A pretty Fair day

Yesterday was a school holiday—not a national or state holiday, just a day off for a time-honored tradition: The Comal County Fair. The Fair is one of the largest in Texas, and for the locals, it is a chance to celebrate with old friends, watch the parade, take in the exhibits, ride some rides, watch a rodeo, dance a jig, drink a little bit, and take in the smell and grime of livestock. It’s fun for everyone.

This year has already turned out to be quite a memorable one for my family. For the first time, my 7-year-old son and 4-year-old daughter entered baked goods for judging. We were as excited as they were when we discovered that my son’s “peanut butter-filled, chocolate delight” cookies won first place, beating out some handsomely decorated graham crackers and a Rice Krispie treat. My daughter’s “Oreo cookie crumble cupcakes won a second-place ribbon, beating out a Little Debbie brownie and a slice of bread from a commercial loaf.

Seriously, though, there were several homemade items, but it was obvious that many entered something from the pantry simply to earn a free entry ticket to the fair grounds. Although my wife helped the kids decide what they should make, with me getting to sample the prospects, my kids actually made their entries entirely by themselves. We are very proud of their efforts.

The next day (Friday) was the big holiday, which meant the grand parade, with the “Pet Parade” being the opening act. Again for the first time, my kids decided to participate. We decorated my daughter’s “Gator” and put our four three-week-old kittens in the back dump bed inside a plexi-glass enclosure. My son pulled our two Pygmy goats in their cage on the wagon. Unbeknownst to us, their entries were to be judged prior to the parade. Well, they were two for two. My son won a first place ribbon for his “Goat Float,” and my daughter took “Best of Show” in the “Baby Kittens in a Dump Bed” category, winning a first place ribbon AND an very nice trophy. The paper took pictures and they made the paper!! I didn’t realize that the kittens would be so popular! Prior to the parade, those poor kittens got more attention than a free ATM machine. Many people assumed we were giving them away, which we weren’t . . . . YET. I mean, we had to parade them first. If I could have sold kittens that morning for a penny each, I could have made at least a dollar!! It was something special to walk with my kids through the streets of downtown with thousands of people along the curbs admiring them. I could have sworn I heard many peoples saying “look at those beautiful children!! They look just like their father,” but I also have a crazy imagination, too!

Tomorrow (Sunday) is the last day for the big event, which means we’ll spend all day at the fairgrounds riding all the rides (or in my case, switching my attention between watching my kids go in circles on the rusty, sticky race cars and counting cigarette butts on the ground within a one-arm radius of the carnival workers.) By the last day at the carnival, all the bolts on the rides have had a chance to “rattle loose,” and the carnival workers are cranky and hung-over. It’s always thrilling to see how close a lit cigarette can get to your kid’s face as the workers strap them in with a dilapidated strap that has more slack in it than our school’s policy on late work.

My kid’s will also be competing in the youth tractor pull, a contest where they have to peddle a small tractor as far as they can as the weight sled slides forward, as all the old-timers with brown polyester Levis and “taco” cowboy hats sit back, watch, and grin while sipping their Schaefer Light Beer, wishing they could still use their legs like those “whippersnappers.”

Yep, things are always interesting at the carnival.

Abacus, anyone?

“It is nothing short of a miracle that modern methods of instruction have not yet entirely strangled the holy curiosity of inquiry.”—Albert Einstein

Yesterday morning at our 6:30 am Math Club meeting, we discussed the Abacus. We watched videos of Chinese and Japanese students demonstrating amazing speed and efficiency using this "retro-calculator." They start students off very early learning to use the Abacus, which helps students understand counting in the concrete, getting their brains churning while their eyes flip back and forth from paper to abacus keyboard, all while their tiny little fingers rapidly manipulate the beads. The claim of the teachers is that ANYONE can learn to use the abacus with the same level of proficiency, and I believe they are probably correct. So why are we not doing the same thing in America? Well, aside from the fact that the abacus requires no power source and the beads aren't made of candy, it is because our culture does not place the same value on learning as the Asian cultures.

This got me thinking of a book a read a few years ago while on our district's math vertical team called “The Teaching Gap,” a book that compares the teaching methods of secondary math education in Japan, Germany, and the United States. Its premise is that math education in the US is failing, not because of the poor quality of teachers, but because of poor and inferior teaching methods, trenchant methods that are part of our culture. Although quick to point out the differences among teaching styles, the book offers little pragmatic tools for any significant change.

In the U.S. math classrooms, the traditional method of teaching is under fire, whereby a teacher demonstrates a procedure, shows a few examples, and students are assigned many similar problems for skill and practice. This has merit in allowing student to become proficient practitioner and executors of very specific problem types, requiring very specific procedures. Well-trained students can that access their mental “list” of learned algorithms, and may even be able to apply them appropriately on structured, standardized tests that have little relevance to anything other than their obtaining their diploma.

This shortsighted type of teaching, although immediately pragmatic, does little to prepare the student for math tests. They often gain little real understanding of what they are doing and why they are doing it. Consequently they never learn to think mathematically, to experience the joy of discovery, and much less, to understand and appreciate the beautiful and great ideas of mathematics. The procedures they are memorizing have their genesis in a deeper, richer mathematical concept, idea, need or theory that were discovered by real people of great curiosity and desire to know. As a result, they come to view mathematics as a boring collection of rules that have no application to the real world, causing the math to become increasingly more incomprehensible as they advance through their coursework. It is no wonder they become less and less motivated and leave high school without numeric skills, agility, and confidence.

So why are we so entrenched in this teaching style? Culture, culture, culture. The teachers of today were taught the same way. It “worked” for them, it can “work” for the next generation, so on and so for ad infinitum. Those who inevitably become math teachers were those who became proficient with the algorithms and were able to climb the ladder of mathematical hierarchy without much trouble. They then have a hard time understanding why “others” can’t handle the procedures as they did. Our culture has an unspoken respect (if not resentment) for those who can “do” math. But math is so much more that a “do” subject. It is a “thinking” subject, if one is only willing to probe below the surface, something most current math teachers likely did not experience in their schooling. These teachers with little interest or a deeper understanding of mathematics will likely not be very enthusiastic about the subject, teach more fragmentally, and are less likely to adopt new, creative teaching methods, which might only reveal their inadequate understanding of the subject.

