s cool. We do believe in diversity with respect. Just look around at how many different kinds of people are in here. And passion with – ” And then he held his mic out to the audience like a DJ as they responded, “Balance!”

“Yeah, that’s right,” Martin continued. “And we believe in community with – ” And again the audience responded, “Responsibility.”

“So, like you’ve heard from Ms. Torres, they’re dealing with the students who did this, but I just think we all have got to think about what this means for our whole community and our reputation out there. We live by our reputation as artists, and if it gets tight out there for us, we won’t be performing…”

We didn’t want students to dismiss the incident as “just something that happened to the music majors.” Dumb, destructive behavior like this is common among adolescents… As sad as I was that BAA students had stolen alcohol, and as disappointed as I was that other students hadn’t turned them in, I was proud of our school’s overall response to the incident. Martin’s leadership meant so much to me. It established a norm that respected student leaders could support school values publicly… pp. 48-51

* Great teachers are empowered to be great by the community they’re a part of. The principal needs to work for the creation and maintenance of this community in order to empower teachers to be great. Building a great school involves “transforming a faculty into a professional learning community.”

Success truly begets success… This plays out in Ms. Chan’s [dance] class, but we see it even more clearly in Mr. Ali’s [humanities class], where students are not all here by choice. Mr. Ali can build on Aleysha’s engaged identity as an artist to encourage in her an engaged identity as a scholar. He has listened to her concerts over the years, and he knows she has a gift and love for music. It is his challenge to create the same set of expectations and joys in his own humanities classroom. p. 78

Teaching at BAA is decidedly not a solitary activity. While I have very little influence on what goes on moment-to-moment in Ms. Chan’s or Mr. Ali’s classroom, I can, and do, work on the schedule (the skeletal system of a school) to ensure that teachers help each other, that worries and questions are shared among team members and the entire faculty. Mr. Ali meets weekly with academic and arts colleagues to discuss students and to develop curriculum. At the end of the year, he will spend two days with his team reviewing and critiquing each other’s units and lessons, and creating notebooks on the year’s courses so that they continue to build a collective archive of work.

Mr. Ali and Ms. Chan are not “one-offs” or “the exceptions” at BAA. I tell their stories here as representative of the ways in which our teachers can be successful. As a leader, it is my job to build a school in which all teachers work in teams, and have the time built into their schedules to talk, to visit each other’s classrooms, and to create curricula as carefully and self-critically as artists create their pieces. pp. 80-1

* A school that wants to make progress on the achievement gap needs to have frank and potentially uncomfortable conversations with faculty and students about race.

There are a lot of really compelling passages to quote on this one but it’s already several hours past the time I told myself I would have finished this post. Read the book.

More info:

Here is a video of a half-hour talk that Linda and some BAA students gave. (At Google I guess??) I found it much harder than the book to follow thematically, but it’s cool because the students do a performance based on the unifying framework (refine, invent, connect, own) and talk about it afterward.

Here is a review of the book written by a former BAA student for feministing.com.

[1] I’m thinking of Malcolm Gladwell (in Outliers) and Daniel Coyle (in The Talent Code), for example.

[2] As an aside, one of the reasons I think The Wire is such a significant show is its persistent exploration across different urban institutions (school, law enforcement, city politics) of the way that numerical “accountability” incentivizes maintaining the status quo and hiding the dirt rather than digging into the problems and seeking real improvement.

Despairing vs. Working: Learning Classroom Management and Learning Math Tuesday, Jul 13 2010 

[Virtual Conference on Soft Skills]

I. Prelude

One of the great challenges of teaching math is the fact that many students walk into class with trauma surrounding the subject. One way or another they have absorbed the idea that the difficulties they have had solving math problems say something important and damning about their intellect.

Trying to do math makes them feel stupid.

J, whom I taught as a junior in Algebra I, was a very developed writer and poet. He would talk about math as a mythical dragonlike beast waiting at the end of his quest to destroy him after he had surmounted every other obstacle. A, whom I ran into on the street two years after teaching her, told me that her life would be great if she could just understand math. O, a professional adult in the financial industry who took a workshop with me, looked like she wasn’t making progress by herself at one point during the workshop, so I asked another participant to join her. She ran out of the room. I found her in tears in the hall. She had fled rather than let someone else “find out how stupid she was.”

If they are going to learn anything, the this tragic association needs to be disrupted, and as quickly as possible. I know you have all already read Dan’s lyrical description of the problem and one part of how to take it on. For now, what I want to call attention to is the mechanism by which this association renders it impossible to learn.

