Wednesday, March 26, 2008

Rambling Gold (the blog, not the dog pictured below)

I realize I haven't blogged in a while, but perhaps that's a good thing. I haven't felt the need to rant or rave, or quietly speak my mind. Add to that the fact that I'm swamped at work, a result of taking too much of a break over spring break (YES, teachers have work outside the classroom.) Why, just yesterday (and early this morning) I had to create two new tests for my BC calculus and PreAP Precalculus classes. Because we have brand new textbooks in all math classes this year, everything I do is from scratch. I don't even have time to work the keys to the exams prior to running them off and administering them, instead, working the key when the first class takes the exam. This means I must work faster than my smartest student so that students are alerted of any typos and (not "or") errors on the exam. Today, I caught one on each test. A BC student had beaten me to the error near the end of their exam (albeit they started on the back page.) I was dully humbled.

I have additionally been using my time and energy to get my new $4000 TI-Navigator system up and running. This is a wireless system that enables all students to plug their TI (Texas Instruments) calculator into a hub so that I can "spy" on their calculator activity. there are several "hubs" that can wirelessly transmit signals from four calculators, although each calculator must connect to the hub via a 6 foot wire-full wire. Just the set-up and tear-down each day (can't have anyone stealing math stuff) takes a while, not to mention the learning curve in implementing the new technology in a way that doesn't make me look like a teacher from the 2005s. One must be a sort of computer guru just to get the wireless router to recognize each hub. Luckily, I'm a quick, independent learner, but it does require a lot of time.

Oh yah! I also keep assigning homework, like an IDIOT teacher, because that only means I have to grade each paper, then enter each grade into the computer. I'm even stupid enough to assign homework to 80 kids each and everyday. Luckily, I don't have to worry too much about lesson planning, since I can teach each lesson from the hip. I know this is not good pedagogical practice, but one thing I AM really good at is speaking extemporaneously about mathematics. Call me Reverend Korpi, the math preacher. Luckily, there aren't too many "breakthroughs" in mathematics on a regular basis. The math stays the same, and I'm proficient at teaching the familiar skills from year to year in a way that requires students to really think, those that actually want to.

So what other lame excuses do I have to you, the faithful readers of this blog (and by "readers," I mean "mom") for not submitting something for your mental pleasure for 4 entire days (that's 96 hours, or 5,760 minutes, or 345,600 seconds . . . yes, almost a half-million seconds without a new blog contribution) . . . lots of lame excuses, but no more legitimate ones. Unless, of course, you count the preoccupation with my finishing all the darn chocolate candy from Easter that I'm going to have to do by myself (my kids LOVE the money in the plastic eggs, and feign interest in everything else small enough to squeeze into them.) I wish my parents hadn't taught me so well about "not to waste." A simple "moment on the lips, a lifetime on the hips," would have done wonders to my fluctuating figure growing up.

Which reminds me . . . I've gotta run . . . literally. Those marathons don't run themselves anymore than math teaches itself.

Friday, March 21, 2008

The Big 05

Yesterday not only marked the 5 year anniversary of the war in Iraq, but also the anniversary of my daughter's birth. Yes, my "pink and purple punky princess" is now officially half a decade old. Thats one-twentieth of a century old! How time flies. It seems like only a few days ago, she was just 4 years old.

To celebrate the day, she, her brother, and I spent the entire day together running errands and having fun together in my tiny little single-cab Nissan truck. Fortunately her birthday coincided with our Spring Break vacation and the weather was gloriously beautiful. Unfortunately, their mother (who also happens to be my beautiful wife) had to work, but that worked out to be a blessing in disguise, 'cause it would have been uncomfortably cramped in that little single-cab Nissan truck with an extra person. We did all manage to celebrate the ocassion together at the "official" birthday party a couple weekends ago, when my daughter had her "Bindi the Jungle Girl" party at the San Antonio Zoo with all of her classmates from school. Yesterday was like a "bonus" birthday for my "sweet little sunshine angel baby muffin cakes."

Throughout the day, her brother and I made it our duty and singular purpose to cater to her every need, desire, and whim. We thoroughly enjoyed spoiler her on her special day (not that we don't spoiler her EVERY day), and she caught on very quickly. "Daddy, can I play with those sharp knives? . . . . . but it's my special day. . . ." How can one say no to that request, especially when she make that little face? Soon afterwards, my son and I were fighting over who made the better tourniquet . . . . Just kidding, it only took a few band-aids.

After spending the morning giving her "race car" rides through the Lowe's store in their specially designed kiddie baskets and picking out 3 BRATZ movies at Blockbuster video, we made a run to the local Dairy Queen to pick up some lunch for ourselves and their mother (who couldn't even take a lunch break from her busy work schedule.) After delivering the burger and tea that would provide their mother with the sustenance she would need to finish her laborious day, my daughter, son, and I went to the park to have ourselves a little picnic. It was perfect except for the absence of my wife and an insufficient supply of ketchup packets.

Immediately after consuming our lunch, my kids wanted hit the playground. Hoping their food would stay down, I agreed against what would have been their mother's better judgment. I told them we'd stay for twenty minutes since my hands were full with drinks, sweaters, and shoes, and because we still had 3/4 of a day of fun left to execute and only 1/2 a day left in which to execute it. An hour and a half later, I finally decided to sit at a bench, as my kids were having too much fun and had incidentally run into their two cousins. I used my time alone in the shade to let my mind wander, taking notice of kid-to-adult ratio, the father-to-mother ratio, the thin-to-overweight ratio, and the courteous-to-playground tyrant ratio. I also mentally cataloged the types and number of trees in the area, counted the number of water spouts, repeatedly waved to the passengers on the park's train, and listened intently to my daughter's periodic reports of what she was doing.

After the park, my "little J" was tuckered out, so we went home to rest, and by rest, I mean watch the BRATZ movies we picked up earlier. I feigned interest in her animated movies as I read my Sports Illustrated magazine. Before we knew it, their mother came home, and we all took turns giving her hugs and kisses. We told her about our day, and she told us about hers. OUR story was much better than hers, but we all wished that we had been able to tell the same story.

