Tuesday, January 8, 2008

Math Describes Everything

I am grateful for many things, but few things more than my love of math. Don't misunderstand me when I say this for I've never been a math prodigy. Indeed, I never earned anything over a C in math between 5th Grade and 12th Grade. Interestingly enough, I earned A's in 5th Grade Math and A's in 12th Grade Calculus. Go figure. But I digress.

My high school taught me many things, and my high school teachers were responsible for 90% of those things, but it was, oddly enough, my 10th-12th Grade math teacher that taught me to love math. It took her three years to do it and I spent most of that time hating math, but when I left her, I did so with the deepest understanding of the universe and how it works as I had ever had to that point in my life.

Math is all about relationships. Xs and Ys, independent variables and dependent variables, and the relationships that exist between them. Numbers certainly are dry and unfeeling and do things that can seem rather pointless to the untrained eye. But tell somebody that musical harmony has a mathematical relationship (quadratic, I belive, but then again, I'm not a math teacher nor a music major) or that food supplies and populations share a unique relationship that can be described with a linear function and, well, if they have any interest in anything, their interest in math will be (at least) piqued.

I spent today as I spent yesterday and as I intend to spend the next week: reviewing my classes for the impending semester exam in my history class. In September, before this Blog began operating and before I had received my textbooks, I decided to teach my students social scientific methodology. Take an observed phenomenon, ask a why question about it, offer a hypothesis explaining it, test it, and find out if you were right. Repeat as required. Obviously there's more to it than that, but I'm not going to write my whole lesson right here. So, after months of indirectly using the method in class, we return to where this all began and review the method itself.

I find myself faced with the need of reviewing independent variables and dependent variables. The kids have learned some things since I first taught this, so it went better than it had in September. Using questions ranging from "Why are students failing Social Studies?" to "Why were people migrating at the beginning of the Iron Age?", we proposed hypotheses such as "Students are failing Social Studies because they aren't paying attention in class" and "People were migrating at the beginning of the Iron Age because food supplies were low."

After school today, two of my students (a Friday girl and a Thursday boy) came for a deeper review of the method. We used the question & hypothesis about the Iron Age so that we could review both the method and the Iron Age (another section on my exam) at the same time. We made up fake food supply numbers (Y) and fake population numbers (X) and we went through the numbers and, after 10 minutes of calculation, we discovered a positive linear relationship between food supply and population. But that wasn't the hypothesis! So we re-attacked the numbers, this time looking at population change from year to year, and came up with a negative linear relationship... with a y-intercept that had to be discovered! 0 = m(18), and m does not equal 0, so there has to be a b.

We didn't know slope (m) or the y-intercept (b), all we had were several points. We solved for b, then we solved for m, then we had the equation of our line! Y=-333 1/3 (x) + 6,000!

The kids loved it. They had never seen math do that before, though they had seen the beginnings of that math before in math class. Both of them immediately came to understand the deeper meaning of math... and they understood that history has math in it. They instantly got the whole purpose of the method, they realized what math is and what it does and how the thinking of math is in everything else. They got how the history could be better understood using math.

They got it. Two of my students had a breakthrough that I did not have until 12th Grade. That's what I did today. Math, history, knowledge... I have to tell you that after that experience, to quote Louis Armstrong, "I said to myself, 'What a wonderful world.'"

Cheers to math from a teacher of history. Cheers to Mrs. Savage. And cheers to anyone who ever came to understand that math describes everything.

Friday, December 21, 2007

"The Greatest History of All is the Kind You Make!" - One of my Students

Yesterday evening, one of my students with a notable disability of some kind (either physical or mental or emotional, I can't be certain myself) interrupted the mundane conversation the school's math teacher and I were having about the usual teacher nonsense (when the meeting or grades or something was going on... maybe we were talking about exams? I don't remember) to tell the math teacher all about how King Xerxes invaded Greece with an army of 2 million men thus sparking the Second Persian War.

I about collapsed.

The math teacher sat there beaming, listening to this student recount the story of three centuries of Greek and Persian history with one of the most excited tones. He repeated me verbatim, acting out the wild battle I had vividly described to his class earlier in the day.

But he didn't stop there. He just had to tell his math teacher (and because I was standing there, I suppose me, too) all about everything he had learned in history for about the last two weeks of school. I knew the kid was smart, but he's always had trouble communicating with me and with others in anything resembling an organized fashion. A month ago, I told him that I was advancing him to the "next level in the video game that is history class". I told him that before he speaks, he should write down what he intends to say and then read that. He was skeptical, yes, but everytime the lad speaks in class now, he gets applause from his classmates. I tried to discourage this, but it was genuine and spontaneous and I stopped when I saw how positive an experience it was for him. Once organized, he is perhaps one of my smartest and most articulate students. And he works hard.