Also, our culture views mathematics as a progression from one “branch” to another. Teachers are expected to deliver the necessary skills to the students that will help be successful in learning the skills at the next level, with Calculus as the ultimate culmination of skill mastery. Students absorb this idea: they see math as a never ending sequence of courses that only get more and more abstract and complicated. The message we are sending is that we only value the habit of industry and work, rather than one of thought and discovery.

Another reason our culture values the current method is due to efficiency. Not only are lessons that focus on discovery and inquiry more difficult to plan, and require resources most teachers feel they don’t have, but they also take longer to implement. One cannot rush discovery, and after all, we have a mandated curriculum to get to (remember, the next course is coming next year!). Motivation and understanding, exploration and appreciation are sacrificed to the more efficient method of the teacher keeping pace by appropriately dispensing the curriculum in a timely manner, requiring the students to take the concepts on non-contextual, fragmented faith.

Efforts to change teaching methods are abound, but still focus primarily on isolated teaching techniques, rather than a paradigm shift in delivering the purpose and beauty of mathematics. The overall message is still the same. Without changing the message, we will never change the culture. Without changing our culture, we will never create the positive attitudes toward mathematics, we will never demystify mathematics, and consequently, we will never expose the students to some of the most profound and greatest ideas of humankind. We must first reform our attitudes before we can reform our methods.

As one of my old college professors, Michael Starbird, said about math: “Knowledge comes and goes, but hatred lasts forever.”

Isn't sloth cute?

I have a character flaw: I'm NEVER on time for anything. But, I'm also never LATE for anything either. Which means that I'm always EARLY. Since being born two and a half weeks premature, I've been keeping the streak alive ever since. In fact, if I'm not somewhere at least 10 minutes before I'm supposed to be, I feel I'm running late. But as I get older, I have begun to see that there are increasingly fewer people who are on time. In reality, most people are late. . . . and it drives me nuts. BUT, there is safety in numbers, so rather than repeat important information at, let's say, a meeting, the start time is usually delayed until all the "others" have arrived. Being late has become a way of life for many. I have also noticed that chronically late people are never ahsamed or embarressed, and some almost seem to savor the notoriety. But here's what their actions are telling everyone who has waited: "I don't respect any of you." What is so hard about leaving the house 15 minutes earlier? Some people live their lives 900 seconds behind. What is so difficult about getting up one day 15 minutes earlier and getting your entire life back on track?

Accepting tardiness is the seed of something much bigger in our society, though. It is the acceptance of mediocrity. It places value on sloth, hedonism, and narcissism. It cultivates the absence of accountability, self-discipline, integrity, and empathy for others. It propagates a deteriation in moral fabric and personal ethics. It is downright sinful and should be categorically unnacceptable. But instead of eschewing this decline in virtuous behavior, our public schools are espousing them, spilling over into our educational system, specifically our upper-level, college-bound secondary curriculum.

PreAP and AP classes have become the last bastion of hope in our school district for adequately preparing students for college, and providing them with the rigor, confidence, and level of expectation they will need to be successful in college and well beyond their educational careers. You would think that rigor, accountability, logical consequences, and repsonsibility would be traits supported by anyone in education, and that those qualities would certainly be the in the best long-term interest of the students, but apparently you (and I) are wrong. The trend has now moved toward empowering students to do less and get more, enabling them to shirk responsibility. The onus of learning has fallen off of the student's shoulders and onto the teacher's, who has now become the stopgap for "curing" every social ill and undesirable effect that is in direct contradiction to educational goals. Legislators, overbearing parents, and the pandering media have somehow convinced themselves that the "bar has been raised" while expectation have been lowering expectations. The incentive for teachers is to "do as they're told." "Free 100s for everyone!"

The latest to affect me personally is a midstream mandate which allows students to turn in assignments passed the due date, overturning a 10+ -year old proven practice of NOT accepting late work in college level courses.

"You're letting the student off the hook by giving them a zero," the argument goes. But what are we defining as the hook in college-level courses? Is this the trend in society? "Do it whenever you feel like, and it doesn't matter what the actually quality is, the whole point is to 'get it done'." What in the heck are we fishing for anyway? The waters have gotton so muddy, who can see clearly anymore?

As a dedicated teacher, I am disheartened by the fact that I am working harder than most of my students, and that the latest trends in pedagogical practice require that I do MORE and the student do LESS. I'm tired of being the only one who is tired at the end of a lesson.

But why do I still swim upstream against the educational current, in search of meaningful results and real nutrition? I'm finding it increasingly difficult to answer that question. Instead of seeking out real food, I am encouraged to simply go for the easy bait that is dangling right there in front of me. Chances are, I'll be let right back off the hook.

In the final analysis, public schools mirror what society values . . . . . . . . . . . . . . . . . . and society is getting what it deserves.

I still have hope, however; I refuse to believe mediocrity's time has come yet. I pray that, like so many these days, it sleeps in and arrives very late.

Winnie the "Who?"

Do you remember watching "The Wonder Years" on TV several years ago(1988-1993). No? Well I sure do. I starred Fred Savage (incidentally named "Kevin") as a kid growing up in Anytown, USA. The young female interest of Mr. Savage was "Winnie" wonderfully portrayed by Danica McKellar. Back then when I watched the show, the actors were about my age, and it was one of the shows I tuned in to watch regularly, primarily because of Ms. McKellar.

Well, today, I watch less TV than I used to and Ms. McKellar does less acting than she used to. I haven't thought of her in years, and she hasn't thought of me . . . . . . . . . . . . ever. But I came across and article today that gave an update on the now 32 year-old former actress. As it turns out, we have had similar career paths after "The Wonder Years." We both earned BS degrees in mathematics (BS meaning "Bachelor of Science," not what you were thinking.) She not only earned a math degree from UCLA, but she also earned it with honors. She was even fortunate enough to have her name attached to a theorem: The "Chayes-McKellar-Winn Theorem." I believe the theorem deals with the unlikely probability that a striking young Hollywood actress will eventually become a mathematician with a theorem to her name.

