Sleepy at the Bat

When people can't sleep, they'll do all sorts of things,
from counting sheep to tossing on springs.

The cure for insomnia is a routine that works.
It may involve dancing, or singing, or various quirks.

For me it's imagining I'm in a game,
on a mound with a ball. On my back is my name.

There's a guy at the plate with a thick piece of Ash,
And with it he hopes, the ball he will bash.

I throw a first pitch coming straight down the pike,
It flies past the batter for a called first strike.

Ahead in the count, I'll catch him off guard,
I'll wind up really big, but won't throw that hard.

The change-up caused a swing ahead of the ball.
It pulled left of third, into the stands for a foul call.

Ahead 0 and 2, I can mess with him a little,
maybe throw him a curve or a ball with some spittle.

Towards home, the ball curves with a twist of the wrist.
The batter stands still. The strike zone is missed.

A good eye on the batter. The ball was a bit wide.
It was a near perfect pitch that just missed outside.

On a 1-2 pitch, a strike can wait.
I don't have to throw something over the plate.

I can slide it away and make him chase it a bit
so he'll swing and miss and won't get a hit.

So that's what I throw, but he doesn't take the bait.
I wish I had that one back, but now it's too late.

2 balls and 2 strikes, the count is all even.
Just one more strike, and from the plate he'll be leavin'.

He'll be defending the plate on this very next throw,
so I'll try to put the ball inside and low.

My forkball is heading right where I want it.
The batter lays off as it enters the mit.

The ball was right there, it should be strike three,
but the ump doesn't see it quite as I see.

And there's no use in entering an objection or plea.
The ump wouldn't listen to a player like me.

So I live with the fact that the count is all full,
and that the umpire's eyes are covered with wool.

The very next pitch is the one for the money.
If the batter strikes out, he won't think that it's funny.

I figure the heater's the best way to end it,
and allow the poor batter to go have a sit.

So I go through my windup and lift my leg high,
and say to myself, "Adios batter. Bye, Bye!"

As the ball rifles home, the batter starts to cock.
I can tell from his stance, he's not chancing a walk.

He swings at the ball with all of his might,
and soon the ball is clear out of sight.

Back behind home plate and into the stands,
In some fan's popcorn, the ball finally lands.

The batter's still alive with his spell of good luck,
and the fans are getting more bang for their buck.

But I have no intention of this lasting much longer,
as my will for a K grows stronger and stronger.

One final pitch is all it should take,
for the chance for this stalemate to finally break.

A final fast ball in the perfect location,
with an exaggerated wind-up to break his concentration.

I'll throw it a hundred so he won't have a chance.
He'd be stuck in his boots in his 3-2 stance.

So I fire the ball to the plate on a bead,
and as it approaches, it picks up more speed.

This last pitch will end this, there is no doubt,
But just before he swings for strike three . . . .I'm out.

zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

Happy Little Halloween Project

Each Halloween, I assign a fun math project (fun in the sense that it doesn't involve math), whereby students get chance to creatively express themselves. Some jump at the chance to show an artistic side of themselves that they don't always get to show in a math class, while others don't bother jumping at all. Still others barely move, griping, "Do we haaaaaaaave to do this?" "Of course not!" I chime. "You could take a free zero instead! What a bargain."

The mathematicians and other math students have two weeks to either write a spooky, mathematical tale using at least 20 math terms, such as "infinity," "indeterminable," "function," and "WRONG ANSWER." The terms don't even have to be used in a mathematical sense, but must be relevant to their story. To avoid long, banal, digressions, and to support concise, cogent efforts, I limit students to one double-spaced, typed page. This instruction is designed to keep the number of single spaced, handwritten stories to the teens.

Some students go out of their way to honor my rule, using large 24 point font, triple-spaced, half-page. Their stories are seldom entertaining, witty, clever, or stories at all. For these efforts, their percentage grade usually matches the proportion of the paper their refuse takes up, with additional deductions for wasting ink and paper.

Every year, I feel fortunate if I get one story that is memorable (and I'm not talking about stories where "the evil Korpi zombie" dies, gets "kicked in the transcendentals" or screams "mother function" at his students.) The true works of art weave a creepy, suspenseful tale of mathematical mastery, filled with puns, allusions, and the classic twisted, unsuspected ending. These gems make the project worthwhile for me.

So what if a math student doesn't feel like he is a Stephen Hawking King and can't express his morbid, menacing, mathematical musings in words? Well, for the M.C. Eshers in my class, I also give students the option of drawing a Halloween scene on a quarter-sheet of poster board, with at least 17 hidden mathematical symbols in the picture and a "solution key" on the back. These are also fun to receive. Fist of all, you would be AMAZED at how many different sizes standard poster board comes in and how creatively a student can take "one-fourth" of it, especially if they are frantically searching around in their locker for one the morning it is due.

I've had projects turned in on standard notebook paper, full-sized poster boards, and 3 by 5 inch note cards. I've had some that were colored, I've had some that were not colored, and I've had some printed out on a computer, then taped to poster board. Very few of them actually meet the criteria, and those that do get LOTS of extra credit.

Then there is the hidden symbol aspect. Well, if they can't cut a poster board into fourths, how adept do imagine they are at "hiding" math symbols? You are correct--they CAN'T! Some are successful and masking a handful of symbols (the infinity symbol works well for ghoulish eyes), but I can tell exactly when the novelty of the project wore off and they were ready to move on to watching the shiny blinking lights for a while. It's like a bagful of math symbols spilled out onto their drawing, falling where the may. SOME students, however, are so adroit at concealing their symbols that I cannot see ANY of them. These are the same individuals who also conceal their ENTIRE drawing, turning in a blank, or "invisible" as THEY claim, paper. If only they put as much creativity into their project as they do in making up excuses for their lack of project, they'd be on their way to valedictorian!

The day the projects are due, which is usually the day of or before Halloween itself, we spend the entire class period presenting both the stories and the illustrations. Students get an opportunity to show off their masterpieces to their peers, proudly heralding their mathematical innovativeness and artistic genius, creating an ambiance of sheer terror and horror as they masterfully work their way through the delivery. No one ever achieves this, but they do it for the free candy I give them for presenting.

In the past, I have even turned off all the lights in the room, put spooky sound effects on, and had students deliver their message via a flashlight under their chin. Apparently, I was the only one who got a kick of the whole thing. Unable to coax presenters with candy, or even with the threat of starting a new math lesson, I gave up this format. Now, a few brave souls stand up, say "This is my drawing of some pumpkins. The eyes are triangles, and there is an infinity symbol here for the ghost's eyes. Can I have a Snicker's bar please?"

