Sunday, December 30, 2007
Case in point:
I was waiting in the car yesterday afternoon waiting for my wife and two adorable children to exit a local pizza parlor after attending their cousin's birthday party. While warming up the car, patiently waiting, listening to peaceful music on the car's stereo, I saw a thirty-something (about my age), frat-daddy-looking man (who looked like he got his money's worth on the pizza buffet) exit with his small son (about my son's age) exit with two elderly people (who appeared to be his parents.)
I took in their sentimental exchange as the grandparents got into their Honda Passport, buckle up, check all mirrors, then cautiously back out and leave their parking spot. "How nice," I thought. "A sweet little grandma and grandpa taking their son and grandson out for a nice meal, which was probably their treat." Having all four of my children's grandparents in the same town where I live, I know how important it is for little ones to know and spend with their parents' parents.
But then, the man and the little boy, after loading into their new Suburban, didn't leave right away. "Couldn't be car trouble. Indigestion?" But then, a woman came up to the vehicle pushing a basket from the Target store about 300 yards away. "Okay, she went shopping, probably, while the dad and son played games in the game room after pizza." My wife and I have actually done the exact same thing before. "He's not a single dad afterall! The little boy has a mommy who likes to dress up in expensive clothes and dis' him while he plays skee-ball."
What immediately entered my mind after figuring out the situation was: "What will they do with the basket when they're done?" Being a stickler for public order, following rules, and in my daily efforts (not just at Christmastime) to be grateful and peaceful and love my fellow man, I always go out of my way to do the right thing and to be kind to people. When I was in the same situation, I met my wife as she approached, loaded the contents of the basket into our car, then ran the basket back all the way to the nearest basket return, which was at least 200 yards away.
I realized after the fact that it would have been faster and easier to drive the car and meet my wife, closer to the store, but I didn't mind the exercise, or the good feeling I got by going out of my way to return the basket to the designated area. Well, my curiosity about the couple, who did not know I was watching them with judgmental eyes, quickly turned to ire as the man, after unloading the basket like a perfect gentleman, looked left, then right, then left again, and proceeded to park his basket at the entrance to the pizza parlor. As if the basket was used to haul excess dough around, the man showed no inhibitions it putting the basket in such an inappropriate location. I felt like jumping out and telling him that I'll get it for him, but not before I offered to help him buckle into his vehicle, close his door, and was his car.
My blood gets boiling easily enough when I see people lazily and inappropriately park a basket withing a much closer radius to a return carrel, but to see someone who obviously didn't mind his wife making the long trip but who didn't think of doing the same to save an employee who had to work over the holiday at a meager wage from having to shag it, well it was one of the most despicable displays of self-righteous, smugness that I have witnessed.
But why should something cause ME so much grief and anguish when it obviously meant nothing to them? Good question! But somehow I refuse to just accept such thoughtless and selfish acts as a sign of our changing times. If that's the case, things are changing for the worse. It's BECAUSE we have accepted such acts that they have become so commonplace. Be turning a blind eye to the degradation of morals, we guarantee that it will continue. We develop an aversion to things that use to be unacceptable or that used to shock us, whereby, it takes an increasingly extreme act to cause us to scoff.
Should I have jumped out and given him a piece of my mind? Would it have changed society's behavior? Would it have changed his behavior? Probably not. But in NOT confronting him, it might have just saved an altercation that could have ended in a no-win situation. The saddest part was that his 7-year-old-ish son watched the entire thing, and to be sure, is taking his cues from good ol' dad. I only wish my son had been in the car, because I believe he WOULD have hopped out and selflessly taken the basket back to the carrel with a smile on his face.
Man, I still have a lot to learn from that boy.
Friday, December 28, 2007
The music would be automatic and would reflect the type of mood you were in. It could be as loud as you wanted, as long as it didn't bother or disagree with someone else's background music. I know you're thinking that's what are imaginations are for, but imagine the blending symphonies that would be tickling our tympanic membranes all day long. It would be like Kepler's idea of the "Harmony of the Universe."
Imagine something as uneventful as watching water boil on the stove: you stir the water maybe as your mind drifts to other things. But if you had background music, you could establish any mood of feeling you wanted. With "Love Story" playing all around you, you could wistfully stir the water with a forlorn look on you face as you contemplate the agonizing wait until the water's temperature reaches 212 degrees Farenheit. WOW!
Or, if you were multitasking in the kitchen, imagine the theme from "Indiana Jones" playing in surround sound. You'd be leaping from stove to dishwasher to refrigerator to the pantry and back to the stove again. All of a sudden, work is fun, interesting, and invigorating as you try not to burn yourself or drop a jar of pickles while you play out your kitchen adventure.
Another situation where I've always wanted background music is while administering a test in school. Most students I've polled said they actually prefer to do math with some type of background music (which is the way I've always worked: in college, I used to read my history text book or do math homework with the radio on, much to the dismay of my roommate), and those that prefer to work in quiet (like my old roommate) just haven't had the chance to get used to it yet. For me, having something quietly playing in the background while I'm trying to concentrate actually stimulates my brain as it takes in more sensory information and actually helps me concentrate better AND makes it more enjoyable.
I've always thought a good Mozart sonata or a Bach fugue would be appropriate until the final thirty seconds of the test, where the theme from Final Jeopardy would kick in. The sound of the kettle drums at the end would signify that it is time to put the pencils down. As each student turned in the test, I would listen carefully to the music playing around them as an indication of how well they felt they did: Handel's "Hallelujah" or a blues tune by Muddy Waters.
There are many other instances where this would be a great asset to daily living. Waiting in line at the grocery store, in the doctor's office, while your watching the oil be changed on your car, during awkward moments of silence in conversation, in a restaurant while selecting from a menu, when you get pulled over by a cop for speeding, or when you're just listening to music.
Think about it today as you go about your business, and you may soon fine yourself imagining that your life is up on the silver screen somewhere, where YOU are the leading actor with an ensemble of supporting actors with the perfect music playing behind you.
Thursday, December 27, 2007
- Now, I can go to San Antonio by traveling 30 miles to the south or by traveling 21,835 to the North.
- These two angles are complementary, watch. “Hey man, you look acute.” “Thank you, you don’t look so obtuse yourself.”
- Let the calculator store the number in its full decimal glory.
