Special Seminar

Yesterday, I found myself surprised while sitting in a math department in-service. Not only did the training extended beyond our contract day, but it also overlapped the time of a funeral many teachers desired to attend. Even the location of the meeting changed at the last minute from our convenient high school campus to the downtown district offices. Oh, and did I mention that we were going to be "taught" how to "teach" to the TAKS test by someone who has had proven results "TAKS teaching."

With all these seemingly negative circumstances going into the meeting, you would think that I would be silently resistant and mentally aloof through it all (my MO for such circumstances), but I was surprisingly open-minded and receptive to the presenter's well-researched and proven insights. Because I teach the PreAP and AP math students, the TAKS test really isn't part of my solicitude. Of the juniors I do have, I expect all of them to pass (and to get commended). Seniors don't even take the exam. Instead, I concern myself with my curriculum and in preparing my students for the rigors of the AP exams and universities.

Perhaps is was the combination of the presenter's professionalism, her sense of humor, and awareness that she was "preaching to the choir," she did a great job of disarming us, rather than angering us, and I was drawn it. In fact, in all my years of teaching, hearing about the TAKS test, and listening to all the petty squabbling over ratings, subgroups, data this, AYP that, etc., yesterday was the first time I got a comprehensive, carefully dissected view of what ALL that means. I even learned something new about the way the test was actually constructed, with the first and last quarter being the easiest questions to answer. This is in stark contrast to the SAT, which gets progressively harder with each increasing integer problem number, and the AP Calculus exam, which has no pattern of level of difficulty.

This knowledge alone arms teachers with a great strategy to pass on to students (without actually having to "teach" specifically to the test questions--of which I am trenchantly morally opposed.) Even the best students tend to work in numerical sequence and can get bogged down, frustrated, or even disinterested near the end of a 72 question test. This means they could potentially shut down before reaching the tantalizingly easy ones on the last 25% of it.

So for the first time in a long, I felt that I actually learned something valuable at an in-service. But just as I thought about calling the local newspaper with a headline, the presenter posed a question to the group: "What makes special triangles so special?" Having prefaced the question by saying she asks that ONE question to all prospective math teachers in her district, I knew she would be looking for an answer that went beyond to obvious or trivial. As many chimed in with what I thought were great characteristics of the special triangles i.e. consequences of them being special. As expected, the presenter quickly dismissed each of the responses. "Thank God this isn't a job seminar," I thought.

I felt that I was in a unique situation to answer the question with what I thought she wanted to hear. Because I have taught geometry, trigonometry, and calculus, I have seen and used many principles that are direct applications of the two special triangles (30-60-90 & 45-45-90) including the unit circle and trigonometric identities. I'm also an avid reader of math history, so I felt I could add a little of that in as well. I thought carefully how I could summarize the underpinnings of my colleagues responses in as concise a statement as possible. Never liking to "sound off" in a group setting at the risk of appearing almighty, self-righteous, or idiotic (besides, I enjoy concealing my knowledge a bit), I had mentally selected my words. I spoke with quite clarity and self-assurance: "It's because they are two building blocks, from which we can find information about any angle in increments of fifteen degrees when used with trig identities."

Proud of the fact that I didn't get into the details, but only alluded to them, I awaited my accolade . . . . only to be off-handedly dismissed as the others had. I immediately got angry. "She must have not heard me," I thought. "Perhaps she didn't realize the depth of my statement," I rationalized. I thought that perhaps I should have conveyed that since the measure of a full rotation is 360 degrees, preserved from the ancient Babylonians sexagecimal (base 60) number system, the angles of 30, 45, and 60 degrees were factors of 360, so that combinations of their angles can be used to develop other angles, though not all. It is for the same reason we only memorize multiplication tables up to, say 12. At some point, for other products, we develop algorithms that allow us to use our knowledge of the "fundamental" products. Sure, we can develop unit side lengths for other right triangles, but it is mentally and mathematically more efficient to use the fundamental "special" angles to develop the other angles as we need them. In essence, they are easy to remember.

Anyway, my anger subsided as I realized there was no "right" answer, any more than being told that vanilla is not my favorite flavor of ice cream (which it is, even if you say "no"). I sat quietly, calming myself, shoring up my argument mentally, and eagerly awaiting the "correct" answer. Second seemed like minutes. The presenter went on and on about "thinking outside the box," "creative answers," and other platitudinous commentary. When she drew a breath, I awaited the answer. Out came information about bugs and spiders--she had moved on to an unrelated activity about scatterplots. Never mentioning why she thought special triangles were special, she left the entire group hanging in mathematical suspense. But to my surprise, no one else WAS! I figured she must have answered it while I was preoccupied with mentally beating myself up. At the risk of making a bigger fool of myself, I bit my tongue and tried to forget about it, figuring I'd ask a colleague later.

Well, she NEVER told us. It wasn't just my imagination. I was apparently the only one that took offense to being "shot down." I wanted to know. That's why I read those damn boring math history books to begin with. If I think some little insight, regardless of how small or insignificant, will make me understand the big picture better, I know it will ultimately make me a better teacher--I want to know. Now I NEEDED to know.

I emailed the presenter the next morning (this morning) requesting the answer, to which she replied that I would have to wait until our next seminar with her in late February. She only hinted that it had something to do with "where" they came from, rather than "how" they are used. My suspicions exactly.

I guess I have no choice but to be content for now with my over-analysis argument. But as my wife reminded me, in today's educational setting, it's really unfair to single out any one group. ALL triangles are special, not just the two. To treat any triangle any differently from all the others is to show favoritism. She's right. In just a few years, every triangle will be "college-ready."

Homework is Hardwork

Each year, I struggle more with my homework policy more than anything else. This is really the most important part of a math course, the individual practice that will allow the student to master the concepts and algorithms; however, it is not the “big game.” The tests are where the real assessment comes. This is where students must "stand and deliver" or "sit" and deliver, whatever the case may be. Many college math courses’ grades come solely from 2 or 3 tests each semester. Homework often counts very little as part of the final assessment. In some classes, it counts for nothing.

This is why I really do not like the current grading system enforced unilaterally for our high school, which not only puts such little emphasis on homework, but also allows students to turn it in late (imagining practicing for a football game AFTER you've lost the game!). When students arrive at the university, professors expect that the student knows the importance of homework as a means to mastery, and that they have the prerequisite skills through the practice of homework. Although this is obviously not the case for all upper-level high school students, we should be preparing them for such an assessment system.

However ideal, it becomes an overwhelming burden to personally grade each student’s homework daily and provide critical feedback. To have each student grade his own in class allows them to immediately see their errors and correct them, but this is a serious chunk of time, meaning less time for the new material, to play with the mathematical kittens, so to speak. I have found that this creates a downward spiral: the more time we spend covering homework, the less time we have for the lesson, the less they understand the new information, the more questions they have the next class period, the less time we have for the new material, ad infinitum. The difficulty comes in finding the balance between holding their feet to the fire, getting them to do the homework everyday and not spending a lot of time going over things they should have picked up on their own. The challenge is to create an upward spiral.

I have found that a combination of completion and accuracy grades, depending on the difficulty of the lesson, the complexity of the solutions, etc., works the best for me. We have a homework assignment daily, without fail. The homework grade should be a reward for the student who exerts the daily discipline required to master the subject. In addition, homework is due at the beginning of class, as soon as the bell rings. Quick quizzes every other class period give me a good idea of who is doing quality individual practice, and who is copying their homework from another student. I never permit students to use notes or homework on quizzes (even though they lobby for this consistently.) This forces students, those that are motivated my grades, at least, not only to go through the mechanics of the homework, but to do it for comprehension as well. When done right, math homework is a very long, arduous, personal triumph of a student over his own limitations, and he walks away from the session sweaty and in possession of something he will never lose.

This is something that is ostensibly lacking in classrooms across the world. I have found that students go through the routine of completing the assignment as if the completion itself was the goal, rather than an opportunity for them to get a better return on their investment of time, energy, and resources. In the end, students reap what they sow. Good grades do not equal learning.

Pedagogical Pizza

Obtaining an education has been compared to the filling of a vessel and contrasted with the lighting of a candle. Without both, however, education would be incomplete. The acquisition of a knowledge base is essential to be a productive member of society and to be culturally literate. But schools should be more that just little learning factories, making pedagogical pizza; they must help students to use their mind well and to put that knowledge into practice.

Much of the specific knowledge, such as important dates or mathematical formulas, will lie dormant after schooling careers. The lighting of the candle, then, is the more valuable gift of a public education. The primary goal of schooling should be to produce graduates possessing informed respectful skepticism. Many schools include qualities similar to this in their ideal portrait of a graduate, but it is a goal that is difficult to assess, hard to measure, and therefore usually left as a hopeful by-product of education. Under the current system, the emphasis is on coverage, rather than depth, on the quantitatively measurable, not necessarily the long-term qualitative results. Due to pragmatics, the emphasis has been on exposing students to a broad spectrum of ideas, rather than a deep, rich investigation of fewer concepts. Which method produces a better graduate? By my definition, the second accomplishes the goal.

There is such a plentiful supply of cheap information in our society that it is more important than ever to teach students how to interpret what is useful and what is not. By honing respectful skepticism, post-graduates and citizens can wend their way through the false platitudes and sophistries spun by politicians. They can discriminate information given by a pandering media. They can sift through the intentions of deceitful advertisements and clever marketing schemes. They can interpret the true intentions of disingenuous officials. Schools should be about the life of the mind. Only the well-trained mind can tolerate the rather paradoxical task of respecting a wide range of ideas, while yet remaining skeptical of their veracity. Skepticism without respect becomes cynicism; respect without skepticism becomes perilous absolutism. Both are needed for a healthy democracy. As Wilson Mizner says, “I respect faith, but doubt is what gets you an education.”

I am a teacher of students, first. My MO happens to be mathematics. We teachers are at the mercy of the current educational trends that so heavily influence the bureaucracy which set the guidelines under which we perform, which can sometimes be frustrating, if not creatively inhibiting. We as teachers and parents can only do our very best under the circumstances. We can find motivation, however, in our students, whose youthful naiveté, uniqueness and diversity, beautiful but awkward dance, and energetic optimism, provide an endless supply of drama, inspiration, and reassurance.

The challenge of today’s teacher will continue to grow as our world becomes more populated, more complex, more regulated, more violent, and more refractory. We cannot afford to take our eyes off the horizon.

Abandon ship?!?!?!

For the past nine years, I have dealt with the usual downside to any job, namely all the crap you have to put up with. A job without crap to deal with is a job that doesn't pay anything. A PAYING job is one whereby one gets paid to deal with crap. But there comes a time where the crap exceeds the reward of being monetarily compensated for it. Call it the "break even" point, but "breaking" point seems more appropriate.

In the past, as a matter of self preservation, I've been able to close my classroom door and take care of my little 20 foot by 20 foot square of the educational edifice. I weathered the monthly, even weekly, bombardment of parent complaints, and administrative mandates. Most of these "disruptions" to my pedagogical paradise came out of hyperbolic, knee-jerk reactions to trivial issues. Others were short-sighted manifestos designed to quell a particular inferno and to foster a genuine sense of cynicism and alienation among those upon who it was forced, i.e. the teachers.

Considering myself a Mathematician first and a teacher second, I let my love of each carry me through the occasional negative aspects that I know any job entails (I spent almost three years prior to teaching a successful homebuilder--believe me, IT'S EASIER TO MANAGE NON-COMPLIANT STUDENTS AND ANGRY PARENTS THAN IT IS TO MANAGE UNDERPAID, OVERWORKED SUBCONTRACTORS.) But slowly over the nine year of my teaching career, I have seen the defined roles of the teacher "devolve" to include more and more things that should be a parent's role. I have seen the burden of education transfer from that of primarily student's responsibility to student AND teacher, to the current status of teacher responsibility. Teachers how now become the stopgap for every social ill. We get the blame and none of the credit. We are viewed as whiny and expendable (what other professional would complain when they have summer's off?)

New educational edicts empower students to be at their worst. We are implicitly enabling students to ride the tide of mediocrity. Without and real standards of conduct, individual responsibility, or work ethic, we are producing a generation of students who are not "left behind" because they are spoon-fed and given piggy back rides across the finish line with no REAL, I mean REAL, DEEP, AND SUBSTANTIVE concern for how they will land beyond the finish line of high school and that standardized test.