Later that evening, both sets of grandparents came over to shower praises and gifts upon the birthday girl. We all shared ice cream and some gross cake I had purchased earlier in the day. My daughter got so many new clothes last night, that I'm pretty sure it will be enough to last her through today (so far, she has changed clothes today only three times.) It's going to be an arduous laundry day this week, that is if I survive the incessant, repeated playing of those all-to- annoying BRATZ movies.

Yep, my daughter has so far spent the majority of her first full day at age 5 watching back-to-back-to-back full-length animated features of spoiled little girls. I hope she doesn't get any ideas . . .

Thursday, March 20, 2008

To Kill a Mocking Bird

Did you hear about professional golfer Tripp Isenhour, yes, that's more than just Adlai Stevenson's 1952 Presidential smear campaign slogan, it's the guy's real name! Well, now he has earned himself an equally ignoble nickname: Kill Squawkinghawk

Last December, while filming a golf "how to" video, a golfer I've never heard of before and from whom I'd be very unlikely to buy a golfing video was repeatedly interrupted during his filming by a squawking, endagered red-shouldered hawk. With his concentration repeatedly broken and being unable to bear that a member of the Aves class was heckling him, Isenhour turned his golfing "how to" video into a hunting "how-to" video, when he abandoned his tips on how to drive and began taking aim at the feathered foe.

I guess the bird didn't realize that the guy taking shots at it was a card-carrying member of the PGA, because it didn't take the hints of swooshing golf balls blazing by it. Instead it remained in the area, preferring a site about 75 yards from the filming area. I guess when you're endangered and under federal protection, you can exhibit a bit of brazen hubris. Well, It took Isenhour only 10 shots before connecting with his target. The bird fell 30 feet from its perch in the tree and died shortly thereafter. Tripp accomplished his fatal fowl feat in one stroke under the 11 stroke par for such a course of action. It was his first birdie of the day! Had Tripp been a better golfer, he might have struck the bird in only 9 shots, but that would have been and Eagle, not a Hawk.

Months have gone by since that fateful day for that frustrating feathered fuss-pot of a falcon, and Tripp has undoubtedly told his story many times to his buddies over a beer or two. But just last week, the "Bird Police" caught up with him, fining him $10,000 and charging him with two misdemeanors--cruelty animals and killing a migratory bird.

Since the incident, actually . . . since being charged with a crime for the incident, Isenhour has repeatedly apologized for his actions. To give credence to his claims that he actually loves animals, his family has adopted some cats from a local animal shelter. Shortly thereafter, the family's parakeet went missing.

Ironically, the name of the video he was filming was to be titled "Shoot like a Pro," but now an alternative title has been suggested: "When Golfers go a fowl."

Wednesday, March 19, 2008

C is for Cookie (that's good enough for me!)

Students always ask me where I get my quotes from, to which, after ignoring the poor grammatical structure of their inquiry, I reply, "from reading, non-reading, and other reading material." At the risk of sounding smug, I do so in an effort to be deliberately vague. A judicious individual never completely reveals his sources, lest he make himself inessential. Actually, the real reason I answer this way is because I get them from so many sources, any attempt to list them would be exhaustive, incomplete, and unappreciated. It's better that the students, instead, merely look forward to the new collection I work hard to bring to them every day.

Which brings me to a book excerpt I recently read entitled, "The Fortune Cookie Chronicles," which explores the history of the cookie and the inspiring message inside. Earlier this week, while out shopping with the family, we stopped at one of the kids' favorite Chinese food restaurants. My daughter literally cannot wait until she finishes her rice just to get at the after dinner "treat." She always reads her fortune, then lets me have her cookie (this particular recipe hinted of vanilla.) Her fortune on this day was something to the point of "Make full use of you talents." Mine had less flavor than the cookie itself. Upon leaving, we immediately stopped at a convenient store and purchased the winning lottery numbers that were marvelously revealed to us. This is, of course, untrue: we stopped only to fill gas.

Although I never scramble for new quotes to post in my class, I DO struggle with inspiration for new blog topics. This "writer's block" is characteristic of any individual, required to mass produce on a regular basis, including fortune writers. Until recently, most of the fortunes read and tossed in the U.S. were the creation of one man employed by Wonton Foods of Brooklyn, New York (which produces about 4 million cookies per day.) His name is Donald Lau, who originally got the fortune writing job because he was the only one who could speak English!

At his most prolific writing rate, he could produce approximately 400 fortunes per month. However, the demands of the job drained him. Writing happy epigrams that are gender-neutral, motivating, yet not perceptually controversial is not as easy at it seems. Like anything else, people are going to have their feelings hurt, even if it's as something as banal, trivial, random, and droll as 10 words inside a cookie. For instance, the company received complaint for the following aphorisms:

  • "You will meet a handsome young man."--an elderly woman complained that she had no such interest.
  • "Lighten up a bit."--an overweight couple read the comment literally and did not see the levity in it.
  • "You will soon inherit a large sum of money."--many interpreted this as prognosticating the imminent passing of a loved one.
  • "It's your turn to pick up the check."--someone found it tactless and impugned their right to the new American way: entitlement.
  • "You'll be going on a long voyage."--a woman was furious after her husband passed away shortly after reading this message.
  • "Be as sexy as you want to be."--Never mind the freedom of choice in this statement, people were offended by this gauche statement.
You can see why Mr. Lau turned in his feather quill and ink well for the corporate board room. Americans are too sensitive to even the innocuous. Today, many others have stepped in to fill the void left by Mr. Lau, drawing inspiration from pop culture, which includes reading, non-reading, and other reading material. Writers are now getting their inspiration from a multitude of sources, opting to re-use "safe" messages that have already withstood the onslaught of acute, histrionic, sanctimonious reaction of the American public including Poor Richard's Almanac (recycling Ben Franklin), the Bible (recycling Jesus), Jewish proverbs (recycling God), and song lyrics (recycling Dylan, McCarntney, and Raffi.) Other popular sources are Bartlett's Encyclopedia of Quotations, Movies, Greeting Card sayings, forwarded e-mails, blogs, and sound-bites from the media.