- Have a good strong end. See you on Monday.
- Y’all have worked really hard this week. I’m proud of you. Why don’t y’all just take the next two days (SAT and SUN) off from school. Y’all deserve it.
- I just can think as lucidly in front of a dry erase board. The refractive index is too high.
- This problem only takes one line, if you start sufficiently far to the left.
- “So the Ferris wheel rider’s position as he approaches the top, Hey I can see my house from here, is 205 ft.
- That last one was a joke grenade. It took a while for you to get the punchline, actually I think that last one was a dud.
- You’ll have to excuse me, for I have very few unspoken thoughts, and my lips cannot usually keep up.
- I know y’all are just really excited, as I am, about being assembled here tonight on our own time to discuss the ever exciting world of mathematics, but I need you to shut up.
- Did you see me at the fair? I was the one wearing my hat.
- Q: Mr. Korpi, why did you take down your students’ Halloween posters? A: Well, first of all, because Halloween is over. Secondly, because they were Halloween posters and Halloween has now past. Do you understand? The Halloween ‘spirit’ is usually not something that lingers.
- The test will look a little different than the review. I think for the review, I used Times New Roman 12-point font. The test will have Times New Roman 14-point font. The problems will be similar though.
- In the spirit of upcoming Labor Day, today we will work our butts off.
- If I have to put the toilet seat down, she should have to put it up. It’s a two-way seat, you know.
- So after all that work, just figuring out the percentage of the swimming pool is filled, we have barely gotten our feet wet. We have much more work to do.
- Label the rate you are trying to find “huh?” and denote it with a question mark. This is your target. Without listing this, you have no target, which means you’re sure to hit it.
- Another good reason to label your target rate as “huh?” is because if the label does not appear in your final equation, you can say, “Hmm, there’s no ‘Huh’.”
- Y’all are awfully quiet today. Are y’all this quiet in all your other first period classes, too?
- In relation to the angle, we want to know the opposite side, and we are given the hypotenuse, sooooooooooooooooooooo, we must use Sine (SOH CAH TOA)
- The bathrooms down the hall are unmarked. The way I remember which door to go in is that Men are always right. This may be untrue, but it takes me to the urinal.
- “SHHHHHHHHHHHHHHHHHH!” That means “BE QUIET,” in civilized societies. Thank you.
- Please solve all of your problems in advance. Thank you.
- So when you see that you are given two angles and a side of a triangle, you say, “OOOO, OOOOO, OOOOOO, Law of Sines!”
- If we call this point C, and the other point Shining C, then we are looking for the distance from C to Shining C.
- If you don’t pay your math dues by the next meeting, don’t consider yourself a member of the math club. We have to distinguish ourselves somehow, if not by our intellectual acumen, then by our fiscal dependability.
- I am my most creative when I am deep in pool of melancholy and self-superciliousness.
- They are hoping that the walls are so shiny, bright, and new, that no one will bother looking up or down.
- So, what do you remember the sine of ninety to be from your past trigonometrical experiences?
- Does anybody in here not know there grade and want to see it, or you know it but it was so stellar that you want to see it again?
- I tried to get a sub for you. I selected the only sub on the list that knew math. Then he called me at home and said, “I’m the only math person on the list, but I can only do Geometry or below.” There’s a career opportunity for anyone interested.
- Thank you for that pointless interruption. Please don’t do that more often.
- “Can we have free day today? Can we have a free day today?” “Sure you can, I’ll whoop your butt for free today. I usually charge 5$ for it. AND on top of that I’ll give you two paper clips, at no charge to you.”
- (overheard) “Mr. Korpi is sooo random!” (my response) “You just haven’t figured out my pattern!”
- When homework becomes classwork, classwork will become homework.
- The greatest triumviri of all time was indubitably Curly, Moe, and Larry.
- You cannot throw your old computers away. Please store them until we have our end of the year technology garage sale. –OK, I will be storing them in that dumpster over there.
- When they did the $3 million overhaul of the school, technology was first. They got there own large lab rooms, full of brand new computers, their own data projectors, new furniture, and get this: floor plugs. They must have thought in advance on that one. The new science wing got theirs, too: new lab equipment and the latest in technology: computer lab testing probes, CPUs, and elaborate software. Even the new home economics rooms got their requisite stoves, ovens, vent hoods, and even a dining area. Athletics got a new competition gym, AND a new practice gym! What about the math department? We got stuck into a leftover space, upstairs, away from everybody, where they wouldn’t have to deal with us. Our rooms are brand new, but small, lack trashcans, pencil sharpeners, bookshelves, storage cabinets, and no floor plugs for our overhead calculators. We did get windows overlooking an apartment complex and very small dry erase boards. It’s like they asked us, “What goes into the ideal math classroom, because we want to make sure what not to put in it.” ‘Tis ‘nuff to drive a man mad!
- You have to be very careful when you are solving problems with sine, cosine, and tangent. Simplifying trigonometric expressions can be pretty triggy.
- I wasn’t in the senior class picture, because I wasn’t asked. Besides, most teachers want to be in it as a level of status: their picture is forever captured in the history of New Braunfels High School. I try to achieve my immortality through my work inside the classroom, not smiling for a camera. But, mainly, I wasn’t asked. Anyway, I think they know that I would be the type of teacher who would run around the back to try and get into the picture twice.
- Q: Can I be in the math club if I’m not a member? A: No, it’s really a club for members only.
- --Your name is Andrew, right? --NO, it’s Tina. –Sorry.
- Live well, eat right, have fun: that’s what I always never say.
- (On being asked to open a fixed window in class) I can open it, but closing it again will be a challenge.
Wednesday, December 26, 2007
Would I make it a marathon day on the new Xbox 360 becoming a guitar hero or battling the Lego version of Darth Vader? Or, would I fold the mountain of clean clothes in the laundry room that somehow went neglected over the weekend? Perhaps today would be the day I begin chipping away at that pile of seemingly reproducing school papers and take-home tests that grading? Or maybe I'll just pick up around the house tidy up all the Christmas litter that's been deposited in every corner of every room over a two-day period? Well, I managed to do ALL of these things. So although I didn't go BACK to work, as in the physical locale, I DID get back to work.