If life-threatening is scary, and scary is good, then the best picture project I ever received was the first year I did the project. That year, not envisioning the variety of interpretations the students would have on the project, I failed to ask the students to keep their stories clean and their pictures tame. I got plenty of stories with foul slang and inappropriate subject matter, but the most frightening picture I have ever received to this day came from an unassuming little girl who was in the exchange student program from the Netherlands. Apparently, the Dutch embrace the horrific as commonplace and benign. I was drawn in a bloody mess in front of my chalkboard (which contained all but one of her "hidden" symbols) with a hideous monster" holding my head in one hand while shooting the "bird" with his other hand. The picture also shows my lifeless bloody body falling limply to the floor, and my "Teacher of the Month" shirt is covered with my entrails. She entitled the picture: "The Precal Monster Strikes Again!" (photo at top of this entry. Click it to enlarge and to see the hideous details.) I was shocked, scared, and really scared. She told me that she actually LIKED math! I gave her a 100 on her project (I was afraid NOT to.) I kept the picture as evidence in case anything was to later happen to me. The little girl was soon after deported back to the Netherlands for an unrelated incident. I wonder if it had anything to do with her history project--she told me she HATED history. By the way, her Monster's eyes were the infinity symbol.

Since that time, I have given more explicit instructions and guidelines for the projects. I still don't mind being the bad guy in the stories, but you aren't allowed to "gouge out my eyes anymore with a circle compass." Although the new parameters and limitations make for tamer stories and drawings, I still enjoy doing the project, because I DO get a chance to see a different side of students' abilities. I have a small collection of the best ones stashed in my filing cabinet (next to "E" for "Evidence.) I think the best part about it is encouraging students to present their creations, which gives me a chance to give away all my old leftover candy from Halloween the year before.

Who says that Snicker's bars aren't better with age. Those who can't determine what a quarter sheet of poster board sure aren't going to disagree (or even notice.)

Muuuhaaahaaa!

A nice night for an evening

This past Saturday I attended the Lonestar Emmy Awards in Dallas. Nominated with two other programs in the Instructional/Informational category, my wife and I got all gussied up, dressed to then nines to look our best with all the news celebrities who would be all around us.

The lady to my left at our banquet table of 12 was a very cordial, amicable field reporter from an Austin network. She was not only up for an Emmy herself for a spot she did on a controversial court case with an unpopular verdict (just listening to her talk about it really made me wish I had seen her two minute piece in the name of justice), but she was also chosen to be a presenter. Knowing it was my first time, and being a little prescient perhaps, she was wanted to impress upon the fact that nobody "wins" the Emmy, we're ALL winners. One can only be "AWARDED" the Emmy. She never offered a phrase for those nominees who are NOT "awarded" the Emmy. If they didn't LOSE, were they just out-awarded?

Whatever you call this 2nd-tier class of nominees, I am now proudly a member of its club--meaning I was "out-awarded" in my category.

The evening started out with the usual apprehension that goes with me wearing a tie, but after we sat and met the people at our table (lucky table number 7), we became relaxed and began enjoying our salads. Then came our main course: expensive little meat thingies that resembled small sirloins. Apparently the more expensive a piece of meat (our tickets were $110 each), the less it is supposed to be cooked. My wife's meat thingie was so red, it could have been wearing a bell (and she's a well-done type of lady)! I'm more inspired by frugality and value, rather than my concerned for taste or acquiring some disease, so I ate all of mine. I thought it would be inappropriate to eat off her plate, so I sadly watched 6 cubic inches and $45 of meat thingie leave the table with the table attendant. Determined not to let this happen again, I showed less concern for Emmy etiquette when it came time for dessert. I'm not a big fan of custard (especially of Flan!), but I'll eat anything if I've paid for it, especially if I've paid too much for it.

So two Flan tower desserts later, I'm done with dinner and ready to receive my Emmy. As the program works slowly toward my category, I'm really not listening very carefully to the self-applauding comments of the celebrity presenters or the the mandated 15 second or less acceptant speeches; I was refining my speech in my mind, trying to trim it down to 15 seconds and make it so memorable that they'd have to give me another Emmy for my acceptance speech performance. I had the opening down, "Four score and twenty days ago . . .", I knew I'd mention math in there somewhere, acknowledge educators in general, thank my wonderful, beautiful wife, all while looking deserving, yet humble.

For the category immediately preceding mine, a new group of presenters emerged: a group of high-school students who won last year for a student production. I thought, "Great! High School students! I TEACH high school--what a great omen!! Come on lucky table number 7!" Then something unexpected happened. After awarding the Emmy, they announced there was another "winner" from that category (which means now that the graph of Emmy winners per category would fail the vertical-line test for functionality.) After the second "winner," they announced that the third and final nominee in that category would ALSO be receiving an Emmy! Wow! No losers! A perfect 3 for 3 in that category. Everything was crescendoing in my favor.

As they announced my show in the next category, they projected the name on the giant, huge, enormous screen for all to see. My wife had been waiting to capture it on digital film for posterity, when some Bozo stood up right as she snapped the photo. Darn the luck.

The tension was building. The students fumbled with the sealed card with the winner's name concealed. They began to read nervously. " . . . and the Emmy goes to" (I began to push my chair out from the table, swallowed hard, and "Here's to your Health." I coughed hard, and pretended to scratch my nose as I wiped what I felt was a small tear of disappointment developing in my eye. Everyone at the table looked over at me like I was an orphaned puppy with sounds of "aaaawwwwwwwwwwwww."

BUT, there was still hope! The last category had multiple winners, perhaps this was a new trend. I didn't hear a word of the acceptance speech for the show that out-awarded me, although I found my hands clapping reflexively. The spotlight soon shifted back to the high-school student presenters. I eagerly anticipate the next sound they would utter . . . . . .

"The next categor. . . . . . I heard no more. My heart sank, my shoulders dropped, I chugged the the last bit of water in my goblet. My wife put her gentle hand on my back and asked, "Are you alright?" "Yes," I lied.

Throughout the rest of the evening, I slowly got back into the celebratory mood, feigning interest in the winners in the other categories. The man next to my wife reassured me that the two other shows in my category were giant, huge, enormous markets with giant, huge, enormous budgets. It was remarkable that I could, with just a side project and a potential viewership of 40 thousand, compete with full-time professionals with markets of 4 million viewers. That really put it into perspective for me. I decided I would let the Academy's spurn spur me on to work harder on my current project, and if I ever had another opportunity, I'd go in with different expectation.