I currently have an unpublished theorem, called the "We're running out of detergent Theorem." It speculates how so much laundry can accumulate over a period of one week without people actually wearing it. (See previous blog on this topic) I'm still working out the finer points, but I think is has something to do with having a daughter who loves to play dress up."

Anyway, Ms. McKellar has now written a book entitled "Math Doesn't Suck." To some, that theorem might sound a bit more difficult to prove. I can see the shelves at the bookstore with bungy straps across them to keep the books in place (as you can imagine they will just be "jumping" off the shelves.) I'll probably pick up a copy someday in a used bookstore. I'm sure it will be labled "Like New!" Seriously, though, it should be a good read for those who wish to reshape their own opinion about the subject. The book apparently is "aimed at helping young girls survive--and even thrive--in math class." She "uses cutesy graphics and teen-magazine staples like personality quizzes, horoscopes and straight-from-the-mall examples to spell out often confusing concepts like reciprocal fractions and prime factorization." Finally, a math book for girls! I can see a problem in it already: "If I change clothes 4 times a day for an entire week, but only change my socks twice daily, and if I leave it all laying on the floor of my room, how many pounds of laundry will be dad have to wash this week?" Thanks Winnie! Call me sometime, I'd like to discuss the real reason why you and Kevin never married? Were you looking for a Kevin who liked math? 'Cause . . .

Are YOU confident?

The one year I had to teach AP Statistics, I stood up, took command, and taught the heck out of that course (although some students did not LEARN the heck out of the course. In fact, many were often heard uttering the phrase, "What the heck?")

Anyway, although I feel I adequately prepared the students for the AP stat exam, if not for a career as an actuary, I never really enjoyed teaching it. It wasn't because it required copious amounts of work on my part (I DID have to relearn it, and there were always many, many, many tables and scatter plots and graphs, etc. to produce for the overhead), but because I didn't like the actual math involved. In other words, I DON'T LIKE STATISTICS!!!

There, I said it. I feel better. I can, however, appreciate how Statistics allows us to make predictions and to make sense of an unpredictable world, but therein lies my distaste for it. I like certainty. I like predictability. I like to be in total control of my variables. With statistics, one can never be 100% certain, only 98% confident that you are 80% right. OOOOOOOO, I'm wincing as I typ whitch is y my tipe ing got badd so sudenlee!

Another thing about statistics that I did not like is that there was not enough calculating or computing (at least at the high school level.) It was more of a verbal class where there were discussions, and opinions could differ. Finding numerical values required either the use of a calculator, which automated everything, or merely plugging into a cute little formula to get an answer. The value of statisticians is then to interpret this number. In teaching calculus, there is plenty of opportunity for interpreting results, but I savor the tedious minutia involved in multi-stepped problems with pages and pages of logically equivalent mathematical steps to arrive at the answer. I love the symbolic manipulation of symbols and numbers because it keeps my mind supple and agile. The algebraic process is as fun as, if not more fun than, arriving at the final product.

Now don't think that I do not challenge the verbal right side of my brain enough. In fact, I love History and English, and I have always thought I might be fortunate some day to teach some classes, but my training in mathematics has always been structured, rigorous, and predictable, and Statistics is in direct conflict with my upbringing. But given the chance to teach it again, I would embrace the opportunity to do it again with fresh eyes and a renewed enthusiasm. I mean, I didn't like coffee when I first tried it, but I eventually acquired a taste for it, a taste which I now cannot live without. Perhaps it is so with statistics.

For now, I am grateful that our current statistics teacher, Mrs. Caradec, absolutely LOVES the class. The students deserve a teacher who is both qualified, energetic, and who doesn't have to feign interest, which is why my role as calculus teacher is safe in the future--the stat teacher likes calculus as much as I like statistics--I'm 98% confident that that statement is 95% correct . . . . I think!

Math Anxiety

Math anxiety cripples if not paralyzes many students. The word "math" itself can cause some to sweat, puke, faint, or run madly for the hills!! It might begin at an early age, or at an early stage in one’s math career. I don't think we are necessarily born with it, although that might explain infant colic. Math Anxiety (now a proper noun) can become an ongoing cycle, leading to increased frustration, poor performance, eventually withdrawal, and acts of desperation. It is a physiological truth that anxiety attenuates our ability to think. Anxiety is a function of our lower, reptilian brain. If the lower brain is not satiated, the upper brain (our cognitive brain) cannot operate. This is severely detrimental to learning math, because the one thing you need to succeed in math is an ability to think, specifically in the abstract. So how can we reduce our math anxiety? To answer this, we must analyze what causes it.

Where does it come from?

From France, of course!!! But serially here, anxiety manifests itself in many different ways. Some students get jittery and flush-faced, while some look calm, pale, and catatonic, resigning themselves to poor performance. Some race through tests and assignments, in the same sense that we rip band-aids off as quickly as possible. Others avoid it as much as they possible can as if math were brussel sprouts . . . with sauerkraut on top. But however it manifests itself, math anxiety is truly unpleasant, if you don't mind the understatement. Psychologists report that when given a choice of pain or anxiety, people choose pain.

"Would you like to solve this linear equation, or would you like me to hit your thumb with this sledgehammer? Great, get your other hand out the way, we wouldn't want . . . " Chalk another one up to math!

There are many causes, but some of it comes from the nature of mathematics itself. Math, more than any other subject, requires us to think clearly, cleanly, and often abstractly. In other words, it demands concentrated effort, and effort, of coarse, takes lots and lots of hard work. What is the incentive for investing this much labor into math? At least at their job, they get a paycheck. In the gym, they can see their abs in the mirror. After a round with a hammer, they can see their bruised, bloody, crushed thumb. Not so with a "math session." There is no royal road to mathematics, no magic formula for us to follow, and it is challenging in ways we can't completely prepare for.