And he wowed me again and made me feel that I had accomplished something. Here is a student that others have written off as "slow" and "awkward" and a pain. He reminds me in MANY ways of Steve Urkel, but in the loveable way (I think I've heard him say "Did I do that?" once or twice). He is in some ways all of these things, and yet he learned the Persian Wars. And he learned the important history leading up to it, including Athenian help for the Ionian Revolt. He personally reenacted the Battle of Thermopylae, which he told the math teacher is Greek for Hot Gates. I had tears in my eyes listening to it all.

When the boy scampered off down the hall to get home, the math teacher and I stood alone in the hallway staring after him in silence for what felt like 30 seconds or a minute. We turned to each other and he patted my shoulder with his gloved hand and said, "Well, you got through to someone." I nodded my stern nod that I've developed, smiled, said good night and walked back into my classroom. The Math teacher turned to leave and said the same.

Christmas break is here and for all of us - students, teachers, staff - it could not have come at a better time. We're drained. I feel like I've emptied myself of every last ounce of strength I have for these kids. I've exhausted myself in planning and in grading and in praying and in disciplining and in just being a teacher for practically every single waking moment of every single day. I have to stop myself from telling strangers on the subway in New York to spit their gum out on weekends when I'm in the city.

I teach history. And I'm beginning to wonder if I've not been making it all along for and with my students. A girl in my homeroom told me today that the greatest history of all is the kind "you" make. I presumed she meant "you" in the sense that the grammatically-correct mean "one", but she corrected me and said, "No, Mr. Cochran, the history you [pointing to me] make." And then she hugged me and left. I was stunned. And many of the other kids said less poignant though equally telling things (not to mention all the Christmas gifts they gave me over my loud objections).

I teach history. My students teach me that being human means more than just being good. It means growing, even when it seems impossible to grow. The moments like the ones described don't happen to me everyday. I suppose I'd write every day if they did. But they happen often enough to remind me that I'm on the frontline of history everyday.

How fortunate am I to be present at such awe inspiring moments as these. How fortunate am I to teach & make history.

Monday, December 17, 2007

Stille Nacht

There was an incident on Thursday last that unfortunately I cannot publish here, but suffice it to say, I made a mistake. The fallout from that day lingered for roughly 24 hours - though I expected it to have lasting implications. I learned from it, my students learned from it, and we've all been able to move on.

But something I've noticed about mistakes before now is that making them some how brings people closer together. It's almost as if they affirm our humanity, they teach us both about the specific instance at issue, but they also teach us more broadly about what it means to be human. Teaching is, in many ways, the science of being human. Teaching itself is an art, but the matters confronted by teachers are for civilized society radically a part of the very fabric of life. To read, to write, to think, to debate, to decide, to conform, to stand out, to cipher, to approach problems logically, to be something distinct while being a part of something larger... education accomplishes these things for young and old alike. When students are told a teacher is a human being and can make mistakes, it is as some fact in some dusty book, detached from reality, other & separate from the here and now.

But when students witness a teacher make a mistake, well... the fact becomes more real. Just as it is far easier to teach students about the Peloponnesian War by having the two (or more) sides of the classroom take sides in the conflict even as it is lectured to them, it is also far easier for students to grasp the humanity of a teacher should they witness that humanity played out in that most "unlikely" of ways, namely, the mistake.

Friday came following Thursday as a million other Fridays have followed a million other Thursdays since time immemorial (though we skipped a week and some in 1582 when Thursday October 4 was followed by Friday October 15). Despite my past observations, this Friday flowed smoother. Students that had never bothered to pay attention suddenly felt compelled to, students that had treated me with indifference showed a new found respect... rule by fear is hardly what I desire or require, but I won't say with certainty that it was fear that drove the new order that has persisted through the momentum destroying weekend into today.

Students have begun to try for me, to push themselves. Certainly I still have the few that are not college prep material, but there again, I have others that I had discounted until only recently. The preparation for Christmas continues in all of my classes as I struggle to bring students forward in time into the Hellenistic Age and the rise of Rome. But with only minor problems, blips as they were, I am making genuine progress that would be written off by any other institution but which I must grab onto for the sake of my own sanity, progress that even I should have called impossible only two months ago. Indeed, my own writing on this blog back in its infancy might well have expressed skepticism at the life I've seen in a few of my more precarious wards.