I feel pretty proud of myself for finding such and agreeable balance to my leisure time, incorporating enough diversion to the bothersome chores that neither became to discordant. The laundry got completely done. The math grading is now 66.365 percent complete. The house was tidy when the kids got home (although now it has fallen back into its usual disarray), and I even managed to pick up my wife and kids and take them to a nice lunch at a local BBQ place.
I didn't even get tired or frustrated as I picked up the curbside garbage that had blown over and down the street as it waited for the garbage man. Each time (3 total), I packed boxes within boxes, with boxes, trying to make everything more dense and less likely to drift off, and to increase the chances that it would all find its way into the garbage truck. I worried if we had exceeded our garbage "quota" for the week, if such a thing even existed. If every household had as many empty boxes and trashbags full off ripped wrapping paper, the poor, overworked trashmen might have to make a couple of runs just to collect it all. With all the garbage we had, it's amazing I was able to find a proper place for the contents of all the boxes inside the house. We really do spoil our kids these days. I sure hope my son appreciates his Xbox as much as I do!
Yep, I couldn't have expected my day to have been any more productive even if my wife had planned it out for me. Best of all, when she got home, I got her seal of approval, the true measure of my ability not to screw things up. I don't think I'm going to press my luck and go for a second day in a row all on my own tomorrow. I consider myself to be lucky it worked out today. No, instead, I'll just follow the list my wife is making for me right now. I just hope she gives me a longer window to write a blog than I gave myself to write this one.
May the garbage man pick up all your Christmas waste in one trip, may you too find a nook and cranny in your house for all the new things Santa brought you that your kids are already tired of , and good luck taking down and packing up all your decorations.
Tuesday, December 25, 2007
My father printed pages and pages of questions from the internet and played "Richard Dawson" as the boys took on the girls. The questions were supposedly current through 2002, but when "Pentax" cameras placed in a survey of most popular cameras while "Olympus" and "Sony" did not, we knew that 1982 was more likely the era of these questions. After adjusting our responses to what we thought was popular 20 years ago, we got on a good role, for instance, when asked the top four video game system, we answered Atari, Colecovision, Intellivision, and Tandyvision (not Xbox 360, PS3, Wii, Nintendo DS).
Throughout the game, it also seemed like the women were getting the easy questions, like "name the top five integers between one and five" while the guys were getting questions like "name the 5 least used characters in the Hebrew alphabet." A question like that is hard enough today, but even more so when you're trying to think which Hebrew letters were shunned 20 years ago!
After what seemed like 2 hours (29 rounds!), the game began to lose its spark, especially since my son and nephew started taking each loss so personally (they couldn't believe that balloons would NOT be on a list of top 5 things made of rubber, or when we lost a round because we went with my "snoring" answer to steal and not my son's "cricket" answer, which we discovered was the number one thing you hear when you're trying to sleep.) We ended the first chapter of the game marathon, took a quick bathroom break, then hit the kitchen table for some more good ol' family fun.
First out of the box was a game we actually got for my mother, a game called "Imaginiff," where you get to decide which of 6 choices someone is most like. For instance, the question might read, "What if Kevin were a type of rug, which one would he be? 1. An area rug 2. An expensive oriental rug 3. A toupee 4. A remnant 5. Auto upholstery 6. With frayed edges and a wine stain"
You can see how a family without a good sense of humor can really get into it with a game like this. Sometimes the answer is an obvious fit, like a person who has trouble following through on their many projects being described as a candy bar that gets stuck in the vending machine, or a person who enjoys a good stiff drink needing champagne at a picnic. Sometimes, though, it's a stretch to come up with an answer that even remotely makes sense, like "If 'so and so' were a color, they would be 1. Chiffon 2. Chartreuse 3. Alizarin 4. Terre Verte 5. Viridian 5. Cyan." I don't even know who 'so and so' is.
After going through half the cards, and repairing bruised egos, we switched to my favorite game behind Trivial Pursuit: Beyond Balderdash, a game where you make up definitions to exotic words, write fictitious movie plots to zany titles, create plausible claims to fames of individuals with interesting names, and give believable meanings to acronyms. Having a pretty creative and witty family, this game always gives big laughs, and last night was no exception. My brother and I quickly abandoned reasonable answers and took the low road to rib-splitting humorous responses. I cannot even repeat the vulgar word my brother got my pious mother to read, but I was glad I was not drinking milk at the moment, or it would have been out of my nose.
At times I don't know if it was the answers themselves causing the hysterics or the hysterics themselves, but the game was interrupted several times by long fits of laughing, snorting, chortling, convulsing, and whooping. The highlight of the evening, and any game session with my family, was when we got my dad to do his unique laugh, whereby he goes into a rhythmic falsetto laugh through closed, tearful eyes, as he barely manages to feed it with air. Once he (and the rest of us) recovered, we're almost too weak to continue anymore, exhausted from our laughathon.
Eventually, I had to take my wife and kids home, as it was getting very late, but I think it's safe to say that we all had a good time. Sure, the gifts and presents we got were nice and thoughtful, but the real gift yesterday was the joy we brought to each other through the healthy activity of laughing not just WITH each other, but AT each other as well, and in MY family, there's plenty of both varieties.
Monday, December 24, 2007
Each May, in an attempt to earn college credit, 1.5 million students from all over the world take about 2.7 million Advanced Placement exams in 22 subject areas. Seeing as how these tests don't grade themselves, each subsequent June, nearly 11,000 college professors and high school teachers meet in one of 5 cities across the nation to hand-grade nearly 10 million free-response questions (apparently, there are machines that can handle the multiple choice portion.)
As the name implies, I will be one of about 500 high school calculus teachers reading the exams this summer, but what the name does NOT imply, I will be carefully evaluating each student's work, anonymously, and assigning them up to 9 points of credit per problem. Reading sounds much too passive for what we actually do. In fact, before we are allowed to score a problem, we are trained in HOW to grade it: what to look for, different ways to justify a portion, exceptions, etc. Although they try to cover many "what ifs," they are relying on (and paying us for) our professional judgment. The work is tedious and repetitive, but it is also stimulating and enjoyable. I'm guessing that type of admission officially classifies me as some sort of geek, but a well-paid geek.