Some of it is caused by a false understanding of what math success looks like, and therefore a false expectation. Many students - and their parents, misinterpret the struggle in math, and equate this with failure. Some blame themselves. Many blame the teacher. They believe that if it doesn't come easily, then either there is something wrong with them, the teacher, or both. They think being good at math means just knowing it. So when they don't, they start to worry that they don't have what it takes. But this is just giving themselves a convenient excuse. They rationalize their behavior with false, convenient lies, which they believe will assuage the pain caused by math. Go math! You evil torturer!

What they don’t realize is that struggling and failing is the way math is actually done! One of the best things we can do for our children, is re-label the struggle in math—struggling is part of the learning process, and failure is just an opportunity to begin again more intelligently. It is a matter of EXPERIENCE, not INNATE BRILLIANCE!!!! Two quotes from famous mathematicians come to mind.

“Perfect clarity would profit the intellect, but damage the will.”—Blaise Pascal

“The study of mathematics is apt to commence in disappointment.”—Alfred North Whitehead

These men were brilliant mathematicians, but their quotes emphasize the both the challenging aspect of mathematics, but also how this same quality should also be a source of motivation for learners. If the most brilliant minds of the day struggled continually mathematics, it is reasonable to assume that most students will too. This is how progress is made. Another quoted brings what I believe the true nature of mathematics involves:

“Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness where the explorers often get lost.”—W.S. Anglin

We need to create a culture of exploration and wonder in the eyes of our math students, encouraging them to take creative approaches en route to their findings. We need to value the process, rather than the product. We need to value and hard thinking and patient pertinacity. Math is not about a flash of insight, or those who are just “born knowing it.” They never learned that it was OK to not know something, which means they never learned how to “fool around” mathematically in exploration of an idea, concept, or answer.

So go ahead, ye students of math, Fool Around!! Fool Around, and see, lest the only fool around be ye!

Vaya con Dios!

Last week, a Nebraska senator decided to sue God. He wanted to bring a permanent injunction against The Almighty for all the doom and devastation he has caused.

http://www.cbsnews.com/stories/2007/09/20/ap/strange/main3283986.shtml

Ironically, the senator is not know to be a religious man, so in essence, he is suing a non-corporal entity which he doesn't even believe exists in a spiritual sense. That got me thinking about all the different "proofs" of God's existence that I remembered studying back in my Philosophy 101 class in college. Here's my analysis of some of the ones I remember:

The question of God’s existence is as old as man/ but who created man? His surrounding history is replete with debate on the subject (Scopes Trials), and much suffering has been cause over the issue (Crucifixion, Holocaust). The issue will likely not end until the end of the world, the 2^nd coming, the Armageddon. What causes people to believe so strongly in God, despite all the bad things that happen in the world and the evil that continually tempts us? Three main philosophical arguments have developed for the existence of God.

The Cosmological argument is put forth partly by St. Thomas Aquinas (c. 1225). He believes that world exhibits change, so a being must exist that is itself unchanging. Things in the world are caused to exist, therefore; there exists a being whose existence is uncaused. The Cosmological Argument attempts to prove a being such as Aquinas’ exists and that it its, in fact, the theistic God. Each of Aquinas’ premises is valid. We would all be guilty of believing that things are caused, changed or contingent. His conclusions, however, are unsound. Contingent things exist in the world, therefore, there is a necessary being that could have not not existed. It is erroneous to conclude that the being Aquinas mentions is God. It is just as easy to say that the being in question is a rock, so long as we define the rock to fit the requirements.

Purdue professor emeritus William Rowe introduces the Principle of Sufficient Reason (PSR) to determine if the premises are true. PSR states that there must be an explanation for each individual in the world, and of any positive fact about the series of individuals. It can be argued that an explanation of each individual’s existence provides an explanation of the series itself. But why did the series exist at all? The second part of PSR is not satisfied. Rowe claims that by a presupposition of reason, God is the reason for its existence. This claim is valid, but again, I can presuppose that the rock caused its existence. If the PSR is true, then something, perhaps God, exists and the argument becomes sound under rational consensus.

The second argument is the Ontological. This is a proof a priori and relies specifically on the definitions of God. Rene Descartes’ Meditation V is perhaps the most famous. He states that God, by definition, possesses every perfection and non-existence is an imperfection, therefore, God exists. The first premise is valid by rational presupposition, but the second premise falls apart. Existence is arguably not a quality at all; it does not enhance our perception of something. Take a dream-home for example. It is not more perfect just because it actually exists. On the contrary, it is actually more perfect in the mind only. Its objective reality is always greater than its formal reality. This would imply that God would be more perfect if he did not exist.

Archbishop of Canterbury St. Anselm (c. 1100) attempts to make a distinction between existence in reality and understanding. To deny God’s existence is to admit his existence in the understanding—valid and true. However, like the fountain of youth, this means only in understanding, not in reality. Anselm’s main premise in his argument is that something existing in the understanding that might have existed in reality is greater if it had existed. I disagree, again appealing to the dream-home example: it can always possess more perfection in a dream than in reality. Things existing in reality are always subject to depreciation and the need for improvement and maintenance. Ontological arguments fail because they do rely on definitions. They can be interpreted differently because, as we all know, a priori, words have more than one meaning, right?

The third major argument is the Teleological. This theory basically claims that the world exhibits design and anything with design has an intelligent creator, therefore; by the theistic definition of God, God exists and created the world. William Paley’s (1743-1805) classic watch example supports this argument. Paley claims that the world is like the watch. We believe the watch had a maker even if we’ve never seen one made, even if it doesn’t run perfectly, and even if it was possibly made by the chance of its parts falling together. This is an appealing argument because it obviously sounds both valid and sound—we can relate to the watch. Despite the objections of metallic nature and chance, the conclusion is true again by consensus of majority rational opinion (the argument depends on facts about the world). I like this argument because it requires a certain amount of faith about the watch. I believe faith provides the strongest “proof” of all.