So now everyone knows where I get my own quotes from, which includes all of the above. I would add one source to my list: fortune cookies.

I hope everyone appreciates the concise, profound density of terse wit. It's not easy. Hawthorne said, "Easy reading is damned hard writing." Gauss said, "I hope you'll forgive me for making this letter so long, I did not have the time to write it shorter." A. Non said "Words are like sunbeams, the more condensed they are, the deeper they burn."

So the next time you snap open that little cookie after polishing off your "Pu Pu Platter," appreciate the time, energy, and effort that went into making your day, and you life a little bit better and brighter, and heed the message contained within:

"When in a melon patch, do not bend down and tie your shoes" 27-36-07-43-13

Sunday, March 16, 2008

Storage Solutions

We humans have a lot of stuff. Too much stuff, to be exactly vague. Currently, I've been troubled by how my children's bikes (at least two a piece), motorized PowerWheels vehicles, scooters, and other methods of Tyke Transportation have overtaken my garage.

Now, I realize that a garage is uniquely designed, if not invented for such an overtaking; however, MY garage was recently (5 years in the making) converted (in my mind) as a full time workshop, and by workshop, I mean WOODWORKING workshop, not BICYCLE REPAIR SHOP (AND STORAGE.) With my wonderfully thoughtful table saw Christmas gift two years ago, I took the opportunity to remodel the entire garage, building custom cabinets to house my woodworking tools and magazines, and to hide a bunch of other junk. I even spent over $600 rewiring the place to accommodate several workstations with several 220 outlets. Yep, the only thing that has been holding me back from making all the beautiful furniture that I have floating around in my head is the price tag . . . and all those darn bikes.

Don't get me wrong, it is very satisfying merely to go into the garage, plug in the 240 volt table saw and listen the the powerful hum of the blade, but in order to push a full 4 by 8 sheet of plywood through that blade, first requires what feels like setting up for an elaborate yard sell. It takes almost 5 full minutes, but what feels like ages, to remove all the "extra, non-woodworking" material from my garage just to get my space required to safely work. When I'm inspired, I want to open garage bay, hit the music, then get after it. I don't want to play "musical bikes," especially when I know I run the risk of getting interrupted by passersby strolling up my driveway expecting a garage sale. If I didn't think my kids (and wife) would mind, I'd probably sell everything on the driveway for one low price to the first "early bird."

Which brings me to my current predicament: Cost- and time-efficient storage solutions. Being the beginning of spring break, and being a former homebuilder, I wanted to spend my week off building a simple "bike barn." But after picking a suitable site, I began adding space and extras to the originally simple plan. Since I was going to be building something, I might as well build it to last and to serve several purposes. Bottom line: I took the idea of a simple 6 foot by 8 foot bike storage shed, and let it germinate into an elaborate two-story 20 foot by 20 foot gambrel shed with a 6-foot wrap-around porch. By quintupling my original budget, I did nothing more than financially prohibit myself from accomplishing my goal: staking claim on my garage shop.

The project grew to one that would exceed the week of spring break, and to one that one prevent us from taking our kids (and ourselves) to Disney World this summer. Giant bike barn or Mickey? What I wanted or what my wife and kids (and I) all wanted. I began doing what any self-respecting person capable of construction abhors: looking at low-cost, pre-fab alternatives.

As of right now, I'm set on traveling to CostCo to purchase a 8 foot by 10 foot prefab plastic (gulp) storage shed to set up on an smaller, different, more convenient pad (see picture above.) It's hard to go wrong with Sam's Club. With this, I'll pay a bit more, lose a bit of self-respect, but I'll be able to have it up and leveled in one day, which means the bikes, Power-Wheels, scooters, and more bikes will be out of my garage, errrr SHOP, in time for me to enjoy almost an entire week designing things I cannot afford, and building things I have no room for.

At least I can listen to the soothing hum of my table saw without "BMX Barbie" looking on.

Wednesday, March 12, 2008

A special request

I definitely don't feel like writing tonight, but I feel I must.

I just found out that a dear friend of mine, someone who is more like brother to me, someone I grew up with, someone who currently lives down the street from me, received some horrible news. His 8-year old son, who is one of MY son's best friends, was diagnosed with a terminal illness. A tumor has wrapped itself around his brain stem. Doctors will treat it vigorously with radiation, but the prognosis is not good. About a year.

I'm so confused right now. This boy is like a nephew to me. I've coached him on two T-ball teams. He's in all our family photos. He and my son are supposed to go through school together. It's not supposed to end at 2nd grade. This is not supposed to happen, not to a healthy, smart, charming 8-year old boy. The incident has left me questioning.

When my own son was severely burned, I was devastated, but I knew he eventually would be okay. When I went through my ordeal with my knee operations and infections, it was overwhelming, but I knew I would be okay. When my father was diagnosed early with prostate cancer, I was speechless, but I somehow knew that he would overcome it, and he has. This news is something that I would like to believe will all my faith and effort will turn out the same way, but currently, based on doctor's opinion, is a tough view to take right now.

Never before has something so immensely grave hit so close to home. I am shaken and disoriented. I don't even know how to react to the family. They need support, but they need their space. I want to do anything and everything I can, but I don't want to do anything too soon or too . . . whatever. I can't wave my wand and change the circumstances. I can only pray so often and so convincingly. I'll hug until my arms fall off, but otherwise feel helpless. I can't imagine the helplessness they feel.

In lieu of commenting, please pray for my friend and his family.
Thank you.

Tuesday, March 11, 2008


As I type this, it's from the comfort of my soft bed at home. I just got a new laptop and wireless router, so I can now waste time needlessly surfing the net with my family much closer by. Previously, I had to retire to the hard-wired PC upstairs in the office (my son's bedroom.) I was always able to HEAR my family downstairs, laughing and living without me, but now I can hear them AND see them too.