You can imagine a large convention center in a major US city filled with these such geeks, coming together to be geeky, and believe me, there are plenty of interesting people that show up. For example, check out the dorky guy in the top photo in the white shirt in the back row!! There is always an interesting array of patchy facial hair, mad scientist hair, and no hair at all. Wardrobes range from full suits, to too short shorts revealing skinny, pale white legs with dark dress socks stuck into white tennis shoes (I saw that on more than one occasion.) The many different facial expressions on the attendees reveal the diversity and extremes of the personalities that attend, from quiet, reserved, socially inept to can't stop smiling and talking about math to anyone that will listen.
Whether because of natural affinity or pure happenstance, last year I was able to meet a small group of guys in the same classification of "normal" as I was in, guys with similar personalities, values, interests, and family situations. Spending the mornings and evenings in the company of these great professionals made the entire week worth while. Whether we we taking early morning runs along the Ohio River, playing late afternoon tennis, or just sitting in a bar watching baseball or basketball, the company always broke the monotony of the 7-day grueling work week.
So this summer, I'll do it all over again. Hopefully I'll meet up with the same guys, meet new people, and avoid paper cuts handling the thousands of tests that will pass through my hand. Kansas City better get ready for the math invasion, 'cause we're coming, and we're making a fashion statemtent.
Saturday, December 22, 2007
My son is apparently a chip off the old block when it comes to thoughtfulness and keeping secrets. Last week, my father-in-law had his birthday. He had been wanting a new juicer to replace his old one whose motor burned up. Knowing this, my son (and daughter and wife and I) decided to get him a new one for his birthday. Having purchased the gift several weeks in advance, we now had the challenging task of "sitting" on our secret. We even coached my son on keeping the gift a secret from his "Poppy." But as any coach knows, you can't simulate "game play" in practice. Apparently, we were not specific enough in all the different situations and scenarios where a new juicer would naturally (or unnaturally) come up.
The very next time we saw my in-laws, my son ran up to his grandfather, whose birthday was still several days away, and said, "Poppy, if you go to the store, don't buy a new juicer! Okay!" Days later, "Poppy" acted legitimately surprised when opening his juicer, and showed true appreciation of the thoughtfulness of the gift and the enthusiasm of his grandson's desire to give him a special gift. They spent the rest of the afternoon making apple juice, carrot juice, tomato juice, potato juice, squash juice, . . . together. It was a pretty special moment.
Anyway, not all stories turn out like that. I was just reading a story about a wife who got a special gift for her newlywed husband and had it waiting under the Christmas tree for him for that special day. Apparently, the husband saw it and anticipated it being something he couldn't resist or wait for. After his wife was asleep, he sneaked into his own living room shortly after midnight last Tuesday and began to open the gift. The wife, who perhaps got up immediately afterward for a midnight snack, went by the kitchen and grabbed a knife, then proceeded to the living room where she discovered he husband with his unwrapped gift--before Christmas Day!!!!!!!!!!!
This was unacceptable to her, a breach of their marriage vows, an act that required immediate action. Did she reprimand him? Wrap the gift back up? Ask him how he liked it? No. . . . she stabbed him in the chest with her knife. As he sat there holding his special gift in one hand and his own blood in the other, she then accused him of having an affair with another woman, then said his socks didn't match, and that she wished he would shave!
The stabbing over the gift was a bit much, but taken with the other infractions, the stabbing was . . . . still an act of a crazy woman!! She was later arrested and charged with aggravated assault and battery, misdemeanor domestic battery, and hysteria. The husband was treated and released from the local hospital, where he raced home to play with his new Radio Controlled car . . . . several days before Christmas. At least his wife wasn't there to stab him again for playing with it inside the house.
So, may you get what you want this Christmas, and may you're stories be more like the story of the juicer and not the dicer.
Friday, December 21, 2007
How dumb can one math teacher be? Leave it to me to assign two different enormous take-home tests and a variety of extra homework problems that were do in the final week before a two-week Christmas break of 107 students, guaranteeing my unavailability to my family or any other activity, because of the perpetual movement of my red didactical wand that is my grading pen over the holiday.
But why did I assign this to begin with? Was it because the students needed the practice? Did I want them to feel an academic pinch (something many of them are not used to). Yes, but primarily, it was because they had angered me by their continual reluctance and to study and recalcitrance to change their poor, lazy habits which were obviously not getting the results I demanded.
So this ultimate “self-flagellation and alienation from loved ones” was because students at the PreAP and AP level are not taking care of business. After grading the final batch of quizzes from the previous week with pathetic scores, when it became obvious to me that my single effort in assessing the students was greater than their collective efforts in producing them, I really began to examine the sum of my frustrations teaching this level of math for the past eight years. “Why is it so hard? Why do so many not get it? My level of explanation has been rewarded and applauded in my short career by students, parents, teachers, administrators, and university professors alike. It had to have gone deeper than just my inability to “teach” the concepts. But what? Here’s what I have finally discovered, although the reality of it is disheartening.
I teach math. I teach math skills. I teach theorems. But, I also teach math humanistically. The implications of math history and philosophy are part of my regular curriculum. I frequently discuss the “discovery” of math, and often structure my questions so that students have the opportunity to make the same “discovery” on their own. Some do. I balance my instruction between pure and applied mathematics: pure being a game involving the manipulation of symbols according to the rules of math, and applied being the study of the beautiful laws of nature. Both of these possess beauty and power. But seldomly in high school does anyone ask, “WHY?” It’s just there: another class they have to take. Some get to appreciate me, without truly appreciating the math at the level I am hoping for.
So why are some more successful than others? Although there is scientific evidence that there is no math “gene,” there is mathematical intuition. You can see it in the students. Some have more, some have less (irrespective of their work ethic.) It can be developed, but it takes toil and sweat and determination. Math is patterns. If a person has no insight into the visual, numerical, and symbolic sense of math, they are handicapped. Math is replete with arcane symbols. “Real” mathematicians are regarded as genius. People respect them for their insight (if not for their abilities to be fodder for an Academy Award winning script) and are cowed at their knowledge and ability to “pry” open the secrets of the natural world.
But, being a mathematician AND a math teacher, I am continually confronted with sequential problems that have nothing to do with math at all. All I can best hope for is to “sell” math to the students on the thin basis that it is “fun.” It is only in this manner that I get through the week.
After discussing my frustrations with colleagues from across the nation (via the AP Listserv), by problems are representative of a classic classroom crisis of understanding versus pedagogy.