As of now, I am very grateful for the experience and the privilege of attending an exclusive function as an initiate. Being competitive and too hard on myself are character flaws that are both gifts and curses. Learning to deal with disappointment is something I don't really ever want to get good at, because that would require a lot of practice, but I think I'm slowly learning to move past them more quickly. My 7-year-old son said it best when I called him on the phone shortly after the announcement: "DAD!!! Second Place is AWESOME!!!" He's sooooo right. Thanks, buddy!

The one thing that is still troubling me, though, is not why I didn't win, but how I could have let that raw piece of expensive steak on my wife's plate go to waste. That will take a bit longer to get over.

TBA (Teaching By Acronym)

Education abroad is like education in Texas
And its policies affect young and old of both sexes.

The field is dominated by theory after theory
and keeping up with them all can make one quite weary.

To help remember these intellectual gems
The theorists and bureaucrats have developed clever acronyms

like TABS and TEAMS and TAAS and TAKS
which all stand for "Texas" something or other (and are more opinions than facts.)

And every few years, a new one replaces the old
that encompasses newer theories and is more improved, so we're told.

"Project this" and "Project that", the waters become so clouded
that teachers trying to implement them become dumbfounded.

The problem is that there are too many people who just don't get it.
They don't want to really solve anything, they just want the credit.

The tide of these philosophies go in and go out.
Old ideas with new self-promoting advocates get a chance to re-sprout.

The power is taken away from the dedicated teacher
who teaches ahead of the standards and gets results (and doesn't need it thrown at him by a pandering preacher)

Those theories are no more than flimsy political stances
by a politician who is trying to better his reelection chances.

But this is the way it has always been done.
And in my opinion, I'd rather have none.

Just give me a classroom and a room full of kids
whether they're rich and bratty or are kids on the skids,

and I'll teach all the things the acronyms contain,
but please, please spare me the obvious and mundane.

It's no wonder that the supply of good teachers is dearth
(besides the fact they don't get paid near what they're worth)

It's all the silly nonsense, red tape, and big hoops
that are put into place by self-serving groups

that leave you jaded and drain your enthusiasm like a leach
Instead of just letting qualified, conscientious, creative, energetic, professional teachers teach!

Mum's the Word

I'm often asked why I don't teach at the University level. My first reply is always, "I don't have an advanced degree." My second reply is, "It would take more gas to get to campus than it currently does," and my final reply (they usually ask me for 3 main reasons, go figure!) is usually much more discursive and personal.

Here's reason number 3. It's because . . . . .

I love the atmosphere of high school. The young, impressionable, teenage students are so unique--their habits and rashness, their awkwardness, their fearlessness and risk-taking, their naiveté and hyperbolic sense of the world. The drama of a high school corridor is always entertaining, with different sagas being told behind impish giggles, gaping incredulity, or with malicious malcontent. The diversions, hijinks, and antics of teenagers always awakens a comical sense of theater in me. Each passing event is a dire emergency for the students involve.

If our school had a daily paper published by students, matters of "who's going out with who?" or "Who did WHAT last night at Starbucks?!" or "I am SO not ready for this Algebra Test!" or "Did you see what's on so-and-so's MySpace page!?" to "Can you believe what happened last night on Grey's Anatomy!?" would front page news . Oh, the timeless, gawky, beautiful dance of youth!

Drama is never greater on campus than during homecoming week, with the dress up theme days throughout the week and the jingling, jangling sounds and fragrant smell of mums on Friday, the day of the big district homecoming game. What's made the energy level greater than usual today, other than the fact that I'm back at school from my day off, is that both teams in tonight's football game are undefeated at 7-0. Now I know homecoming games are chosen at the beginning of the season, and are ideally chosen so that a victory is all but guaranteed (losing the game tends to be a bit of a downer to everyone except the happy King and Queen who get to wear a large, silly crown and pose for the real paper), but I don't think anyone envisioned tonight's game would be a clash of district titans. There is much at stake tonight for our team's confidence and playoff aspirations. Go team!

So you see, I never think I would make the jump to the University level, because I'd be losing the intensely entertaining sub-culture of the high school histrionics, a culture that mirrors my own personality and tastes. Even if I ever DID finish my Master's degree and earn a Ph.D. in mathematics (which IS a personal yearning), I'd still teach right here at the high school level. I have always thought it would sound kind of neat to hear a giddy student ask me, "Dr. Mr. Honorable Kevin Korpi, Ph.D. Sir, would you mind dressing up in drag and dancing the Macarena at the pep-rally this Friday?"

I've got my prepared response: "I'd be happy to! I'll do anything to help pep up the dance of youth. Should I bring my own pumps?"

Doctor Daddy

Yesterday I wrote about missing my first math club meeting as its sponsor. Today I get to write about missing my first day of school this year. Tomorrow my ship is scheduled to set sail. I'm beginning to wonder if I'll be missing that (just a metaphor, I'm not taking to the high seas anytime soon.)

Last night, for the first time since our children were infants rising to feed every two hours, I was waking up every 1.523 hours (that's every hour, thirty one minutes, and 22.8 seconds--approximately, of course) thanks to my daughter's body's desire to regurgitate its stomach contents--in OUR bed. It was like beautiful clockwork. And by beautiful, I mean abhorrent.

She was always kind enough to give us an unintentional warning. She'd start moaning and whining. Then she'd start yelling "trash can, trash can, trash c-aaaaaaaaaa-bllaaaaaaah-aaaaaaaa-bbllaaaaaaah" *cough* We were always able to catch SOME of it, namely the two subsequent episodes that shortly followed.

After her third fulmination of Kraft's finest macaroni dinner, she'd settle down, we'd clean her up, change the sheets, and take out the liners in the trash can. Then we'd all lay down for another nice, uninterrupted 1.523 hours of sleep, not including the actual time it takes to fall BACK asleep, which for me is around 1.513 hours, give or take 0.01 hours.

It is really hard for me to see my "Beautiful Sweet Sunshine Angel Baby Pink and Purple Punky Princess Muffin Cakes" be in so much agony. I kept thinking that if only it were her BROTHER that were sick instead of her. Just kidding, it's just as hard for me when he's the one crying like a little girl, perhaps even much, much harder.

No, if someone's got to be sick in the family, I'd like it to be me, although my wife would gladly step in for me, since she claims I'm the biggest baby of them all. It's really the thought that counts, though. I mean, we can't actually get sick in someone's place. But we certainly MAY get our turn.

Which brings me back to what I might be missing tomorrow . . . So far, I'm still feeling just fine, and my little patient seems to be doing much better as well. It's probably because I make such a great can of Campbell's Chicken Noodle Soup and the extra doses of medicine I "prescribe" to her take to her body like someone much older and heavier. I don't think those three Barbie videos we watched hurt her any, either.