The mechanism is this: when you feel stupid, you are not thinking about math. Like driving a car and playing basketball, it is not possible to think about math and feel stupid at the same time.

I am using “thinking about math” in a strong sense here. It is possible to execute an already-known algorithm like the multiplication algorithm while feeling like the biggest dumb*ss in the world, although it is harder than doing it when you’re feeling better about yourself. What it’s not possible to do is solve a problem new to you, think creatively or resourcefully, see a surprising connection or a pattern, notice your own curiosity, or any other type of thinking that would cause you to grow mathematically. What I am claiming, in short, is that the activity of feeling stupid excludes all activities that allow you to grow.

To make this concrete:

In the workshop for adults I mentioned above, I had posed the sums of consecutive integers problem in a fairly open-ended way. (What numbers can and can’t be represented as sums of at least 2 consecutive natural numbers? Why? What else do you notice?) Most of the participants in the workshop were having conversations with themselves and each other along the lines of:

“What’s going on here?”
“Can I get this number [as a sum of consecutive naturals]? How about this one?”
“Is there a pattern in the numbers I can/can’t get?”
“If you give me a number is there a system I can use to represent it [as a sum of consecutive naturals]?”
“What patterns are there in the representations I’ve found so far?”
Etc.

Here are the conversations O was having with herself before I asked someone else to join her and she ran out of the room:

“Everybody else is having all these insights. Why am I not?”
“What’s wrong with me that I’m not?”
“What will they think of me?”
Etc.

I didn’t realize this by looking at her, although perhaps I should have. I thought maybe she just wasn’t making progress for whatever reason. She is a pro at hiding it (along with all other people who have this type of conversation with themselves). Lots of practice. But the point I’m making here is this:

The conversation that O was having with herself was of a totally different character than the other participants. The thoughts she was having, and the work that she needed to be doing in order to grow mathematically, live on different planets. When students begin to have this conversation with themselves, they have gone to Mars as far as learning math is concerned.

I listened to O talk about how she was feeling, gave her a hug and told her something to the effect that it made me mad to think anyone had ever made her feel bad for taking her own time to explore something. I brought her back to the workshop and partnered her with another participant who hadn’t come up with a whole lot yet (and who was also very empathetic). She let O explain herself and vent a bit; I let this happen for a few minutes and then said I thought it was time to get back to the math.

Maybe you have seen this miracle yourself: when that traumatized person unloads their pain and finds it accepted and not judged, or just plain has the cycle of self-doubt/paralysis/self-doubt interrupted in any way at all, and then takes a fresh look at the problem… the natural dynamics of the process of problem solving take hold and they instantly become a frickin genius.1 Not by everyone’s standard but by the only standard that ought to count: they start to see the problem from new angles. This amazes them. I’ve lost count of the number of times I’ve seen this happen and it’s breathtaking every time. They then often invalidate their accomplishment through an unfair comparison with others, but that first moment of seeing-the-problem-in-new-light is there, available, and needs to be highlighted. “When you said, ‘oh, I could simplify the other side first’ and that opened up a path to make progress… that’s what being a mathematician is. That’s the whole game right there. Looking at what’s there and playing with it and working with it till you get a new angle. There is one secret to ‘being good at math’: do that as much as possible.”

O, a reflective grownup, got the lesson in a powerful way. How much of her mathematical paralysis was really entrapment in the self-doubt cycle. How much she was capable of, that she didn’t even know about, whenever she could switch off that cycle and be present to the problem.

The key word there is presence. If you are present to a mathematical question, and the reality it is asking about; in other words if the question and its reality are available to you, vivid for you, there before you to touch and probe; then doing math is the most natural thing in the world, and growth is inevitable.

But you can’t be present to the math when you are busy thinking/worrying/stressing that you suck. This takes your attention away from the actual problem and the process of looking for a solution stays shrouded in mystery.

II. An Analogy

All of this is set-up for what I really wanted to talk about.

In my six years as a full-time public school classroom teacher, I spent a lot of time and emotional energy thinking about and struggling with classroom management. I was, of course, not alone here. It’s a major issue for beginning teachers.2 Everybody knows this.

I learned a fair amount about classroom management in that time, but there’s something important that I don’t think I ever understood, till this year when I worked as a teacher trainer. I feel like I could have accelerated my learning curve immensely and spared myself and my students a lot of pain if I’d understood it earlier. Consider this true statement:

Struggling with classroom management made me feel like sh*t as a person.