Under the guise of "the best interest of the student," we adopt policies that help the student "feel good" about turning in late work. We reinforce that it is "Okay" to fail several times, as long as they eventually try, whenever they feel like it. We are sending a message that the world revolves around THEM, and that the safety net will always BE there. How far from the truth that is, but by the time they realize it, if they ever do, they are no longer part of our "data," so . . . . good luck to them after that.

Take for instance the scary, threatening comments from my "Tackle TAKS" video (see it here) I did last year in an effort to "boost" student moral as they went into their state standardized test. I busted my butt in the classroom preparing students for that darn test, and even got my butt busted in my efforts to be a part of the game in which we all play. Here are the comments of one viewer who came to the realization that public education has come down to "passing one test" and not so much about espousing real learning. He responded three times within 24 hours.

• fu@$ the taks I faild math part and dint graduate cuz of it why dont you fu@$s show us how to make money taks dosent make money it just makes familyes worry more
• my teachers was to petrafide in class to teach
• I know you teacher put all these thumbs down we are just speaking the truth you dont need taks I make about 500 a day from my own online bussines its not wat you know its who you know fu@$ school they left me I didnt leave thim im from the dfw were lots of theachers see bad thing so they are perafide every year i think teachers in the hood are one of the best cuz they see a young kids strugle

Or take this comment:

• I think TAKS is a waste of our time!!!I think that teachers are too busy preparing children for the TAKS and not for college!!! Also children are still being left behind. I think that we shouldnt have the TAKS test but instead just Final exams to see where we stand. TAKS testing puts alot of pressure on us students. We want to go to school to learn something thats going to carry us through life, not to prepare us for the TAKS!!! Thats my honest oppinion!!!

Unfortunately, we are going the other direction. Currently, the AP exam is a cumulative, comprehensive, rigorous exam that requires a students to demonstrate real understanding of, in my case, calculus, for which they can earn up to 8 hours of college credit for passing (BC calculus.) It is nearly impossible for someone to pass the test by merely being "taught the test" itself. I have had great results in both teaching this subject, preparing students for college, AND, coincidentally, getting them to pass this exam. I pour my heart and soul and every energy into doing this effectively. I have been certified by the College Board to teach both AB and BC calculus, I have attended week-long summer institutes training to be more effective, and I have even been selected as an AP Calculus Reader, a prestigious appointment where I get to actually grade the AP exams.

The current, back-breaking, decree on table is that the most intense, most rigorous, fastest-past math class on campus, BC Calculus, a class that I started at the request of students in the top 10 of their class (not just top 10 percent--students who are applying for Harvard, Princeton, Yale, MIT, UT, Rice, etc) and their parents has been suddenly mandated to be a dual-credit class. This means that I, not having a Master's degree, will be unable to teach these awesome kids with whom I feel I connect so easily with, but more importantly, it means that a small, local, private college with mediocre status, will accredit the course, whereby students can simultaneously earn college credit. It's essentially "take a high school class, and get college credit, as if it were a college class." Unfortunately, the accrediting college does not have much control over the quality in which it's delivered. They, instead, rely on the "professionalism" of the high school to maintain the college standards. This really equates to a crap-shoot on the dedication and qualifications of the teacher, with at least a Master's degree, teaching the class. It's not surprising that few major Universities actually accept these hours towards a degree. Some might offer "general elective credit," but the students who will be taking BC calculus, they will get NOTHING, but instead will have to start back at ground one: Cal I

Compare this to the 9 students out of 14 last year that I had earn 5s (the highest score possible) on the BC Calculus exam. These students went off to UT, Villanova, University of Virginia, and MIT with 8 hours of RECOGNIZED college credit. Some retook Calculus II (not I), and several went directly into Calculus III, where I can happily report that they are doing superbly.

I can't help but take a step back and think of how the captain (or captains) commanding the ship are steering it into such shallow, shallow waters. I believe it's either time for mutiny on the grand seas, or as I fear, it's time to abandon the ship altogether.

Arrrrrrrrrrrrrrrrrrrrrrrrg!

Too Young To Feel This Old

It seems only natural after planning my funeral on the last blog, to give equal time to talking about my birth on the next one. Having said that, "Happy Birthday to Me." Yep, exactly 34 years ago today, in the SouthTexas city of McAllen, born as the second of three children to a loving family, I came into this world. My how the years have passed since then. As I now make my living "preaching" the word of math on a daily basis, at birth, I was so excited to be in this world, I was literally speechless for about 15 months. Quickly learning to talk and walk, I've been doing it ever since: talking the talk and walking the walk.

I think about all the great things I've done in my relatively short time on Earth, and I think about all the many things I'd still like to do before that funeral plan is implemented. But seeing how the last 10 years has gone by about as quickly as the previous five, it seems like time is accelerating as I get older (positive second derivative, or concave up.) At this rate, I'll be 55 by the time I'm 40, or at least feel like it. With something new aching each day, from bad knees, to pulled hamstrings, to shooting pains in my shoulder, stiff neck, piercing headaches, blistered feet, crooked spine, and ingrown toenails, I actually look forward to soaking in Epsom salt, and I know I couldn't function each day without my 6 pills I take each morning from my "old people's" pill library dispenser.

Had I been as wise as I am today 15 years ago, I'd be in much better shape. Unfortunately, with my myriad of skateboarding injuries from my youth, ranging from 6 concussions, compound fractures of the left radius and ulna, broken front teeth, and too many cuts and scrapes requiring stitches, staples, glue, or butterflies, to the consequences of my cliff diving, rope swinging, and diving board injuries, I didn't take care of my body. It's funny how I'll be feeling that short phase of my life for the rest of my years. What's more, I was so timid and craven as a small child (less than or equal to 10 years old), that I was too scared to even get on the kiddie coaster at Astroworld. Little did I know than that I would turn that overly-cautious, cowardly disposition around pi radians (180 degrees) when I became a teenager, throwing caution to the wind, doing anything for a cheap thrill and the attention.

I'd like to think my wife for awakening me to the senses of my pre-adolescent years (with one, small ACL-tearing incident aside), whereby I have returned to the cautious, calculating, responsible person once again. In fact, as I see my seven-year-old son and four-year-old daughter exhibit the same guarded temerity, my desire for them to be assertive and adventurous are overshadowed by my relief that their temperaments will minimize the distress in my life, as I don't need to worry about what dangerous act they're doing behind my back. If only my mother could have been so lucky.

But then again, they ARE both still just pre-adolescents who are more like their mother. Only time will tell if they go through their father's stage of reckless abandon. For them, that's still some time away. For me, it will be here tomorrow. By then, I'll be taking a few more pills and looking into hair transplants.

Korpi, the Musical

I saw a commercial the other day that reminded me of my mortality. It was a commercial for funeral insurance. Although I wasn't intrigued by the sales pitch for something my life insurance already accounts for, I was interested the the "gift that was mine to keep" if I "called now." It was called a "last wishes planner," basically, a pamphlet in which one could fill in details of one's own funeral, so that your survivors don't have to guess what Michael W. Smith song to play.

With recent tragedy all too fresh in my mind, and never really thinking about how others will react in the event of MY passing, I became really interested in getting that free gift. So I did a quick "Google" search for "planning ahead for a funeral" and clicked on the first link: a .pdf document that was a similar version of the one offered for a "limited time" to the "first 100 callers" with "no obligation."

I've decided to answer the questions here, so that when my time comes, whenever that should be, there will be a cyber-record of my intentions. At first I thought this to be a morbid, ominous task, but then I thought it might be kind of fun, if not necessary, to plan my "dream" funeral.

As Churchill said, "Plans are useless, but planning is invaluable," so here it goes:

Type of Service: Funeral, Memorial, No Service, or Other
I'm going with the traditional "guy in a box" arrangement. I've heard its very important for some people's closure to see and touch the body. Since the service is really for the survivors, this is an unselfish decision.

Location of Service: Church or Temple, Funeral Home, or Other
I guess a math classroom would be a bit unconventional or crowded and the Rocky Mountains always poses a risk of bear attack on the attendants, I suppose I'd opt for a Temple . . . or at least a church. I'll let the Catholics and the Baptists fight over who wants to host me.

Location of Reception: Church or Temple, Funeral Home, or Other
I'd definitely like a change of venue for the after-party. Once the burial is done, it be neat if everyone met at someone's house to relax, eat, drink, and remember what a great guy I was.

People to Give the Eulogy: If David Letterman is not available, and if Abraham Lincoln is cannot make it, and if Ray Romano doesn't really know me, I'd like some good, close friends have a word: Trent, Gordon, Lauren C., and Dad. Don't make it sad, guys. I'll be listening, and I'll need a good laugh.

Music I'd like Played or Sung:
This would be cool to play these songs before and during the ceremony. I really like a lot of songs, many of which are even appropriate! This event could almost be a musical, especially if the people giving the eulogy decide to sing it! Or perhaps this could be the background music for a PowerPoint photo Montage, that would be a crowd pleaser!

Sonata Arctica-"This Ain't Your Fairytale"
Iron Maiden-"Die with your boots on"
Andrea Bocelli-"Time to Say Goodbye"
The Beatles-"Let It Be"
Conway Twitty-"The Rose," "Sweet, Sweet Spirit"
Bon Jovi-"Never Say Goodbye"
Midnight Oil-"Forgotten Years"
Guns N Roses-"Knockin' on Heaven's Door"
James Blunt-"Goodbye my Lover"
Michael Card-"Joy in the Journey" and "El Shaddai"
Los Lonely Boys-"Heaven"
David Gray-"Shine," "The Other Side"
David Kauffman-"Be Still," "Out of Darkness"
Monty Python-"Bright Side of Life"
Roger Miller-"You Can't Roller-skate in a Buffalo Herd"
Nat King Cole-"Unforgettable"
REM-"Everybody Hurts," "The Great Beyond"
Seether-"Broken," "Rise Above This"
U2-"Beautiful Day"
Don Henley-"Heart of the Matter"
Fandago USA-"Charanga"
Tina Turner-"The Best" (pretty selfish, huh?)
John Denver-"Sweet Surrender," "I want to live," "Flying for me," "Looking for Space," "Perhaps Love," "Season's of the Heart," "How Can I Leave You Again," "Goodbye Again,"It Amazes Me," and any others
The list would go on, and on, and on . . .

Readings:
Being raised Catholic, I'm not really a Bible scholar, but I think the verse about "walking through the valley of death" is a good one. There's another I recall from Jeremiah about "I have gone before you . . ." or "I have plans for you . . ." Something from the Old Testament about how far the outhouse should be from the food-prep area is probably inappropriate, as would Lincoln's Second Inaugural Address. I vaguely remember a verse stating "I have prepared a place for you . . ." Some Ogden Nash poetry would be nice, or some Shel Silverstein. For sure the poem "If," by Rudyard Kipling. Please also read the poem I wrote for this occasion. I'll file it under "Kevin's original funeral poems."

Arrangements at the Altar:
Flowers: daisies are all too appropriate, Gerber variety, please
Photograph: If one looks descent, use it. The one from the Algebra 2 show would be humorous. I'd like one of me with my kids, though.
Religious Image: infinity symbol, equation: e^pi*i + 1 = 0, cross

Flowers and Monetary Donations:
No Additional Flowers or Wreaths from guests
Monetary Donations to establish a memorial scholarship fund for future math educators

Burial Instructions:
Dress me in the only suit I own with my "Archimedes is my Homeboy" t-shirt beneath
Put a picture of my wife and kids in my suit pocket
Celebrate the occasion, 'cause I'll be watching.


That's it. That felt both necessary and weird. Excuse me now while I go knock on some wood.