I really do hate missing school. It's almost more work getting things ready for a substitute, and even harder finding one that can teach upper-level mathematics (too bad the math doesn't just teach itself), not to mention being up at school at the ghostly hour of 4:30am when the school is empty, the lights are off, and there's no one to come help me with the paper jam in the photocopier.

Nonetheless, my daughter and I had such a silly, good time today; it was a very nice, unplanned, fortuitous quarantine. If laughter is the best medicine, then my fortunate daughter shouldn't get sick again this year, and I'm inoculated at least through the weekend. Yep, Dad is the MAN!

I should probably go check on her pretty soon, though. That Barbie double feature is bound to be over by now.

First Time For Everything

I turned over a new leaf this morning, not intentionally, though: I missed my first Math Club meeting as its sponsor/co-sponsor. In the nine years that I have been the faculty member of record for the club, I have never missed a meeting. These included "wild" toga parties at 7:30 in the evening, "crazy" white elephant gift exchanges late in the evening, a meeting a a student's house WAY out in the boonies (although late, I DID make it), and several early morning 6:30 am meetings here on campus. I must have attended at least a hundred meetings in succession, but the streak ends today.

I think my work is finally catching up with me. Having come in a bit early today (5:30am), my wife agreed to fill in for me today in my role of dropping off my kids at her mom's. I thought I'd have plenty of quiet time to catch up, but I'm usually wrong on these things, as an overly-inquisitive student, with nothing more to do that meander around my room and ask me non-mathematical, non-educational, nonsensical questions in a tiny voice. I must have answered, "The math club meeting starts at 6:30 this morning" 5 times . . . . . . per minute!

All this is going on while I'm trying to fine tune my Algebra II show that I have to film today after school. It's the big Halloween episode, a real audience pleaser, if you consider two viewers and audience. Today I'm dressing as a pirate, and doing the entire show in character, including the voice. I was scrambling this morning for some funny (clean) pirate expressions, jokes, names, etc. while frantically searching for an appropriate pirate-themed background for my green-screen shot.

Checking my email, I see a message from a former student with a subject of "mathematical emergency," he knew how to get my attention. I've been preparing my whole life to handle something like this. I opened up the email to discover that he has a major project due today and has no idea how to start. Either he was as busy as I was, or he was a prodigious procrastinator. Nonetheless, I decided to drop everything and help--for the sake of the problem and my peace of mind, not the student's. Anyway, his project was a giant word problem he had to read, extract the relevant information, solve the problem at hand, and write a solution in mathematical and layman's terms. My interest was piqued.

After brooding over the problem, I had the insight, and the solution, which involved calculus and optimization, flowed easily from there. As I scanned in a very partial solution, a hint if you will, to send to the student, I found myself muttering without realizing it, "the math club meeting starts this morning at 6:30am." I sent the hint to the student and got back to my pirate affairs.

As of now, it's almost 7:00 and the math club meeting is happening as I type . . . . . . . . . in fact a student from the meeting just came in form some math help, so I guess it is over.

Oh well, there's always next month's meeting, which "will begin at 6:30am."

Less than or equal to 1000 uses for an Emmy

This Saturday evening is the big Lonestar Emmy Award Ceremony in Dallas. My wife and I are attending the formal event as the sole representatives of "That Geometry Show," which got the nod in the "Educational/Instructional/Shows nobody watches" category. Although we are excited about attending, there will be a small issue regarding where to sit. Most TV networks will have undoubtedly reserved entire tables for producers, executive producers, executive vice-producers, assistant executive vice-producers, etc. As the only representatives of our district, not that we HAVE an assistant executive vice-producer, although my son Tate proudly wears the moniker of "best boy," we will have to either squeeze in a table between Randy Beamer and Ursula Pari (husband and wife newscasters from San Antonio), or we will be cast into the singleton section in the back corner of the hall behind the men's restroom. It's sure to be a very comfortable evening, made increasingly so by the tuxedo I'll be wearing.

But then there is the good possibility that I actually WIN the Emmy in my category (I hope they don't announce it while I'm in the men's room or sleeping. I hope they DO in fact announce it at all, and that it's NOT one of those categories that they deemed was not important and either did the day before in the lobby of some cheap Hotel 6 or got rid of altogether in the sake of saving time. In the event that they DO announce it while I'm there, and that I AM the winner, and I'm NOT in the men's room, I've already thought about who I would thank: the usual suspects with some random, esoteric references just to appear "Jack Nicholson-esque."

What's really been on my mind is what to do with the trophy AFTER I win it. Here's what's been running around in my head.

• Offer it to one of the other nominees in the category as a humble act of shameless modesty and humility, then at the last minute say . . . . . . . . . "Psyyyyyyyyy-ch"
  
• Put it in my classroom at school next to my certificate for Phase II technology proficiency at my school district.
• Use it as a paperweight on my school desk. I have two fans going at all times, and I'm always looking for something that will help my papers stay in place.
  
• Hold it in my hand forever. Left had for trophy, right had for chalk, grading pen, pumping fist, etc.
• Attach a chain to it and wear it around my neck as Bling.
  
• Put it in the trophy case at school next to the 1976 bi-district 4A football champion trophy.
• Display it in the front office at school next to the peppermint candy bowl. I think this would set the tone for any visitors at our school--programming excellence and fresh breath.
• Keep it at my parents house on their shelf next to all my little league trophies. After all, they WERE the ones who tripled the viewership by having the show on in every room of their house.
• Keep it in the basement studio where I film the show. The lack of light and atmosphere would guarantee its preservation. The producer lives there, too, so she'd keep a close eye on it. I also think she'd polish it up regularly for me.
• Display it downtown at our district offices at the receptionist's desk. Here in the dimly lit entryway, it would surely go unnoticed as it collected dust. But a small sign COULD be hung from it saying "Complimentary peppermint candies. Please take one!"
• Auction it off at a school-related function to raise money for a worthy cause, like Communities in School, Project Literacy, Head Start, or the Korpi Checking Account.
  
• Keep it at home in the kid's play room next to their action figures and Barbie dolls. I kind of think the trophy would look cute dressed in bikini bathing suit riding "My Little Pony" to a beach party with "Strawberry Shortcake."

And finally

• Put it at home in my dedicated trophy room on a pedestal in a glass case next to the empty pedestals where my anticipated Oscar and Nobel Peace prize will soon go (Hey, that seems to be the trend right now.)

Wish me luck! I'm going to need it if I expect to sit at Randy Beamer's table!