The grim esotericism, in which even the best of us sometimes fall, the preponderance, in our current writing, of those dreary textbooks which bad teaching concepts have put in place of true synthesis, the curious modest, which, as soon as we are outside the study, seems to forbid us to expose the honest groping of our methods before a profane public . . .”—Marc Bloch, The Historian’s Craft
Invariably, a certain fraction of my instruction is devoted to proving theorems. This fraction is certain to be greater and deeper than that of a basic algebra class, and increases with the level of mathematics. One of the true objectives of teaching/showing proofs is to hope to convince students by unimpassioned reason, by psychology, by intuition, of the truth of a statement. Frequently in more elementary-level classes (those below Precal)—and it is experienced by all educators—that some confused student interrupts the proof in earnest with the cry (should they be so bold and eloquent): “I don’t see why you did what you did. I don’t even understand why what you say is so, is so. Additionally, I don’t comprehend how you came to do what you did!”
This is where we teachers of higher-level mathematics are confronted with a crisis of understanding. How should we/do we deal with it? Unfortunately, not very well (those of us with patience, that is.) Maybe we go over the sore spot again in a less technical, slightly different way, using terms and analogies, OR perhaps, anxious out of a mandated requirement to cover a certain amount of material, we overtly brush the student aside with a cursory explanation stated with the additional advice that understanding will surely come if only the student will go over the material later on his own, including reading, (that’s right, reading!!!) the math textbook.
OR (as dedicated teachers, such as I and my many colleagues throughout the world), we alter the course of the lecture/lesson completely, going for depth and the expense of breadth, and hoping for no fire drill and other frequent modifications to the schedule that severely limit our already sacred 3 to 4 hours with the students each week) until we have explored the mathematical difficulty until the students understand.
My first reaction to a crisis in understanding is to think: why are they confused right here at this spot? This is only a definition! This isn’t even the “hard” part, yet! This is the straw that breaks the camel’s back. We have been piling up sophistications upon theorems upon corollaries upon lemmas upon conjectures. Are they confused with the notation? The hypothesis? The conclusion? Do they know the difference between necessary and sufficient? At best, I have moved on, bludgeoning my class into, at least, accepting the proof without understanding it. But is has become clear that, having created an initial barrier; the theorem/concept/idea would not be cleared up by simply restating it in excruciatingly fine detail. Another approach was required.
It is a general consensus in the math educational community that the road to understanding is the way of the initial discovery: if one knows and sees the way some idea or concept was originally though out, then this is also a good way for presenting it in the classroom, but this is not entirely true. The initial discovery may have been obscure, buried within a specific context, or made unnecessarily difficult. Many of the presentations in a textbook are glossy, up-to-date versions that can, themselves, be obscured in their conciseness and generality. In such a case, a presentation that retraces the original problem and the historical, humanistic framework can offer more insight.
Ultimately, a proper education is the collaboration of efforts from teacher and students working, thinking, exploring together. Both must be willing to admit faults, make errors, and exchange information and ideas in a safe, non-judgmental environment. The true beauty of learning is the process itself.
Thursday, December 20, 2007
We're never that good, but nobody has ever thrown tomatoes at us (and we HAVE sang for the cafeteria workers before!) It's all about being creative, having fun, and spreading Mathematical, Christmas joy before the holidays.
Here's a song I wrote after very few students opted to write a carol. It's to be sung to the tune of "Feliz Navidad" WITH hand clapping and maracas where you deem appropriate.
We love doing math
Oh ya! We love doing math.
We love doing math,
We even do it when we're taking a bath.
We need some more math.
We've gotta have more math.
Can't get enough of math,
It'll lead us down that primrose path.
We want to wish you a merry mathmus! "What the heck is a 'Merry Mathmus?'" We don't know, but we can discuss it Over many math prob-lems. So when you're out having merry mathmus, Remember math on this special mathmus. and please don't get mad or make a fuss If you can't find and infinite su-um.
So now we must go.
We're getting looks, you know.
So in leaving, "Ho, Ho, Ho!"
Good luck on finals and a mathy new year.
We want to wish you a merry mathmus!
Don't ask us "What is a 'Merry Mathmus?'"
'Cause we're not sure, but we think it might
be something about Pi!
So when you're out having merry mathmus,
Remember math on this special mathmus.
And thanks for putting up with all our mathmus
Adios, so long, and goodbye!
Wednesday, December 19, 2007
The spirit of Christmas is about giving, and not just giving your hard-earned dollars to the large corporations that market their expensive wares so that you can have a stockpile under your Christmas tree, but also a time to give to large non-profit corporations who pay their expenses and salaries with your donations, then distribute the rest to the needy families without stockpiles beneath their tree. Groups such as United Way, Goodwill, and the Salvation Army typically set up "giving stations" in conspicuous, high-traffic shopping areas to make it convenient to donate, and to make you feel guilty if you don't.
The people working the donation stations are all volunteers, and are very cheerful for the most part. Some are passive and grateful, some are ardent and zealous in coaxing your money from your wallet. None are more noticeable than the Salvation Army's strategy: bell ringing, non-stop bell ringing. I have been so aggravated by the sound in the short walk from my car to the store's entrance that I have been glad to drop a buck into the bucket just to get the ringing to stop.
Because of the toll it takes on the wrist and one's sanity, bell-ringing shifts are usually short, an hour or two, before another volunteer takes over. I've been fortunate to have actually seen a shift change. It is a remarkable feat how they are able to pass the bell from one ringer to another without missing a single "ding-a-ling-a-ling." It was executed with such jolly perfection, I doubted whether these were actually volunteers, rather than professional bell-ringers. Such skill and coordinated agility must take hours and hours of practice, and being able to do it so reflexively after the ceaseless tintinnabulation makes it all the more impressive.