Oh, the wonderful, marriage-saving conveniences of wi-fi! The technological advance of a broadband routers will definitely allow me to be both a better husband AND parent. I haven't been this excited about the absence of wires since the second coming of the wireless screwdriver, that is, the cordless drill (the first cordless screwdriver being an actual screwdriver.) When I got my first "Makita" 9-volt drill-driver, I was drilling holes all over the place for no reason at all. I was screwing and unscrewing all kinds of things, like VCR shells, dining room chairs, and fences. The novelty DID eventually pass, but to this day, I don't know what I'd do without my 18-volt Bosch cordless drill. Ditto that for cell phones. In each case, I was late getting into the market, waiting until the cost came within my reach.

Which brings me back to this new wireless breakthrough: Talk about a win-win situation: my memory foam mattress that is my bed offers much better support than that uncomfortable office chair upstairs. I'm even getting quite used to the absence of the mouse, navigating with the "touchpad." I can't believe I didn't jump on this bandwagon much earlier.

Wheras in the past, I'd drive past such fine eateries as Dairy Queen an laugh at their marquee which read "Oreo Blizzards $1, with free Wi-Fi." "Who," I seriously wondered, "would go into a Dairy Queen with their laptop? Surely enjoying a fries, burger, and blizzard was still an "offline" experience, right? Well, now that I'm so portable, I can actually see myself biting into a hungerbuster while checking out the lates scores on

I used to think the same thing about .mp3 players, that they were being used far too often . . .but that was before I owned one. Once they became affordable, I bit the bullet and purchased one, now I too, have things sprouting ourt of my ears in previously unthinkable circumstances . . . . (what was that honey? . . . . can't you see I'm jamming and blogging? . . .Yes dear. . . )

Ok, I'm back now. See, if I were upstairs, I would have totally missed out on that intimate exchange with my wife.

Come to think of it, I'm getting a little sleepy laying here all comfortablyyyyyyyyyyyyyyyyyyyyyyy. . . .zzzzzzzzzzzzzzzzzzzzzz. . .

Excuse me, there, I nodded on the keyboard.

Yes, my family will be the true beneficiary of this new wireless setup, as they get their dad back. I also believe it will make me much more productiveeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee. . . zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

Monday, March 10, 2008

Memory, Mental Arithmetic, & Mathematics

What is the integral part of the square root of 3x10^40? What is the product of 79532853 and 93758479? What are the first 2000 digits of Pi? These are all questions posed by mathematics. Some people cannot answer any of them. Others may be able to answer some of them with the help of a calculator. A select few can answer all three with the assistance of a calculating device. Believe it or not, there are some, though, who can not only answer all three questions without any assistance, but can do so accurately and relatively quickly. These individuals certainly would classify as genius, if not odd.

What actually separates those who can perform these feats from those who cannot? Is the genius a product of the ability, or vice-versa? Is the mental agility involved in the calculations a skill that can be learned, or is it an innate trait that only few will ever possess? Is this type of ability requisite for being successful at math, or does it have anything to do with math at all?

These amazing feats of memory and extraordinary mental powers have been exhibited by a select few well-educated mathematicians including Ampere, Hamilton, and Gauss, as well as a number of people who had no mathematical skills, little or no education, and yet were able to perform the same feats. Von Neumann, particularly, not only was a master at complex mental arithmetic, but had extraordinary mental capacity and displayed amazing feats of memory, as described by his colleague Herman Goldstine.

As far as I could tell, [he] was able on once reading a book or article to quote it back verbatim; Moreover he could do it years later without hesitation. He could also translate it at no diminution in speed from its original language into English.

Only one mathematician, A.C. Aitken, has ever described in detail how he was able to perform his incredible feats of memory and calculating. His methods will be analyzed later in an attempt to answer some of the questions posed above. One thing that is known is that his “nearly perfect” memory played a large part in his ability to calculate.

In order to understand memory, it is first beneficial to discuss other elements related to memory. Intelligence is the capacity to learn. Each individual has a limitless capacity to store information. Learning is based on the acquisition of new knowledge about the environment. Memory is simply the retention of things learned. This model implies that anything that is learned is stored in our vast and endless memory bank. The problem most individuals face is recalling the information they have learned appropriately. Research has shown that memory can be improved through enhanced learning techniques and a variety of recall cues. Memorization is enhanced in the course of acquiring understanding. The more interest one has in a subject, the better one is able to later recall information about the subject.

Modern research has concluded that memories are stored electrochemically. The exchange of information takes place at the synapses. The more of these connections in the brain, the quicker and easier it is to store and transfer information. These connections are developed in the early years of childhood. Some evidence supports that the more young children are exposed to positive, intriguing inputs, impulses, and information, the more nerve cell connections are made in the brain. The extent or implications of these findings are arguable, but it is known that the first five years of life are critical to the development of the brain, although connections in the healthy brain continue to be made throughout life. In other words, someone who had a positive experience with math, showed early interest and ability, and was supported throughout, would have a better chance of developing into someone who could perform quicker calculations.

Researchers acknowledge two types of memory systems: locale and taxon. Locale memory is based upon natural learning or learning in context. For example, remembering last night’s dinner is very easy, although no formal thoughts occurred to remember the menu. It is based on schema, or mental maps. It is the memory that stores our life experiences and helps us become who we are. The items stored in locale memory exhibit a complex set of relationships among each other. Schema formation is motivated by novelty, curiosity, and expectations. Because it is intrinsically oriented, those who become curious about math at an early age, for whatever reason, begin learning using the locale memory. It becomes insufficient by itself, though, to produce the abilities described at the opening.

Taxon memory is based on the information-processing model. It is the area of the brain where lists, categories and numbers are stored, including the majority of mathematical tables and formulas. The most pervasive characteristic is that taxon memories must me rehearsed. Information stored here requires rigorous learning. It is more difficult for information to be stored in this matter, requiring long repetitions and rehearsals. However, once information is stored in the long-term taxon memory, it is very difficult remove or change and tends to last much longer.