God and Math

I recently came across a calculus course syllabus for the Castle Hills Baptist School in San Antonio, Texas (my own backyard!) It states the following:



Students will examine the nature of God as they progress in their understanding of mathematics. Students will understand the absolute consistency of mathematical principles and know that God was the inventor of that consistency. Mathematical study will result in a greater appreciation of God and His works in creation. The students will understand the basic ideas of both differential and integral calculus and its importance and historical applications. The students will recognize that God created our minds to be able to see that the universe can be calculated by mental methods.


Gustave Flaubert once quipped, "Le bon Dieu est dans le detail," In the same spirit as Luther's "sola fida" interpretation of the Romans 3:20-28 in the St. Jerome's Vulgate, this aphorism now apparently translates two different ways into our English language: "God is in the details" or "God is in my calculus class." As a calculus teacher, I have to admit that I'm kind of intrigued with the class described above, and I am actually of the opinion that the beauty and utility of math give evidence of some divine creator.

Although I could never get away with teaching my calculus class from this angle in public school, nor would I necessarily want to, I respect the private school for approaching the study of this beautiful mega-structure we call mathematics from this perspective. Here's why.

If you studies the history of mathematics, you might find yourself falling asleep repeatedly, but if you manage to stay awake, you will discover that there has always been a close connection between brilliant mathematicians, mysticism, and religion/theology.

The Pythagoreans, led by their fearless leader, Mr. P, believed in the divinity of numbers so much that their entire existence was based on the trenchant tenet that "all was number," and by number, they meant rational number. They believed that the world was created in such a way that everything was in perfect harmony with each other, or mathematically, that measurements of natural objects always were in a perfect integer ratio to each other. For example, the perfect toga wrap was exactly 1.5 times longer than it was wide, or in a perfect ratio of 3:2. Unfortunately for them, by their discovery of one of the greatest mathematical relations of all time, the theorem bearing their name, actually tore at the very rudimentary fabric of their entire belief system. When the unit square was looked at, they discovered that the diagonal was the irrational number, the square root of 2, which CANNOT be expressed as a ratio of two integers. Consequently, they were the first group to collectively exclaim the word, "CRAP!" in unison. As any good secret mathematical cult would naturally do, they tried to keep a tied lid on the square root of 2, denying its existence. But . . . . you cannot keep a good number down, and it eventually got out to the public. The Pythagoreans quickly crumbled and were ridiculed by all the populace proletariat. To make themselves feel better and perhaps show the public that they weren't just toga-wearing, wimpy, shallow, superficial math geeks, they murdered the mole who leaked the truth, after which, they went to confession and took up croquet.

Even Gottfied Leibniz, a Lutheran Deist and one of the co-founders of calculus along with Newton the Great, had a small following of religious math fanatics with big hair. He built an entire binary theology based on the numbers 0 and 1, where 0 represented the null (Satan) and 1 represented the infinite (God). A less popular tenet in his mathematical dogma was that the 5.5 represented "Bimbo" the clown.

The great Leonhard Euler, the most prolific mathematician in the history of prolific mathematicians, discovered a beautiful equation that, to this day, many argue is a concise, teleological proof of God's existence: e^(pi*i)+1=0. This beautiful equation is not only true, but it contains the 5 basic, ubiquitousness numbers in mathematics. And WHO invented this consistency?????? "God was the inventor of that consistency," Euler only "uncovered" or "discovered" it.

Even Newton, has intimate ties to religion and theology. Born prematurely in Christmas Day in 1642, sharing a birthday with another famous, influential man in history, Newton survived his entry into this world against the odds. Being so tiny, his mother purportedly kept him in a small cooking pot as an incubator. Some observers believed that Newton thought himself to be divinely inspired. This is a polite way to say he had a "God complex." But who can blame him? He had a relevant birthday, he was amazingly brilliant (pardon the extreme understatement.) A scribbled note on the bottom of one of his math papers is a translation of an anagram of his name: "Isaacus Neutonus--Jeova sanctus unas" or "God's holy one!" Throughout his career he spent much of his time writing about theology, church history, and labored over a meticulous exegesis of the Bible, leaving behind 4 million words on the subject. He was probably a teleologician, believing that the nature and design of mathematics and the natural world itself gives proof of God. He spent his entire life trying to find the Divine Creator of the universe, and even mused on his deathbed that he was "but a little boy, playing on the sea-shore, and diverting myself, in now and then finding a smooth pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."

So whether you do or don't believe in the divine manifestation of mathematics or whether you agree or disagree with the curriculum at a private, Christian school, if you wake up and do the research then wake up again, you will see that history is replete with unconventional ideas and viewpoints, which although unpopular if not blasphemous at the time, are part of our mainstream accepted beliefs today.

Preach on, mathematicians!!

2 Quarter Limit

I once took a coin, a quarter that is

And added to it another half a coin

This totaled thirty-seven cents

And a half (when they were joined)

But I wasn’t content

With such and odd amount

So I added another half of a half

And started to count

“One plus a half plus a fourth

is 43 and three-fourths cents.”

So now with 1 and ¾ quarters

I proceeded to commence

So I added a half of a half of a half

(Another eighth of a coin)

Plus half of that is a sixteenth

And all these halves I did join.

I kept adding more and more halves

Of the previous amount

Thinking I was amassing

And enormous bank account

But as I kept counting

My head grew quite numb

And I began to think

My method was dumb.

For although my money kept growing

It grew more and more slowly

The amount I was adding

Was more and more lowly

My sum grew closer and closer

To a mere fifty cents

That only two quarters!!

It didn’t make any sense.

So, to that first coin, there’s no limit

To the halves you can add, it is true.

But there is a limit to the total of coins,

And, precisely, that limit is two!

So many, many halves makes two quarters

But two quarters is exactly a half

This strange and puzzling truth

Can only make you scratch your head and laugh.

Rhyme Time

I got a lot of feedback on yesterday's poem, mostly of the "it didn't rhyme" variety. I congratulate everyone's powers of perception. Not ALL poems have to rhyme, they don't even need to have form, although I'll admit they really lose interest as they get increasingly "original." I actually prefer rhyming poems, just ask my wife, who's been fortunate enough to get a "Korpi" original the last 10 years on our wedding anniversary (she just wants flowers, but flowers don't rhyme, so she still gets a compilation of limericks and ab-cb rhyme schemes.)

I'm a HUGE fan of rhyming poets like Ogden Nash, Shel Silverstein, and Doctor Seuss--those guys were/are lyrical geniuses. Their poems were playful, light-hearted AND poignant, so the rhyme-type poem was a perfect vehicle for them (although Wordsworth and Keats managed to pull off their serious tone in perfect rhyme.) Other serious, more dry, poets like Goethe, Whitman, and Maya Angelou mostly stay away from the rhyme and from the whimsical tone.