Mathematical Musings: Part VII

More of what I have (purportedly) said in class (these are funny ones):

• S: Mr. Korpi, if I have Cosine of blah, blah, blah, over Cosine of blah, blah, blah, can I cancel them out? K: Not unless it’s the same blah, blah, blah.
• Whew, all that running wore me out. We either need to do that more often, or less often, preferably less often.
• My favorite website is any old Haunted House: lots of spiders.
• OK, it is called the ambiguous case because there are three cases, meaning number of triangles. Let’s number the cases. One is zero, two is one, and three is two. You got that?
• So after the plane switches his heading from 180 to 225, he is flying Southwest: the direction, not the airline.
• So in the right Right triangle, Sine of A equals h over c. In the left Left triangle . . . no wait, that doesn’t work. In the left Right triangle . . .
• QUIET! My mouth is very, very close to my ear. See? But, I can’t even hear myself talk.
• If you sit in the back of the room, the numbers on the board in the front of the room probably look smaller to you. So a nine probably looks more like a six.
• Here are all the formulas for areas of triangles you need to memorize. You will have to know all of them for the test, however, you will only have to use one of them. So, you really don’t have to memorize all of them, just one. You figure out which one.
• S: Mr. Korpi, I made my poster bigger than a quarter size. I couldn’t fit all the information on just a quarter size. Is that OK? K: Sure it is. You used half a poster board, but that’s nothing more than a quarter size of one that was originally twice as big. I never specified the original size of poster board of which a quarter should be taken. Most people assume standard size, which is the only kind.
• Some people see the number 2304 and think, “Hmm, that’s two thousand three hundred and four.” I see it and say, “Hello forty-eight squared!”
• That was a fabulous tune (Baby Elephant Walk) from the late, great Henry Mancini. Now back to the Law of Cosines.
• I think I’m rather quotable, but don’t quote me on that.
• I like how the tiles are made to look like real terrazzo, but each 12 by 12 tile is laid with the terrazzo grain perpendicular to the next, thus completing the obvious fact that it is fake.
• As little as your study patients see Doctor H, they probably wonder if he even really exists. I think we should open our own practice with under an assumed practitioner’s name, something catchy that will bring the patients in, but they’d never see him. Something like Dr. Bon Jovi.
• We’re going to find area here. Does anyone have an exotic unit of measure we can use? The perch? OK. Then the final unit will be purchases? Squared? I guess if you’re a fisherman, the unit of perch is directly related to the number of witnesses.
• Have y’all ever been to Sam’s? It’s dangerous. You go in there not needing anything, then three hundred dollars later you get out of there going, “Dang! That sure is a lot of mayonnaise.”
• There’s a joke about a turkey in there somewhere that I’m not even gonna touch, not that it would be funny or anything.
• Come on, listen to me now. I’m cereal.
• So here’s our equation. With a little algebraic finagling, we can get it in the form we want.
• Let’s say a pair of calculus cops are set up together to catch speeders, one at point A, the other 5 miles down the road at point B. You know, like Roscoe P. Coltrain and Cletus trying to catch them Duke Boys, ‘Kyuuu-Kyuuu.’
• The commutative and associative properties of multiplication allow you to play a kind of shell game with the factors.
• You have two options for this class period: you can either work on the review, or if you don’t want to, you can fake it, and pretend that you are working on the review so convincingly that I cannot tell the difference.
• There’s about four minutes left in class, maybe a little less, maybe a little more, but around four.
• The insane are a good case to study, because they are committed.
• Semi means half; half a circle is a semicircle, half a perimeter is the semiperimeter, and half of a 36 wheeler is a semi.
• Is everyone all squared away on area, then?
• If you’re here, that means you’re back from vacation.
• Another day, another dime, another difference made.
• Subtraction makes all the difference when you’re adding two things.
• It’s just that nose sniffling, phlegm hocking, snot slurping time of year.
• Today’s the day you get the chance to show off your acquired precalculus knowledge. After grading the other classes tests, there has been quite a bit of showing off, even some trash-talking and victory dances.
• I seemed to have lost that information somewhere between gray mater and cyberspace.
• Let’s have a little fraction action.
• At the end of a proof, you can write Q.E.D., which is Latin for Quid Erat Demonstratum (that which has been demonstrated), or “Dorothy’s Dog” (es todo = it’s Toto.)
• Even though I’m telling you that you cannot distribute the cosine to each of the two angles, I have full faith and confidence that many of you will still do it at some point. I really believe in each of you.
• Here’s a pre-class disclaimer. I’m high on antihistamines. Please disregard anything that I say that is surreal or doesn’t make sense, unlike usual.
• When we multiply by 180 over pi, we get rid of the pi’s, which never is a problem at my house at Thanksgiving.
• Being able to find exact trig values is very, very important, for instance if you were trapped in the dessert doing precal without your calculator!
• Math club members, come decorate the Landa Professional building Saturday at 9:00 sharp. Be there or the fourth root of b to the eighth.
• Mrs. Jones, I don’t think your son is overwhelmed with the material, nor do I think he is underwhelmed, as you have alluded to. I do believe that he suffers from a chronic, full-blown case of the Lazys.
• Everybody please come to the next math club meeting ready to have fun. I guarantee we’re going to have a sphere.
• Unless you are going into a very technical field, you probably won’t use the specific information obtained from earning your college degree. Your degree, then, becomes a symbol to prospective employers that allows them to say, “Here is a person in collegiate caliber. He/she must be capable of enduring a bunch of crap. That’s the kind of person we need to hire.”
• The last class they were exhausted after the last lecture. Imagine how I felt, and I have to give it 3 more times.
• You must take turns when speaking out. I can’t understand a thing any of you say when you all speak at once. (to a quiet class, too timid to speak)
• Whoever didn’t just speak, I’m sorry, you’ll have to repeat yourself. I couldn’t hear you over the deafening roar of all the others who weren’t screaming out.
• The test is two pages, front and back. Don’t worry. I’ve got you covered. You won’t run out of Calculus.
• Korpi: What’s that awful smell? Student: Math! Korpi: I wonder if they make that scent in a candle, then. I could put them all over my house and get you one for your house!
• You don’t need your calculator for the fractions on the quiz, quit whining. The fractions are small anyway. If you think they’re too big, write smaller, but no calculator.
• This semester I have three goals for you all. First, I want each of you to have a renewed and enthusiastic rigorous love of learning. Secondly, well I don’t want to tell you that one, and thirdly, I want you to figure out what the second goal is.

It's what I do

Yesterday, as the new semester got underway, I welcomed a new class (and a new kind) of class into what is essentially my "homeroom" class. Called "Unicorn Time,"(UT) it is a block of 21 minutes where students meet to watch announcements, receive report cards, meet for assemblies, take standardized tests, watch TV, and catch up on gossip. Although students do not earn grades during UT, they don't take it seriously either. They are only accountable for their attendance. We teachers were encouraged to use this time with these students to form positive relationships, becoming their mentor, role-model, and hero. On paper, this is a great idea. In the classroom, it's still a great idea, but one very unlikely to ever fulfill.

With no more recourse than holding students in low esteem and possibly yelling at students who are unwilling to follow directions, the time slot has no teeth for anything of any value, other than convenience for administrative tasks. I tried several times to come up with exciting mini-lessons on various subjects from number theory, word origins, presidential trivia, and magic tricks to make the time productive for all involve, but I became increasingly weary of inventing topics and acting them out for an audience that was less than captive. Overall, the kids grew to respect me, and I learned quite a few neat things about them.

This semester, however, the UT structure has changed for a select group of math teachers who volunteered to take on struggling math students, those who need help passing the state's standardized test. With my old class dispensed to other non-math teachers (many of whom were actually quite sad that they had to now watch Sportscenter in a different UT classroom), I welcomed 8 new students with a lot of mathematical and academic baggage.

So why would I give up my cushy role of attendance taker and babysitter during this 21 minute period for the new role of math teacher for students who are not only bad at math, but who are self-proclaimed "haters" of math? Because it's what I do! I LOVE math, and I LOVE teaching. Out of the same motives a philanthropist gives his resources to a worthy cause, so am I willing to contribute my talents and time to making a difference for some kids who really need it. Although I will not get that hospital wing named after me, maybe I can help one of these "elite eight" students to pass tests, learn and love math, and get fired up about school and learning once again. I have rediscovered the joy the last two days of teaching these types of students, who have totally different needs, backgrounds, and expectations of the AP calculus students I am used to. To be able to go back to the very rudiments of mathematical notation and syntax, and explain concepts and skills in such a concrete way is invigorating and exciting for both me and my students.

For instance, today we reviewed the basic rules for combining exponents. There are three simple rules that can often be memorized, buy not so easily recalled and used correctly. I went way back to addition and how multiplication if short-handed addition. I saw a spark ignite in their quiet, thirsty eyes. Next I showed them that exponentiation is merely short-handed multiplication. After a few examples, they all understood the methods behind the rules, and why we'd want to use the rules to begin with. They suddenly knew when to use each rule, as they now had the mental framework for employing the rule. It was an intense 21 minutes filled with enlightening, pleasing grins.

Yes, I do think I am going to enjoy my UT class this semester, even if I have to find another time to watch Sportscenter.

Meow!

Here's a repost from one of my favorite websites: www.straightdope.com

On this website, readers can send in intellectually inquiries directed at the smartest man ever to live, a man called Cecil Adams. Although some question whether he is an actual individual or a conglomerate of researchers, his answers are always well researched, well spoken, and memorable. Below is one of my favorites regarding his answer, in verse, regarding Schroedinger's cat. As a little background, the silly little experiment in quantum mechanics was proposed by Erwin Schroedinger in 1935. It attempts to illustrate the theory of superposition, and serves to demonstrate the apparent conflict between what quantum theory tells us is true about the nature and behavior of matter on the microscopic level and what we observe to be true about the nature and behavior of matter on the macroscopic level.

Here's Schrödinger's (theoretical) experiment: We place a living cat into a steel chamber, along with a device containing a vial of hydrocyanic acid. There is, in the chamber, a very small amount of a radioactive substance. If even a single atom of the substance decays during the test period, a relay mechanism will trip a hammer, which will, in turn, break the vial and kill the cat. The observer cannot know whether or not an atom of the substance has decayed, and consequently, cannot know whether the vial has been broken, the hydrocyanic acid released, and the cat killed.

Since we cannot know, the cat is both dead and alive according to quantum law, in a superposition of states. It is only when we break open the box and learn the condition of the cat that the superposition is lost, and the cat becomes one or the other (dead or alive). This situation is sometimes called quantum indeterminacy or the observer's paradox: the observation or measurement itself affects an outcome, so that the outcome as such does not exist unless the measurement is made. (That is, there is no single outcome unless it is observed.)

We know that superposition actually occurs at the subatomic level, because there are observable effects of interference, in which a single particle is demonstrated to be in multiple locations simultaneously. What that fact implies about the nature of reality on the observable level (cats, for example, as opposed to electrons) is one of the stickiest areas of quantum physics. Schrödinger himself is rumored to have said, later in life, that he wished he had never met that cat.

Here's the reader's inquiry, followed by Cecil's poetic explanation.

Dear Cecil:

Cecil, you're my final hope
Of finding out the true Straight Dope
For I have been reading of Schroedinger's cat
But none of my cats are at all like that.
This unusual animal (so it is said)
Is simultaneously live and dead!
What I don't understand is just why he
Can't be one or other, unquestionably.
My future now hangs in between eigenstates.
In one I'm enlightened, the other I ain't.
If you understand, Cecil, then show me the way
And rescue my psyche from quantum decay.
But if this queer thing has perplexed even you,
Then I will and won't see you in Schroedinger's zoo.
--Randy F., Chicago

Dear Randy:

Schroedinger, Erwin! Professor of physics!
Wrote daring equations! Confounded his critics!
(Not bad, eh? Don't worry. This part of the verse
Starts off pretty good, but it gets a lot worse.)
Win saw that the theory that Newton'd invented
By Einstein's discov'ries had been badly dented.
What now? wailed his colleagues. Said Erwin, "Don't panic,
No grease monkey I, but a quantum mechanic.
Consider electrons. Now, these teeny articles
Are sometimes like waves, and then sometimes like particles.
If that's not confusing, the nuclear dance
Of electrons and suchlike is governed by chance!
No sweat, though--my theory permits us to judge
Where some of 'em is and the rest of 'em was."
Not everyone bought this. It threatened to wreck
The comforting linkage of cause and effect.
E'en Einstein had doubts, and so Schroedinger tried
To tell him what quantum mechanics implied.
Said Win to Al, "Brother, suppose we've a cat,
And inside a tube we have put that cat at--
Along with a solitaire deck and some Fritos,
A bottle of Night Train, a couple mosquitoes
(Or something else rhyming) and, oh, if you got 'em,
One vial prussic acid, one decaying ottom
Or atom--whatever--but when it emits,
A trigger device blasts the vial into bits
Which snuffs our poor kitty. The odds of this crime
Are 50 to 50 per hour each time.
The cylinder's sealed. The hour's passed away. Is
Our pussy still purring--or pushing up daisies?
Now, you'd say the cat either lives or it don't
But quantum mechanics is stubborn and won't.
Statistically speaking, the cat (goes the joke),
Is half a cat breathing and half a cat croaked.
To some this may seem a ridiculous split,
But quantum mechanics must answer, "Tough @#&!
We may not know much, but one thing's fo' sho':
There's things in the cosmos that we cannot know.
Shine light on electrons--you'll cause them to swerve.
The act of observing disturbs the observed--
Which ruins your test. But then if there's no testing
To see if a particle's moving or resting
Why try to conjecture? Pure useless endeavor!
We know probability--certainty, never.'
The effect of this notion? I very much fear
'Twill make doubtful all things that were formerly clear.
Till soon the cat doctors will say in reports,
"We've just flipped a coin and we've learned he's a corpse."'
So saith Herr Erwin. Quoth Albert, "You're nuts.
God doesn't play dice with the universe, putz.
I'll prove it!" he said, and the Lord knows he tried--
In vain--until fin'ly he more or less died.
Win spoke at the funeral: "Listen, dear friends,
Sweet Al was my buddy. I must make amends.
Though he doubted my theory, I'll say of this saint:
Ten-to-one he's in heaven--but five bucks says he ain't."