The individuals mentioned earlier who have displayed the amazing feats of memory have attributed their skills to practice, practice, and practice. Zerah Colburn is interesting because his abilities diminished when he underwent education. This may be due to the simple fact that his abilities required continual practice for hours a day, which he was unable to afford with his studies. A demonstration of the permanence of taxon memory is illustrated by an anecdote from the life of A.C. Aiken. When he was proceeding to recite the second 500 digits of Pi, he uncharacteristically hesitated and sometimes corrected himself. When asked why he found the second 500 much harder than the first, he had an interesting answer.

Before the days of computing machines there was a kind of competition in seeing how fare they could calculate Pi. In 1873, Shanks carried this to 707 decimals; but it was not until 1948 that it was discovered that the last 18 of these were wrong. Now, in 1927 I had memorized those 707 digits . . . and naturally I was rather chagrined to find that I had memorized something erroneous. [Later], I re-memorized it, but I had to suppress my earlier memory of those erroneous digits.

Aiken’s problem was that he could not forget the incorrect 180 digits. (By the way, the current record for pi recitation is 100,000 digits, by Japan's Akira Haraguchi. a feat which took him 16 straight hours.)

It is best to study the methods for storing information and calculating through the methods used by Aiken, for he is the only one who could actually described some of the methods he employed. But first, it is appropriate to discuss general methods of improving memory and recall.

There are three requirements for information storage: registration, consolidation, and retrieval. Registration is the input of information from our environment received by our senses. Once we have registered the data, we must organize or consolidate it into either our short or long-term memories. After it is stored, we must be able to have access to it when we want it. There are several ways to improve the way we store information and retrieve it, ranging from mnemonic devices, chunking, association, rehearsal, and even eating certain foods.

It should not be surprising that the individuals who possess the amazing mental abilities share the characteristic that they actually ENJOY doing the calculations. This implies the cooperation of the locale and taxon memories. Each began developing their skills as either a hobby, pastime, or for enjoyment. The genetic predisposition they may have possessed for calculations would never have developed if they were not given the chance to practice. The question whether this “predisposition” for calculations is specifically math related or simply a learned respect for diligence and detail is unclear, Aiken himself offers some sort of explanation. “Familiarity with numbers acquired by innate faculty sharpened by assiduous practice does give insight into the profounder theorems of algebra and analysis.” Without the discipline, no ability would ever develop into talent.

One of the most commonly employed calculating strategies and memory aids is regrouping or chunking. It is believed that most human calculators use this technique to some extent. Regrouping involves the synthesis of numbers and rewriting sequence of operations in terms of equivalent expressions. Chunking requires the association of equal values and expressions taken together, rather than singularly. Aitken used these techniques to aid his calculations. He did not begin to develop this skill until age 15, when he would continually practice until he acquired enough taxon memories that these calculations became easier and easier. For example, when Aiken was presented with the number 1961, he instantly saw a variety of ways of expressing it.

1961 = 37 x 53 = 44^2 + 5^2 = 40^2 + 19^2

By doing this, he was able to use the property of the smaller numbers and combine them to achieve the desired result. When asked to multiply 123 by 456, Aiken provided the following explanation.

I see at once that 123 times 45 is 5535 and that 123 times 6 is 738. Then 5535 plus 738 gives 56088. Even at the moment registering 56088, I have checked it by dividing it by 8, so 7001, and this by 9 gives 779. I recognize 779 as 41 by 19. And 41 by 3 is 123, while 19 by 24 is 456. A check, you see; and it passes by in about one second.

These types of algorithms provide insight into the shortcuts involved in mental calculations. Most students of mathematics rarely develop a memory for such sophisticated tasks. Some more common mathematical memory aides are those used in number sense competitions, such as divisibility by multiples of 3, multiplying by eleven, or squaring powers of five.

It is interesting to note that most of the mental abilities associating with calculating and memorization relate to sound rather than sight. Many of the individuals capable of these feats have attributed their storage and recall as having a particular rhythm or cadence that helps them “keep the beat” as they perform these feats. Much attention and praise has been given to those individuals who seem to have a “photographic memory.” The truly astounding people claim that visualizing the information slows them down and prefer not to “see” the problem. Indeed, Aiken was slower when forced to visualize. When asked to recite Pi backwards, he was forced to visualize the numbers and recite them from his visual image. The speed was still impressive, though. The last 50 digits required 18 seconds to recite them forward using his audio cadence and 34 seconds to recite them backward using his mental image.

The conclusions that can be drawn from research and the explanations of such calculating wonders as Aiken offer insights into math, memory, and calculating ability. The pattern is sequential. The early years are the most crucial to the development of the brain and establishing the necessary neural connections for the best memories. Without these early experiences, it is doubtful if one would ever be able to reclaim the lost opportunity to produce the necessary connections. The interplay of both the locale and taxon memory is important for the continuation and pursuance of learning and development. The locale provides the initial interest and intrinsic motivation, the taxon provides the storage capacity and recall algorithms required for the amazing memory feats. Diligence and discipline are required to continually improve and practice calculating and memory-improving skills. Hard work and continual effort ensure that one stays sharp and able to recall quickly and effortlessly.

As these skills progress, one begins to gain insight into the complex workings of mathematics and develops a deeper understanding. He can begin to form his own specific memory aids and calculating algorithms, capable of making authentic contributions to the field, regardless of any formal training, using only his own immense mental abilities. Memorization and Calculation are both skills. Skills can be learned and forgotten depending on the amount of practice. The prolific mental calculators will always be few in number, but there is hope for all individuals who wish to increase their mental capacity. I cannot remember when I heard anything so hopeful and promising.

Perhaps with a bit of practice you can come across 1,588,533 and say, "Hello there, 589 times 2697!"

* Final Note on Aiken: His perfect memory was his glory as well as his demise. His horrific memories of his youth in the battle of Sommes, in which he fought, vividly haunted him all of his days, as he was unable to forget about them. His journals reveal that the bad memories contributed to his ill health near the end of his life and eventually led to his death. Oh, the curse of genius.

Sunday, March 9, 2008

Liberating Vice: An Oxymoronic Poem

I’m afraid I’ve been too brave again.

I gone overboard and come to terms with me

I let her down and now she’s fed up

I’m happy that I’m sad again

It sucks so bad here that it blows

I’m so hungry that I can’t eat a thing

There’s nothing left that feels right.