Yesterday, I was in a serious, reflective mood, brooding over my role at preparing students for life beyond school, often against the support of the students and their parents who tend to focus on the here and now, and who question my methods. It was a very purgative. Today, I'm feeling more playful and mischievous. So here's a "rhymer." Call it, "Ode to Joe."

Coffee is a dear part of my life,
even though it is bad for my spleen.
The start of each and every one of my days,
requires a high intake of caffeine.

Just one cup a day is all that I need,
If indeed it's a big enough mug.
No sugar, no creamer, and no fancy blend,
The blacker--the better the drug.

Some tell me to cut back, I'm drinking too much,
That I've got to curtail my addiction.
But I see it quite different, as a matter of fact,
I believe its a salubrious affliction.

Without it I can't even manage to think,
And the headache I get is severe.
But just one sip of the dark warm, elixir,
and my head and my mind are all clear.

It's even been said of mathematical folks,
That we transform the caffeinated serum,
from a hot, steaming cup of black Java,
into an abstruse mathematical theorem.

This much I can tell you is true,
That it helps me to think much more deeply.
But as much of it as I drink daily,
It's not a price that really comes cheaply.

But it's definitely worth the high price,
I'm not throwing money away,
'cause it's all that I have in the morning,
My breakfast's a coffee buffet.

When I'm alone in my room each new morning,
I relish the quiet time alone,
with just me and my theorems and coffee,
I'm in my mathematical zone.

The small warming sips from the rim of my mug,
Fill me with quiet assurance.
For I know when the students finally arrive,
It'll give me the proper endurance.

Who cares if it makes my breath stinky and foul,
It's nothing some gum can't repair!
Besides, it is nice when I run out of gum,
It's keeps the kids out of my hair.

So "Here's to you coffee! Thanks for all that you do,
I appreciate your stimulant feature.
Your affect on my life has been profound indeed.
Without you, I'd be a cranky, math teacher."

Confession

Oh, the sound of pursuit by our youth!

The groans. The moans. The ear-splitting glares.

You pull in one direction, they in the other.

There are so many of them and only one of you.

You must be powerful to resist and overcome the conglomerate force.

The blood is shed on their behalf,

Although they would all naively disagree.

Expectations abound. Some low, some even lower.

The relativity scale is relatively low.

Even the high is relatively so.

To take them from point A to point B is one thing.

But when it’s Z where you’re trying to take them,

And trying to look at and appreciate the scenery along the way,

When the terrain is overgrown and seemingly indomitable,

Then it is as if we travel with a grain of sand in the shoe.

Yet we must move on foot toward the end.

Stumbling and aching along the way.

Just when we feel we can’t go on,

More is required than was before.

And only I have my eyes on the horizon.

Many give out, long before their prime

Taking shorter more traveled routes to nowhere.

Those that remain write home

Hoping home will intervene

And save them from what they are told they should do.

Home reads the letters with mixed emotion.

Why does the journey have to be so demanding?

Can I travel it for them? Can they take a plane?

Why is their leader so ruthless and unrelenting?

If only I could send milk and cookies!

As if I enjoy being looked upon as a necessary evil,

Home tries to keep it’s distance. . .

Until they realize that even though we all forge onward,

We have no guarantee of reaching our destination.

I am a mad leader on an unnecessarily perilous odyssey.

Yes, I must admit.

Onward I push in the face of criticism and antagonism.

I don’t need praise to sustain me.

For I can see far beyond others

And I know the rewards are there.

Yes, I admit

I am sometimes filled with self-doubt

But never am I deterred from the pursuit of leading the proselytes onward.

Yes, I confess, I am a math teacher:

I torture kids for a living.

Math Emergency?!?

I just read an interesting article about the origins of the space race, and how it influenced public education here at home. 1957 was a wake-up call for America. The Soviet's successful launch of the first artificial satellite into orbit became the impetus for a change in science and math education in the United States. In an act of perhaps fear, embarrassment, and pride, America took steps to secure their future as the leaders in the space and technology race.

Today, however, we are losing the race, and there may be no catching back up. Public officials and bureaucrats pay lip service to bettering our public education, but their actions (and spending) show that our nation's priorities lie in other domains. International and Galactic peace keeping is a very important and noble goal, it's nice not to have to worry about a bomb falling on your head while you are trying to solve a differential equation, but I think we as a nation are merely reacting, rather than responding, to the fact that our nation's 15-year-olds rank 24th in the world in mathematical literacy. We talk of improvements, a better education for all, and leaving no child behind, but band-aids cannot stop a sucking gut wound. Remediation has become our curriculum. It's almost like our philosophical vision has become "the faster we fall behind, the more time we have to catch up!" We're going to need a lot of time a the rate we're heading.

Mandates, edicts, decrees, and other trickle-down orders for academic improvement do not empower teachers or students in the classroom to actually meet the demands the bills spell out. You cannot legislate excellence. It must be built up over time through training that actually reinforces content and that repose educators with a sense of professionalism. This is not happening, as much of the training of teachers happens on the local level and which focuses on abstruse, theoretical, platitudinous, double-speak, but not necessarily any practical, helpful information that comes first-hand from experts in specific disciplines.

As a math teacher, I want to know more about mathematical underpinnings, concepts, history, and subtle connections among topics that will help me better understand the big picture of mathematics and how it fits into the curriculum at each level. I'd also be a captive listener to any discussion on proven methods of instruction or proven mathematical programs. What I DON'T need is any more paperwork that documents my efforts to remediate the worst students or any information that targets improvements specifically in the very worst cases. I'm not interested in the latest medical diagnosis that gives a student another excuse to be mediocre (such as caffeine-induced insomnia--duuuh), or the latest label for special students that allows them to get by with less. If that's the way we are heading, we'll ALL soon have a special label that requires private treatment--in this is PUBLIC education.

If public education is going to be so compartmentalized and specialized, where an increasing amount of responsibility is falling into the teacher's court, while less and less is required of the student, we are going to see it get a lot worse before it ever possibly gets better. This is the trend that I have seen in the last 8 to 10 years. With all the new paperwork, documentation, IEPs, 504s, IPGs, and countless other cute acronyms that require reams and quires of paper to fill out, I'm starting to personally feel that I am transitioning from being a mathematics teacher to a bookkeeper with bad math jokes. It's no wonder why, in 2003-2004, more than 8 percent (269,000) of the nation's teachers left the profession. Of these, 56% (150,640) did so to pursue another career or because they were dissatisfied, disgruntled, or just exhausted.

