## Saturday, March 31, 2012

### Let me count the ways

On the bus to work everyday I watch men and women with newspapers spread across their laps and pens in hand pondering sudoku problems.

Suduko is a logic puzzle. In each row, each column, and each box the numbers 1-9 must appear exactly once. The challenge is finding – through trial, error and numerous erasings – the singular solution. For serious Sudoku players there are entire books of puzzles to solve.
But for those who want a real challenge I would argue that the greatest Sudoku grid is a classroom-seating chart.

Consider:

Daniel cannot sit next to Maria, for when bored, he has a tendency to bully. Nor can Emily and Vanessa sit side-by-side for they are prone to dissolving into fits of giggles. Anna needs a desk at the front owing to her bad eyesight. Sara is self sufficient, easy to work with; she can successfully be placed anywhere. Michael is tricky. I have tried the edge: he zones off. I have tried the very front of the class, right up next to the board with mixed results: at times he is unnerving in his focus, and at times he slips into acting the class clown, front and center.

The list of seating-chart stipulations is unending.

When I read how the fifth grade teacher in Tracy Kidder’s book “Among School Children” agonized over seating charts – how she devoted much thought to which students when placed beside each other could draw out the best – I was incredulous. Clearly, she must be over-thinking the issue.

I was wrong.

I started off this year with a musical-chairs approach – new seats daily. I experimented with combinations. Could one of my best students focus one of my worst? What if I executed a 180 and put two trouble-makers together? Could they, like two negatives, result in a positive?
But with ever-changing rotations I found myself bombarded daily with my students’ seating desires. This semester each student has just one assigned seat. I hoped, after careful consideration and balancing, I had reached an equilibrium.

Daniel is in the back, slightly isolated to encourage focus. Andy is in the front, easy to watch and redirect. Joseph is also near the front so as to discourage excessive pencil tapping. I have deployed calmer and quieter students to occupy the center seats and arranged the most rambunctious around the periphery.

Yet despite all my careful calculations, in two months I see the lines fraying. Like a field general, I find myself having to re-arrange the troops, draw up treaties, form alliances. Students have begun negotiating with me. “If I’m really good this week can I sit in the back?” I extract promises, “If I let you sit together I have to see amazing focus.” Even my best students are starting to chafe from sitting to long next to the same peers. I catch them poking each other, purloining pens and pencils, and I know, I will have to go back to the drawing board soon.

There are twenty-five desks in my classroom and, if everyone is present, eighteen students. All told, I calculated that makes a bit more than 3x1021 possible seating charts. To try them all, at one a day, would take me about billion times the age of the Earth. Unfortunately there are only fifty days left in the school year to experiment.

#### 1 comment:

1. What if you made the seating chart itself an exercise in logistical thinking? It's a perfect example of a real-world problem. It involves math, understanding other people's needs, communicating your own needs, and understanding the goals of the classroom.

You could do it at the beginning of the year (or in the middle I suppose) and have the kids submit proposals of seating charts. Maybe they would have a different perspective if they designed the seating from a teacher's point of view?