For someone so hot she is colder than ice

I have felt way too much that I now feel numb

The only smart thing to do is to play dumb

I’m so tired that I cannot sleep

I’ve been assisting my self in my helplessness

Wanting something more and absolutely nothing else

Come over here and leave me alone

Come listen to me think, but not so loud

Of my lack of confidence, I’ve become quite proud

I love to hate you and hate to love you

I lied to you before like I’m lying here now

Without the worry, I think I’d go mad

The stress puts me at ease and puts calm over me

I can only discover what I’ve already found

Please help me to live by myself without you

Oh the pleasurable shame this act would produce

The tighter I get, the more I feel lyrically loose

I can’t slow down quickly because I’m too fast to be slow

When I get myself highest is when I feel the most low

When things are at there darkest do I begin to see the bright light

Why are things bad when they feel oh so good?

The more I please myself, the more I hurt us

Friday, March 7, 2008

How we can learn math, part I

Do you think in words? Is it in your native tongue? I know when I have certain thoughts, it's as if I'm talking to myself in my mind, but that's not always the case. One of my old college German professors told me that I will have turned a corner in my study of a foreign language when I no longer need to mentally "translate" the language, but rather begin thinking in the new language itself. Back then I agreed with him, and I still see his point, but not ALL thoughts, at least mine, are in any particular language at all.

This is most evident when I am working with technical information such as a math equation or designing a piece of furniture. When engaged in this type of activity, which I would include the act of teaching, itself, words and language are entire absent from my thoughts. I am consumed with forms and shapes and esoteric images that help me to process the information in the dark corner of my mind. Apparently, I'm not alone in this capacity.

Einstein, himself, wrote:
Words and language, whether written or spoken, do not seem to play any part in my thought processes. The psychological entities that serve as building blocks for my thought are certain signs or images, more or less clear, that I can reproduce and recombine at will.
Jacques Handamard, French mathematician and author of the book, The Psychology of Invention in the Mathematical Field (1945), a ground-breaking publication in which he analyzes what mathematicians think of when they actually do mathematics, said this of his own methods:
I insist that words are totally absent from my mind when I really think . . . even after reading or hearing a question, every word disappears the very moment that I am beginning to think it over.
If this is a common trait shared by those with an rational, analytical mind, that is, by those who are "good" at mathematics, then it should be surprising why most great mathematical minds cannot adequately describe their internal methods for their mental calculations.

One person who actually CAN describe how he accomplishes his remarkable mental calculations is Daniel Tammet, a 29 year-old Autistic Savant. His descriptions of his thoughts are also devoid of words or language, but instead, are full of unconventional imagery, consisting of shapes, colors, emotions, and even tastes! Known as Synaesthesia, in his mind, he says, each number up to 10,000 has its own unique shape, color, texture and feel. He can intuitively "see" results of calculations as a synesthesic landscapes without using conscious mental effort, and he can "sense" whether a number is prime or not. He has described his visual image of 289 as particularly ugly, 333 as particularly attractive, and pi as beautiful (he has event painted it--see picture above.) 6 apparently has no distinct image. In earning the European record for recitation of the decimal digits in pi (22,514 digits in 5 hours), he merely told the "story" of the synesthesic landscape he was seeing.

Although his feats are extraordinary, and attributed to his savant "disorder," his methods do offer insight to how the brain works, and possibly reveal some methods that extends well beyond mnemonics that the average person can employ to increase his/her mathematical abilities.

It would appear that analytical thought is independent from linguistic thought. Most mathematicians, physicists, chemists, inventors, etc. who have discovered something great, have not done it in one sitting. In fact, as many describe it, it came after months or years of careful study and analysis, during which time the solution eluded them. The solution, itself, often came rather unexpectedly, through no deliberate, conscious thought process. This is how Kekule discovered the Benzene ring configuration and how Gould invented the Laser. These "flashes of brilliance" were nothing of the sort. Their mind was prepared for a solution, and it processed the seeds of study and diligence to produce the fruitful discovery.

Now I'm no Einstein, Handamard, Tammet, Kekule, or Gould, but I am a math educator interested in reaching more students. So I ask the question: do any of these scenarios offer any insight into why so many students struggle relentlessly with mathematics and how to remedy it? How can we educators communicate, not only about the results of mathematical thought, but about the thought processes itself if we don't think about it linguistically? How can we concretely communicate about the abstract? How can we teach beyond the symbols, but reach to the fundamental mental abstractions of mathematical objects and ideas themselves?

It requires us to "invite" our students into a "fake reality" where things are strange and unfamiliar, a realm of pure abstraction and imagination. We can do it! We as humans have developed the capacity to visit this world, in which there is no direct or simple link to our real world. We cannot touch thing with our hands. We cannot smell things with our noses. We cannot see with our eyes, nor hear with our ears. We can only escape within our own mental landscapes and explore the terrain. This is a strange land for many, but as with anything, with frequent visits, it becomes less fearful, more comfortable, and even enjoyable.

Thursday, March 6, 2008

Deja Vu, he's right on cue!

Yesterday was a great day in local television. It was Wednesday, the day I usually film my Algebra 2 show for the my district's local cable network, but it wasn't a usual taping. No, yesterday was the annually filming of the Spring Break episode, an episode that runs for two weeks, rather than one, which gives home viewers more opportunities to miss it. Consequently, it's a show that I put a bit more effort into, hoping to make a bigger "splash," but in actuality, since people on Spring Break typically don't watch math programs, the show affords me the chance to experiment with style, props, images, and using my son, Tate.

Yes, my 7 year-old loves the camera, and he's rather good at it, so I wrote him into the show, which will premier on Monday night. He's already began arrangements for his viewing party. The episode's premise is that I am on vacation, for Spring Break of course, so Tate is left to fill in for me. Donning a bow tie, glasses, and a sport coat, he conducts the show in the same fashion I would, corny jokes and all. Periodically, for the math instructional bits, he pretends to go to me "Live Via Satellite" from different parts of the world like Las Vegas, China, France, Rome, and Dubai. Of course, I'm standing beside him in front of a green screen, but I thing the affect will be understood.