This is a costly consequence of where our schools are heading. I believe the solution to restoring America's place in the scientific and mathematical elite of the world comes down to the proper training, recruitment, and retention of qualified teachers who specialize in their subject area. That is, a math teacher has at least a bachelor's degree in Math, with a desire for advanced degrees. It seems like everyone is an expert in pedagogy and teaching methods these days (or at least has an opinion about it), but many teachers in secondary education are teaching courses they are either not certified in, are not comfortable teaching, or lack even a minor in their area. In order to stop the "sucking gut wound", there needs to be a serious investment in the education of teachers that goes beyond staff or professional development training. Teachers must become absolute experts in their content area. All it takes is appropriating the money to treat the disease and not the just the symptoms.

So what must we remember from Sputnik? Building teachers up so that they can build up their students just makes sense. Expert teachers who can inspire future generations with the passion, vision, skills, and the realization of the importance of math in solving many of society's problems (many of which we haven't yet encountered), should be the primary educational priority to safeguard the future of our great nation.

What's in YOUR fridge?

Every so often, I open up the refrigerator door and something falls out on my foot. The throbbing toe and cursing (“Sweet Gherkin Pickle”) signify one thing and one thing only—it is time to clean out the refrigerator.

I don’t know how we acquire so many leftovers, nor how the plastic resealable containers never seem to fit into the drawers without the lids bunching up, making the drawers impossible to open, but how they do always seem to fit into the refrigerator (as long as there is at least one spoonful of food in them.)

Blame it on my upbringing, but I cannot waste food. I usually eat as much as I can before any given meal is over, which includes finishing off my kids’ plates, just to avoid the possibility of leftovers. But as there is a finite capacity to just how many half-eaten chicken nuggets I can put down, there is always something leftover, which means that last half spoonful of macaroni and cheese gets put into the smallest sealable container we have. Besides, if the kids want a snack later, or tomorrow after school, I figure I can reheat their leftovers from the day before, right?

Wrong! They never want the same thing twice unless it is FRESH! Consequently, leftovers get pushed further and further into the back of the fridge as new ones take their place in the front. This insures only one thing—the things that should be eaten FIRST are at the most inconvenient place, if not hidden in some back, secret area of the fridge behind the sweet gherkin pickles that I didn’t even know we had, which means they, if eaten at all, will likely be eaten LAST. And by LAST, I mean that by the time they are found, since I cannot throw anything away, it will likely be my LAST meal, as I die from some bacteria which has decide to populate that little piece of rib-eye from last month.

Then there’s the milk phenomena. At my house, we drink milk very unpredictably. Some weeks we drink a gallon or two (when the kids want cereal and don’t want to eat their soggy, leftover cereal from yesterday) and some weeks we’ll stare at an unopened quart all week. This means we usually have at least two containers of moo juice in the fridge at one time. The one that is due to expire today is the full gallon on the bottom shelf behind the leftover macaroni, again, hidden by the sweet gherkin pickles (which I am starting to believe is a secret refrigerator agent for the food protection program) and the one that does not expire for another week is the single quart that sits so precariously on the front edge of the top shelf in the refrigerator that it almost pours itself when you open the door (although it does NOT replace its own cap!) What this means is that we are guaranteed to have at least a half gallon of spoiled milk on hand at all times.

It can be kind of fun to actually play, “What WAS that?” when going through the Tupperware dishes.

“Oh, I think that was the leftover broccoli-rice casserole we had at Thanksgiving. I don’t think those green things are broccoli, though.”

In our fridge, if it’s not in storage bins, it’s in Styrofoam “doggie boxes” from restaurants. We typically have two or three of these crammed in the fridge at any given time. The third one, however, can be hard to spot, as the gallon of spoiled milk is SMASHING it down flat behind the sweet gherkin pickles (whose jar is permanently stuck to the surface by some mysterious sticky substance that I hope, although don’t doubt, leaked through the glass jar!) To give you an idea of our methods of preservation, we only eat out once a week, so it’s safe to bet that the French fries in at least one of the doggie boxes are at least three-weeks old, which means that they will require a little bit of extra ketchup to help them go down. Luckily for me, there’s plenty of ketchup to be found on every shelf in half-empty bottles.

At the end of a refrigerator restoration activity, our refrigerator is clean again and my belly is full of a smörgåsbord of leftover cuisine. Oh, I DO manage to throw SOME things away--you don’t expect me to eat squashed Styrofoam, do you?

Now old squash . . . that’s a different story.

Shine my little light

Each year I see new teachers who enter the demands of public education with a catalog of pedagogical theories, a portfolio of unproven curricula and lesson plans, and a sparkling enthusiasm accompanied by a certain sense of naiveté. What most are lacking is any practical wisdom that can only come from experience. So, I thought I would shine my little light and reflect on what I could do to strengthen the profession for new and current teachers.

I believe the single-most important thing I can do to strengthen the teaching profession is to be a shining example of what I think a good teacher is.

For fellow teachers, I believe my youth, enthusiasm, and sense of humor can help be effective medicine against demoralization, frustration, and becoming jaded. Being a teacher of AP, I also feel an obligation to keep my colleagues, both at the high school and beyond, informed of current trends in mathematical education, in terms of curriculum emphasis, instructional methods, and vertical alignment. I have given presentations on the local level (my math department) and at the state level (Council for the Advancement of Mathematics Teaching: CAMT).

For future educators, by being an unrelenting, enthusiastic, caring, and knowledgeable example of a teacher, I hope to inspire a new generation of quality educators, who can then do the same for additional generations. After all, I’m in this profession because of the effects that four great teachers had on me. These were respected teachers who mastered their subject areas, but who also shared their life-lessons, innocuously delivering an inspiring curriculum that can never be measured on a standardized test.

I think the teaching profession will continue to improve if teachers are hired as professionals, treated as professionals, then empowered as professionals to work their “magic” in the classroom. They say you can lead a horse to water, but you can’t make him drink. Teachers must be willing to salt the horse’s oats. They must be willing to admit their faults, stay abreast of (or at least not fall too far behind) the technology curve, experiment with methods, and realize the ever-changing dynamic of our society, and how their discipline fits within the larger context. Teachers must be willing to learn as much, if not more that what they are teaching. The best teachers will be those that are, themselves, life-long students.

Speaking of learning, I gotta go learn the next lesson before my students get here!

Mathematical Musings: Part I

Through the years, in my attempts to illustrate my points in the classroom, I have reportedly said some oxymoronic things and some pretty plain moronic things. Many are malapropisms, pleonasms, and tautologies. Here is a collection of the latter type of quips, quotes, and quarks that students have collected or tried to forget that I have allegedly said in the classroom. I neither confirm nor deny saying these things.