--CECIL ADAMS

Guess the number!

Read the following two verbal descriptions and think of the number each represents:

• "One hundred and ten thousand and one-tenth"
• "One hundred ten thousand and one-tenth"

"Do they represent the same number? different numbers? Does one imply an operation?

Currently on an Electronic Discussion Group (EDG) or AP calculus teachers to which I subscribe, there has been much discussion and debate regarding a trifling use of semantics in mathematics: how to interpret the above verbal statements. I would personally indubitably interpret each statement to represent the number 110,000.1, my favorite fraction between 110,00 and 110,001, but not everyone would agree with me.

Although there are several, undebatable equivalent ways to mathematically write the answer (110,000.1 = 110,000 1/10 = 1,100,001/10) there is much debate on how to pronounce it. How would you read it? I know in my upper-level math classes, when writing the number, I would omit the commas, and when saying it, I would merely say "one ten oh oh oh point one." No student would misinterpret what I'm saying, because they understand place value and understand mathematical "slang" at this stage in their mathematical careers. But if I were teaching place-value and the correct procedure for precisely stating numbers (something my son is study

If I told you that both verbal statements are equivalent as written, would you get all ruffled up, get mad and upset! If you do, you are either extremely anal retentive, are and attorney or banker, or write a lot of checks (or all of the above.) People who disagree with the equivalence of the two statements may interpret them this way.

The first one: "One hundred and ten thousand and one-tenth"
The anal purists would say the word "and" is reserved for the fractional part of a number, expressed with the decimal point in the actual number. This description, then, literally means 100.10,000.1 which, with its TWO decimal places is meaningless (even when read in Europe, where they use decimals instead of commas.) There other extremists that go one step further, saying that the description actually implies the operation of addition! Do you see it? They argue the statements is 100 + 10000 + 0.1, interpreting the word "and" as the operation of addition.

Here's my take. The latter argument above is more genuine in the spirit of what is actually taking place. When students first learn place-value, they do so by "dissecting" the number into the sum of its respective parts as powers of 10. The number would be written as

110,000.1 = 100,000 + 10,000+0.1

If the "plus" sign is read as "and" then the we can read it as "One hundred thousand and ten thousand and one-tenth." Because this would be an awkward way to use the number in conversation, in the context of discussing quantities or magnitudes, we understand this to be equivalent to "One hundred and ten thousand and one-tenth." Example: "Did you see that the NASDAQ closed yesterday at one hundred and ten thousand and one-tenth?"

However, if we were discussing this number verbally in the context of amassing or listing a quantity or magnitude, we would interpret differently: "I need to find the sum of one hundred and ten thousand and one-tenth." This sum would be quite a different number:

100 + 10,000 + 0.1 = 10,100.1

Are you now more confused than you were at the beginning when you read the two statements originally? Let's try to re-clear it up.

The second argument: "One hundred ten thousand and one-tenth"

Some would argue that the context in which a number is used should not be part of how to interpret it. These people claim that, with the two "and"s in the description is always equivalent to the smaller number obtained from the addition: 10,00.1

I certainly see their point, but I can't say I ever lose sleep over it. Being a strict grammarian myself, with all the more egregious misinterpretations of verbal statements, I think this one is rather benign. I think students would see pursing this distinction would qualify for "making a mountain out of a mole hill" category.

This would essentially equate to listing three or more things in a sentence and the use of commas. In recent years, the keepers of the laws of grammar have accepted the omission of the final comma in a list: "I like to eat apples, bananas, and watermelon" is now correct to be written as "I like to eat apples, bananas and watermelons." Being more old school, I prefer the first style, additionally because it provides better clarification. To me, without the final comma, the last two, bananas and watermelon, should be treated as a single group rather than separate items.

For example, decide from this sentence exactly what I like to eat:

• "I like to eat chicken and rice and peas and carrots."

This statement (with no commas) lists only two dishes: the chicken and (with) rice combo and the peas and (with) carrots combo. It gets more vague when written the following way:

• "I like to eat chicken, rice, peas and carrots."

By the new, acceptable rules of grammar, you can read this as me liking four separate items (with peas and carrots being distinct side dishes) OR only three separate dishes (with peas and carrots being ONE dish--which means the sentence could actually read "I like to eat chicken, rice and peas and carrots.")

So have you figured out what I like to eat yet? If you were REALLY interested and were unsure, you could ask me to clarify (I like them all in any combo or casserole.)

In the end, I don't think it matters how the number is written or spoken, as long as the true intention can be discerned from the context. Grammatically, there is no consensus as to which is correct or "more" correct. We individuals are free to express ourselves within the constraints of what is acceptable, and this case is no exception. We use our personal judgement (and "YES" it is still acceptable to include the "e" after the "g.")

Now, the misuse of reflexive pronounce, is one I, myself, really get fired up about! Just ask myself sometime.

Empty Classrooms

Today officially marked the end of the first semester at our high school. It is the first time the semester has not ended prior to our Christmas break. This year for the first time in my nine years of teaching, because of a new state law prohibiting schools from beginning school before Labor Day, we had two additional weeks of school after our two week winter break. Most students put in the usual complaint prior to the break about having to remember everything when they got back (because most don't actually learn it well enough to begin with.) But it almost didn't matter that they forgot what they learned.

This year we also had a very generous semester final exam exemption policy, which meant that many, many students did not have to study, learn, or relearn everything from the previous 18 weeks for their comprehensive exams. Students who earned exam exemption not only did NOT have to take their cumulative exams, they did not have to come to school during the period in which the exam was given. So this last week, being an academic "dead" week (no more new material covered so that students could prepare for their upcoming exam exemptions by playing more video games or having meaningless conversations with their friends in coffee houses after school) was artificially LONG. I, however, made the most of it by squeezing in chapter tests at the beginning of the week and forwent any review for the finals. There's nothing I could have done, though, about Wednesday, Thursday, and Friday, which were officially exam days.

Since nearly half the school was exempt, the halls and classrooms were mostly empty on these days. Those unfortunate students who were NOT exempt, mostly because of failing grades or excessive absences, were enjoying a little more elbow room. I had about five students in each class take my final exam, a 33 question, mulitple choice exam, whose questions were pulled DIRECTLY FROM OLD CHAPTER TESTS, tests that we had gone over in detail in class. Even though the students were fully aware of this, knowing that I was not even going to change numbers or rearrange answer choices, very few passed, and nobody scored a perfect score, even though I had a few highly-motivated, top-notch students electing to take the exam, even though they were exempt. I'm convinced that if I had given the final exam with all 33 correct answer choices highlighted, that I STILL would have had several preAP (college-bound) students fail.

The most unusual part about the whole exemption idea was that the eight exams were spread out over three full days, meaning that Wednesday and Thursday had one "dead" class during the lunch period where ALL students were expected to attend, including the students who did not have exams the rest of the day. If that doesn't make sense, then get this! Today was the last day of exams, with two exams in the morning. The last two periods of the day were non-exam classes . . . at the end of the semester. . . . that ALL students were expected to attend. So after EVERYONE was done with their exams (or exemptions), as their final semester averages were pretty much locked down, there were two full class periods full of absolute nothingness. Most exempt students took the unexcused absence (which is unfortunate they had to do), but I think I would have done the same thing. Of the 10 people I actually had in class, we watched an Isaac Newton video for the first half of class, then picked our noses the last half.

It would have made more sense to have exams over a two-day period, with no "dead" periods on any day OR to have made the last day an early-release half day (which would have required a little planning and forethought in making the calendar LAST year.) But I gotten quite used to the whole "reacting" to circumstances and "trial and error" leadership style. I have to say, it is an exciting and entertaining (although sometimes frustrating) environment in which to work. You never know what tomorrow will bring. Heck, tomorrow, that might even be the new National Educational Motto!

My Bucket List

Rob Reiner's latest film, starring Jack Nicholson and Morgan Freeman in familiar roles, is called "The Bucket List." In the film, two actors play cancer patients who, while sharing a hospital room and staring at death, decide to make a list of all the things they want to do before they "kick the bucket." Having not actually seen the film, I can predict how the story unfolds, what they likely included on their list, and how it will end.

Although the movie did not make me want to see it, DID make me want to start my OWN "bucket list," not that I'm planning on meeting the Grim Reaper anytime soon. Here's what I've come up with so far. They are all things I believe I have some control over (as opposed to saying, "I want to win the lottery," or "I want to end world suffering," or "I want to cure student apathy.")

• run a marathon (currently registered, haven't yet run, but moving closer to the goal--see yesterday's blog)
• Perform in a leading role in public theater (having done minor roles in the past as a member of chorus, looking for chance to actually have speaking part)
• patent something (lots of ideas, but paperwork and expense can be daunting)
• win a prestigious, national award (have come close with Texas Teacher of Year race and Lonestar Emmy nomination)
• Spend an entire summer in the Montana wilderness
• Take an Alaskan cruise
• Travel to Finland and research ancestry
  
• Go ghost hunting in a haunted, ancient, historical castle
• Skydive . . . . solo
• Ride in a hot-air balloon
• Snowboard a half-pipe
• write and publish a book
• learn to fly (an airplane or helicopter)
• Discover/prove a mathematical theorem
• Tour historical New England
• Brew beer and create savory recipes
• Hang Glide with the Eagles (birds, band, or football team)
  
• Write a song for popular radio
• Write a play/movie script and watch it from audience
• Do stand up comedy
• Be a guest on David Letterman's show
• Play "HORSE" with Larry Bird
• Play catch with Brett Favre
• Ride a motorcycle
• Learn to juggle
• Learn to play guitar (well)
• Learn to play piano (also well)
• Be in a part-time garage band and play a few gigs
• Own a large tractor with a bucket and backhoe
• Ride in a submarine
• Climb a famous peak
• Have rock-hard abs and pecs
• Visit all the Abraham Lincoln historical places
• Visit all the Theodore Roosevelt historical places
• Canoe down the Amazon
• Design and build my own home and dream workshop
• Have a fruit orchard
• Take a dirt-bike ride on a motocross track
• Fly in a fighter jet or race car
• Maintain a garden
• Learn Spanish and German well
• Have a giant salt-water aquarium
• Experience weightlessness (the vomit comet?)
• Scuba Dive a sunken ship
• write and draw a regular comic strip
• Travel to Europe, especially Greece, Italy, and Egypt

I'd better get busy. While I'm checking off my list, think about what YOU want to do?

The run of my life

Well, I've gone ahead and done it!

Yesterday, I became an official entrant in the Austin, Texas Marathon. Originally wanting only to run the half-marathon, I thought, "what's an extra 13.1 miles at the end of 13.1 miles?" and registered for the whole race. I think one of the deciding factors was my trenchant desire for value and practice of making the most of my money. You see, the half marathon had an entrance fee of $75. Being twice as long, the FULL marathon would, therefore, be $75 times 2 = $150 . . . you would think . . . but it wasn't!!!! It was only $110!!!!! That's a bargain I couldn't pass up. That's a savings of $45 on the second half of the race. A 30% off sale on distance races, if you will. By stretching out the distance I now have to run, I am essentially stretching my dollar.