In fact, it is only through the magic of the green screen that I can travel the globe so quickly and effortlessly in a 30 minute globe, only to be left standing at the end, with Tate now by my side, on the beautiful shores of the Persian Gulf in Dubai. It was pretty fun to get the chance to work with Tate again (he had a small role on a previous show as my Vet assistant) and to give him a chance to be on TV (wow), but to see how the entire writing, rehearsing, filming, and editing process comes together for the finished product. Who knows, perhaps someday he'll invite ME on one of HIS shows.

Of course, being only seven and not having much experience reading a teleprompter, he was not as polished as, let's say . . . his dad?, but he did a great job. Writing jokes into the script for the general population, with punchlines and puns that a small boy who loves to embellish his words, has its perils. At the end of the show I say, "Remember . . . seven days without out math make one . . .," and Tate was supposed to say, "Weak," a pun on "Week," but what he actually said, perfectly on cue was, "Long Week." I laughed on camera, went with it, and reassured him that he was also correct. It was such a nice way to end it that we didn't reshoot the scene. Yes, kids do say the darnedest things.

It was a great experience he and I will always share. Tune in Monday, 6:30pm on Time-Warner cable channel 98 and learn a bit and laugh a lot.

Wednesday, March 5, 2008


Tonight is the season premiere of one of my favorite shows: Ghost Hunters. Airing on the Sci-Fi Channel, it's about to guys who are plumbers for Roto-Rooter by day and paranormal experts at all hours outside of that. Recycling an acronym from their failed "Trans-Atlantic Plumbing Society," they founded TAPS (the Trans-Atlantic Paranormal Society), which travels across the nation (and now internationally) investigating claims of headless apparitions, strange occurrences, and other mysterious, paranormal events.

Do YOU believe in ghosts? I certainly do. I also believe in aliens and Leprechauns, but that's a different blog. My credence in the supernatural has fed my imagination and interest. Needless to say, I love trying to scare myself, especially from the safety of my own how with a handgun nearby in case I need to "re-kill" and unfriendly apparition. Which is EXACTLY why I love the "Ghost Hunters:" they go on location for me and bring the evidence to my own television. There's no need for me to have to crawl underground in an cramp bunker in pitch blackness at 2 in the morning at some haunted prison where my only "gun" is a thermal camera--they do it for me, and I get to watch THEM shriek and squirm.

Over the last few seasons, they have caught some remarkable evidence including strange EVPs that have responded to the investigator's questions, thermal images of humanly shapes that only appeared after the fact, and video footage of chairs moving, doors opening and closing, vases breaking, wires being lifted and thrown, cameras jumping up and knocking cameramen out, and strange shadows in a lighthouse moving across the metal lattice stairs only to peer over the railing to look down (see the St. Augustine Lighthouse episode.) For believers, its fascinating entertainment. For non-believers, it can still be the same.

In fact, I've got my 4 year-old daughter and 7 year-old son hooked on the show. Their mother didn't think this was such a good idea, but I figured if they could confront their fears, even if they're fears that I implanted, with enough education and understanding of what ghosts really are (or might be), they'll be unafraid. So far, we haven't been able to get them to sleep anywhere but in our bed on "Ghost Hunters" night, but we'll keep trying to persuade them that the spirits upstairs in their rooms are only there to play with them.

On tonight's season premiere, the team travels to Philly to investigate one of the most purportedly haunted places yet: Fort Mifflin, (picture of team at top) a fort where many died during the Revolutionary and Civil War. From the commercials, it looks like it should be a good one. Perhaps they'll even catch a Leprechaun on camera! Who knows.?

Although I know it makes for better TV to explore these places at night, I wonder if the ghosts are out during the day as well, or if they ALL sign up for the graveyard shift? Are they like Gremlins, afraid of the light, or is it just that WE are afraid of the night?

Tuesday, March 4, 2008

Getting Jiggly With It

Last week was a great week for fat guys, as the Florida Marlins of Major League Baseball, looking to replace their overweight slugger Miguel Cabrera, held tryouts for a new performance squad called the "Manatees." In honor of the sea cow, the squad will eventually consist entirely of overweight, but agile, men. In advertising for the try-outs, the professional organization rad ads stating the following
The Florida Marlins are looking for big bellies with the biggest jiggle, big feet with the best dance moves and enthusiasm that will rock Marlins fans out of their seats. Auditions will be held to find a few big men for the Marlins Manatees, the first-ever dance/energy squad in Major League Baseball. The Marlins Manatees will perform at Friday and Saturday Marlins' home games throughout the 2008 season. Manatee hopefuls do not need prior dance experience-just the willingness to learn routines and have a great time dancing and cheering in front of thousands of fans.

It turns out that the overweight energetic couch potatoes were rewarded simply for showing up to the try-outs, making the team simply by being their. With the try-outs taking place at 1:00 pm, the Marlins simply rewarded all the overweight guys who had enough resolve to roll in to immediately after their all-you-can-eat lunch buffet at the pizza joint down the street. I wonder if the 15 new members of the Manatees celebrated by watching the Saturday Night Live video of Chris Farley dancing with Patrick Swayze as a Chippendale's dancer.

It's hard for me to imagine how desperate the Florida Marlins organization really is to stoop to this level of corpulent debauchery. Watching sexy women in cute, revealing outfits genuinely lifts the spirits of baseball fans, which is why the Marlins have the "Mermaid" cheerleaders. But does the organization really think that fat guys in wigs and exposed hairy bellies will produce long-lasting positive effects on fan enthusiasm? Wouldn't this scenario serve better as a gimmick during the seventh-inning stretch? After all, I though Chris Farley's dancing on SNL was hilarious, but if that skit had lasted any longer, I think I might have puked. If my stomach had already been filled with warm beer and cold stadium hot dogs, I know I would have.

