Thursday, June 27, 2013

The Four Most Important Words in Teaching

My co-blogger, John, often mentions that a crucial part of his practice is standing at the door, greeting students as they come in.  Although this practice started as a way to keep order in the halls, for him it's persisted because it gives him an opportunity to check in with students individually.  I don't have anything like that kind of discipline, but I have to agree that the 3-5 second "touch" is incredibly important, wherever and however you make it happen.  So my candidate for the four most important words is "How are you doing?"

As a math teacher, I don't "get" the opportunity to talk with my students about their personal lives; I have to make that opportunity.  But I think that the kids who most need to talk are often the most fearful of actually opening up; the biggest secrets are just below the surface.  "How are you doing?" is a low-stakes way of saying "I'm interested, and if you want to talk, we can."  When a student has already opened up to me, "how are you doing?" is really a statement: "I know it's been rough, and I'm concerned."  It doesn't demand an extended exchange.  "Not so great thanks" -- "I'm sorry; find me at lunch if you want to talk" is almost always as long as it gets: five to ten seconds.

It's easy to misjudge the amount of effort needed to care for our students' social and emotional health on the basis of that very small number of students whose drama is like a riptide, dragging in friend after friend and teacher after teacher.  But most students aren't like that.  And I find that especially when a student is in crisis, or just coming out of one, regularly asking "How are you doing?" makes a huge impact--probably more than an hour-long "session" would, at least with this nonskilled practitioner.

This impact was demonstrated to me by an unusual coincidence during this last week of school.  I said goodbye to two boys who had been going through rough times this year (one just for the summer, one who is graduating); both were practically in tears.  One wrote in my yearbook that my checking in with him had made it possible for him to finish school and graduate, and he meant it.  Literally--I promise you--no conversation with this student had lasted more than five minutes.  Then our graduation speaker was an alum who, five years ago, had told his entire class and their parents (he was the graduation speaker at his own graduation, too) that my "How are you?"'s had been a lifeline during difficult times.  (And again, at the time, I was bowled over:  none of these conversations lasted more than 3 minutes, and only a few were even half that long.)

When I first started teaching, I envisioned long, soulful one-on-ones with students about all the bumps and pitfalls of adolescence, of which I'd had my own share.  But I've come to realize that most students don't want those conversations most of the time, and that they can't be forced.  Two of my mentors, at Andover, pointed me in the right direction.  Craig Thorn (beloved house counselor and English department chair) told me his secret the day I arrived: just be around, in their rooms or wherever, so that they see you and know you and talk around you.  Doug Kuhlmann, who was the math department chair, said something like this: when you ask a student a personal question, you need to be aware of your own stake in the answer.  What he meant, roughly, was that when you ask a student a personal question, you need to be aware of your own reasons:  are you asking because talking will help the student, or for the emotional buzz of reinforcing your relationship with the student, or to validate your own self-image as "the teacher who cares." It's easy, he warned, to think of yourself as asking for the student's benefit, when really it's about you, which is problematic:  as an authority figure, you're in a position to demand a response, even when you shouldn't. 

"How are you doing?" largely avoids this pitfall: asked in the hallway, or when you're checking in homework, or outside the lunchroom, it doesn't demand much, if anything, of the student.  Just saying "Okay" is enough--in fact, it's standard protocol.  The first couple of times, I might follow up with "Really?  Doing okay?" -- to indicate that I am really asking, not just following the script.  But then it's up to the student.  So "How are you doing?" is empowering, not disempowering: it says "Remember, I'm here if you need me, but I'm not going to push it if you don't."  And it's a "touch" I can make in front of other students, who may or may not know the backstory.

With 140 students per teacher, it's easy to fret about how little we can do.  But what I take away is that it only takes a little.  The key is -- to circle back to John -- to keep asking, to make it a regular routine.  The kids who thank me for it later remember this:  I asked them every time.  And that regularity--and the care behind it--mean more than you'd expect.

Tuesday, June 11, 2013


In my first several years of teaching, when things did not go as expected,  I thought about how to improve results. This [what] often meant adding another rule or expectation [to what], because my students were not doing what I perceived they needed to do in order to learn. After a few years, I had created a bureaucracy that was unmanageable for me as well as for my students. The worst part was that these rules and expectations had not helped improve instruction.

I came to realize that my job was not to tell students what to do. My job was also not to show them how to do a problem. My job was to create interesting situations where they could think about mathematics and learn from the work and discussions that followed. My job was to assist students in anyway I could to develop their own understandings of important mathematics.  I have documented these thoughts and processes many times in earlier posts. Here is a new thought for me.

This same process applies to teacher improvement. Those in charge of teachers at the local, state and national level are ill served by piling on more and more rules and mandates about how teachers should teach. If they really want to improve instruction, they must follow the same model that I followed in my classroom. The supervisors need to see that their job is to do whatever they can to facilitate teacher learning (therefor student learning), as opposed to requiring teachers to do certain things in a certain way. Teachers, with proper resources, will find ways to reach students. As things stand now, those in charge are working very hard to make a teacher's job as hard as possible.

