LJ Idol Exhibit B.8-1: When I was young...

I was not "the sharpest tack in the box," as the expression goes, back in elementary school.

In my defense, however, I think it's fair to say that—if my role could be described as that of a "tack"—I had no idea I was supposed to be "sharp." Furthermore, I would have had no idea how to achieve sharpness had I been aware there was a need to do so. But I digress, and the metaphor has taken enough punishment…

As do most, I did figure out, early on, that right answers were better than wrong answers, and so I did what I could to come up with right answers as often as possible. Sometimes, however, the task was beyond me, as was the case in learning simple arithmetic.

Now, somewhere along the line, I had managed to learn to count, forwards and backwards, and for better or worse, I would entertain myself at home by seeing how high I could count (in my head) during the commercials that interrupted my enjoyment of afternoon cartoons on television. (There was something about the pattern of counting that appealed to me, and as a side-effect, I developed an ability to count very quickly.)

Obviously, I had a native understanding that adding one to a number made it the next larger number, but I didn't really recognize what I was doing as "addition." So when it came to learning to add a number other than one to some number—say 6 and 5—oh, I was an endless source of wrong answers (or shrugged shoulders), as I had no idea how to do it without counting and using my fingers.

I was reprimanded for using this approach and told that it was "wrong." Apparently, the answer was supposed to appear inside my head, but how that worked wasn't exactly clear. The teacher proceeded to drill me using flash cards, which merely sped up the rate at which I provided wrong answers. I recall I wasn't bothered so much by how I kept coming up with wrong answers as much as by how the other kids in the class apparently knew the answers (and without hesitation), not to mention the fact that they laughed at me.

As it turned out, it was good that I had no idea of the "right" way of going about addressing the problem, which apparently involved simply repeating the information over and over until it somehow got stuck in your head. (To this day, that kind of rote learning simply has no effect on me.) This left me in a state of blissful ignorance, free to figure out a way to get the right answer on my own. The result wasn't particularly pretty, but it worked.

For each number between 2 and 9, I created a mental "constellation." For the numeral 2, I visualized two stars, one at the top of the curve of the 2, and the other in the middle of the horizontal part at the bottom. In my visualized numeral 5, two stars were located at the ends of the top horizontal and the other three lay equidistant along the loop of the 5. The numeral 9 had three stars along the top of the loop, another three along the bottom of the loop, and the final three along the bottom, "hook" portion of the number.

Basically, I had—without knowing it—created a mnemonic device that broke every digit down into the corresponding number of stars, and since I could count like a demon by ones, all I had to do was add one as I mentally visited each star of a number's "constellation." So when I was asked, say, "What's six plus seven?" I would start with the six, visualize the seven, and instead of using my fingers, I'd visualize the constellation for seven, and as my "mind's eye" landed on each star, I'd mentally count sev-ate-ni-ten-lev-twel- and announce "Thirteen!" as the answer.

There were a couple of times (especially when the number to be added was a 9) when my answer came late enough to prompt my teacher to ask if I was still counting by ones in my head when doing the addition. By that time, I knew that if I answered in the affirmative, that it'd be... the wrong answer.

And so I gave... the right, if untrue, answer. Soon after, however, that answer became the truth, for while I still used my constellations, I had begun to count by twos and threes as easily as I had at the beginning of my journey, by ones.

I was young and, as they say, just learning to get by. I didn't fully grasp addition—at least, not in the way my teacher had wanted—until some time in junior high school.

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This week's entry is a two-parter! View the second part, about a 'design flaw', here.

LJ Idol Exhibit B.8-2: Design flaw...

There was, during my time spent learning multiplication in elementary school, a very curious incident involving this one flash card.

What made it curious was that I could provide the correct answer to this flash card but to no other, which in the grand scheme of things, was a little like having a witness who gives every indication of being blind provide an intricately detailed suspect description, down to the density of whiskers in the suspect's five o'clock shadow. For you see—and apologies for having heard me say this before—I wasn't much for flash cards in elementary school. They made no intrinsic sense, at least not to me, but I digress...