I applaud my wise decision based on its financial soundness, regardless of whether it makes sense physically. It's like going to Sam's Club or CostCo and finding the 5 gallon tub of mayonnaise too irresistible to pass up. Even though you know only need one small jar of it, you realize that the same amount of mayo in the local supermarket would cost twice that much, so you make the purchase, feel proud about it, then tackle the problem of USING it later.

That's how I currently feel about the race. I'm excited and nervous at the same time. I've never ran that distance before. Although I've averaged about 30 miles per week for the last year and a half, my longest distance was a paltry 12 miles--not even a HALF marathon. I'm not worried about my stamina or conditioning, but rather the daunting psychological battle I will have to face, running without my beloved headphones. The real object of my solicitude is my knee--both of them. My "bad" knee, the one without an ACL in it (long story involving three surgeries and two MRSE bacterial infections), has now become my "good" knee. My previously "good" knee (the one WITH the ACL) has now become my "bad" knee.

I have been unable to run for the last two weeks because of an excruciating pain that feels like my femur and tibia are crashing together with each step, causing me to limp and wince even when I walk. I went for a run last week from my house and couldn't even get out of my driveway before I was grimacing and aching. I'm guessing that all the accrued miles spent pounding the pavement the last 18 months has taken a toll on my 33 year-old body. I know I sound crazy, in light of this information, signing up for even a 100-yard dash, much less a marathon, but that is EXACTLY why I did it. I feel my window of opportunity slipping away.

Not really interested in surgical attempts to fix the knee (I have a surgical "aversion" now), I figured if I'm every going to do it, now is the time. I would just have to force myself through any discomfort (discomfort = aforementioned excruciating pain.) With the race exactly one month and one day away, I now have the undesirable, paradoxical challenge of training for the race by running, running, running AND resting my knee by NOT running, running, running (which seems to be helping, somewhat.)

I think when the time comes to actually run, I will find the strength, with the support of my family, running partner, the exuberant crowd lining the course, my adrenaline, and large amounts of pain medicine. I keep telling myself, "If Oprah can run a marathon . . . . . If Will Ferrel can run a marathon . . . . If JoDee Mecina can run a marathon . . . . If Ryan Hall (the current US marathon record holder, crossing in record time above at the recent Olympic trials in New York) can run a marathon . . . . then so can Kevin Korpi.

Without my music to carry me through (headphones are not allowed), I truly believe that when needed, I can draw inspiration from acclaimed author, Holocaust survivor, and Nobel laureate Elie Wiesel. Although he never ran a marathon with a number on his bib, he did run for his life, in much worse, almost indescribable conditions. In Night , his memoir of his survival of the Holocaust, there is a unforgettable story of how he, his father, and the other Jewish prisoners, in switching to a different concentration camp near the end of the war, had to run mile after mile after mile, hour after hour after hour, through the night, into the unknown, through the snow and freezing temperatures, through their hunger, through their malnutrition, through their pain, and through their fears, knowing that if they fell, or fell behind, they would be brutalized, or even killed, by the armed German guards. Many did not make it.

He was running for his life. I'm running for glory. He survived. I will prevail too if I have even a fraction of his courage, determination, and hope.

Write your answer next to mine

I would like to thank everyone who reads this blog for NOT emailing me yesterday when you noticed that a new installment failed to appear for the first time since I've been creating my blogs (and my fan base.) To think of fielding ALL those electronic messages would have only increased my tremendously busy schedule, the very reason I never got around to writing a new entry to begin with.

But enough of my delusions of grandeur and my misconception of some imaginary readership. The fact is that I was the only one who likely missed because it was not there. Most people missed it because they did not look for it.

But enough of me going on about me saying that I've said enough about it.

Yesterday I pulled off a feat that I have never done before in my 9 years of teaching: I gave students a test with the answers on the test itself!!! Now I know that that sounds like bad educational practice, but I realized afterwards how brilliant it actually was--it made it more unlikely that people would fail, which is one of our district's goals!!!

It wasn't as bad as I'm exaggerating it to be, though. First of all, only one had answers printed on 25 percent of the test, so the students still had to "guess" the answers to the other 75 percent. Secondly, not everyone taking the test immediately realized what I had done. Some even worked the problems and boxed their "wrong" answers right next the the printed "correct" answer. Perhaps they were too afraid to ask me. Perhaps they thought they were the only ones with the answers printed and didn't want to exploit it. Perhaps they didn't even know.

Finally one girl had the integrity (and the perplexity) to quietly walk up to my desk to ask me what "those numbers" were. I could see all eyes in the class curiously looking at me, awaiting my response. At that moment, I felt embarrassed and let out a giant laugh. The cat was out of the bag--I told the entire class about my mistake. Somewhere in the room, the erasers went into action, changing their answer to the correct one I had given them. I told them that I would still count the question as part of the test so, in essence, they were getting a 25 point curve. Everyone, still laughing from such an egregious oversight on my part, transitioned to a victorious shout of approval.

Here's why it happened. I thought I would put the numeric answers to the free-response question directly on the test, so that when I used it in subsequent years, I wouldn't need a hard copy. Having highlighted the correct answers to the multiple-choice sections, I remembered to un-highlight them before printing the test for mass photoreproduction. What I FORGOT to do, however, was delete the answers to the second section of the test. The result of my blunder was the guarantee that no student would score below a 25 on the test (an some barely ended up beating that out!)

I now realized that even with limited hard-drive space on my school desktop that, as small as the file was, it was worth saving it in two forms: a printable, student version (without answers) and a teacher, key version (with answers). Or, I could just be more thorough, which I usually am.

The reason behind the reason it happened was that this week is the end of the first semester, and I'm trying to desparately squeeze in one more chapter test in each my three different subject areas. Creating my own exams from scratch, this takes quite a bit of time in deciding what I want to test, how I want to ask it, and how difficult do I want to make it. Even after this is pinned down, the actual typing of math symbols in a Word document takes a while too. Once I've got the test made, I need to work all the problems to make sure it is an appropriate length and to catch an mistakes I might have made in its creation. Only then do I run-off copies for each student. Oh, yeah, and all those tests must be graded once they are taken.

This is what I had to do this week, and since it is also Final Exam Week . . . . . I also had to create a 33 question multiple choice for each the three courses, something even more time-consuming that creating the chapter tests. I'm glad, though, I caught the blooper during one of the first tests I gave; it made me a increasingly aware of it as I created the other exams.

I sure would have hated to give a final exam with all the answers on it. That would have been catastrophic--someone might have actually passed!!!!!!

Santa Gets the Cold Shoulder

Life can be lonely some times. Even lonelier when you're alone. Add to that, the stress from a demanding job. Let's also say that you were also chronically, uncomfortably cold. Throw in the holiday season and you've got the ingredients of severe ennui. If that weren't enough, imagine you were all the above AND suffering from cabin fever! Need some help putting this one together? Let's let the highly-educated, devoted staff and scientists on the remote Antarctic research stations demonstrate.

Remote, isolated, and frozen all year, Antarctica is arguably the most untouched and undisturbed region on the planet . . . until now. Apparently out in the middle of nowhere with nothing but snow, high winds, and the occasionally monotony-breaking (and bone-crushing) polar bear, even Ph.D.s can lose control now and then, painting the town red and the snow yellow.

It is reported that several Christmas parties at more than one research site good a little out of hand recently. A Santa Claus groped several female scientists. This was not even a Santa for "hire" but an "in-house" Santa, a fellow scientist. Perhaps the suit gave him the confidence he needed and just the right amount of anonymity he incorrectly thought he had to do something he'd probably been researching for some time. Maybe he just thought red suit gave him a green light to to be jolly. Whatever the motivation, the female gropees apparently did not appreciate the unsolicited stimulation, and likely retired to their private research closets for the remainder of the evening.

Another drunken researcher went on a wild joy-ride on a four-wheel-drive vehicle. How would even you spot a drunken driver in the frozen tundra? Would he be straying across the snow? Would he have hard time keeping in between the white? That would have fun to see. . . from the window of the research hut where the party was going on. "Hey, isn't that Dr. Johanasson out there on the snow cat? Yeah! Let's go put black oil on his microscope eye-piece before he gets back! He is sooooo owned!"

At one party, two individuals, brimming with all sorts of holiday cheer, resorted to violence. Punches flew, and a jaw was broken. Who knows what drunken scientists in Antarctica could have been fighting over at a Christmas Party? Maybe each of them wanted to be Santa Claus (who can blame them for wanting to wear the warm suit)? Maybe they didn't like their gift of "unlimited snow" from the other? Or perhaps they were fighting over who was prettier: Miss Antarctica or Mrs. Claus.

To be sure, is was the most disturbance Antarctica has probably seen in it history. Being good scientists, though, they will probably use the folly and the fall-out from their polar escapade as a valuable learning experience so that they don't repeat the same mistakes next year. But until then, it's back to the cold and lonely research.

Real Fun with Fake Money

It looks like one can make an honest living out of frivolous lawsuits.

Last Wednesday, an article was published revealing that our Federal government was hit with 489,000 lawsuits stemming from the 2005 Katrina disaster totaling $3,014,170,389,176,41. That's 3 + QUADRILLION dollars. Being a math teacher, I occasionally come across very large numbers (not when counting my paycheck), but even I had forgotten what comes after a billion. Because of this beyond-astronomical number, I will not likely soon forget that it is quadrillion.

After my initial shock at such an unfathomably huge dollar amount that was, I did the math to find the AVERAGE amount of each lawsuit, hoping this would bring the number into the realm of reasonableness--it didn't. With 489,000 claims, that comes out to a staggering 6,163,947,626 per person. THAT'S 6.1 BILLION DOLLARS EACH FOR ALMOST HALF A MILLION PEOPLE!!!!! That's equivalent to EVERYONE in Atlanta, Georgia being a multi-BILLIONaire, including toddlers, rugrats, criminals, middle school students, and yes, even every school teacher!! The population of New Orleans was only about 230,000 at the time of Katrina.

But wait, there's more . . . . . .

One claim in particular stood out from the others. It was a staggering $3 quadrillion itself! How much damage can one person suffer to feel they deserve to be compensated by an amount that is more than three times the United State's Gross Domestic Product? I'm guessing they got more than a little water damage. If the diagram above doesn't put a quadrillion into perspective (the cubed stack is made up of 1 quadrillion pennies), this example ought to. Based on the thickness of a penny, if the amount of $3 quadrillion was paid in pennies, and those pennies were stacked, the stack would make 150 round trips to SATURN (or 300 one-way trips.) With Saturn being about 746 million miles aways, the stack would be 300*746 million = 223,800,000,000 miles (that's 223 billion miles.) If you'd rather make fewer round trips, the pennies can make more than 30 round trips from the sun to the once-planet Pluto.

Once you through out this frivolous statistical outlier from the total sum of Federal claims, the average claim amount drops to

($3,014,170,389,176,410 - $3,000,000,000,000,000) / (489,000 - 1) = $28,978,360.23

That's somewhat better, but it still means giving almost $29 million dollars to everyone in Atlanta, Georgia minus one guy (perhaps Ted Turner.)

But who can really put a price tag on human suffering? Is "cold, hard cash" really a proper description of the money these victims seek? Does something cold and hard really comfort? NO! Their seeking warm, soft, cuddly cash, the kind they can snuggle up with and use for toilet paper, or burn if they get too chilly.

It is likely that many of these claims were merely unnatural, punitive acts against the Federal Government by victims who feel slighted by the lack of protection or intervention by a blind act of nature, but the U.S. Army Corps of Engineers, who are taking full responsibility for the levees that eventually failed, are diplomatically claiming in public that they are not passing judgment on the merits of each claim, while they are secretly popping one Advil after another to ease the pain their cheeks are feeling from the laughter produced by each new claim.

It will be interesting to see how this one ends up playing out, and to see how much money is actually award to which individuals.

Mathematical Musings: Part VI

More things I've allegedly said in class.

