Algebra I: I Scream

Algebra I

Day I

I am an English teacher with a math anxiety, and I have gone back to Algebra. I explain it more fully here.

Linear functions, scattered data, and probability, and apparently, I have just about the worst timing ever. The chapter test is tomorrow, so the students were reviewing. As I can't remember what a linear function is, I was at a slight disadvantage.

Today's problems concerned coin flips, lottery problems, factorial problems (another concept I can't remember) and dice rolls, complete with histograms.

Okay - here's my first question. Histology is the study of organic tissue. Histo- comes from the Greek and means "a warp or web," literally "anything that stands upright" from histasthai, "to stand." Medical writers in the 19th century decided that this root was the best candidate for medical terminology concerning itself with "tissue." So how the heck do we get to a place where a histogram means a mathematical graph?

I did not want to raise my hand in the first five minutes of my first Algebra class. I wisely sensed that an etymology lesson might just derail poor Alison from her homework corrections, so I wrote it down in the corner of my notebook and did the research later on.

A mathematical histogram is a visual representation of the distribution of data, specifically for probability. According to the research I did after class, Karl Pearson, who coined the term in 1895, took histo- as "anything set upright, as the mast of a ship or the bars of a loom" and gramma-, meaning "drawing, record, or writing." Another source says that Pearson just went with histo- from "historical" and gramma- "drawing," and meant to create a drawing that shows a historical representation of statistical data.

Whatever. My point is that my first question in math class was an etymology question. You can see what I am up against here.

I liked the next problem. Vermont license plates use a combination of three letters, followed by three numbers. How many possibilities are there for Vermont licence plates? Well 26* 26* 26 10*10 *10 (I am just going to assume here that I did not represent that correctly; give me a break, it was my first day) = 17,576,000 possibilities for Vermont license plates. As there are about 28 people living in Vermont at the moment,* I think the state is in the clear where motor vehicle registrations are concerned. 

The third problem really threw me for a loop and not because of the math - no, that threw me, too, but only because I could not get to the math part.

3. Chris Cross si 14 months old, and is just learning how to walk. He zigzags across the 12-by-15 foot room shown in the figure, eventually falling down. The ice cream cone he is carrying spills either on the 9-by-12 foot rug or on the floor around the rug.

Okay. Before I can even begin to think about the math, what sort of parent gives a 14-month old an ice cream cone and lets him walk around on a carpet? This entire mathematical quandary could have been avoided with better parenting.

But, as I am here in remedial math class due to my superhuman ability to avoid math, I forced myself to get past this appalling lack of judgment. I gamely participated in the problem and did not even point out that any intelligent mom would have that kid on the hardwood floor OUTSIDE the perimeter of that carpet. Oh - and hey! I know what the perimeter of the carpet is!

1. Bill Ding [clever] constructs quality homes. He figures that a house built on a particular lot should be sold for $373,000 if it has a floor space of 3,000 square feet. A 4,000 square foot house constructed on the same lot should be sold for $483,000. The selling price is the sum of the construction cost, at a fixed number of dollars per square foot, and the cost of the lot.

The problems after the example tested me. I was able to figure out the number of dollars per square foot it costs to construct the house, and the cost of the lot. I was actually quite proud of myself. However, two minutes later, I had to ask another student explain the terms "domain" and "range," terms I must have known when I was 13 or so when I had Mr. Davin for Algebra. I tried to sketch the graph, but my graph was just sad and looked nothing like the students'.

In the end, I'm okay with how things went. My students saw me go out on an intellectual limb and dare to admit I don't know something, and they got to feel good about teaching me something. It's win-win.

Items to look up tonight: factorial, linear function, domain, range, cleaning products that remove dairy from carpet.

*also look up how many people actually live in Vermont.

Part III of my math odyssey can be found here.

When a Man Teaches Latin

This Latin teacher thing. It freaks me out sometimes. My Latin teacher in middle school and high school was, well, a stereotypical Latin teacher. She was five feet tall, gray-haired, and insisted on teaching Latin as a spoken language. Because being able to speak Latin is about as useful as being able to speak Klingon, so drill those verbs! Harden those consonants! Roll those Rs!

I shelved the oral Latin for a long time, but then I moved to Italy during my Junior year of college, and as I had only had one semester of Italian before I moved to Siena, my French and Latin helped me more than my sad, elementary Italian. I asked for French bouteilles of water and inquired as to where I may find the tonsor who would cut my Roman hair, but at least I was close and could (mostly) be understood by the Italians in my neighborhood.