I say, “to hell with the proofs of God’s existence.” They will always have flaws and inconsistencies. Faith, and faith alone, is reason enough to believe. Fideism, belief that reason is irrelevant to religious faith, should prevail in this case. As Blaise Pascal, the Fideist (inventor of the barometer, the first calculating device, pioneer of probability theory, and awesome mathematician), said, “It is the heart which perceives God and not the reason. The heart has its reasons which reason knows not of.” His Wager shows the infinite payoffs for believing in God at such negligible cost and effort. His “proof” is stronger than any of the other three mentioned above. It is also the only one that preserves the Christian view of salvation through faith. John 20:29 says, “blessed are those who have not seen and yet have believed.”

Vaya con Dios!

Student Motivation

In order to influence motivation, it is important to first understand motivation. Motivating individuals is impossible. Everyone is motivated. The person who sits in a recliner doing nothing but watching television is motivated—motivated to lounge. If he wasn’t, he would be doing something else, and that would be his motivation. No activity can ever commence without the first necessary ingredient called motivation.

We can, however, discuss types of motivation: positive motivation and negative motivation. Positive motivation would involve the desire to do something beneficial, constructive, to produce, to make something or someone better, to grow, to learn. This is what we hope each of our students possesses, but some are motivated to passively lounge in their desks, albeit they are less comfortable than a recliner.

It is these La-Z-Boys (and Girls) who need to have their motivation influenced if not redefined. The man will not turn off the Boob Tube and get out of his easy chair unless he believes that there is something better for him. People will always do what they would rather do than not do! This is the genesis of their particular motivation.

Now, most people’s motivation resides in them wanting to feel good, whether it be physically, emotionally, spiritually, mathematically, or mentally. If any one of these areas goes unfulfilled, we are cast into a state of panic, frustration, turmoil, and great stress. We will often do anything, regardless of how irrational it harmful it might be. This is what we see in the rebellious math student who demonstrates recalcitrance in learning to solve for x, and who exhibits obstreperous, if not disrespectful, conduct in class. He is injuring his opportunity to learn and master a new skill that might promulgate him into greater things for the sake of “saving face” or “sticking it to the man.”

To motivate students, we must convince them that changing their behavior will help gratify some specific need or desire. That the benefits of their actions will outweigh the price they will have to pay for them. For me an my students, I can dangle the carrot of better colleges, better jobs, the joy of understanding the natural, beautiful, holistic concepts of mathematics that intricately weave all of our existences together . . .

My students are motivated to get the grade. I want them to be motivated to actually learn and retain. How can I inspire them to reshape their entire paradigm of what school is all about, that it is more than just jumping through hoops or “playing the game?”

This cannot happen by me telling them what they “need,” “should,” or “must” do. Threats, force, and coercion only inspire short-term behavior that is altered only for the temporary convenience of getting you off their back. This reminds me of one of those funny quotes: “The beatings will continue until moral improves.” Ha! I wish. This would eventually even force a masochist into depression and rebellion.

This is why I try to inspire positive motivation innocuously. Creating a healthy, safe, learning environment, where questions are encouraged, mistakes are treated as just part of the learning process, where process is valued as much as the product, tolerating healthy off-topic discussion . . . These are all things that send a message to students that you care and that you are dedicated to helping them fulfill their own potential. We must “pull” them to where we want them be so that they will want to stay. “Pushing” them only makes you the teacher exhausted and the students bruised (as in egos).

This process is slower, but has more permanent and lasting value. If we can make sure that we are creating an environment where their emotional, mental, physical, mathematical, and even spiritual (Bible Lit Class) needs are met, only then can real learning take place. It is a fact that the cerebral cortex cannot function if the lower, more-animalistic, brain structures are not placated. Reptiles cannot learn to do algebra!

Math is . . .

I love teaching. I love teaching kids. I love teaching kids math. I love teaching kids math on a high level. Aside from parenting, it is the toughest and most far-reaching jobs that one could ever love.

Math is . . .

· Filled with many wonderful discoveries

· Lends itself nicely to the development of useful habits of mind

· Is not open to arbitration or subjectivity

· Is replete with humanistic tales and historical accounts of mysticism, deceit, and even murder

· Helps one think more analytically and heuristically

· Is useful in its utility in daily activities

· Is a Universal language

· Is the language of Nature, our surroundings, and the Universe

· Is the handmaiden to the sciences

· Is something everyone should learn how to do and appreciate

· Makes one a better person for life

· Doesn’t require the use of a calculator

· May be used outside of a math classroom

· Improves performance in all other academic areas

· Should be practiced and reflected upon daily

· Power

· A beneficial skill that never leaves you

· NOT just a bunch of dry rules and equation

· Not just about “finding x.”

· Not a four-letter word, in a certain sense.

· Not about just what is going to be on the test

· Not just another class to go to

· Not the primary source of income for the Sylvan Learning Center (well, maybe it is)

And finally . . .

· FUN!!!!!!!!!!!!!!!!

Now, If I can only convince my math students!!!!!!!!!!

Fire Up Blue, Fire Up

Now into the fourth week of school, I have already seen some of the energy of the new year fade from some students. Many are already falling back into old patterns and habits that aren't necessarily good ones. Most noticeably is the diminishing enthusiasm for learning new skills and developing newer, more salutary habits. Watching all this happen before my eyes, I was reminded of a speech I gave two years ago as the keynote speaker at our school's National Honor Society Induction. See if it fires YOU up.

NHS Induction Speech

January 30, 2006

**A special thanks to the 2006 NHS officers for selecting me as their speaker. Also, a special thanks to Mrs. Cary Gray for setting the standard of a faculty sponsor and for putting on a fabulous ceremony.

Here it is . . . . . . . . . Please . . . . don't laugh at me.

---

Introduction by Rachel Thebeau (Madaam President of NHS):

Our guest speaker tonight is a man who still looks around for his father when addressed as, “Mr. Korpi.” He is a 1992 graduate of this very high school, who liked it here so much, he decided to come back to stay. It’s our math club sponsor, our UIL “mathlete” coach, and the math teacher of many students here tonight. It’s Mr. Kevin Korpi, son of Wayne!

Speech:

(Tapes an odd math symbol to the front of the podium, "I have a prop," he reassures the crowd, as they laugh at his inability to locate the front of the podium . ..)