Is this what the Marlins want happening in the stands, assuming there ARE any people the stands? The Marlins have had the poorest attendance the past two seasons. I guess they're thinking that if they're having problem filling the seats, why not attract a crowd that require two each. Have they no respect for other people's eyes??!! Babe Ruth is turning over in his grave.

Honestly, If I was an actual manatee, I'd be downright offended. Of all the sea mammals of various sizes, amount of blubber, and levels "testosterone", wouldn't the Sperm Whale have been a better choice for a mascot?

Monday, March 3, 2008

Sample ELA TAKS questions

This week at school, we are gearing up for the first official TAKS test of the year, the English-Language Arts Exam, affectionately called the ELA TAKS by those ALPs (Acronym-Loving Pundits.) On Wednesday, students will sit down, read long passages about uninteresting topics, then answer a slew of multiple choice questions, such as,

In the first sentence of this blog, the author's tone is
A. Jolly
B. Sardonic
C. Forceful
D. Facetious

If you answered, "A," you are not only optimistic, but have a hair trigger. If you answered "B," you'd be close, even if you didn't know that Sardonic means "acerbically mordant and scornfully derisive." If you answered, "C," you are incorrect, but are statistically selecting the answer choice that is most frequently correct (unless, of course it's incorrect.) If you answered "D," you are correct. This word most closely reflects the author's (my) tone, which is somewhere between Jolly and Sardonic.

See how the test goes? Kind of fun, huh? Well, there are many questions that follow a passage, such as this complementary question to the first.

In the first sentence to this blog, the words "gearing up for" could be replaced by all of the following except
F. preparing for
G. anticipating
H. dreading
J. bracing

They all sound so tempting, don't they. But which one is the BEST answer (and did the TAKS people forget their alphabet?) Although "dreading" sounds the MOST appropriate, it is NOT a synonym for "gearing up" in the context of the sentence, therefore, the correct answer is H, as in "Holy Crap! this is going to be a boring test."

Want some more?? How about this one . . .

In the first sentence to this blog, the word "we" is what part of speech?
A. Dipthong
B. Pronoun
C. Sound
D. Dangling Modifier

Were you thinking a different word when you read the first answer choice? The test makers are banking on your association of this word with something enticing, like snuff or string bikinis, so that you will answer the question incorrectly. In this sense, the ELA TAKS tests much more than ELA, it tests EQ (Emotional Quotient) and your SFEBTOEI (Stamina For Enduring Banal Tasks Of Exaggerated Importance.) Notice choice "C" is technically correct, but is only a sound, per se, if you had read the question out loud, which is strictly forbidden during the test. Choice "D" is the "giggler" answer choice, designed to be intellectually humorous to the test taker who has already clearly identified choice "B" as the correct answer, but reads on as a matter of recreation and personal growth.

Would you like some more? OK, one more, but I'm in writing this, I'm weakening my own SFEBTOEI, so this will have to be the last one.

Which of the following is a major conflict for the author?
F. Taking anything seriously
G. Writing anything worth reading
H. He fear of failure is stronger than his desire to succeed
J. Reading TAKS instructions to students without sounding like a robot

The previous would be a horrible actual question, as all answers are correct, but wouldn't THAT be a GREAT way to raise test scores!

Sunday, March 2, 2008

A Lady's Man?

DISCLAIMER: I've been exceptionally busy lately, not getting much sleep and finding little time for quality thought to this blog, so here's one that is just philosophical rambling about a man I just read an article about. I know you'll find it as lame as always.

A dilemma arises when we consider whether our actions are caused or whether they are not caused. If they are caused, then it follows that we are not morally accountable for them. If, however, they are NOT caused, it still follows that we are not morally accountable for them. This result concludes that either way, we are not morally accountable for our actions.

The leading proponent of this belief was the hard determinist, Arthur Schopenhauer. In the most general sense, he prescribed to the philosophical branch called "Idealism," where it is believed that reality depends upon the mind. Idealists, such as George Berkeley, Immanuel Kant, and "Shopey" himself rejected the simple idea that there is a world of objects independent of human perception. This means that the tree falling in the forest really doesn't fall, or even exist, unless we're there to see it, and even then, according to the specialized branch called transcendental idealism, we're not seeing the ACTUAL tree fall, but rather the mere appearance of the ACTUAL tree falling. Confused yet?

For Schopenhauer, the ultimate nature of reality is a singe, undifferentiated Will (yes, her personified it)--a blind, striving force--which appears to us as a would of individual things ins space and time. Claiming that his origins of transcendental idealism are found in the purusharthas philosophy and literature of Hinduism, which he believed only exists in an pseudo-quasi-artificial appearance of what it would actually be if it actually existed . . . outside the mind. For him, the Will exists a priori, and prior to, the intellect of the mind, i.e. desire is believed to exist prior to any thought, and, in a parallel sense, Will is said to be prior to existing. The role of Will / desire in Schopenhauer's philosophy is similar to the role of Kama, sensual gratification, which is treated as one of the goals of life relating to the second stage of life in the purusharthas Hindu tradition. Which leads us back to the original fortuitous conclusion to the opening dilemma: we are NOT morally accountable for our actions, even when we first seek the pleasurable pursuits of our Hedonistic Will / desires.

Wow! It sounds like Shopey went out of his way to rationalize a life of pleasure seeking, making it seem downright noble to do so. Being also a hard determinist, he espoused the belief that at any instant, there is exactly one possible outcome. This sort of morally binds him to seeking his pleasurable pursuits, although he would also argue that there IS no moral obligation (read from the beginning.) Since all events are caused, then we cannot determine what the course of events will ever be. Schopenhauer said that, after the fact, the only thing left is the essence of that action (and maybe a linger skin rash.)

"The ultimate aim of all love affairs ... is more important than all other aims in man's life; and therefore it is quite worthy of the profound seriousness with which everyone pursues it."

A misogynist his whole life, he took interest in several young woman. Some he rejected, many rejected him. He thought that "marrying means to halve one's rights and double one's duties," and never realized that he was never able to take advantage of his conveniently defined philosophy because of his inconveniently defined philosophy.

I, myself, find the "Wolverine" look from the X-Men, pretty cool, too bad he was jerk.