• Every discipline you enter into has its own challenges. Going into medicine is not necessarily more difficult than going into mathematics. There were several times I wished that I was just memorizing all the nerves in the human body, rather than prove a particular theorem.
• The whole idea of assigning writing journals, yah, that was a bad idea. It looks good on paper, but because of the paperwork generated . . . yah, bad idea.
• We found out we were having a girl: the first girl in four grandchildren. I told my wife that she was going to have really long arms being tugged on between the sets of grandparents.
• We found out it is a girl, so starting today, I’m saving for the wedding . . . and a sawed-off shotgun.
• Having a girl isn’t so bad at all. She’ll just have to get used to wearing her older brother’s hand-me-downs.
• Having a girl is actually ideal. I’m looking forward to choosing a son-in-law someday.
• I think we decided on the first name of Jenna. It’s the middle name we’re still contemplating. We want it to be in honor of a family member: Jenna Wayne, Jenna Lynn, Jenna Rose, Jenna Elaine, Jenna Leslie, Jenna Valeska, Jenna Dora, or Jenna Oma. We like the last one; her initials would be J.O.K. We are expecting her to be a great athlete.
• One grows fat when one’s intake exceeds one’s expenditure. One grows financially thin when one's expenditures exceed ones intake. One cannot expect to be healthfully fit by allowing the two to balance each other: over consuming and over spending. All this achieves is being fat broke.
• When we are looking for the absolute extrema on a closed interval, we can think of it as playing the “BIGGEST AND SMALLEST y-VALUE” contest, where the contestants are going to be the two endpoints, and any critical values in the interval. The winners get the title, the losers get some nice parting gifts, like a broken toaster.
• Keep it straight in you head and always bear in mind that Headings and Bearings are the same thing, unless you’re referring to compositions and axles.
• Be quiet and listen. I’m standing right next to him, and I can barely hear him!
• 37.652 is my favorite value of x.
• Student: “Mr. Korpi, I didn’t do my take home test.” Korpi: “That’s pretty dumb. You’d better have a good excuse!” Student: “I’m getting married tomorrow, and I have just been a nervous wreck getting ready for it.” Korpi: “Fine, but you better bring it to me as soon as you get back from your honeymoon!”
• Q: “Do you know why when geese fly in a ‘V’ formation, the V is longer on one side than the other?” “Does it have anything to do with the sheer winds or anything?” “No, it’s because there are more geese on one side.”
• And so we put the x all by itself on this side of the equation, although he is not alone, since he’s squared, there are really two of them, so he’s really there, with himself, keeping himself company. (on setting up the law of cosines)
• So it doesn’t really matter which angle A, B, or C we find first. Let’s just do it in random alphabetical order . . . starting with C.
• Student: “Mr. Korpi, there’s an error on the assignment sheet. The assignment due today had 12 problems. You wrote 11 down.” Korpi: “Thank you, you are so correct. Give yourself 0.4 points for that one, then round.”
• So let’s say I’m on the beach sunbathing, and I get the inkling to measure the distance between two oil rigs out in the seascape. I pull out my handy-dandy angle-measuring device, which I always keep handy while sunbathing, and take some measurements. I only need to take two angle readings from two separate points along the beach. I must also know the distance between these two points, say 2000 seashells long, mostly broken seashells. Using the Law of Sines and Cosines, I can determine the distance between the two without having to swim way out there with a huge waterproof tape measure, and, most importantly, I can get back to my sunbathing.
• I heard that the tanning salons now offer a service where you stand in front of a paint machine and it blasts you with golden paint. That can’t be good for you, especially when it must be done weekly, and that’s if you don’t bathe. At least the paint on my house is guaranteed for 20 years.
• When experiencing my personality, you cannot fully appreciate or be properly effected by it by brief intense exposure to it. Much like sunbathing, in order to keep from reacting adversely to it, you need to experience it small daily doses. Under these circumstances, I provide a healthy glow to other people’s lives, rather than a painful, nasty burn.
• The only thing mathematical about the math club this year is how membership has multiplied from last year. (from 14 to 64, as people joined just to socialize and eat food.)
• Student: “Does Little Korpi play trumpet, too?” Korpi: “Heaven’s No! He’s not even 2 and a half years old. He’s barely got the piano and guitar down.”
• Korpi is listening to “Crazy little thing called love” by Queen. A student says, “Man, you’re old, Mr. Korpi.” Korpi quickly replies, “Let me guess. You prefer Dwight Yoakum’s version.” Student assumes look of befuddlement and bewilderment.
• Did you think these variables here were just to decorate the equation?
• Be on the lookout for irrelevant information in the problem such as the sexual preference of the pilot of the plane that isn’t even mentioned.
• I feel like I’m looking at the penguin exhibit at Sea World. (Gliding across the floor, leaning on the roller cart. Students very quiet and sitting very still, room is very cold.)
• If you finish making your Golden Ratio rectangles, measure your faces and see if you and Liz Hurley have something in common.
• Student: “Why is everybody wearing College shirts today?” Korpi: “Well, because it’s college day. But that’s OK, we can tell you’re an Aggie without a maroon shirt.”
• I heard next Friday is “wear your pajamas to school” day. I hope the people who sleep in the nude are sick that day so the rest of us won’t be.
• If you have physics, you’ve probably done this calculation in class. If you don’t have physics, you probably haven’t done this in physics class.
• One thing I can tell you about the conference I attended was, even though it really sucked and the presenter was boring, I still stayed quiet and appeared to be listening as he spoke. It is the obligation of a student.
• So let’s say we’re trying to move this piano. We tie two ropes to the foot pedal and the two of us pull at different angles and forces. The resultant force and direction will be the diagonal of the parallelogram, which means we know exactly where the piano is going; it can hit a target, which I guess is pretty important in piano bowling.
• You can’t say, “Just because I drew it like a right triangle, it must be so."
• We use implicit differentiation when we either cannot solve explicitly for y, it is too difficult to solve for y, or we’re just too plain lazy.
• The case of SSA is called the Ambiguous case, or something like that.
• Someday I’m going to invent a new and improved fly swatter.
• Brady, please wake up! Every time you lay your head down on your desk, a little piece inside of me dies.
• The official name of this course, as far as the state of Texas goes is, “Independent study in mathematics,” although we call it Calculus. I’m terribly sorry I have been depriving you of your independence to learn it on your own. If I get fired, it will be for teaching in a class where I’m not supposed to.
• And so, if we were to jump off the building and calculate or speed, we would yell as we leapt, “BEEEEEEEEEEEEEEP.” (the bell to go to lunch chimes in).
• You! You are tardy, and I need to talk to you about all the classes you have missed this six weeks. Please stay after class. S: I can’t, I have to leave early to take a friend to a doctor’s appointment! K: So, either you don’t come at all, but when you do, you come late and leave early. Let me simply state it then: YOU’RE A BEHIND!!! Did I say "A?"
• We call this theorem the Mean Value Theorem because it deals with average values and because he is quite a bully.
• In response to a playful question at the end of a difficult test involving the rate of change of a deflating balloon, “What color is the balloon?”—Student: The color of the balloon symbolizes my feelings towards this test—ASS BROWN.
• Here’s looking at Euclid.
• The Calculus Cop’s job is to enforce the law of Cosines.
• The other day I looked in the mirror. I sure look funny with my eyes closed.
• Why yes Principal F. , the Math Club IS having a raffle. Would you like to buy a ticket? First prize is a dozen dead AAA batteries from our calculators. Second prize is a handful of dried-up dry erase markers which we generate daily!
• Someday I’m going to write an Autobiography, if I can authorize it.
• Please remind me to remind you to tell me when I have forgotten to mention something I should have remembered to tell you about.

Buying Expensive Band-Aids

One of the latest optimistic, hopeful attempts on our high school campus of raising standardized test scores is to purchase very expensive technology, specifically a calculator system that allows teachers to monitor each student's progress in terms of key strokes from a convenient hand-held. This is in sharp contrast to the plight of the current situation which requires a teacher to walk around the room and actual look at what a student is doing.

Personally, I am very skeptical whether it's worth spending the exorbitant amount of money to get these devices, when we currently have high-powered hand-held calculators in each of our math classes. Merely purchasing and acquiring something new does not mean that it will be the panacea for all the ills, namely poor test scores, that are drawing so much attention from the non-initiate administrators and public. It surely feels good, though, to spend money on the latest and greatest, because it is an easy thing to do which you would EXPECT to be fruitful and beneficial, creating a record of an earnest attempt to fix a problem, thereby creating an alibi against apathy and ambivalence.

But what SHOULD be done is a thorough analysis of WHY standardized math scores are low. Only then and a real, long-term, meaningful solution be sought out. Rather than merely treating symptoms, the underlying cause of the illness should be conducted if the goal is to eradicate the disease. Treating the symptoms only makes the Band-Aid company rich, as the demand will always be there. How many Band-Aids does it take to cover a sucking gut wound? Wouldn't surgery and stitches be a better option? Sure, it takes more know-how and more time to heal, but healing DOES eventually take place.

Take for instance a brand new piece of exercise equipment that an eager individual purchases for a grand amount with the hopes of losing weight and living a healthier lifestyle. Does the mere possession of the expensive equipment guarantee that he we lose weight or will even use it once the novelty and the guilt of spending too much on it wears out? Absolutely NOT. This is why so many people have the same New Year's resolutions year after year--intentions and fancy equipment or gym memberships do not guarantee any results. They are Band-Aids to a deeper problem, usually a dearth of will-power and a surplus of excuses.

Or imagine another case that fails for a different reason. Perhaps an individual is excited about jumping on the technological bandwagon and buys a brand-new, high-dollar computer with all the bells and whistles. Assuming this person has high motivation to learn how to use the computer, including turning it on, opening programs, loading software, troubleshooting problems, etc. There is a GIANT learning curve in being able to go from no computer to being computer literate. I've seen this reality first-hand in the last 10 years as school districts have become increasingly dependent on computers: many of the "old school" teachers were very reluctant, hesitant, and afraid to adopt and learn the new methods.

Such dramatic transitions require a great deal of training and encouragement along the way. Would it be prudent if, after failed attempts to master everything about the modern-day computer, one simply abandoned the device and purchased a brand-new one? Should we expect different results? It would be foolish, irrational, and wasteful to think so. The problem is not the computer (or the exercise equipment), it is in USING them!

My point is that our school and math department are currently equipped with the appropriate "calculator" technology. Each student has daily access to a hand-held device that can do almost as much as a high-powered computer. We even have the technology to effectively display screen commands and to teach its appropriate use. The problem is NOT with what we have, it is in HOW we use them and HOW we teach our students to use them. Spending more money on newer, more powerful, more complicated calculators will not "magically" solve any problems. What we need is proper training for teachers about all the amazing things these calculators can do, and how they can be used as TOOLS, rather than CRUTCHES--how to use them for exploration, but not as a substitute for original thought or calculations such as 5+7 (which I've seen kids reflexively reach for their calculator when confronted with.)

I feel fortunate to know quite a bit about the true utility of these computational devices, but I also make a deliberate effort to learn about them, and then pass this on to my students. In fact, many of my college-bound students know their calculators extensively and occasionally teach ME something I didn't know about them. Unfortunately, students are handed a calculator at a very early age, too early in my opinion, and are never give real instruction on HOW and WHEN to use them. It's the equivalent of handing a ripe teenager the keys to a car for the first time with the instructions of "Don't crash."

Empowered with nothing more than a vague intention, given as an inflexible command, the only thing that is likely is that the car will crash. I'm afraid that's where our curriculum is heading. Which means, after that happens, we'll likely keep replacing the old with "shiny new" ones, with no better training, guidance, or instruction than we did previously.

I'm going to go online to E-trade now and buy stock in Band-Aids. It looks like the demand will be there for a while.

Mathy New Year!

The first day back at school after a long two-week holiday break is always a bit difficult for students and teachers alike. Most knowledge learned, or at least exposed to, prior to the break has been dormant in students' minds, as they have resorted to staying up late, sleeping in late, perhaps working to earn some cash, drinking coffee with friends at 3 in the afternoon, and playing the occasional video game. In other words, they are a bit "rusty" when they get back to the classroom.

Some teachers, too, need a little time to get back into the full swing of assigning homework. Even I needed a good thirty seconds at the start of first period this morning to get my mathematical bearings after my two week hiatus for mathemagicland. I think it took my students a bit longer to adjust, as most were in disbelief that I was able to pick up exactly where I left of in 2007. I know they were hoping for a more gentle transition back into the academic environment, perhaps a nice discussion on what they did over the break or a comparison of cool Christmas gifts or unusual New Year's resolutions, but in my class they don't really expect it.