But then, I discovered the secret to the perfectly executed maneuver: there are clear instructions for ringing the bell and the changing of the bell written in large, glaucoma-friendly, print on the back of the "Salvation Army" sign. Feeling somewhat naughty for reading such privileged information, but taking advantage of the opportune angle of the sign that allowed me to sneak a peak, I read inquisitively. Here's a summary:
1. Ring bell
2. Keep ringing the bell
3. Don't stop ringing the bell
4. Smile through the maddening sound of the bell
5. If your hand falls off from ringing the bell, ring bell with other hand
6. Ring bell until relief comes, or until forever
7. If thinking about stopping the bell ringing, do so while ringing the bell
8. If deciding to stop ringing the bell, change your mind
9. Remember that you are a volunteer who has volunteered to ring the damn bell
10. It's all about the bell ringing
11. No unauthorized individual may touch, much less ring, the bell
12. Remember, the more annoying you are, the better you are helping the needy
13. The bell must remain ringing during the transfer of ringers--DON'T MESS UP
13. Bell ringer may pilfer 10% of donations acquired during bell-ringing session
Yes, there's nothing quite like Christmastime.
Sharing is caring, need knows no season, and the memory of an unrelenting ringing bell haunts indefinitely.
Tuesday, December 18, 2007
I should have known when I woke up with a sore back from another restless night that the day would go downhill from there. When I got to school, I noticed that I had made the not-so-uncommon "guy" mistake of thinking that we can actually dress ourselves. Having donned what I thought were my ebony trousers early that morning, I proudly accesorized with a fine shirt with black accents, slipped on some black socks with my black shoes and even opted for the black belt over the brown. "My wife would be proud that I dressed myself again today."
Well, my black slacks never left the hanger, but my Navy Blue slacks sure looked suddenly blue in the fluorescent lights of my classroom against my black shoes. I thought I even heard my belt laughing at me in my wife's voice. Throughout the day, as students mentioned it, I reminded them that the math problems on the board were not going to work themselves.
I had also expected to get some much needed grading done on an early Monday morning, thinking that few, if any, students would show for tutorials at 6 am after a weekend break--wrong again. Luckily, I was sitting behind my desk as the eager students, more focused on why their homework wasn't working out than on why my wardrobe was incongruous, entered the room. One question after another. The SAME question one after another. By the end of the morning, I think I was the only one who had mastered that problem, although most of the students had mastered the art or color-coordinating their outfits. I guess we're all good at something.
During my first period conference, I thought my chance had come to do some grading, but instead was taken up by other administrative tasks and time spent with my Mentee (who was kind enough not to comment on my fashion faux-pas.) Then I fought through the throngs of student gossip depots during the passing period to arrive back at my class in time for homeroom, where I was immediately bombarded with requests for ribbons, scissors, construction paper, markers, tape, blah, blah, blah. I couldn't process the requests from the spirited sophomores who obviously remembered that it was homeroom door decorating day. I had forgotten the event, so my supplies were not on hand. By the end of the 25 minute period, our door looked respectable with the odds and ends we were able to pull together from other people's doors, only to see my neighbors finished project which looked like she had contracted it out to the Disney Imagineers! She apparently remembered the event, even planned before hand, as she had posted photos of each of her students wearing Santa hats. When it comes to door decorating, I'm a third stringer in the pee-wee leagues.
As I got into my teaching routine after that, I expected things to get better, much better, but for whatever reason, I felt disparately alone in front of the classes all day long. I was working harder than usual to deliver an invigorating, enthusiastic, witty, bombastic lesson, but with each increased effort on my part, the students' became increasingly listless and sleepy. During my lunch period, as a drew a breath a few minutes before the bell to release them to eat, I heard a raucous cheer in the back of the room, "Come on lunch, come on lunch." Not wanting to disappoint, I sat down at my desk for the remaining three minutes. By last period, nearly half of the class had their heads down on their desk. One student was even mopping it with his tongue.
An exceptionally bright young student who was fighting off the peer pressure from her hibernating peers offered an explanation, saying that she only got three hours of sleep the night before. Although I was really unsympathetic, figuring that the lack of sleep was self-induced due to procrastination and because I get very little more than that on a regular basis, I was grateful that at least she was awake to actually offer up the confession.
After school, I thought I'd check my phone messages. For the past week, my display has shown "one message," which I previously checked and was saving. Still showing "one message," I decided to check it anyway--10 new messages--All parents of students needing to talk. Some called multiple times, and had a noticeable growl in their voice. OOPS! Never again do I trust the conveniently misleading digital read-out on the phone.
With no time to return them then and there, I raced off to my doctor's appointment, where I did not want to be late for my 45-minute-sit-in-the-waiting-room-before-we-call-you- then-wait-20-more-minutes-in-the-patient-room-before-the-doctor-gets-to-you session. After only 5 actual minutes with the doctor, he told me I was in great shape, and wrote me a prescription for my blood-pressure medicine and a pair of black pants.
With an hour to kill before I had to pick up my daughter from her "dance" lesson, I went back to school to face the phone. The first call lasted almost 45 minutes and wore me out, but ended amicably. Like a criminal on trial taking the stand in his own defense, I justified my teaching methods, my personality, and my fashion sense until by mouth went dry. After the first call, I had time for one more quick one. The man said "hello," I talked non-stop for 5 minutes, after which the man replied, "that's all I needed to know. Thanks." Whew! An acquittal.
Racing to the dance studio, I arrived 36 seconds late. Feeling horrible for my tardiness, I apologized to the instructor, who couldn't discern if I was serious or jocular--neither could I at that point. And that's how the rest of the evening went. I was in a restless, cloudy state all night.
As I threw the football with my son, watched television with my wife on the couch, and played with my daughter, I couldn't concentrate on anything else but how wearing matching pants the next day would make tomorrow much better than today.
Monday, December 17, 2007
On television, where REPORTING the weather supersedes the actual study of weather, where no change in the weather is bad for business, weathermen have advertised themselves over the range from full-fledged meteorologist to "forecaster," a euphemism for "windy guesser." With their high-tech equipment and fancy computer graphics, these teleguessers are in a high-stakes competition with other networks for viewership. As a result, they try to outdo each other in their sensational reporting of mother nature's temperament by giving you updates on the half-hour (in case you don't have a window to look out of), or by offering a 10-day outlook (in case you want to know what it won't be like in a week and a half from today.)
If it's hot, they talk about eagerly anticipating some relief in the form of cooler weather. When it's cold, they encourage their viewers to "hang in there! Warmer temperatures are coming." They seem incapable of just reporting the facts without adding their colorful, subjective opinions. I wish for once that they would just enjoy the current conditions, instead of trying to plug their next forecast.
