I have taught algebra and geometry at a public high school here in Columbus since September of 1977, which makes this my twenty-third first day of school. I am not a poet by training. I took the one required English course in college and got a B.

About six years ago a student teacher left a paperback of poems on my desk, and in it was a villanelle, nineteen lines with two of them repeating over and over, and I sat at my desk during my free period and worked out the pattern on graph paper the way I would work out a sequence. Then I tried to write one. It was terrible. I tried again. That was the end of my free periods.

The old fixed forms give me the same pleasure as a proof. You are handed certain things and you may not change them. You must get from the givens to something true, using only legal moves, and when it works, you feel the click. Free verse is a fine thing and I admire people who can do it, but for me it is like being handed a blank sheet and told to "do some math." I need the givens.

So here, one form to a section, is how each one works, written out the way I would put it on the board, and one of my own. My subjects are not exciting. I grade papers, I shovel snow, I grew up in my father's hardware store, and the clock in my classroom is broken. You work with what you're given. That's rather the point.

The form as we have it comes, oddly enough, from one French poem written around 1600, which later writers took as the model and turned into rules. The trick is that the two refrains have to be written first, and they have to be good enough, and flexible enough, to survive being said four times in four different places. Everything else bends around them. The rhyme on b is the hard part in English: you need six words that rhyme with each other and don't sound like you went looking for them. (You did. The reader shouldn't know that.) Since a refrain has to carry the most weight, I write mine on an index card and carry it in my shirt pocket for a week before I start.

The letters on the left are the scheme, so you can check my work.

Check: a-rhymes night, right, polite, fright, despite, white, sight. b-rhymes four, swore, more, for, shore, before, six of them, no word used twice. I did use "four" only once as a rhyme, which took most of a Saturday. The clock really is in Room 114, it really did stop in March of 1994, and the work order really is still open. I check every September.

The sestina was invented by a troubadour named Arnaut Daniel in the twelfth century, and I like to think he was a math teacher at heart, because the rule is a permutation. Take the last word, then the first, then the next-to-last, then the second, and so on, folding the list in from both ends. Here is what that does over six stanzas:

Read down any column and every number appears exactly once, so each word gets one turn in each position. Apply the rule a seventh time and you are back to 1-2-3-4-5-6, which is why there are six stanzas and not seven: the permutation has order six. I showed this to my Algebra II class last spring and two of them were interested, which is two more than usual. Notice also that the last word of each stanza is always the first word of the next. That is where the poem gets its feeling of circling something it can't quite put down.

Choosing the six words is most of the work. Pick words with more than one meaning ("change," "count") and you'll have room to move. Pick "parabola" and you won't. I learned that one the hard way.

My father ran a hardware store in a small town north of here from 1946 until 1987, when the big store opened out by the interstate. He died in 1993. I worked the counter every Saturday from the time I was nine.

Check: 39 lines. Stanza endings, in order: 1-2-3-4-5-6, 6-1-5-2-4-3, 3-6-4-1-2-5, 5-3-2-6-1-4, 4-5-1-3-6-2, 2-4-6-5-3-1. Envoi: drawer and change, count and bell, hands and nails. I went over it with a ruler. If you find a mistake, I will give you extra credit.

The pantoum comes from the Malay pantun, by way of some nineteenth-century French poets who admired it. Every line but the first two and the last two gets said twice, so the poem moves forward two steps and back one, like a person walking through deep snow. Which is why I used it for a snow day. Rhyme is optional; I left it out. Small changes in punctuation are allowed when a line comes back, and you'll see I took a few, but the words stay the same.

Check: 20 lines, 10 different ones, every one of them used exactly twice. (Deb is my wife. She approves of this poem because she comes off well in it.)

This is the oldest form on the page and the one I understand least, so I say so up front. The ghazal began in Arabic and was carried to its height in Persian, by Hafez in the 1300s, and in Urdu, by Ghalib in the 1800s. The couplets are like beads on a string: each one is its own small thing, and the refrain is the string. They don't have to tell a story in order. That was hard for me. My instinct is to make line 2 follow from line 1, and couplet 3 from couplet 2, like the steps of a proof. The ghazal wants you to stop doing that and trust that the string will hold them together.

Here the refrain is "at this table," and the rhyme just before it is eight, wait, calculate, straight, celebrate, hesitate, late. The table is the kitchen table, which was my father's, and the time of year is any Sunday night from September to June.

Check: 6 couplets, refrain in lines 1, 2, 4, 6, 8, 10 and 12, a new rhyme each time, name in the last couplet. People who really know the form will say my lines are too long and too plain. They are probably right. I'll keep trying.

A medieval French form, and the most efficient poem ever devised: eight lines, three of them new. I have suggested to our guidance department that it be required. The difficulty is that line 1 has to mean something slightly different each of the three times you hear it, or the reader will feel cheated. A question works well for this, because the answer can change.

The ones above are the ones I'm least embarrassed by. There's a second page with a few others: a triolet about chalk, a pantoum about Open House night, and a cinquain, which is the shortest form I'll admit to, plus the story of the sestina I gave up on.

People write to ask why there are no sonnets here. The honest answer is that the sonnet is the one fixed form everyone already knows, and I'd rather spend my evenings on the odd ones. The other honest answer is that my meter is not good enough yet. If you want sonnets, go to The Sonnet Workshop, where a retired professor explains how the form is built, walks through Shakespeare's Sonnet 18 line by line, and gives you homework. I did the homework. I'm not posting it.