In fact, the only New Year's Resolution that was announced was my own proclamation of my efforts to move more quickly through mathematical content and to talk more rapidly during class. Although that's not what I resolved to do (I really intend on assigning more homework, especially from sections I haven't yet covered-MUHAAAWAAAAHAAA), it was fun to see the reaction on the students' faces when I announced it and began talking faster than the guy on the old Micro-Machine commercials.

After I got the reaction I wanted, I plugged away at the math, reviewing the concepts we covered prior to the break (knowing that NOT doing this would be more counter-productive than proceeding with new material), and even eventually got to a point where I actually asked about cool Christmas gifts (my excuse to tell everyone about my cool Xbox 360 my son got from me.) One student was excited to say that he got three games from his parents for the Nintendo Wii System, but he doesn't have a Wii System, nor did they get him one. I shared that I once got a Compact Disc from my parents without having or getting a CD player. I spent a week spinning the disc on my finger and listening carefully for music before I realized the problem. Although it was entirely fictitious, it related well to the student's predicament, and we all got a good laugh at this as we wrote down the next math problem from the board.

So tomorrow, being the second day back from our break, I hope the students will be back in full academic form as we hit the ground fast and hard in the game of public education, where Milk break, Recess, Nap time, and Movie Day are an archaic thing of the past (and possibly the present and future for some.) In my case, the math does not teach itself, and for me, that's job security.

Mathy New Year!

An evening with Denzel

Yesterday, my wife and I celebrated our 11th year of marriage, although celebrated is a bit of an exaggeration. With Cedar Allergy Season (Yes, a Proper Noun) in full swing, my wife has been putting in long hours at the Asthma and Allergy clinic she works for. So if you consider her leaving the house at 6:30am, working straight through lunch, and returning home around 6pm, all while I ran around town getting her oil changed (on her car that is) and running errands, then celebrate it we did.

Even my two children, who perhaps didn't realize that our spending weekdays together was almost over, even though I reminded them repeatedly, wanted to spend the day at their grandmother and recently-retired grandfather's house. This meant I spent most of my anniversary alone, at home--just me and Guitar Hero III.

Later in the evening, I met my wife, the kids, and her parents for dinner at a Mexican restaurant. Having snacked on high-carb, Guitar Hero food all day long, I wasn't very hungry, so I just sat at the table watching everyone else eat their enchiladas, tacos, chalupas, rice, beans, chips, tortillas, salsa, and queso while chopping on an occasional ice cube. After we got the leftovers put away in the take-home boxes and refusing the waiter's invitation for dessert (I guess he thought we might want to stuff some sopapillas in our doggie bag with the leftover enchilada), my in-laws were kind enough to pick up the tab--a nice anniversary gift.

The best anniversary gift they gave us, however, came later in the evening when they offered to keep both of our kids (on the condition that they give them back today), so my wife and I were able to go back home and have a quiet evening to ourselves. Well, we decided to share our evening with Denzel Washington and Dakota Fanning who starred in "Man on Fire." The four of us spent two and a half hours together in a riveting, glued-to-our-seats saga of redemption and revenge--perfect motifs for 11 years of marriage.

After the movie, we kept the inappropriate themes going by watching an episode of "Intervention" on A&E on Demand. After watching a former NBA star lose his wife, his two daughters, and his life to his heroin addiction, we were really appreciative of what we have and how we have been able to stay away from heroin for 11 blissful years.

The themes of our programming all came full circle as we were reminded of the fragility of life, the unconditional love and pure innocence of children, and how we are making wise financial decisions by deciding to buy food, clothing, and shelter with our earnings, rather than bodyguards and crack-cocaine.

Yep, it turned out to be a rather nice anniversary after all.

The search for X

Algebra may divided into "classical algebra" (equation solving or "find the unknown number" problems) and "abstract algebra", also called "modern algebra" (the study of groups, rings, and fields). Classical algebra has been developed over a period of 4000 years. Abstract algebra has only appeared in the last 200 years.

The development of algebra has fallen under the following major influences: Egyptian algebra, Babylonian algebra, Greek geometric algebra, Diophantine algebra, Hindu algebra, Arabic algebra, European algebra since 1500, and modern algebra.

Since algebra grows out of arithmetic, recognition of new numbers - irrationals, zero, negative numbers, and complex numbers - is an important part of its history, and will be an important part of any Algebra course.

The development of algebraic notation progressed through three stages: the rhetorical (or verbal) stage, the syncopated stage (in which abbreviated words were used), and the symbolic stage with which we are all familiar.

Babylonian Algebra

Preserved in cuneiform written on clay tablets, the mathematics of the Old Babylonian Period (1800 - 1600 B.C.) was more advanced that that of Egypt. Their math utilized a sexagesimal base number system (base 60) which led to a highly developed algebra. Our custom of giving 360^o to a circle, 60 seconds in a minute and 60 minutes in an hour are cultural artifacts passed down to us from the Babylonians. They were able to solve quadratic equations and worked with systems of equations with more than one unknown. There was some use of symbols, but not much. Like the Egyptians, their algebra was essentially rhetorical, and they only accepted positive, rational (fractional) solutions. Negative and irrational solutions were rejected.

Greek Geometric Algebra

The Greeks also rejected irrational numbers and insisted on representing quantities as geometrical magnitudes. They focused more on form, such as triangular and square numbers. Although this period ultimately gave us the Pythagorean theorem and many great ideas, the geometric approach to algebra was of little practical value and actually slowed the development of symbolic, algorithmic algebra for several centuries.

Diophantine Algebra

The later Greek mathematician (250 A.D.) is regarded as one of the first to move from geometrical algebra to a treatment which did not depend upon geometry. He is, therefore, regarded as the “father of algebra.” Although the rhetorical, verbal style was still in use, he introduced the syncopated style of writing equations, where words were abbreviated and symbols were used.

In his Arithmetica, he gives a treatment of indeterminate equations - usually two or more equations in several variables that have an infinite number of rational solutions. Such equations are known today as "Diophantine equations". Although the use of symbols and abbreviations was a major leap from the rhetorical style, Diophantine did not develop general methods for solving his equations. In fact, each of the 189 problems in the Arithmetica is solved by a different method. He, too, only accepted only positive rational roots and ignored all others.

Hindu Algebra

The successors of the Greeks in the history of mathematics were the Hindus of India. The Hindu civilization dates back to at least 2000 B.C. Their record in mathematics dates from about 800 B.C., but became significant only after influenced by Greek achievements. Most Hindu mathematics was motivated by astronomy and astrology. A base ten, positional notation system was standard by 600 A.D. They treated zero as a number and discussed operations involving this number.

The Hindus introduced negative numbers to represent debts. The first known use is by Brahmagupta about 628. They recognized that a positive number has two square roots. The Hindus also developed correct procedures for operating with irrational numbers.

They made progress in algebra as well as arithmetic. They developed some symbolism which, though not extensive, was enough to classify Hindu algebra as almost symbolic and certainly more so than the syncopated algebra of Diophantus.

Arabic Algebra

While much of Europe was in the dark ages, the Arabs preserved the Greek learning and flourished in the study of arts and sciences. They took over and improved the Hindu number symbols and the idea of positional notation. These numerals (the Hindu-Arabic system of numeration) and the algorithms for operating with them were transmitted to Europe around 1200 and are in use throughout the world today.

In algebra, the Arabs contributed first of all the name. The word "algebra" come from the title of a text book in the subject, Hisab al-jabr w'al muqabala, written about 830 by the astronomer/mathematician Muhammad ibn Mūsā al-Khwārizm. The book was a systematic exposé of the basic theory of equations, with both examples and proofs. It is interesting that our word "algorithm" comes from a corruption of al-Khwārizm 's name.

While ancient civilizations wrote out algebraic expressions using only occasional abbreviations, by medieval times Islamic mathematicians were able to talk about arbitrarily high powers of the unknown x, and work out the basic algebra of polynomials (without yet using modern symbolism.)

European Algebra after 1500

At the beginning of this period, zero had been accepted as a number and irrationals were used freely although people still worried about whether they were really numbers. Negative numbers were known but were not fully accepted. Complex numbers were as yet unimagined. Full acceptance of all components of our familiar number system did not come until the 19th century. Algebra in 1500 was still largely rhetorical. Renaissance mathematics was to be characterized by the rise of algebra.

In the 16th century, the main focus was on solving polynomial equations. During this time, there were great advances in technique, namely the general solutions to cubic equations. There were also at this time many important improvements in symbolism which made possible a science of algebra as opposed to the collection of isolated techniques ("bag of tricks") that had been the content of algebra up to this point.

Publication of many of these results in 1545 in the Ars Magna by Italian Renaissance mathematician, physician, astrologer, and gambler Girolamo Cardano is often taken to mark the beginning of the modern period in mathematics.

The landmark advance in symbolism was made by François Viète (French, 1540-1603) who used letters to represent known constants (parameters). This advance freed algebra from the consideration of particular equations and thus allowed a great increase in generality.

Viète's algebra, however, was still syncopated rather than completely symbolic. Symbolic algebra reached full maturity with the publication of French mathematician and philosopher René Descartes' La Géométrie in 1637. This work gave the world the wonderfully fruitful marriage of algebra and geometry that we know today as analytic geometry.

Work continued through the 18th century on the theory of equations, but not until 1799 was the proof published, by the German mathematician Carl Friedrich Gauss, showing that every polynomial equation has at least one root in the complex plane. This was to be known as the Fundamental Theorem of Algebra.

By this time, algebra had entered its modern phase. Attention shifted from solving polynomial equations to studying the structure of abstract mathematical systems whose axioms were based on the behavior of mathematical objects that were encountered when studying polynomial equations, such as complex numbers.

So the next time you're searching for x, know that there is a great history behind its search, and the beauty of the endeavor, is that it is a different experience and a unique result every time.

61 cool, cool years

61 is the integer following 60 and preceding 62. It is also the 18th prime number. It is the atomic number for the element Promethium. 61 corresponds to the Messier number for the constellation Virgo, and the constellation Pisces in the NGC catalogue. You must dial 61 to place a direct call to Australia. 61 was Richard Nixon's age when he resigned the Presidency, and the age of his successor, Gerald Ford. 61 is the number of home runs Roger Maris hit in '61, breaking Babe Ruth's record. Tom Seaver and Nolan Ryan each had 61 career shutouts.

61 is also how many years New Braunfels Radiator Works was in business.

Yesterday was a landmark day for my father-in-law, a bittersweet day filled with a little regret and great relief. After 61 years in the radiator repair business, one started in 1947 by his father after WWII, he signed the papers that sold his repair shop and the land it sits on. As with anything that has had such a long and prosperous run, it is a bit difficult to see it end, but it was time for it to go.

The radiator repair business in New Braunfels has had a stalwart presence for so long. People from from far and wide stopped in over the years to have their automobiles repaired. "If it's hot, we'll cool it," was more than a slogan, it was a way of life for two generations of families. Working over his vat, alone, my father-in-law labored for years and years getting people back on the road, fixing thousands upon thousands of blown head gaskets, damaged fins, and leaky coils. He took pride in his work and his name, like his father before him, and had a reputation for being the best (and having the best prices.)

Shortly after I began dating my father-in-law's daughter, I remember once telling my grandmother, who lives in a neighboring city, of the best place to go if she ever had radiator problems. Like a good stubborn German lady, she cut me off abruptly and said, "I don't care where you tell me to go, I only go to one place, and I've been going their for years: New Braunfels Radiator Works." Needless to say, I didn't try to convince her otherwise.

But throughout the years, the radiator repair business has been in decline. More and more radiators are plastic and disposable, making them difficult and not cost-effective to repair. With the proliferation of auto parts stores, who sell cheap radiators to the average Joe, the business has taken on more of a radiator replacement, rather than repair business in recent years. Even the large industrial radiators that still were repairable quit coming in. As a result, the once thriving prosperous little shop, whose business earned enough money to raise 6 children over two generations, now was struggling to make a profit.

I had consistently urged my father-in-law to diversify into other areas like Air-conditioning or heat coil work, but he told me that would only create ill-will between his business and the businesses already doing that type of work (who sometimes sent him a customer or two.) But that's the type of honorable business he ran, which is why the business was so reputed and respected, but also why it was so hard to see the writing on the wall.

Having researched the prosperous shops nationwide that were still doing well, I even entertained the idea of going into business with him, hiring some people, and making the business expand in size and scope. He always told me know, telling me it was a "dying business." I guess he was trying to protect me, and I can see his point, but my motive was the same as his many, many years ago when he went to work with HIS father. I couldn't see letting such a long-standing, reputable business with a equally reputable name just count the days to its ultimate end. But after several years of being told "no," I eventually gave up the idea.