My intention is for this sentence to have landed with some echoes in the background, but just in case:

… Trying to do math makes them feel stupid.

Like math itself for so many of our students, classroom management struggles have left many teachers traumatized. And with reason. Math’s power to hurt is based on the perverse culturally taught belief that accomplishment in math is a manifestation of some important inborn intellectual attribute and struggle to understand is evidence you don’t have it. The power of struggles with classroom management to make you feel bad are likewise amplified by the current cultural milieu, in which the idea that teachers need to be more minutely and exhaustively judged is the coin of the political realm. But the fact is that the experience of being treated rudely by a room full of children pretty much bites, whatever the cultural context.

Reasonableness aside, though, just as math trauma paralyzes the growth of the math learner, feeling bad about yourself because your kids aren’t listening to you is an activity essentially different from, and incompatible with, in fact on a different planet than, growing as a classroom manager.

Let me make this point more concrete. This year, as a supervisor for an MAT program and as the math coach at a high school, I had the privilege of witnessing a lot of different people teach and thinking with them about how to improve their teaching. Frequently this role called upon me to help them think about their classroom management. I found myself, to my surprise, with lots of advice. What was happening was that it was much easier to perceive the dynamics of the classroom as a third-party observer who knows what they look and feel like but is not presently involved. If you’ve got at least a few years experience but have never stepped into the classroom of a fellow teacher with the intent to give management advice, do it – you’ll be surprised how useful you are. It’s the essential awesomeness of what not actually being caught up in it lets you see.

What really threw me, in a good way, is that the suggestions I was making were things that by and large

a) I was sure I would have benefited from during my own full-time classroom practice; and yet

b) most of them were in areas I had never thought about. They were like a whole new angle on the classroom. More specifically, they were smaller and more concrete than most of what I had thought about in all those years of stressing about management.

When things went badly in my classroom, and I thought about what to do about it, my questions were most often like:

“How do I convey strength?”
“What’s the appropriate response to insubordination?”

On bad days,

“What’s wrong with me that they don’t listen to me? (and is it possible to fix? probably not…)”

These are big, abstract questions. What I’ve come to understand this year is that this abstract level is not where the answers live. They live in the minute-to-minute, real-time interactions that constitute a class period. They are solid, tangible, low to the ground. A discipline problem would develop, and then boil over, so that I found myself furious with a student or multiple students, and feeling like a failure. I would then ask myself these big abstract questions. In so doing, I would totally divert my attention from the tiny incremental steps by which the problem had built itself, and from the tiny, concrete things I could have done to head it off before the axe fell. I would also make myself feel horrible for no reason. I felt weak, as though the difficulty I was having had been caused by my fundamental inadequacy as a human. In reality, it was caused by a chain of extremely small and concrete failures of technique. These techniques can be taken on and learned one at a time. They are all individually too small to be worth feeling bad about.

To get specific. Here are some of the suggestions I found myself giving to teachers repeatedly this year. They may be individually useful to you if you are struggling with management and recognize your classroom in the situations they are designed to address. But the big thing I am trying to communicate is that these suggestions do not relate to anything it makes any sense for a teacher to feel bad about. They’re just bits of technique. If your class is messing up because you’re not doing one of them, all this means about you is that you haven’t learned this bit of technique yet.

* In the 1-3 minutes following a transition in which you issue an instruction to the whole class, do not converse with any individual kids. Keep your attention on the whole class. Make it your only job to see that your instruction gets implemented.

(I gave this advice, for example, when I saw teachers give an instruction and then immediately begin to help or reprimand an individual kid, while the rest of the class implemented the instruction inconsistently or not at all.)

* If you have assigned classwork and are trying to help the whole class through it one desk or table at a time, stop the work and call the class back together. The work wasn’t ripe for doing yet it turns out.

* Do not communicate disappointment when a student fails to do something you didn’t communicate a clear expectation about. Communicate your vision of how the class should behave before they have an opportunity to fulfill or disappoint that vision.

(This piece of advice was usually coupled with specifics.)

* Do not make capricious decisions about your students’ attention. For example, if you set them to work 3 minutes ago and someone asks you a question that you think deserves the class’s attention, don’t take lightly the decision to interrupt the work to share the question. If you want to be able to direct students’ attention you need to be willing not to ask too much of it.

(This is a piece of advice I could really have used myself.)