With Christmas only a week away and as time continues to slide forward, I pause and reflect at the night that reigns. But even as I do, I cannot help but picture the three burning candles of the Advent wreath that my religion class and I gathered around this morning. We sang "Adeste Fideles" in the original Latin (the little troopers gave their best shots) and "O Come O Come Emmanuel" and then we sang one of their favorites, "Silent Night," but I printed up lyrics for several of the stanzas and I added in a Spanish stanza for my Hispanic students and for the others to practice. And then I finished with the original verse that had been written in German.

They stood and listened with wide-eyed awe at the sound of the other language as it came from my mouth. I'm not the best singer in the world, but years of choir (including one Christmas when I sang "Stille Nacht") put me in a position to bring the carol to them in a meaningful way.

I was able to get students in a Newark High School to listen to me sing "Silent Night" in German, to appreciate it, to admire it, to ask me to sing it again... I don't know how many times I will experience moments like this in my life.

However many times it is, for now, I'm just going to sit back, grade papers, and enjoy the quiet of the Stille Nacht.

Monday, December 10, 2007

What I've learned in the interim

Sorry to all my loyal readers who've felt left out of my teaching experiences without my frequent reflections. I should be able to get back on some semblance of a normal routine now that progress reports are done and my planning and grading are caught up.

Since last writing, I've learned a few practical things: first, don't collect 120 journals all at once and then expect to read them all thoroughly in a brief amount of time; second, it is vain of a teacher to believe they've taught their students something after only once teaching it, especially when that something falls under the category of "modern political discussion material." Even if the issue under discussion is misunderstood in wider society and that is why it is discussed anyway, do not presume to think you can clear away the fog and lead people to understanding just like that. If people are already believing the world was created in 7 days, then simply telling them that Genesis is not a scientific description of the creation of the universe is not going to end the problem.

I've learned it's very easy to feel like a failure even when you're not. It's also easy to come out of that feeling so long as you have people around you who see the same thing you see and tell you that you're not a failure. Teaching is very much an art. Not that I think I'm a master, but even the great masters of painting and sculpture reviled some of their own greatest masterpieces even as the rest of humanity basked in their beauty. I've reflected before on the need to focus more on the big picture, but it is so hard to live beyond the immediate moment when the student will not behave, will not follow directions, will not be serious about a given situation, just wills not to comply. It is so hard.

I've also had the experience of dealing with the old cliche, "You can lead a horse to water, but you cannot make him drink." Last week, as I sat to prepare progress reports, I found myself facing the fact that one of the students in my home room had not handed in either a history journal (participation grade) or his religion journal (project grade). I sat him down after school and just put all the cards on the table and told him, "Look. You're failing almost beyond recovery for not handing in your work. The time to hand these things in has more than elapsed, but I'm going to break my own rule and let you take until this coming Monday [today, 12/10; the conversation happened on 12/5] to get these things done." He cried and thanked me for giving him the extra time. I saw a genuine desire to do better.

He didn't have his journals today. He "had a game to go to this weekend."

I put the zeros in my grade book right in front of him and let him watch his average change. He cried again, but this time I had no pity. I asked him, point blank, if he cared. His response was, "Of course I care!" and my response, flatly, was, "It certainly doesn't look like it, does it?" pointing to his averages.

When I was in high school, I was public enemy number one when it came to not handing in math homework. I would start out the semester doing it, but way would lead onto way and I'd get caught up in my other classes and I'd try to do my math homework but it would take me too long and I would rarely understand all of it until we had moved on to the next section - by which time it would be too late to do the old homework anyway since I now had new homework to do. So I just didn't do it.

I tried to put this student into that same mold, but in this student's case my class isn't math, it's history and religion. And the assignment isn't problems 1-49 every-other-odd, it's write a page worth of reflection on a given prompt that he is given time in class to write on (not to mention a great deal of time at home). The excuses I gave in my discussion of math homework were not sufficient then and are not now, but they explain why I didn't do it. For this student, I'm left with the conclusion that either he cannot do the work - and his general writing ability that I've seen does not reflect this - or he will not do the work. He "has a game to go to."

I told the student that, one way or another, he would learn from me before he left my class: either he would master my class's curriculum, or he would learn a very important life lesson. I didn't tell him that I had to learn a comparable life lesson in high school myself. I'm really hoping I don't have to teach him a lesson about failure, but then again, I suppose it's better he fail me now on a report card than he fail a job later and lose his house.
Since last post, I've aged a year further and I've come to realize that adults aren't really that much smarter than kids. I know adults that are much less intelligent than some of my students. The difference is in the experiences, the mistakes, the lessons learned. The great tragedy is that with all the brainpower that humans have, we're rarely smart enough to learn from the mistakes of others, especially from others who have authority over us. For someone like me, teaching is as much a Purgatory as it is a Paradise; every time I get on a student for not handing in work, I feel my inner voice getting on me for the same reason. I have no idea what to do about that, assuming it's even something that needs attention.

