More on the Sieve

Meant to mention this before.

I really don't understand freshmen.

Paying attention and staying on task are not my students' strongest skills. They were continually getting off track when I was defining the prime numbers, reviewing the arithmetic that we'll use on Friday, and telling them about Eratosthenes and the library at Alexandria. I would have thought that the biographical information would have held their attention.

And so I have this feeling of dread as I hand out the xeroxed grids. I had used Excel to list the numbers from 1 to 300, each number in its own little box, and I start giving the directions:

"Cross out 1 because we said that 1 is not a prime number. Leave 2 because we all know that 2 is a prime number. Now, I want you to cross out all the even numbers (except 2) because they are multiples of 2, so they can't be prime numbers."

Absolute silence in the room. Forty freshmen diligently cross out 150 boxes.

"We leave 3 because we know it's a prime number, but we have to cross out all the multiples of 3. Maybe as you're crossing them out you can see a pattern that will allow you to cross them out more efficiently. Remember, we're crossing out every number that we're certain is not a prime."

Still silence. Almost 50 multiples of 3 remain on our grids, and the freshmen cross them out, one by one. No one cares that as you go down the vertical columns on our grids you cross out one and then skip two.

We move on to the multiples of five; I still have their complete attention. They keep following my directions and keep crossing out boxes. There are fewer than five minutes left in the class period, and no one is packing up to leave. Everyone is sitting quietly, crossing out boxes. We move on to the sevens, they continue, as if in a trance. And they kept at it until the end of class; I had to tell them when time was up.

It was the weirdest thing.