When I returned home to the United States, I had a challenging semester ahead. I had to catch up on some of my comparative literature requirements. I signed up for intermediate Latin so I could take at least one class that offered the chance of an easy-ish ‘A’. My Latin teacher was a very bored graduate student, kind of cute in his dorky way, but so traumatized by his 4-year sentence in undergraduate hell that as long as we showed up and didn’t debase him with our improper pronunciation (Drill those verbs! Harden those consonants! Roll those Rs!), we passed.

So when I interviewed for my current post and gleefully informed my now-boss that I’d studied Latin in middle school, high school, and college, she asked me to teach Latin as well as English.

(Note to self: some skills are better left un-shared.)

The good news is that I only have to teach my students enough Latin to prepare them for Latin II in high school. The bad news is that I have to know far more than the simple Latin II material in order to answer challenging questions from my students.. As Latin teachers are thin on the ground in my neck of the woods, I have come to depend on my colleagues across the world to help me understand the whys and wherefores of the Latin language and ancient Roman world.

A while back, I posted about the wonder of the Latin teacher listserv and the weekly Latin teacher digest. I have learned so much from these seasoned Latin teachers and thanks to them, I am not afraid of the hard questions. This week, I was intrigued by an email that fell into my inbox from one of the Latin teachers, mostly because the subject line included Marilyn Monroe. A Latin teacher – Steve Perkins, from North Central High School in Indianapolis – shared his methodology for teaching Latin poetry according to the alliteration, themes, and rhythms of popular culture and song lyrics. This particular email was about a Roman poem’s resemblance to the specific pronunctiation of Marilyn’s p’s and t’s in her “Happy birthday, Mr. President” performance, but I was even more fascinated by comparisons between rock and Rome.

As I was curious, and love a good cultural literacy tie-in, I emailed Steve and asked him to elaborate on the connections between popular music and Roman poetry, and he sent me a brilliant email describing his top ten hits. He teaches Horace’s Odes III.10 and Ovid’s Amores I.9 to the melody of Percy Sledge’s “When a Man Loves a Woman,” particularly the line “sleep all night in the pouring rain if that’s the way it had to be.” He explains that both poems feature a man “enduring the harsh weather by spending the night on his beloved’s doorstep.” According to Steve, this type of poetry is sometimes called paraclausithyron, which comes from the Greek words meaning “door” and “to lament.” He will bring in the 80’s hair band Whitesnake if he has to, but he admits that 1987 might render the band a bit dated. You know, as opposed to 50 B.C.E.

He goes on to explain that he teaches Ovid’s Amores I.9 and others with Pat Benetar’s “Love is a Battlefield,” Horace’s Odes I.25 with Rod Stewart’s “Maggie May,” and Caesar’s De Bello Gallico I.8 with the film Boys ‘n’ the Hood. Thanks a semester with Sir Christopher Ricks, my first poetry professor, I teach Bob Dylan lyrics during my poetry unit, but Horace and Rod Stewart? Brilliant.

My favorite of his suggestions is a reference to the band Deep Purple in the midst of  The Aeneid II.246-247, the section about Cassandra during the Trojan War. In Steve’s words:

“Cassandra was the priestess of Apollo who, after she spurned his love, was cursed that she always foretold the truth, but that no one would believe her. I bring in the title song to the 1973 album Burn by Deep Purple. The lyrics run, ‘The city's ablaze, the town's on fire.  The woman's flames were reaching higher.  We were fools, we called her liar.’ Cassandra was known as a firebrand, and in fact, Marion Zimmer Bradley wrote a novel called The Firebrand, which is a telling of the Trojan War from Cassandra's perspective. Although the lyrics of the Deep Purple song support my interpretation quite well all the way through, I have had emails with the song's author, David Coverdale, and he says he was not inspired by the Cassandra story.”

Dude. Steve’s no outdated, gray-haired, Latin teacher with a penchant for oral Latin. This guy is my new hero.

GEEKINESS ALERT! GEEKINESS ALERT!

You may go watch this extravaganza of geekiness if you promise to come back for my new post in praise of my new hero. I tried to incorporate this wonderfulness in the post, but it didn't fit. So come back. Soon. 

The Supersizers go to ancient Rome….warning: they eat guts, vomit, and enjoy garum. Don’t say I didn’t warn you; it rocks.

Part I:

Part II:

…and Part III:

Lovely. Just lovely.

Now I know that one takes out the sting of a jellyfish with salt in order to serve it for a banquet. And how to barf with a help of a feather wiggled in my throat by a slave to aid in the ingestion of additional courses.