And that's what I've learned in the interim.

Thursday, November 29, 2007

How many Lights do you see?

Every morning, I arrive within five minutes of a quarter to 7 (6:45-6:50) unless the day is a non-routine day. There have not been many of those.

I appear at the back door to my school and peer into the inky blackness of the main hallway artery of the building, my own classroom door immediately inside to the right. There is a light switch on the inside immediately beside my room entrance. I turn the key and walk into the dark and reach for the first switch by the light of the streetlamps shining through the barred windows.

At the beginning of the year when I first did this, I didn't know what light swith controlled which set of lights. I have them all memorized now, yes, but the point is, I was always caught off guard, (mesmerized may be too strong a word) startled by which set of lights came on first. The thing is, with one switch, only two of the nine flourescent lights hum to life after I flip the switch (light #2 and light #7). The other seven activate with the other switch. There were times that I flipped the switch controlling the set of seven and thought I did not need to flip the switch controlling the other two because it's not necessarily easy to notice they're not on. Then again, what a surprise to flip the other switch first and have only random parts of the hallway light up.

I'm certain there is an engineering/electrical reason for this discrepancy in the hallway lights. It happens on the administrative hall as well. But whatever the reason, it made for interesting mornings way back when and it makes for good analogy now.

With one lesson - the correct one, mind you - I can turn on the minds of 78% of my students, give or take. But there remains that 22% that just don't come on with the first switch. Or, then again, sometimes I have that lesson where only roughly 22% get it. The other 78% of my students remain in the dark. A minimum two-pronged approach has been necessary for sometime and I suppose is always necessary seeing as how no student learns the same as another.

I wish teaching were as simple as the two-switch conundrum I face every morning to illumine my school's hallways. I like to read the little green sign that says simply "Christ the King Prep" on the glass door before I go into the morning darkness. I've taken to saying a little prayer, "Bring light to those in darkness, O Lord," as I flip the first switch. It's one of those fun moments where I get an immediate response to my prayer because light always floods the hall immediately afterward - though sometimes more light than other times. I used to never know whether I would get two lights or seven. Now I do, but I still have trouble guessing whether my 22% of my students will get it or 78% (or however many) when I teach a lesson. I come pretty close, but I'm always, somehow, surprised by somebody.

Teachers, by profession, bring light to darkness. This is why the abstract concept "scholarship" is normally represented by the "torch of knowledge" which itself is an abstract come to life. We cast away the darkness of ignorance, the darkness of evil, the darkness that creeps in and chokes good ideas and frightens those who have no defense against the bitter cold of inepitude. Teachers must do this daily, make the abstract concrete, make the untenable reachable... they must flip the switch and bring light to those in darkness.

I flipped my switch this morning and seven lights came on. I flipped it off because at that moment this post occured to me. I flipped on the second and stared at the two lights burning in the near darkness. I turned them off and then back on a couple times before finally turning them all on and then basking in the glow of the old, dirty flourescence.

I watch the lights come on... and I'm watching some lights go out. And unlike with real lights connected to real switches, I don't know what to do with some of my little lights that are flickering out on me. My poor little lights... my poor lights. How many... how many lights have to go out? How many Lights do I see?

Wednesday, November 21, 2007

Thanksgiving

"Know that the Lord is God. It is he who made us, and we are his; we are his people, the sheep of his pasture. Enter his gates with thanksgiving and his courts with praise; give thanks to him and praise his name. For the Lord is good and his love endures forever; his faithfulness continues through all generations." Psalm 100:3-5.

Today marks the nice little half day before Thanksgiving, and might I say, Thank God. I have so much to do this weekend -- relax is only a small fraction of it all, unfortunately. The school is almost empty; only the Admissions Director and I remain as one of my students has finally departed after a nice pre-next-Tuesday-test review session. Two classes took quizzes today. And the school's prayer service, while perhaps not as "revival" in spirit as what I had originally envisioned when I pictured what would take place, was a pleasant affair. The students were well-behaved, paid attention, and participated in the worship experience.