I would love to tune in one day and hear that freezing rain and high winds are awaiting me on my morning commute without the reminder to "bundle up!" and without the negative framing of the whole situation: "we should be getting some relief by early this afternoon." Relief from what? Freezing rain IS a relief . . . . from NON-freezing rain. As infrequently as we GET freezing rain, why not embrace and savor it instead of pining for the glory days of the soft, wet rain rather than the piercing, painful kind?
And what's with all the NAMING of weather events. Will anybody ever remember "Arctic Blast Severe Sleet Storm Saturday: 2007?" We're more likely to remember the gaudy digital effects, the grave sincerity of the reporter who fears the end-of-days, and the outrageous appellation rather than the conditions outside our door.
When the weather changes, it's the lead story, but only as a teaser advertisement for whats to come later in the broadcast. Oh sure, they'll tell you immediately what the weather was like for the past few hours, this is when their forecasting at their best, maybe they'll even read their thermometer for you while mentioning their Doppler Deluxe X-3000k machine, but if you want to know how to dress tomorrow morning, you'll have to wait until the end of the broadcast.
So will it freeze tonight? Well, that all depends on the weather.
Remember to bundle up!
Sunday, December 16, 2007
- The other day, I slipped and fell up three flights of stairs.
- Label your intentions
- In the equation f(x)=100, the f(x) acts as an introductory adverbial phrase.
- For any given angle in a triangle, two of them can be considered Adjacent sides, but we only consider the Non-Hypotenusal Adjacent side as being called Adjacent.
- I get my quotes from books, other books, and non-books, such as conversations and non-conversations.
- Most people who mispronounce “New BraunSfels are out-of-towners or locals at Wurstfest, who are ‘soaking up’ the local culture.
- Is this regular hexagon (drawn in black) what a stop sign is? Of course not, stop signs are red.
- I think it would be neat if the same groups that “adopt a highway” and pick up trash, carried with them magnet clothes to dress up the Mom and Daughter on the school crossing signs.
- Related rates are called such, not be cause they are brothers, or sister or anything, but rather because they are more like 2nd cousins, twice removed.
- I don’t like to run. With every step I take I say, “Gosh-this-really-sucks-I-wish-I-was-driving.”
- I’m working on my first film. It’s taken me a while. They are probably going to charge me a late fee at Blockbuster.
- Mr. Korpi, can we please not learn anything new today? Well that’s up to you. Do you think you can convince your classmates not to pay attention to the lesson which I will be giving today?
- If we travel around the first parallel, could we claim that we have traveled around the world? If so, this would be true for any latitude. I choose the 90th, although I have to travel around the world just to get there and back.
- What a beautiful day today. I’d like to have class outside today. All in favor, meet me outside after class.
- This is about the easiest section we will do all year. As a result, we will spend an extra day doing it.
- We can’t afford to slow down, not for anything. We have a set amount of curriculum to cover. Q: What if the school blows up? A: That may slow us down a bit.
- Now for the next problem, we will be blowing up balloons. That’s inflating them, not filling them with lit dynamite.
- This problem is not right. I don't even think it is wrong.
- Who stole my “Math Counts” Frisbee? I will not tolerate such shenanigans.
- I’m sorry, I don’t have any cash on me. I’ve been meaning to buy some more.
- How silly is to punish an act of truancy with suspension or expulsion. This would be tantamount to paying criminals for robbing banks.
- It is a sad day in the world of education, when we use the absence of learning opportunities as a punishment for unrelated misbehavior. This reinforces the wrong concept of learning.
- We are soon fixing to get ready to make plans to begin.
- I always like to carry a quarter in my pocket just in case anyone ever comes up to me and says, “hey, you ain’t worth a dime.”
- Today is national “pronounce the silent letter in words” day. In H-onor of the event, we will be discussing Isos-k-eles triangles, inspecting them so closely increasing our K-nowledge of them so much, we are practically dissecting them with a K-nife.
- The calculus is the easy part. It’s the algebra that will kick your butt.
- All right, Let's Do it To it.
- Ready, Set, Go, Stop. Who’s done?
- Don’t forget units. Millions of points throughout history of math tests have been lost because units have been overlooked. Don’t be a statistical footnote in history.
- Look, it says 23 percent of Americans don’t believe a thing that Al Gore says. It also says that Disney’s patent of Mickey Mouse will expire in 2003. Look for Al Gore’s percentage to increase as he claims that he invented Mickey Mouse.
- I got out of homebuilding into teaching because I figured it would be easier to manage students than subcontractors. I found out that this is not necessarily true, but they do show up more regularly.
- Have no fear about having your ears shot out as I turn on the television, for I have been to teacher school, where they teach you to turn the volume down before doing so.
- If you’re going to get up in front of someone to teach, especially a very typically boring subject, you’ve got an obligation to at least make it entertaining, if not educational. The same goes for educational consultants at teacher in-services.
- Leave them laughing. That’s what I always say. Please laugh now as I turn and go.
- I have lateral tibular fibulitis. I’ll take your word for it.See you next time, or before then.
- Does it matter if we find side a or side c first? No, It really comes down to our preference: do we prefer Apple Pie or Cherry Pie? Acid or Coc. . .Never mind.
- Now little g is not only the length of the side opposite angle G, the acceleration due to gravity, but also a rapper out of Compton.
- Now just because I’m drawing planet Earth with a red marker doesn’t make it Mars.
- The answer is 47. 666. OOOh. That creeps me. Let’s make it 47.667, the Neighbor of the Beast.
- So the answer is .411. That’s some good information
- This road we’re going down is not the scenic route, in fact it’s not even a road. We are clearing our own path. Watch out for tempting serpents.
- We can verify this triangle is correctly solved by using the triangle inequality, Pythagorean theorem, and using Trig functions, but I think we can see that it’s correct, so let’s not do that, and say we did.
Friday, December 14, 2007
One of them is telling another, "These problems really aren't too bad."
I immediately reply, "but you're saying it IS bad, but just LESS bad than worse things."
"Yeah, I guess so. But I guess anything less than death is not TOO bad."
Another student quickly chimed in, "I can think of SEVERAL things less than death."
"Like problem 34!" said another.
Oh, I love the taste of math in the morning!
I did start thinking, however, that perhaps calculus should carry a warning label, much like cigarettes, alcohol, and superhero costumes.