And garum? The Romans’ favorite condiment? You don’t even want to know. Oh – wait – you DO? Take oily fish guts, salt them, deposit them in a huge pot and let them sit for truly questionable periods of time, then apply liberally on every dish served on the Roman table. The host of the aforementioned video described it as “apple sauce in which a goldfish had died.” I mentioned “lovely,” yes?

And I Can Hardly Speak, My Heart is Beating So

Bad news stinks, and getting bad news at work really stinks. But for most people, temporary solace lies behind the door of an empty office or in a walk around the block or, as a last resort, a quick cry in the lavatory stall.

When bad news arrives in a teacher's inbox, solace is harder to find. There are all those students - lots of eyes, lots of needs, lots of questions, and they need their teachers to be present and emotionally in tact. If my students get freaked out by seeing me in the grocery store buying toilet paper, you can imagine how upsetting it would be for them to see me come emotionally unglued. Teachers learn to keep their highs and lows to themselves, to remember that the kids have to come first. Students depend on their teachers to be stable, and like a parent protecting her children from the boogeyman, a source of strength and courage.

There's so much I could not have anticipated about this job when I signed my first contract. Late night phone calls, crying students, crying parents - I didn't enter this profession lightly, but I did underestimate the challenges inherent in being under a microscope all day long. Students look to their teachers for all kinds of support, and often we have to subvert our own emotional impulses in order to help them manage theirs.

The first year I taught full-time, my best friend died very suddenly. She had battled depression for years, but her final trip into the abyss proved to be too much for her, and she took her own life. The morning after I got the phone call from her housemate, I taught. My eyes were swollen and I had to excuse myself a couple of times and just stand out in the hall by myself, but I made it through that day without breaking down in front of my students.

Two years later, 9/11 played out, and we acted as parent, therapist, EMT and crowd control, as we were all they had when the bad news hit. The teachers and staff wanted to freak out, but we couldn't. The students looked were watching, and if we held it together, they stood a much better chance of holding it together.

This morning, I sat down to run the sixth grade homeroom, and the little red "new email" dot appeared on my toolbar at the bottom of the screen. Tim was traveling to his clinic in Manchester, so I checked quickly to make sure it wasn't an emergency. Unfortunately, the subject line "Mom" and the sender, my mother-in-law, were all I needed to see to grasp the news of that email. My grandmother-in-law has been very ill, and while we thought she had about a week left, she died this morning.

I got the email just as our regular homeroom routine was beginning - psalm, moment of silence, flag. Yes, psalm. Crossroads Academy is not a religious school, but we consider biblical literacy (along with all other subjects of cultural literacy) to be one of the most important elements of our students' education, regardless of any personal religious conviction.

I am not a religious person. I do, however, love words, and today's psalm, 139, held some nice moments for me, particularly the part about being truly known.

            O Lord, you have searched me and known me.

            You know when I sit down and when I rise up;

                        you discern my thoughts from afar.

            You search out my path and my lying down

                        and are acquainted with all my ways.

Being known was comforting to me, as I was in the middle of faking happiness in the middle of my private sorrow. Thanks to the current cold and flu season, there are boxes of tissues spread all over my classroom, and I hid my sadness behind the facade of a cold. I covered pretty well, so well done, me. I successfully ushered the sixth graders through the pledge of allegiance, and they headed off to history class. As a reward for my stoicism, I allowed myself a couple of minutes of unrestrained tears in the middle school office before blowing my nose, taking a deep breath, and teaching composition class. Grammy Eileen would have liked that transition. She was a kick-ass writer, and she would have told me to buck up, get my butt in there and teach those kids how to use a darn comma.

Middle school students are rumored to be self-absorbed, selfish, and so hopelessly awash in hormones that they can hardly see past the end of their pimply noses. Sometimes, this is true. But sometimes, they know. Sometimes they leave notes on their teacher's desks, wishing them a good day. Sometimes, despite my best efforts, they know me.

Quantifying the Unknown

I have a recurring dream: I am in college, or law school - sometimes high school - and I have not attended classes all semester. I don't know where my locker is, let alone the combination, and I'm not sure where the classrooms are. I certainly don't know what material we have covered. It's exam time, and I know I won't even be able to find the classroom so I can take the exam. I know that if I don't pass the exam, I will not be able to graduate, so I have to find the main office and I can ask them where my classes are. I wander around the school, often in that slow, stunted, underwater way, and get nowhere as the minutes of the exam period tick by.

One fun twist on last night's version of the dream is that while I was digging around in my materials, looking for any clue as to my class schedule, I found an application for an internship with Billy Collins. Despite that nice surprise, I still woke up nervous and flummoxed.

