May 25, 2010

The Inclusion-Exclusion Principle

Filed under: Classroom Management — Adam Glesser @ 5:59 am
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During my first semester at Suffolk, I noticed there were several Spanish-speaking students in my classes. As my position wasn’t permanent, I figured it would be useful to add “Bilingual” to my CV and that I would have several students around who would be more than happy to feel intellectually superior to me.  The good news is that a year and a half later, I still enjoy studying Spanish; the bad news is that those students still feel intellectually superior to me.

Michel Thomas and Me

The best system I’ve used for learning Spanish (and I’ve tried a lot of them) is the Michel Thomas method. What make his tapes unique is that the recordings are of him teaching two people. You get to hear their (often incorrect) answers and how he responds to them. His style is a wonderful combination of humor, clever mnemonics and carefully planned repetition that constantly adds just a bit more to what the student already knows. With other programs, I would get bored or weary after 20 minutes, but with Michel Thomas, an hour goes by and I whisper, “Tell me more.”

The Michel Thomas Method and the Classroom

Here is the revolutionary, groundbreaking, innovative idea (that I stole from someone, but I can’t remember who) that I’ve come up with all on my own this summer: Stop teaching 25 kids at once. My plan is to take three students from the class and only teach to them. By this, I mean that they will sit at the front of the room and I will teach them. My usual style is to lecture to the class, but no more. Now, I will build the subject in tiny increments, continually asking my three students questions and assessing their understanding. A typical exchange might be:

AG (looking at all 3): Consider this plot:

(to Student 1) What is the y-coordinate of point A?

S1: 1

AG: (to Student 2) And what is y-coordinate of point B?

S2: 4

AG: (to Student 3) How much did the y-coordinate change?

S3: By 3.

AG: Good. How much did it change if I ask you first about point B and then about point A?

S3: Still by 3.

AG: Yes, but it is a curious thing here. From A to B, the y-coordinate goes up and from B to A, it goes down. We don’t want to lose that distinction. So we agree that if it goes up, we call it a positive change; if it goes down, we call it a negative change.

(to Student 1) When we go from point A to point B is the change positive or negative?

S1: Positive.

AG: (to Student 2) And from point B to point A?

S2: Negative.

AG: (to Student 2, again) How about in this picture—again from point B to point A?

S2: The change is negative.

AG: From point A to point B, the change in the y-coordinate is negative. What about from point B to point A?

S2: From point B to point A? Oh, yes, backward. It is positive.

AG: Now the way we will write the change in the y-coordinate is to use a Greek letter \Delta (writes it on the board). The change in y is written \Delta y (writes it on the board).

S1: But how do you know if you’re going from point A to point B or the other way around?

AG: You need to specify. Let’s make an agreement, though. If I don’t say anything, we’ll mean left-to-right, the same way we read.

(to Student 1) What, then, is \Delta y in the first picture?

S1: 3

AG: (to Student 3) And what is it in the second picture?

S3: 2

AG: Are you going left-to-right or right-to-left?

S3: You didn’t say which, so I’m going left-to-right.

AG: And does it go up or down?

S3: Down.

AG: When it goes up, the change is positive; when it goes down, the change is negative.

S3: So, is it -2?

AG: Of course.


What’s the Problem?

So, already I see some issues.

  1. There are 22 other students; what if one of them wants to ask a question? The simple response is that I’ll answer it.
  2. Won’t those three students get a better education than the others? Yes, but I plan to rotate the students daily.
  3. What if a student doesn’t show up when it is his or her turn? Their performance in this setting is graded. If they don’t show up, their grade reflects that. Also, I can always do it with two students (it might be more effective that way!)
  4. What if a student shows up under-prepared? Again, it is a part of their grade, so I expect some of them to take it seriously. But, I can imagine a student who is clearly not working at the same level as the other two students and this could be a problem. I would probably phase him or her out as the lesson grew in complexity and then discuss it with him or her outside of class. I need to take care in putting together these groups of three: if done randomly, I might end up with three slackers who could ruin the class.
  5. The three at the front will pay attention, but what about the others? How do you keep them engaged when you’re ignoring them? This is the toughest question for me to answer. I hope that I can make the dialogue interesting enough to keep their attention. Ideas here would be really appreciated. One retort I have is that even if I lecture conventionally, I still can’t keep their attention the entire time. How many more would I lose this way? I don’t know.


  1. Sounds like a good experiment. I’m sure that over time you’ll be able to refine your method and thereby improve the technique. We’ll be anxiously waiting to hear the outcome.