As a point of interest before I end my half-day post, many of you may remember my post regarding the Student Senate's first meeting with a quorum. Well, like the Italian government, the President has lost her command of a majority confidence in her legislature and the CTK Prep government has fallen after a majority of the student Senators failed at least one of their classes the first marking period. There was enough time for them to organize a food drive and carry it out. And then they fell. New elections of eligible students (meaning none who failed any of their classes) resulted in two of six seats being filled in two classes, five of six in another, and all six with a few to spare in another class. The Senate now has 15 seats filled out of a possible 24. Presidential elections will be next week and then we'll see how long this government lasts. Quorum obviously will be tougher to get, so the school may be facing an uphill battle. But those ejected for academic reasons now understand how serious the school is about academics. And those who remain, well, let's just say that I'm pleased with their hard work and attitude.

Now then, time for my four day weekend. Thank goodness.

Tuesday, November 20, 2007

Who Watches the Watcher?

Today I was observed in class for perhaps the 6th time this year, the third time by my Masters Program observer. Looking back to the first time I was observed, I must say, I was going into it with no small degree of trepidation. I had lain in bed the night before wondering what the next day would bring. I frequently reflect on what I do -- and what I fail to do -- so that I can spot my mistakes. And goodness knows I'm making them. I spot them constantly. And lest, gentle reader, you think me overly scrupulous, I am, after all, a novice. However much "presence" or "poise" or natural instinct I may have, I have made mistakes on a nearly daily basis since the beginning of the year. They are certainly little ones, but I had always assumed that if a neutral & objective outsider were to enter my class, I would get called on the carpet for them.

"Like what?" you may ask? Well, I sometimes speak with my back to the class at the chalkboard. Never for longer than a few words, but anybody with any knowledge of education (or theater, and trust me, there's little difference) knows you don't turn your back. I have tried to compensate by keeping the students on their toes, the seating positions in the room, and so forth, but I'm supposed to always be watching. And I am sometimes not.

Then there are the times when I overreact. A student gets out of their seat for the 800th time without permission. And it was just to go to the trash can. And I kick them out. What did they do? Was that the best way to handle it? And me losing my temper, well, I don't blow my top over just any little thing. But I have. And I do. The virtue "temperance", meaning to moderate our activities and emotions, gives us the phrase, "to lose one's temper." For if you lose it, you lose your rational control over your emotions. Indeed, one could become inconsolably sad and be said to have lost one's "temper," though it is hardly if ever used in that context in English. I have seen it in myself and I have tried to work on it. But that doesn't mean it doesn't happen.

Lest I make this my public confessional - my Confessor gets that enough already - I digress. My observations have instead tended to focus on the "big things" about me, rather than the "little things" already mentioned. They remark on my professional style of dress, of speech, etc. They mention my organization and preparation skills. They comment on how much the students respond to me, how they obey me, how they laugh with me, how they respond eagerly to my questions. They comment on how clean my room is. They point out how wise I am to begin my class with a quote and how much that must assuredly encourage the critical thinking I so hope to engender in my students. They tell me I'm aware of everything that is going on in my classroom. They give me applause and comments such as, "You would never know it's his first year."

They give me the big picture.

And, without realizing it, they give me an important criticism that I had not before today really noticed. I focus so much on details. It's my nature. In a very real sense, it's my job. It's what I received my first M.A. in (International Relations) since the social sciences are so dependent on details to make valid points. I have an undergrad minor in Economics. I am OBSESSED with the pieces that make up the puzzle almost to the point that I forget the big picture that I'm supposed to have when it's all said and done. (And before you think I'm better at Micro, I prefer MacroEconomics... but my micro-management style bleeds into my studies there, too)

I get upset that I lose my temper with a student (as well I should), but the other students who witness it are now more likely to tote the line. I obsess over the fact that my back is to my class, but my students are learning the material. My kids have terrible reading comprehension, but it's tenfold better in some cases than it was when they first met me. They're learning to think, to write, to speak, and I'm upset that they haven't mastered the English language? My mother used to tell me on a daily basis, "Don't sweat the small stuff." I do anyway. But I'm quickly figuring out that sweating small stuff only uses up the energy that could be spent on big stuff.

I am, by profession, a Watcher. I watch the time. I watch students. I watch TV. I watch (read) books. I plan so that I can watch some more. I watch others for signs of growth, for signs of deviousness, for signs of gum chewing, for signs of sincerity... I watch for triumph so I can praise it. And I watch for failure so that I can correct it. And I watch myself with the same "watchful" eye.

It's good to know that when I'm being watched, the person(s) doing the watching likes what they're watching. And not only that, they're watching what really matters about me. My students should be so lucky to have me watching them with the same macro-vision eye. If others can see that big picture in me, well, that might be a lesson to me that even the "Watcher" still has some things, some good things, to watch for -- not just in himself, but in his students as well.