The equations reads: Su = (Sc + Le + Se + Ch)x

Which stands for "Success equals Scholarship plus Leadership plus Service plus Character all times x."

Thank you, Rachel for that introduction. Very nice distinction between me and my father. Sitting there, I was starting to think it was a remarkable coincidence that he was going to be speaking here tonight, too!!!

So, good evening ladies, gentlemen, students, and others. ( if you’re out there).

Now some of you are squirming in your seats at the sight of this equation; some of you might even be getting a little excited; some of you just might be getting nauseous. Fear not!! I will explain the equation in front of you, and trust me, there will be no test over it . . . . perhaps only a short quiz, so . .

Let me start by thanking the current members of this prestigious organization for asking me to be the guest speaker here tonight. Aside from the obvious honor of being selected by group of students, to whom I have dedicated my most ardent efforts, it’s a good excuse to get all prettied up and out of the house.

Of course, the reason we are all out of the house tonight it to recognize and congratulate each of the new inductees into the most notable, highly-regarded league of high school students—The National Honor Society, and looking out among you, I can clearly see that each of you are in a very select group. Since I was inducted into the New Braunfels High School Chapter of NHS 15 years ago . . . .(pause) wow, 15 years. Time seems to accelerate as you get older. Pretty soon I’ll BE my dad!! . . .anyway, I believe they have raised the standards for getting in. Back in 1991, among the requirements for induction were to name a few collective nouns, such as “fly-paper,” “garbage-can,” and “vacuum-cleaner.” Let’s see . . . we also had to know that the Declaration of Independence was signed . . . at the bottom. And finally, if my goldfish memory serves me correctly, we had to know how to spell “N-H-S” . . . . . . . (slowly) backwards. –Yep! That kept a lot of people out.

Well, the point is—the bar is definitely higher. Each of you has been carefully selected from a large field of applicants, by a distinguished panel of educators, based on four key characteristics: Scholarship, Leadership, Service, and Character, and I do see many scholars, leaders, servants, and ahh, yes, even some characters among you. But your desire alone to apply to this society means that you are a cut above your peers, that you are a caliber of individual with unlimited potential, great expectations and awesome supportive parents . . . (nodding) square that last one. Good job parents!

But, unfortunately, it also means you have the hapless fortune of listening to me tonight. But, ohh wait. . . There is another perk--It also means you’ll get to wear a cool white cowl at graduation, a fashionable accessory to any full-length gown, which means people will know at a glance of your vast knowledge of important historical U.S. documents and your BACKWARD spelling prowess.

Why if George Washington were here tonight (rub chin), he would not only be noted for his old age, but he would be so proud to see each of you sitting there, embodying the qualities that prepare you for a productive and successful life ahead. And I’d have to say that I’d share his sentiments.

But I don’t want to speak to you tonight about former presidents, but I also know that I can’t use words that I’m used to speaking to a group, such as “don’t forget to simplify your fractions,” or “have you tried rationalization conjugation?”, and “Please wake up, this will be on the test.” Those wouldn’t suffice. So I thought long and hard about something that would be more interesting, rather than boring. Something with more mass-appeal and less mathematical. . . . (pause) but . . . I came up with nothing. So instead I thought I would just stick to topics I know best: Chinese whale frogs, and equations.

As for Chinese whale frogs, well, they are large, rare, imaginary, hopping, mammphibians that dwell in trees in China. Yah. . . . not that motivating! And Equations . . . well they can also sometimes be large . . . and only marginally more motivating—relatively speaking.

So here’s where the math comes in—you knew it was coming. Think of success as an equation (please refer to exhibit “1-a-i”). Every equation has inputs, parameters, and variables, . . . and an equal sign. Now think of the four components of NHS: scholarship, leadership, service, and character: as variables in the equation—add ‘em all up and it will likely equal, “Su,” success. BUT . . .there is another variable in the equation, as you can see. Another multiplier, that will increase each of the four traits by its factor. One that will amplify the effects of the others. Something that will give you different levels of success. It is denoted in the equation as variable “x.” Have a lot of it, increase your chances of success, have zero of it . . . well we all know what multiplying by zero does!! (exaggerated laugh).

Guess what that trait is!! What could x be??? Here’s a hint: it’s not pattern baldness. That should narrow it down.

Well in the interest of time, I’ll just tell you. X equals . . . “Enthusiasm!!!!!!!!!!” That’s ENTHUSIASM for y’all in the back row.

You see, enthusiasm is a powerful trait. It’s the difference maker. As I hope this speech will come to bear, even a simple man, like my father’s son, who is fired with enthusiasm can be more persuasive than a more eloquent man, like George Washington’s father’s son, without it. It is perhaps the greatest asset on Earth, better than power, influence, money, and dare I say, math skills. A person with enthusiasm has nothing to fear in this world—except perhaps those whale frogs. He is bold in his actions, brimming with confidence, and he effuses an infectious spirit around him that can set the world ablaze, even more easily in dry conditions—and by dry I mean lack of leadership, creativity, spontaneity, moisture, etc. . . .

Now, enthusiasm alone can be an asset in the absence of others, but as the equation clearly illustrates, it becomes something else entirely when it is combined with the traits that have brought you here today. Those traits represent power. Enthusiasm is the trait that pulls the switch, unleashing that power. It’s the yeast in the bread that makes the dough rise. It’s the carbonation that causes the fizz in the soda. It’s the flame in the hot-air balloon that makes it go up. It’s the ink in a pen that makes it write. It’s the punch-line in a joke that I’m always lacking. It’s the quality that can prevent you from realizing you’ve made enough analogies and it’s time to move on.

It becomes the life force that drives you onward to greatness and sustains you at the same time. It awakens your senses to possibilities and adds vim, vigor, and vitality to all you do. As my old football coach said more than once, it puts “blood in your eyes and snot in your nose.” Although I never knew why he thought these afflictions were so desirable, I realized in writing this speech that he was talking about tenacious enthusiasm . . , I think.