    Comment by Allen Glesser — May 25, 2010 @ 12:26 pm | Reply

  2. Hmmmm, very interesting. Even though you won’t be “lecturing” you will still be very heavily guiding all conversation. Is there a way to have students work through a really similar conversation without you? It seems like with the right prompts, your groups of 3 (or 4, maybe one of them gets “hints”?) could work through this while calling on you only when they’re really stuck.

    I could really see the value of the modelling you’re doing with the smaller groups at the beginning of the year, especially if you’re working with a group of students who doesn’t know how to questions well, but after a little practice I see it being pretty exciting for the students to take over. This would allow you to have these mini-assessment conversations with every group almost every day, and also allow you to focus more heavily with a group that is lagging if needed. You’ll always need to direct teach the vocabulary & notation, but for all the great observations you’re pulling out students could do that mostly without your prompts.

    I switched to “podding” my students in groups of 3/4 this year and learnt something really valuable along the way – switch your seating plan, at random, every single day. Students will work with anyone for an hour, but they don’t want to get “stuck” working longer term with someone they don’t like. It’s been awesome for our class dynamics as well, things feel much less “clique-y”.

    Since I’ll be on leave next year I look forward to seeing how this goes 🙂

    Comment by park_star — May 25, 2010 @ 4:26 pm | Reply

    • This is a really interesting point, you raise. I’m having trouble getting my head around it, actually. Since my plan is to teach all the material in this fashion, if I break up the students into groups, what would the students in other groups be doing when I’m not with them? However, I do it, I’m also a little worried about time. Since it is a college class, I get about 47 hours of class time. Given that I have to keep to a reasonably strict schedule (it is a coordinated course, so I don’t have complete autonomy), I’m worried that if I’m not in control, then we’ll fall behind.

      Am I letting fear get in the way of the natural conclusion of an idea?

      Comment by Adam Glesser — May 26, 2010 @ 9:03 am | Reply

  3. I guess that depends on just how much the class following your depends/expects to “master” the course objectives. Depending on your department people might have different opinions on this… Even if it’s strict, you know where your hotspot are and what “just needs to get covered.” Sometimes I feel that I can be a little freer with my curriclum since typically students don’t remember much between courses anyway. I’d rather do some really good work with them and avoid the “we never learnt this!” conversations that inevitably follow, but I’m guessing you can make students a little more accountable to review/catch up on their own at the college level. I’m also really lucky (sometimes cursed!) in that I also get to follow groups through from one level to another, so I know where their strengths/weaknesses are in regards to previous curriculum.

    Maybe shelve your fear for a bit, but still have a good idea of what an acceptable pace is for you – if you find yourself getting offtrack, simply reign it back in for a day or two. As much as we like to live in the best possible scenario, somedays you just have to run the show so sh!t gets done. My hypothesis would be the more you & your students do this, the less and less help they’ll need from you. As for what the other students will be doing while you work exclusively with 3, what would they be doing if you were lecturing and throwing out the occasional question to the whole group? While not ideal, you’ll have those who want to learn paying attention and those who are prone to disengaging disengaged… Your witty dialogues with the other students have to be more interesting than what they’re getting from the majority of their other classes – someone droning at the front 😉

    Comment by park_star — May 27, 2010 @ 2:17 pm | Reply

    • The one thing working in my favor is that this is the terminal math class for most—if not all—students in the course (unless I do such a good job that it convinces them to take more math classes!). This means that if I mess things up badly, I only need to make sure they can pass the final exam and I’m on record as saying I can teach anyone who qualified for the course how to pass the exam in two hours or less.

      Anyway, thanks for food for thought. Until I actually get in front of the class and try this, I probably shouldn’t get too worried. I just need to remember that, “I’m Good Enough, I’m Smart Enough, and Doggone It, People Like Me!”

      Comment by Adam Glesser — May 27, 2010 @ 7:56 pm | Reply

  4. That’s the perfect situation for trying whatever and making many many messes 🙂

    Comment by park_star — May 28, 2010 @ 1:03 pm | Reply

  5. […] gawd, what am I doing” part. This last bit is called Oral Evaluation. Way back in May, I mentioned my desire to teach only three students, instead of twenty-five. Well, I’m giving it a shot in one of my […]

    Pingback by Cleaning Out the Gutters « GL(s,R) — September 6, 2010 @ 11:26 pm | Reply

  6. […] the few students who have commented on my system of lecturing to only three students are an indication, the idea  is a success. I’ve had at least three students volunteer to do […]

    Pingback by Collecting Unlike Terms « GL(s,R) — September 21, 2010 @ 8:31 pm | Reply

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