Incidentally, I read an article yesterday describing the wackiest warning labels. There's even a website full of them. The winner, chosen by an anti-lawsuit group, was found on a John Deere skid-loader tractor, reading, "Avoid Death." Great! I'll try to do that. I guess that means no doing calculus while driving that tractor.
The other candidates were:
- Found on an iron-on T-shirt transfer decal: "Do not iron while wearing shirt."
- Found on a storage pouch on baby stroller: "Do not child in bag."
- Found on a letter opener: "Safety goggles recommended."
- Found on a Tide Bleach pen: "The Vanishing Fabric Marker should not be used as a writing instrument for signing checks or any legal documents."
- Found on a phone book: "Do not use this book while operating a moving vehicle."
- Found on a cell phone box: "Do not dry out in the microwave."
- On a waverunner's fuel cap: "Do not use a lit match or open flame to check fuel level."
- Found on Apple's website: "Do not eat iPod shuffle."
- Found on a Razor scooter: "This product moves when used."
- Found on household cleaner: "Read all instructions prior to use. If you cannot read, do not use product."
- Found on Vet pills for a dog: "This drug may cause drowsiness. Use caution when operating a car or dangerous machinery."
- On a chainsaw: "Do not hold the wrong end of the chainsaw."
- On a blow dryer: "Do not use while sleeping."
- On a life-vest: "This is NOT a life-saving device."
- On champagne bottle: "Remove label before placing in microwave."
- On bottle of peanuts: "This product contains nuts."
- On Liquid Plummer bottle: "Do not reuse this bottle to store beverages."
- On a Toilet Plunger: "Do not use near power lines."
- On a box of hair dye: "Do not use as an ice cream topping."
- On eye drops: "Use before expiration date."
- On Bayer Aspirin: "Do not use if allergic to Aspirin."
- On a bottle of Nytol Sleep Aid: "May cause drowsiness."
- On Christmas lights: "For indoor or outdoor use only."
- On a box of matches: "Contents may catch fire."
- On a road sign: "Do not hit this sign."
- On McDonald's Happy Meal toy bag: "This bag is not a toy.
- On child's Superman cosutme: "Cape does not enable wearer to fly."
The intent of specifically defining ridiculous scenarios is to curtail frivolous lawsuits, which is precisely why McDonald's now prints "Caution: Hot Coffee" around the rim of its hot coffee. Some might argue that the labels themselves give people ideas of what to do, but the sad reality is that the labels exist because someone ACTUALLY did the very thing the labels warn against--and SUED because they were not explicitly instructed NOT to do that-AND WON!!!!!!!
I think one new warning label can effectively replace all other labels:
"Don't be an idiot!"
But then, why are we trying to protect idiots. Why not let natural selection run its course? It's because idiots have more rights than the rest of us. The courts pander to the lemmings. We are effectively trying to legislate common sense, which is like trying to beat someone until their attitude improves.
I'm serious, though, about that calculus textbook warning. Don't say I didn't warn you!
Thursday, December 13, 2007
An father was returning his 6 year-old and 13 year-old daughters to the house of his estranged wife's house Wednesday evening. After his wife refused to come out onto the porch to talk to him, he pulled out gun, pointed it at his daughter's heads and fired a single shot into each of them, after which, he put one into his own head and died right there beside his two daughters on the front porch.
With all the violence on television, the movies, and even in the streets, we have become numb to tragedy. But stories like the one above manage to shock us out of our insensitivity. In fact stories like this make me want to puke in disgust. Any loss of human life is tragic, but when innocent children are the victims of senseless violence, is there anything worse? Not since the Susan Smith case have I actually been moved to tears by a story of such senseless, needless loss. The incidents surrounding this latest tragedy are hard to imagine. What father would turn a gun on his own children? Why couldn't he have shot HIMSELF first, THEN turned the gun on the girls????? What makes these heartless lunatics feel like they need to take innocent victims with them. Did he thing the girls would be there for him in the afterlife? Was he just trying to make a point to their mother? I don't even know what questions to ask in a case like this.
Tragically, filicide, as the deliberate killing of one's progeny is called, seems to be a growing trend nationally, as there are seemingly more and more cases involving parent killing their own children, or seriously injuring them in their attempts. A quick check of Wikipedia shows and alarmingly high number of filicide cases. Here are some headlines from the last few years:
Man Gets 40 Years In Infant Son's Death
Teen Mom, 17, Charged As Adult In Death of Infant Son
Infant Dies From Methadone Overdose
Mother Gets 15 Years, Likely Deportation
Man Charged In Beating Death Of Infant Daughter
Statistics have shown that the majority (70%) of the motives for filicide-suicide were identified as altruistic, that is, the parents (90% of the mothers and 60% of the fathers) were motivated by the desire to alleviate real or imagined suffering in their children. Does that make it any more noble or less criminal?
Watching an episode of Dateline NBC last night, I saw how the McCoy septuplets were doing now at age 10. Two of them have cerebral palsy and have endured 10 painful years of physical and occupational therapy and numerous surgeries. Science and empirical evidence show that there is an extreme risk of CP in multiple births, and the McCoys were facing odds that all but guaranteed that one of their seven children would suffer the debilatating disease. When asked if they regret carrying all seven to term, they broke down in tears and said, "How could we. We have never encountered anyone who loves living as much as their daughter with CP."
The response was so heartfelt and poignant, that I fell my heart swell in empathy for their decisions (although I was cringing during the story about the details of the surgeries to correct the CP.) This heart-warming story aired just prior to the story about the double murder-suicide, and really put me on an emotional roller coaster that kept me up much the night thinking about it. How can some people be so strong, compassionate, and hopeful in the face of adversity, while others are so weak, punitive, and savage in the same situation?
Our world is so unpredictable situations and unpredictable people. The McCoys had their faith to guide them through. Others are tremendously misguided. I believe it all comes down to one simple concept: LOVE It's what we as humans really can never get enough of is love, but sadly, it's the one thing we cannot give enough of.
The lack of love and compassion, especially in such tragic portrayals, leaves a horribly rotten taste in my mouth.
As Charlie Brown once quipped, "Nothing takes the taste out of peanut butter quite like unrequited love."
I don't imagine ol' Chuck ever thought the consequences would extend past the deprivation of the taste buds.