And so, he continued opening the little two-bay shop on the city's west side each morning at 7:30, worked straight through lunch until closing time at 5:00 each afternoon, 5 days a week. Some days he would have a little work, sometimes nothing at all. But you could always drive by and get a friendly wave from him, whether he was standing over his vat, squatting out front puffing on a cigarette, or sitting behind his counter with a picture of his father over his head, watching traffic go by.

In the end, I think he finally decided that he would not be letting his father down in any way by closing the shop, but rather, he realized that his father would have done the same thing in the same circumstances. There's a difference between "Open for Business," and "Open for Nostalgia." It was time to close the doors on a way of life. And so it was on January 2nd, 2008, the "Best Place in town to take a Leak" was no longer New Braunfels Radiator Works.

Does God Exist???? Part I

A while back, I posted a blog arguing the different philosophical arguments of God's existence. Here are some more concise arguments, many more of which to follow. If you don't believe in at least one of them, please go to penance and ask for forgiveness.

1. TRANSCENDENTAL ARGUMENT
   (1) If reason exists then God exists.
   (2) Reason exists.
   (3) Therefore, God exists.
2. COSMOLOGICAL ARGUMENT
   (1) If I say something must have a cause, it has a cause.
   (2) I say the universe must have a cause.
   (3) Therefore, the universe has a cause.
   (4) Therefore, God exists.
3. ONTOLOGICAL ARGUMENT (I)
   (1) I define God to be X.
   (2) Since I can conceive of X, X must exist.
   (3) Therefore, God exists.
4. ONTOLOGICAL ARGUMENT (II)
   (1) I can conceive of a perfect God.
   (2) One of the qualities of perfection is existence.
   (3) Therefore, God exists.
5. MODAL ONTOLOGICAL ARGUMENT
   (1) God is either necessary or unnecessary.
   (2) God is not unnecessary, therefore God must be necessary.
   (3) Therefore, God exists.
6. TELEOLOGICAL ARGUMENT (I)
   (1) Check out the world/universe/giraffe. Isn't it complex?
   (2) Only God could have made them so complex.
   (3) Therefore, God exists.
7. ARGUMENT FROM BEAUTY, aka TELEOLOGICAL ARGUMENT (II)
   (1) Isn't that baby/sunset/flower/tree beautiful?
   (2) Only God could have made them so beautiful.
   (3) Therefore, God exists.
8. ARGUMENT FROM MIRACLES
   (1) My aunt had cancer.
   (2) The doctors gave her all these horrible treatments.
   (3) My aunt prayed to God and now she doesn't have cancer.
   (4) Therefore, God exists.
9. MORAL ARGUMENT (I)
   (1) Person X, a well-known Atheist, was morally inferior to the rest of us.
   (2) Therefore, God exists.
10. MORAL ARGUMENT (II)
    (1) In my younger days I was a cursing, drinking, smoking, gambling, child-molesting, thieving, murdering, bed-wetting bastard.
    (2) That all changed once I became religious.
    (3) Therefore, God exists.
11. ARGUMENT FROM CREATION
    (1) If evolution is false, then creationism is true, and therefore God exists.
    (2) Evolution can't be true, since I lack the mental capacity to understand it; moreover, to accept its truth would cause me to be uncomfortable
    (3) Therefore, God exists.
12. ARGUMENT FROM FEAR
    (1) If there is no God then we're all going to die.
    (2) Therefore, God exists.
13. ARGUMENT FROM THE BIBLE
    (1) [arbitrary passage from OT]
    (2) [arbitrary passage from NT]
    (3) Therefore, God exists.
14. ARGUMENT FROM INTELLIGENCE
    (1) Look, there's really no point in me trying to explain the whole thing to you stupid Atheists -- it's too complicated for you to understand. God exists whether you like it or not.
    (2) Therefore, God exists.
15. ARGUMENT FROM UNINTELLIGENCE
    (1) Okay, I don't pretend to be as intelligent as you guys -- you're obviously very well read. But I read the Bible, and nothing you say can convince me that God does not exist. I feel him in my heart, and you can feel him too, if you'll just ask him into your life. "For God so loved the world that he sent his only begotten son into the world, that whosoever believes in him shall not perish from the earth." John 3:16.
    (2) Therefore, God exists.
16. ARGUMENT FROM BELIEF
    (1) If God exists, then I should believe in Him.
    (2) I believe in God.
    (3) Therefore, God exists.
17. ARGUMENT FROM INTIMIDATION
    (1) See this bonfire?
    (2) Therefore, God exists.
18. PARENTAL ARGUMENT
    (1) My mommy and daddy told me that God exists.
    (2) Therefore, God exists.
19. ARGUMENT FROM NUMBERS
    (1) Millions and millions of people believe in God.
    (2) They can't all be wrong, can they?
    (3) Therefore, God exists.
20. ARGUMENT FROM ABSURDITY
    (1) Maranathra!
    (2) Therefore, God exists.
21. ARGUMENT FROM ECONOMY
    (1) God exists, you bastards!
    (2) Therefore, God exists.
22. BOATWRIGHT'S ARGUMENT
    (1) Ha ha ha.
    (2) Therefore, God exists.
23. DORE'S ARGUMENT
    (1) I forgot to take my meds.
    (2) Therefore, I AM CHRIST!!
    (3) Therefore, God exists.
24. ARGUMENT FROM GUITAR MASTERY
    (1) Eric Clapton is God.
    (2) Therefore, God exists.
25. ARGUMENT FROM INTERNET AUTHORITY
    (1) There is a website that successfully argues for the existence of God.
    (2) Here is the URL.
    (3) Therefore, God exists.
26. ARGUMENT FROM INCOMPREHENSIBILITY
    (1) Flabble glurk zoom boink blubba snurgleschnortz ping!
    (2) No one has ever refuted (1).
    (3) Therefore, God exists.
27. ARGUMENT FROM AMERICAN EVANGELISM
    (1) Telling people that God exists makes me filthy rich.
    (2) Therefore, God exists.
28. MITCHELL'S ARGUMENT
    (1) The Christian God exists.
    (2) Therefore, all worldviews which don't assume the Christian God's existence are false and incomprehensible.
    (3) Therefore, God exists.
29. ARGUMENT FROM BLINDNESS (I)
    (1) Atheists are spiritually blind.
    (2) Therefore, God exists.
30. ARGUMENT FROM BLINDNESS (II)
    (1) God is love.
    (2) Love is blind.
    (3) Stevie Wonder is blind.
    (4) Therefore, Stevie Wonder is God.
    (5) Therefore, God exists.
31. ARGUMENT FROM FALLIBILITY
    (1) Human reasoning is inherently flawed.
    (2) Therefore, there is no reasonable way to challenge a proposition.
    (3) I propose that God exists.
    (4) Therefore, God exists.
32. ARGUMENT FROM SMUGNESS
    (1) God exists.
    (2) I don't give a crap whether you believe it or not; I have better things to do than to try to convince you morons.
    (3) Therefore, God exists.
33. ARGUMENT FROM META-SMUGNESS
    (1) Up Yours!.
    (2) Therefore, God exists.
34. ARGUMENT FROM MANIFESTATIONS
    (1) If you turn your head sideways and squint a little, you can see an image of a bearded face in that tortilla.
    (2) Therefore, God exists.
35. SLATHER'S ARGUMENT
    (1) My toaster is God.
    (2) Therefore, God exists.
36. ARGUMENT FROM INCOMPLETE DEVASTATION
    (1) A plane crashed killing 143 passengers and crew.
    (2) But one child survived with only third-degree burns.
    (3) Therefore, God exists.
37. ARGUMENT FROM POSSIBLE WORLDS
    (1) If things had been different, then things would be different.
    (2) That would be bad.
    (3) Therefore, God exists.
38. ARGUMENT FROM SHEER WILL
    (1) I DO believe in God! I DO believe in God! I do I do I do I DO believe in God!
    (2) Therefore, God exists.
39. ARGUMENT FROM NONBELIEF
    (1) The majority of the world's population are nonbelievers in Christianity.
    (2) This is just what Satan intended.
    (3) Therefore, God exists.
40. ARGUMENT FROM POST-DEATH EXPERIENCE
    (1) Person X died an Atheist.
    (2) He now realizes his mistake.
    (3) Therefore, God exists.
41. ARGUMENT FROM EMOTIONAL BLACKMAIL
    (1) God loves you.
    (2) How could you be so heartless to not believe in him?
    (3) Therefore, God exists.
42. ARGUMENT FROM SACRIFICIAL BLACKMAIL
    (1) Jesus died for your sins.
    (2) Therefore, God exists.
43. ARGUMENT FROM INCOHERENT BABBLE
    (1) See that person spazzing on the church floor babbling incoherently?
    (2) That's how infinite wisdom reveals itself.
    (3) Therefore, God exists.
44. OPRAH'S ARGUMENT (I)
    (1) The human spirit exists.
    (2) Therefore, God exists.
45. OPRAH'S ARGUMENT (II)
    (1) Check out this video segment.
    (2) Now how can anyone watch that and NOT believe in God?
    (3) Therefore, God exists.
46. CALVINISTIC ARGUMENT
    (1) If God exists, then he will let me watch you be tortured forever.
    (2) I rather like that idea.
    (3) Therefore, God exists.
47. ARGUMENT FROM CROCKERY
    (1) Pots don't go around giving orders to the potter.
    (2) Therefore, God exists.
48. ARGUMENT FROM MASS PRODUCTION
    (1) Barbie dolls were created.
    (2) If Barbie dolls were created, then so were trees.
    (3) Therefore, God exists.
49. ARGUMENT FROM PAROCHIALISM
    (1) God is everywhere.
    (2) We haven't been everywhere to prove he's not there.
    (3) Therefore, God exists.
50. ARGUMENT FROM UPPERCASE ASSERTION
    (1) GOD EXISTS! GET USED TO IT!
    (2) Therefore, God exists.

Happy New Year

Yesterday while I was out running on the last day of 2007, I got many encouraging looks and even a few thumbs up from people driving by or out walking. At first, I thought they were just being friendly and encouraging, but then, as I always do, my mind began to wander, investigate, and over-analyze their motives.

What I surmised is that those people must have thought that I was getting a jump start on my New Year's resolution, and they felt compelled to boost my motivation. So in either case, I say "thank you" to those people whose bright smile put an extra spring in my step.

Last week, the local newspaper published the top 5 New Year's resolutions from a reader poll, and the list contained the usual suspects. The number one goal was to lose weight. Others were exercise more and consume less alcohol. These are very admirable goals for any person, but because they're all related and each is very difficult to do, many people with the best of intentions to fulfill these goals don't stick to the exacting, demanding rigor of making them last. I know this personally, as I have been doing it now for 1.5 years, and although I have lost about 40 pounds and feel better than ever, it still must force myself to run daily and conscientiously think carefully about what I'm consuming.

At the beginning of each year, I always see an increase in the number of people out jogging, but after a week or two, I don't see them any more. What does this mean? Does it mean they lost the weight they desired in a mere week and quit? Does it mean that they bought a membership to a gym and are now training indoors on a treadmill? Most likely, it means that the anticipation of losing weight, the energy of a new year and new hope was swallowed up by the reality that running is hard work and takes daily discipline. It also means adjusting one's daily schedule to make time to do it. In a world with super-sized combo meals and daily planners filled to capacity, it all too easy to let oneself off the hook when it comes to diet and exercise.

The mindset of "going on a diet" has made many savvy individuals very wealthy by offering unique ways to temporarily change eating habits to results. But most people will tell you that once they go "off" the diet, they typically gain all, if not more weight back. Some people are unsuccessful on their diet: "I ate Brussels sprouts and raw bacon for fourteen days, and all I lost were two weeks!" For a diet or an exercise program to work, they cannot be something that one goes on and off of, they must be a way of life. A diet is WHAT you eat. Exercise is WHAT you do.

So whatever your resolutions are this year, may they be more than vacuous words and hollow goals. May you be empowered to change your mindset and your habits to effectively change your health, wardrobe, and lifestyle.

If I see you out running, I'll be sure to give you a big smile and and a reassuring "thumbs up!"

Have a great 2008!