The class I fail in my dreams is usually math, which is absolutely predictable if you know me at all. I have never done well in math, and as a result, I have serious math anxiety. I can grade papers and calculate percentages, but anything more complex than that brings on the shakes. So when I woke up this morning at 4:32 A.M., drenched in sweat, I decided to return to the place of my defeat (again) and go back to school.

Fortunately, the math teacher at my school is amazing. She's the math teacher I wish I'd been lucky enough to have when I was in middle school. She's organized, demanding, witty, and kind, and every time I poke my head into her classroom, her students are enjoying themselves.

I know! That was a new concept for me, too.

I checked the middle school schedule and realized I have a prep period during her Algebra I classes on Wednesday and Friday, so starting next week, I'm back in school. I will have my own textbook, and I will even try to do some of the homework once I catch up to the kids (if that even happens).

It's time to put my money - well, my pride, I suppose - where my mouth is. I encourage my students to be brave, diligent, and never back down from an intellectual challenge. I try to model a love of education, a genuine thirst for knowledge that drives what I read, watch, and listen to. They know I am a frequent buyer at The Teaching Company, and that I listen to lectures on my iPod when I stack wood, fold laundry, and chop vegetables for dinner. Currently, I'm listening to a course on the evolution of the English language, and I love to share the tidbits I've gleaned with my students. They know I listen to courses on English, history, and science, but they also know about my math aversion. They joke about it. I joke about it. But it's not really that funny; it's actually quite sad.

I am hoping that my efforts to remedy my math anxiety will put weight behind my words. I hate math, yes. I hate the obsessive attention to plusses and minuses. I hate the inflexibility of numbers. But the excuse that "my brain just does not work that way" doesn't cut it when I simultaneously tell my students that they can do anything - anything - they want to do.

Well, dammit, so can I.

Part II of my math odyssey can be found here.

Food for Thought

The most wonderful thing happened to me today. A student asked a question, and I did not know the answer.

Don't misunderstand - I am at a loss for answers all the time. Every day, I affix a new index card to the front of my plan book so I will have a place to write down the all questions I need to look up. Tonight, for example, I have to look up the etymology of the word "hypocrite" (Greek, hypokrites, stage actor, pretender, dissembler), find out why Castor and Pollux wear skull caps (remnants of their hatching - long story, involves their father Zeus in the form of a swan), and whether the limerick ever achieved high scholarly status (not really). The last one on my notecard, though...it's a doozy.

There I was, in the middle of a poetry lesson in my seventh grade English class. We were talking about cliches - cliche similes and metaphors, specifically. If a poet were to write that someone is as white as a ghost or meaner than a junkyard dog, readers will understand, but some cliches are so familiar, they don't mean much anymore. They don't stop the reader in his tracks or offer up a new way of looking at something.

But, when a writer reports that "purple is black, blooming" or that the ladies were "like soft tea cakes with frostings of sweat and sweet talcum," I can see that dark blue blooming into purple and the cloying heat of a Maycomb Sunday afternoon.

And then, there it was:

"If phrases can be cliche because they are so overused, why aren't stories like the journey of the hero cliche, too?"

Huh.

First of all, HALLELUJAH. Hallelujah. Hallelujah. Haleleeeeeeeluuujah. What an awesome question. Once my shower of lavish praise ended, however, the room grew very quiet.

Where are Carl Jung and Joseph Campbell when I need them? Flitting about on their angel wings, interpreting Steve Jobs' dreams, no doubt.

We all thought about the question for a while. They looked at me to see what I would say, I looked at them to see what they would say. Class went on like that for a while. I have some really great students, kids who understand that quiet is not merely something to be filled up.

Finally, a girl - one who rarely speaks up in class - raised her hand. She offered that maybe, if the journey is a little different each time, it's still exciting to us. Another girl agreed - Bilbo is after the booty in Smaug's cave, Pip seeks Estella and his expectations, Dorothy has to reveal the man behind the curtain - it's all the same story, in the end. And yet we keep reading because the details are different.

It was about time for class to end, so I wrote "journey=cliche?" on my index card, and promised to think about it overnight and get back to them.

And then, as they filed out of the room, a student offered up the most lovely cliche I've ever heard: "Maybe it's because the journey is the important part, not the destination. That's why we keep reading."

Out of the mouths of babes, ladies and gentlemen. Out of the mouths of babes.

Happy Birthday Charles Dickens!