• When I can't think of how to express myself personally, I often quote myself instead.
• I can guarantee that you might not understand this.
• OOPS! Tall Carper! (after stumbling and nearly falling while moving around up at the chalkboard.)
  
• I’m coming to you live, not prerecorded!
• MMMMMM. That was a good lunch, but I digest
• The good news is, we can treat each term separately. The bad news . . . well, there is no bad news . . . So that’s just more good news.
• I love to eat lint in the morning with my coffee. It gives me a warm-fuzzy feeling.
• (While writing on the chalkboard) your problem on your paper should look exactly like this . . . except much smaller.
• Don’t erase. Don’t erase. You haven’t made a mistake. You have just discovered a method that successfully will not work.
• The main difference between the TI-83 and the TI-83 +, is that the 83+ has more RAM, so it plays game much faster.
• There’s a first time for everything. Believe it or not, this is the first time I’ve made a mistake on this problem today, in this class. You all are witnessing a historical event. Come back next time for another.
• So I was driving down the road and I glanced at my derivativeometer . . .
• Remember, just because a function is peculiar, doesn’t mean it’s odd.
• The method is called logarithmic differentiation. Once you master it, you can refer to it affectionately simply as Log Diff.
• We call the family of basic functions from which we can obtain others through transformations, Mother Functions. Not all functions are Mother Functions, though some can be a booger.
• Any student who wishes to solve the Riemann Hypothesis will receive a $1million prize from the Clay Institute and 5 bonus points on a test from me.
• I wouldn’t doubt it if they came on the intercom and just said, “Teachers and students, please pardon this interruption.”
• Don’t mistake my sense of the ridiculous for ridiculous sense.
• What I meant to emphasize when turning in your test corrections was to make sure your problems are CORRECT!
• We will be having a pop-quiz next time in class.
• So the answer is 5x . . . “you forgot the square,” quickly chimed a student . . . squared. You didn’t let me finish.
• How many of you have ever seen or not seen a record player?
• Let’s verify this Identity with a number, any number, say 5.621752189617613694768147654664 . . .
• This assignment is due Wednesday, a week from today. Be sure to start it by the weekend, or at least by next Wednesday morning.
• Growing up, I was kind of fickle. My favorite number was x.
• OK, let’s say there’s a drag race, and when I say drag race, I don’t mean two guys wearing tutus and running shoes.
• It’s not like Fermat gasped the words with his final breath, “I believe that for integer values of n larger that two, the sum of two non-zero integers raised to the nth power cannot be expressed as a single non-zero integer raised to the same power.” (On Fermat’s last theorem)
• The main thing to remember when taking this test is to read the directions carefully, don’t rely to heavily on your calculator, show all your work, round to 3 decimals, simplify radicals and fractions when appropriate, leave no negative exponents, and, oh yah, get the right answers.
• Raise your hand if you’re not here. (taking attendance)
• There is an isomorphism between the words synonym and isomorphism, but they are not synonymous.
• Is the inverse also a function? Does it pass the vertical dry-erase marker test?
• It’s kind of oxymoronic that radical notation is actually more conservative that rational exponential notation.
  

Can you build a bridge?

In teaching mathematics, I hope that students become more than just proficient with effective methods of practice. In the real world, getting the correct answer is the ultimate goal (who wants to drive over a bridge where only 70% of the structural calculations are correct?), but there are also deadlines in the real world that have to be met.

In this sense, there are really two factors at play: effectiveness AND efficiency. Students must learn to work toward the correct solution, but also to do it under a time-pressured environment, an environment that rewards a concise, efficient solution. There are numerous ways to solve any particular problem, some are more direct, while others are more "scenic," while some are not even intuitive. So how do we as teachers encourage exploration of concepts and difficult, multi-stepped problems, which obviously require a substantial amount of time to grasp, wrestle with, and try new approaches, while insisting that students perform a comprehensive test or quiz in a prescribed amount of time? The answer is quite easy. Homework, Socratic lectures, and class activities are the primary vehicles for the tedium of drawn out examination. Students must learn to practice on their own so that they feel comfortable with their new-found discoveries, methods, and insights, so that when it comes time for the test or exam, all they need to do is apply their newly acquired skills.

I don't think any civil or structural engineer (who is employed by anyone) would ever show up to the jobsite and begin building that bridge without having first invested hours and hours in his office laboring over every detail of blueprints, specs, revisions, and revisions to addendums to revisions. He has built the bridge repeatedly in his head and on paper, anticipating situations and potential problems. In other words, the bridge building activity is NOT the practice. Now certainly, an engineer who has done his homework will likely be highly solicited for his expertise, which generates more experience, which yields more expertise, which makes him increasingly effective, efficient, and filthy rich.

I'll admit that there is no such monetary incentive for students to do their math homework, nor is there the possibility of sizable penalties and pecuniary lawsuits for the collapse of their "bridges," but assiduous habits formed now are habits that will eventually put the student in the position to build that bridge.

But before they become efficient, them must learn to be effective. This means going slowly in the beginning. It is much easier to speed up once we've learned it correctly than it is to slow down and learn it over. My son learns piano this way, not that I'm fond of hearing "Yankee Doodle Dandy" played at a snail's pace, but hitting the right notes in a slower rhythm is imperative to learning the right notes at the proper speed. Just as he gets faster playing a piece once he's learned it well, math students get naturally faster at problems and procedures, after they've struggled with it, stretched into it, and really learned it.

Ironically, the students who often have the biggest struggle learning as the math gets harder, are the ones to whom it came quickly. Not only do they not know how to slow down, but they don't think they're supposed to. They think deep thinking, struggle, and the need to take more time indicates a problem, when in fact, it's the best way to learn math.

Motivated students should embrace challenging, multi-stepped problems from which they can develop mathematical stamina and learn general methods. One of the biggest problem students face is a lack of stamina to really delve into their problems. If the answer is more than a "click" away, they lose interest and return to their X-box. As teachers and parents, we must help students to develop a patient pertinacity and praise them for rolling up their sleeves and staying with the problem, especially when they are so frustrated that feel their pencil surpasses them in intelligence. THIS is the true value of mathematics: the vigor it adds to the mind, the problem-solving insight we gain, and the habits of mind we create. All these skills transcend the classroom, and will help students in any pursuit or endeavor, whether they are building a bridge, a family, a relationship, or a submarine sandwich.

As the great philosophical mathematician Alfred North Whitehead quipped, "The study of mathematics is apt to commence in disappointment." He is correct, but there is a flip side to the "math is hard" coin: those who actually invest the effort and develop their mathematical abilities develop unshakable confidence and a reassuring comfort that they are equipped to handle anything the world should through at them.