Administrators need to observe teachers teaching. Administrators need to listen to what teachers have to say about the difficulties they have, and administrators need to work hard to help the teachers solve their problems. I have had to good fortune of working for a few such supervisors, and it makes more of a difference than I would have ever imagined. And the very best supervisors worked hard to help the top-level administrators understand that learning to teach well is a very difficult process, that it takes time, and that it requires support and nurturing. Learning to teach well does not require demands and punishment on the part of the Administration.

It is part of the job of experienced classroom teachers to facilitate this process with newcomers and to help administrators understand what they need to do to be effective.

The importance of Content knowledge

I was asked a while ago to write a blog for the National Council on Teacher Quality. I agreed and here it is. This is also posted on their website This is re posted here with their permission.

During my forty-two years of teaching high school mathematics in Evanston, Illinois, I concluded that an essential ingredient for providing quality learning is that the teacher be well versed in the subject that the student is learning as well as the content that comes before and after the subject being learned. This may sound obvious, but it often happens that teachers have mastered what is in the textbook they are using without having knowledge far beyond. I believe this greatly inhibits their ability to help students make connections and often such teachers make poor choices about instruction because they fail to see the entire picture.

I taught a two semester Algebra 1 class, Empirical Geometry, Mathematics--A Human Endeavor, as well as Traditional Euclidean Geometry, Trig, Calculus, Multivariable Calculus and Linear Algebra. I found deep knowledge to be useful at all levels, all the time.
A teacher who has mastered the material well beyond the course being taught will understand why certain topics are presented the way they are and will anticipate what's next. A less prepared teacher will emphasize tricks and shortcuts that will get the students through Friday's test, but leave them ill-prepared for future courses.  For example, a student who learns to multiply binomials using FOIL (First, Outer, Inner, Last) instead of the distributive property of multiplication over addition may do well on the problems involving multiplication of two binomials, but will be hopelessly confused when multiplying more than two, or when one of the factors is a trinomial.
Part of good teaching involves understanding the importance of what is being taught and how it can be applied. Sometimes application of the content does not come until the student studies physics, or calculus, but a teacher who is not well versed in those subjects will not understand their importance. For instance, a teacher who is not familiar with Linear Algebra will not understand the importance of row-reduction of matrices and probably will not present it as the tool of choice for solving systems. In fact, many of those teachers will never ask their students to solve two equations with three unknowns because they do not see the big picture, limiting their students.
I have also observed that students can have remarkable insights into the subject at hand, but those insights may not be well formed. A teacher with deep content knowledge will be able to see the gem the student has noticed and clarify it for the rest of the class. A less prepared teacher will not. I found that by giving students a problem and walking around observing their work, I could find the teachable moment for the concept I was trying to teach, and I could make intelligent use of student work in bringing that moment to life in the class. This would have been very difficult if I was not confident in recognizing good and bad mathematical work.
To ensure that our students receive a rich math education rather than a string of rules, I think we should move forward by insisting that certified math teachers know a lot more mathematics than what they will be expected to teach and that they know it well. 

— John Benson

Wednesday, June 5, 2013


The Shanghai Metro website is terrific: you can look up stops, fares from point to point, in nearly-flawless English.  But while doing some browsing I came across the instructions you see at right.  In case you're having trouble reading the image, they are:

Take the Metro

  1. get into the station
  2. buy the tickets
  3. move to the platform through turnstile with ticket
  4. wait for the train
  5. get on the train
  6. get off the train
  7. move out of the platform through turnstile with ticket
  8. get out of the station
What struck me as funny about these instructions was that I couldn't figure out who they might be for.  I mean, if you can't figure out that after going through the turnstile, you have to wait for the train, what use is that instruction going to be?  I could imagine one of our students with autism using these kinds of instructions ... but also with lots of practice and review.  What I can't imagine is someone who really needs these instructions being able to go on the web, download them, and then use them to actually successfully navigate the subway.  Anyone who can do all that can probably figure out the subway.

To be fair, another page on the Shanghai Metro website gives really helpful, step-by-step directions with warnings and pictures.  It's still a little funny to me to think of someone needing to be told things like:

but I can imagine saying them, so I guess it's worthwhile.  (And the instructions for using the ticket machines are actually excellent.)

But I was left wondering how often we as teachers make this exact same mistake, namely, give directions that would only be useful for people who don't really need them.  For example, when we "teach" kids to write research papers ("teach" being a term I use loosely in this context), we often say things like:
Step 1: Identify a topic.  Pick something that interests you that you can write about.
Step 2: Research the topic.  Keep track of your sources so that you can footnote them in your text.
I'm being a little facetious here, but not very.  Instruction about selecting a topic might include some platitudes about not being too broad or too narrow, but how often do teachers actually sit with each kid and talk about the topic for 3-5 minutes to help the kid learn what is too broad or too narrow, and how to widen, narrow, or pivot the scope?  We teach the mechanics of how to research ("This is how you use the online database" "This is the card catalog") but do we actually model the process of finding a source and using it to find others, or to supply background knowledge, or questions for further inquiry?   Do we model the process of constructing a paragraph in which information from two different sources is combined in a synthetic way, so that students can actually see the difference between copy-paste and genuine research?

The same is true about other kinds of products.  I've never yet seen an elementary school teacher workshop students' written fiction.  Neither of my children has actually designed an experiment in science class.  These challenging processes require actual instruction--not just assessment--as much as any other.  We need to be sure that the directions we give are useful to the students receiving them.