How about a quote from someone who spoke less allegorically and with less imagery: Dale Carnegie, the pioneer in self-improvement and corporate motivation. He said, (in voice)“Flaming enthusiasm, backed up by horse-sense and persistence, is the quality that most frequently makes for success.” Now, I don’t know if he actually talked like that, but in math terms this is “HS +P is approximately S.” So his equation was a little different from mine and doesn’t fit as nicely around the four pillars of NHS. But according to him, it worked. Notice also that in his equation, success requires enthusiasm . . . and horse sense. Now I know for a fact that each of you has a tremendous advantage over even the most brilliant equine.

So fill your words with encouragement and enthusiasm, any you’ll often find people and circumstances lining up in your favor. Anything will seem possible, when you put your passion, energy, and enthusiasm into everything and anything you do.

Now enthusiasm costs nothing, yet it can help bring to you just about anything you want. People will lend their support and rally around a leader with enthusiasm. Who wouldn’t want such a powerful force . . . for free even. You can’t go wrong with enthusiasm. AND . . . it’s contagious: once you have it, you can infect others. But negativity is also contagious. So who better to infect other people? You! with enthusiasm? Or them!, with ldfjelkejr (make a distasteful sound)? If you get yourself and others around you infected with enthusiasm, you’ll soon have a lot more of it—all for zero dollars and twice as much cents!

So what can you do to get going with enthusiasm?

Drink a Mountain Dew? Do your math homework???

What will it take to get you excited and fired up every day?

Jump out of bed each morning on a pogo stick?????—that seems to do the trick for me . . ., except for the splashing coffee, . . and making holes in the ceiling, . . . AND scuffing up the floor, BUT . . . it may not work all that well for you either.

So, what will it take to get you excited and fired up every day?

I want you to sincerely think about that question, and as you do, your thoughts will give birth to a real and indisputable enthusiasm within you. You see, enthusiasm lives and grows and is felt in your mind, which means, as Mr. Kilford says, you can “fake it ‘til you make it!!” Carry your own sunshine with you wherever you go. Put a smile on your face, a spring in your step, and think big, and don’t be afraid to show some real enthusiasm.

Welcome it into your mind, every day, and soon you will develop the habit of enthusiasm, and it will become part of your character.

You see, this is your life. Anything you do is worth your best efforts and is important enough to invest your commitment, your attention, and . . . (YEP, you guessed it . . . ) YOUR ENTHUSIASM. So don’t just complete the assignment—learn! Don’t just work—achieve! Don’t just glisten—sweat! Don’t just hear—listen. Don’t just sit there—stand and applaud!! (wait ‘til the end please.)

But please don’t just exist—live!! Live with enthusiasm.

Almost done . . .

Now almost anyone over the age of 30 would like to be, in some ways, perhaps in some small, very small way . . . maybe, younger again. I know I would, just ‘cause I think it’d be neat to go back to high school again and have students say, “isn’t it weird that our classmate is our math teacher?” But hey, that’s what REM sleep is for. Seriously though, why would anyone want to be young again?

Think of this multiple choice test question, umm, I mean “quiz” question: “What is one of the primary attributes of youth?

a) Enthusiasm b) Old age c) radioactivity

Now while the ability to glow would be a cool superpower, enthusiasm is a natural characteristic of youth. That means choice A) was the correct answer and would receive full credit. Choices B) and C) were incorrect, and would consequently only receive PARTIAL credit.

Anyway, what I’m getting at is, as we get older, somehow we get the idea or tendency to let go of enthusiasm. But we shouldn’t. We should strive to be enthusiastic throughout our lives, everyday, even when the pressures of reality and the stresses of all our obligations weigh down heavily upon us. Enthusiasm is exactly what we need to carry us through our difficult times; it will push us forward and will add a brilliant neon glow to all we do.—Hey I guess we can have that superpower after all. Imagine that! “Hi! I’m Captain Enthusiasm, and I’m here to help and infect somebody. Need a light?” Wouldn’t that be Cool!

So in closing, I want to encourage each of you to be glowing superheroes in your own life. Remember the “x” factor from the equation (pointing to the equation). Be your best, and your life will be too. Live with integrity, a generous spirit, and a positive enthusiasm, and the world will reflect it all back to you. And remember this bit of wisdom from another famous football coach, Hall of Famer Vince Lombardi: “If you are not fired with enthusiasm, you may find yourself fired . . .with enthusiasm.

Thank you, congratulations again, and have a great, enthusiastic tomorrow!! . . . ohh, and do your math homework.

Building Lives

Teaching math is one of the most challenging and rewarding things a capable and able-minded individual can enjoyably endure. Although I really don’t teach math, I do teach kids. And what is mode of my madness? Nothing other than math, or mathematics (as it is know to those who like to sound pompous and pretentious).

So Why did I switch out of Chemical Engineering during my junior year of college, just prior to a lucrative internship with Dow Chemical??? Because I didn’t want to live in Houston, or Springfield, or wherever I was likely to work. I was a graduate of NBHS, as well as my then girlfriend, now wife. I wanted to stay close to home, where I could obtain cheap, quality day care (via grandmas and grandpas) for my family I envisioned. So why math? I had more math credits than any other, chemistry was a close second. To assuage the anger of my parents, and boy, were they upset, I needed to get out of college in 4 years. Math was the only expedient choice that would allow me to sit at the “big people” table at Thanksgiving.

And . . . I didn’t even go into teaching directly out of college. Why. . ., I took my BS in math from UT and I did the obvious: I took a job as a residential construction manager (CM) with a home building company out of San Antonio. The money was great. With a cabinet-making and framing background from college, the learning curve was not that great. I was soon the leading CM in the San Antonio area. But . . . the opportunity came with the great flood of ’98 to go into business for myself, primarily doing flood-damaged remodel jobs. A good friend of mine and I did all the work ourselves. The money belt tightened up. Self-employment was a difficult thing. I gained great respect for the entrepreneurial-minded business man. When it comes to business, I am an infant, and always will be.

I will never forget the day that the cell phone rang, “Dang it!!! Another complaining homeowner or subcontractor!!!”