Happy 200th birthday Charles Dickens! In honor of The Man's bicentennial big day, I post this tale about the teaching of Dickens. It had previously been over at the Core Knowledge blog, but as I have moved on to poetry in both of my English classes, I'm reposting it here. 

We are currently reading A Tale of Two Cities in the eighth grade, and things are heating up in France. Dickens is deep into his fire and water metaphors – the French Revolution as rising fire and rising sea, “the firm earth shaken by the rushes of an angry ocean which had now no ebb, but was always on the flow, higher and higher, to the terror and wonder of the beholders on the shore…”

Today’s discussion will focus on chapter 24, “Drawn to the Loadstone Rock.” I asked them to look up the meaning of “loadstone rock” over the weekend and to think about how it might figure in the chapter, why Dickens might use that title for this particular chapter. I happen to be a big fan of titles, particularly chapter titles, and Dickens is at his metaphorical best in A Tale of Two Cities. The symbolism and allusions lay thick on the ground, and even the youngest students can’t help but stumble over a couple by the time the Reign of Terror begins.

I adore teaching this novel. This novel is where even my most literal-minded students make that leap from the literal to the figurative. Students who have been steadfastly rooted in the facts and just the facts (“why doesn’t the guy in ‘The Tell-Tale Heart ’ just move his chair somewhere else when the heart starts beating again?”) suddenly emerge from the darkness, and see. They see the Fates in the guise of Mme. Defarge and all that knitting, they see that wine is more than just wine, blood more than just blood. Gorgons, scarecrows, resurrection men. Their eyes widen, breath quickens, and hands shoot up in the air, and it’s like watching a small miracle take place. I call it their Dorothy moment, the moment black and white text switches to Technicolor.

This transformation happened to a young 8^th grade girl last week, and she’s been on a roll ever since. This morning, I gave over a period of composition class so we could listen to a CD of Patrick Stewart performing A Christmas Carol. We got to the part where two children emerge from under the cloak of the Ghost of Christmas Present. The children are grotesque personifications of humanity’s Ignorance and Want.

“Yellow, meagre, ragged, scowling, wolfish; but prostrate, too, in their humility. Where graceful youth should have filled their features out, and touched them with its freshest tints, a stale and shrivelled hand, like that of age, had pinched, and twisted them, and pulled them into shreds. Where angels might have sat enthroned, devils lurked, and glared out menacing. No change, no degradation, no perversion of humanity, in any grade, through all the mysteries of wonderful creation, has monsters half so horrible and dread.”

As the scene ended, one student raised her hand, and I paused the disc. “Those children – they are like The Vengeance in A Tale of Two Cities. She’s the personification of the vengeance in the people of St. Antoine, and those children are the personification of the bad stuff in people.”

Sweet. The day has been a success.

This was a girl who, just two months ago, could not identify the simplest metaphor. She was not the student who asked the question about “A Tell-Tale Heart,” but she may as well have been. It’s not her fault; those neurons responsible for identifying and interpreting figurative speech simply had not joined up yet, but then, about halfway through A Tale of Two Cities, they did. And there was light.

I am looking forward to today’s discussion. For the record, a loadstone rock is a naturally magnetic rock, the sort that were used in marine navigation. Here, Dickens is referring to the inexorable magnetic pull of France that will eventually lead Darnay to his imprisonment and death sentence. Dickens is not referring to just any old loadstone rock, he’s referring to the loadstone of Arabian Nights fame. In that novel, a ship was drawn to a gigantic loadstone rock, one so powerful that the nails were pulled from the wood of the hull, and the ship sank. I show my students a beautifulengraving of this scene, and hope someone will make some sort of connection between poor Agib, clinging to the loadstone rock, and Darnay, about to step on to the shores of France.

The students are always exasperated by Darnay’s decision to return to France, even to save his employee, Gabelle, from prison. They know what is going to happen – it’s inevitable, fated. It’s been registered in the knitting, after all. Today should be a good class, as the metronome of those hundreds of footsteps is picking up and the climax of the novel draws near. I still have still five or six literal-minded 8^th graders, and one or two may well have their Dorothy moment today. There’s some good stuff in store for them, plenty of fertilizer to fuel those branching neurons:

“The unseen force was drawing him fast to itself, now, and all the tides and winds were setting straight and strong towards it. He left his two letters with a trusty porter, to be delivered half an hour before midnight, and no sooner; took horse for Dover; and began his journey. “For the love of Heaven, of justice, of generosity, of the honor of your noble name!” was the poor prisoner’s cry with which he strengthened his sinking heart, as he left all that was dear on earth behind him, and floated away for the Loadstone Rock.”