What made this flash card different, you might ask?

Well, you see, it had a mark on it, above and to the left of the "question." The mark may have been a spot of ink, a flaw in the design of the card stock, or a drop of student blood—I never got close enough to find out. But I very quickly made a mental link between that smudge and the answer on the reverse side of that card.

Though young, I had been in school long enough to feel, deep in my heart, that this did not represent an altogether above-board approach to learning, but such a detail could not stand against the importance of "providing the right answer," and so I did not dwell on the matter. Alas, I was too young to understand that, completely by accident, I had stumbled upon a learning mechanism that can harness the power of a thousand Niagaras, once it is understood.

In the days before the wide availability of paper and printing presses, development of "the art of memory" was considered an essential part of education. Indeed, our spoken (and written) references to "in the first place," "in the second place," and so on are remnants of a technique—called the method of loci, or "places"—in which speakers traced a mental path through some space—real or imagined—where images of what they were going to talk about were visualized "in the first place," "in the second place," and so on, of that space. The technique was ancient when it was set down in writing in Latin by an anonymous author in a book known to academics as the Ad Herrenium, and only fell out of use with the advent of technologies that relieve us moderns of having to memorize all the information we require to function in our daily lives.

In distinction from the techniques described in the Ad Herrenium, the Roman rhetorician Quintilian took a somewhat different approach, exhorting those who want to learn information to use "the same tablets on which [they have] committed it to writing." In this way, the learner focuses not only on what is to be learned, but also on all of the visual aspects of that writing, including places where it is "interrupted by some erasure, addition, or alteration." My experience with the flash card was an extremely simplified example of that kind of learning, with my jumping in to take advantage of the technique only after the creation of an "erasure, addition, or alteration" (that spot) by somebody or something else.

Among other things, Quintilian's approach provides a foundation for "mind maps," in which knowledge is represented visually, and where colors, styles of lettering, highlighting, arrows, and graphics are combined to create a unique visual representation that depicts the interrelation of constituent elements. However, I can duly attest that the act of simply writing down what you want to learn (and paying attention while doing so) can also do the trick. I did this recently after deciding it was high time I finished memorizing the Gettysburg Address.

Memorizing Lincoln's most famous speech was a requirement somewhere in my public school years, and in truth, I had no problem memorizing the first several sentences (because the speech was telling a story) and the last part (beginning with "that we here highly resolve…"). Fortunately for me, the method our teacher used to "test" how well the class had memorized the speech consisted of going around the room and having each student, in turn, recite the next sentence. Miracle of miracles, each time it was my turn, the sentence to be recited was one that I knew. Unfortunately for me, I was left with an imperfect knowledge of Lincoln's words.

So on the recent 150th anniversary of the Battle of Gettysburg, I sat down with a pen and piece of paper and wrote down the two passages that had given me so much trouble so many years ago:

It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us—that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion…

I will freely admit that I deliberately made all manner of "alterations" to the words I wrote on the paper. I did this to highlight the difference between "It is for us the living, rather" and "It is rather for us," between "to be dedicated here" and "to be here dedicated," and between "the unfinished work" and "the great task." After letting all of it sink in, I was finally able to recite the entire speech without stumbling. And yes, I realize that with this accomplishment under my belt, I can buy the most expensive cup of coffee Starbucks has to offer, provided I have enough cash. But that's not the point, which is that there are certain things—simple things—that one can undertake to improve one's ability to learn.

My "fortunate accident" with that flash card escaped the notice of my teachers then, and almost certainly would do so now. Over the course of my lifetime, educators have gone from being adherents of rote learning to proponents of, it sometimes seems, not requiring students to memorize anything at all. And yet, the knowledge of how to memorize, and do so effectively, is there, waiting to be discovered..

Or maybe just "remembered."

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This week's entry is a two-parter! View the first part, about when I was young, here.