“Hello (softly and professionally). This is Kevin. Mrs. Birdwell!! My gosh!! I haven’t talked to you since I totally aced your PreAP Precal class my junior year. How have you been? Really? How’s my math? Well, I have a BS in Math, and just between me and you, that’s exactly what some of those upper-level courses were. I mean, the numbers started disappearing and more and more letters took their place. I’m sorry, I went off on a tangent . . . you get it . . . a tangent!!!!! Anyway. You need a Calculus teacher!! Nobody wants the job? Really? Why not? I’d have to think about it . . . . really? Nobody wants it???!!!!!!!!!!!!!!! Well, I’m not certified, only this BS in math thing. OH!! You’ve already talked to the principal and the job is mine if I want it!!! (Pssssssst, “oh no”) Nothing, the air-nailer just mis-fired and now I have a sheetrock repair.

Well, I guess it might be easier managing parents than homeowners, and students might be more responsive than subcontractors, so . . . . . you got yourself a deal. I start in one month? Good, my partner will be overjoyed!!! Post-graduate certification . . . here I come.”

So it was by a fateful, determined act of fate (or a god, or even God) that I ended up where I’m at. And to answer my own naïve, incredulous question from above: 1) Parents are more emotional about their children than their homes and thus harder to “manage,” and 2) Subcontractors are often more responsive than students (because of a little thing called greenbacks).

As it turned out, I took a tremendous pay cut, but I fill richer now than ever, for teaching is the last, greatest, unappreciated profession in the world. To come into class on a daily basis and impart wisdom to a captive audience (mostly, and this must be earned), is the greatest and most awesome responsibility, privilege, and rewarding experience that I can imagine.

Previously, I made homes. But, it was always the people that made the house a home. Now I get to make the house, although they will not be built for awhile.

Set the Bar High

It is a funny thing about life; if you refuse to accept anything but the best, you very often get it!—W. Somerset Maugham

This simple platitude seems obvious and lacks the profundity of more abstruse observations, but therein lies its puissance. We as teachers have the obligation and responsibility to expect the best from each of our students, as well as from ourselves. When we refuse to accept anything but the best, we set our expectations high. In the end, after all objections and deliberations have been exhausted, individuals will rise to the level that is expected of them.

Minimal expectations are abound in education, and provide the framework for achievement. For example, at the national level, teachers are expected to leave no child behind. At the state level, students are expected to pass their exit-level exams to graduate. At the local level, teachers are expected to be proficient in their subject area. In the classroom, students are expected to come to class with a pencil. These minimal expectations establish the rudiments of accountability in the profession, but the real difference is made when these expectations are raised beyond what legislation and funding or budgeting mandate. It happens at the most personal level, in the classroom, when we as educators expect more than what is required, when we expect more than what even the students believe they are capable of doing.

For student learning, teachers must set high, almost idealistic expectations for students. Most students by nature are very adept at doing precisely what they need to do to meet a teacher’s standards. Setting the ceiling too low can cause students to become complacent and unmotivated. Thomas Fuller expressed it well: “Good is not good, where better is expected.” Expectations are everything. A good teacher has high expectations for the student, but the great teacher arouses the student’s own expectations. The daily, personal interactions between teacher and student provide one of the most significant opportunities to positively influence the life of a child, but the channels of learning cannot be opened without first establishing relationships and trust. Relationships cannot be built without mutual respect. Mutual respect comes from establishing and maintaining clear expectations for teacher and student alike. On the surface, students expect teachers to show up for class regularly, dress appropriately, know their subject, and admit their mistakes. Teachers expect students to make it to class on time with their materials, participate in their own learning, follow rules, and do their homework. But students also expect their teacher to love kids, to be kind, have a sense of humor, to be fair, to care, and provide them with a safe learning environment. Teachers expect their students to develop a passion for learning, to develop critical thinking skills, to acquire problem solving abilities, to exhibit group concern, and to be tenacious and persistent in the face of adversity. Excellence is expected.

Although high expectations give us all something to continually strive for, experience tells us that we must also be realistic in the possibility of falling short of them. Some goals have uncertain outcomes, while others have more predictable outcomes. So, what can we as teachers expect for ourselves? We can expect a dedication to continual excellence, to constant self-improvement, to life-long learning, and to a life of purpose and meaning. We can expect to work many thankless hours. Expect change. Expect intense highs and joys. Expect disappointing lows. Expect frustration. Expect fire drills in the middle of a test. Expect school pride. Expect to behave yourself in public. Expect to have the heart of a servant. Expect new educational standards and legislation. Expect success. Expect to cry tears of joy. Expect to cry tears of sorrow. Expect to laugh. Expect to laugh a lot. Expect to acknowledge your mistakes and limitations. Expect technology to continue to advance rapidly. Expect to make the required relationships with each student to open the channels of learning. Expect to make a fool of yourself. Expect your passion to rub off on students. Expect high blood pressure. Expect to teach outside your comfort zone. Expect a masterpiece. Expect high-drama. Expect in-services. Expect to learn every day. Expect the best from each and every student. Expect the best from yourself. Expect that not everyone will learn it the first time, or the second time, or the third time. Expect to be moved by the spirit of a pep rally. Expect to memorize 120 new names each year. Expect to know your pharmacist well. Expect to buy red pens in bulk. Expect to have a chalk line across the back of your pants or overhead marker stain down the side of your wrist. Expect many of the students to drive a newer car than you. Expect part of your salary to go for supplies for your class. Expect students to look up to you. Expect miracles. Expect that you will positively influence each of your students. Expect your students never to forget you. Expect to get tired and weary. Expect to persevere. Expect that some days will be better than others. Expect a better day tomorrow.

Ultimately, the success of public education lies in the success of the students it prepares, which lies in the hands of the teachers who prepare them. Maintaining high standards in the classroom each and everyday can be a difficult and demanding task, but we can derive our energy in the belief of the magnitude and importance of our vocations. We can find strength in the hope for tomorrow. As Thoreau so eloquently stated, “we must learn to reawaken and keep ourselves awake, not by mechanical aid, but by an infinite expectation of the dawn.” Our expectations, then, become both a source of our languor and a source of our vitality.