Again, the point is not about these specific suggestions, which I gave to particular teachers facing particular challenges that may or may not be yours. The point is that each suggestion connects to a bit of learnable classroom technique that can be taken on one at a time; that there’s nothing here to feel bad about, since each bit of technique is nothing more than that; and lastly that the big heavy questions of self-worth that plague so many teachers struggling with management are really distractions from these techniques. They pull your attention up and out, to the broad and abstract, and carry you away from what is actually happening in your room between you and your students.

Now I want to be clear: it’s not that the individual techniques are easy, and it’s not that you can just learn them by deciding to. Sometimes, the techniques involved get deep into your being. One of the deepest: communicate the intention that your instructions be followed. This bit of technique is totally natural to some teachers before they walk into the classroom. Others (I’ve been one) need to learn and sometimes relearn it, and learning it may not be as simple and external as the other techniques I’ve listed.

The point is that in spite of this, it’s still just a technique. You just learn how to look, sound and feel like you mean it when you tell your students to do something. This skill can be broken down into smaller components that also can be worked on individually: relaxation and confidence in the tone of voice; relaxed posture; steadiness in the body; a steady gaze. Follow-through: the maintenance of all this personal force in the second and the minute following your instruction. Doug Lemov’s “stand still when you’re giving directions” is the same thing. You can get better at each of these components. Because they have to do with deep habits of your body and social M.O., they may be hard to work on. It may help to videotape yourself or work with a coach, mentor or colleague. But the point is just this: there is nothing mysterious in improving these skills. They are nothing more than techniques. Underdevelopment of any one of them, or many of them, is simply something too small and concrete to feel bad about. That heavy burden of self-doubt is ironic because it’s simultaneously an awful experience and an obvious gambit by the lazy-bum part of our brains to distract us from the real job of learning these techniques. (Isn’t being a lazy bum supposed to be kind of pleasant?)

So: the kids are battered by self-doubt because they think struggle with math impugns their intellectual worth. This cycle distracts them from the math. Free them from this cycle and they grow. The teachers are battered by self-doubt because we think struggle with classroom management impugns our worth as people/professionals. This cycle distracts us from the real job of getting better at the techniques that comprise classroom management. Free us from this cycle and we grow.

I hope if you’ve been there that this post can be part of helping you stay free.

III. Related Reading

* I started to put together the thoughts in this post in some comments I wrote in response to a beautiful post from Jesse Johnson.

* Jesse and Sam Shah, who have been at PCMI the last 3 weeks, have both been writing about teacher moves, and distinguishing teaching from teachers. Meaning, learning to focus on the actions that are being taken in the classroom, rather than on judging a person. This distinction seems to have been introduced at PCMI in the context of looking at video of other teachers, but both Jesse and Sam recognize you can use it on yourself as well. This is closely related to what I’ve talked about here: the realization that just like a kid learning math, getting present to the real, actual, concrete process of teaching both empowers and is empowered by letting go of judging yourself.

* Here’s a 3-year-old post from Dan Meyer drawing an analogy between the process of subdividing our job into small, concrete bits that can be worked on one at a time, and integration (as in, \int). Closely related and very cool.

* When I looked up that New York Times Magazine article about Doug Lemov to link to it, I realized that some of the same issues are being dealt with there. Maybe this is part of why (except for acting like Lemov is the first person to wonder how good teachers do their job) that article was so refreshing to me.

IV. In Other News…

The New York Math Circle has their Summer Workshop coming up in a week! It’s about the Pythagorean Theorem and based on talking to the organizer, Japheth Wood, I think it’s going to be both mathematically and pedagogically interesting. (Y’all know this theorem is the greatest single fact in K-8 education. If I may.) The program is housed at Bard College and doesn’t cost very much for a week-long residential thing. ($375.) Clearly the place to be.

Notes:

[1] Assuming that the problem is at an appropriate level of challenge. Another way to put this is, assuming that the reality the problem is asking about is available to the student. (This could be a physical reality or a purely mathematical one.)

[2] Totally unnecessary citation: “A significant body of research also attests to the fact that classroom organization and behavior management competencies significantly influence the persistence of new teachers in teaching careers.” Effective Classroom Management: Teacher Preparation and Professional Development, p. 1 (issue paper of the National Comprehensive Center for Teacher Quality, 2007), citing Ingersoll & Smith (2003), The Wrong Solution to the Teacher Shortage. Educational Leadership, 60(8), 30-33.