## Multiplication eureka

From the What I Learned Yesterday files…

I have always loved numbers, especially in terms of manipulating them. Remember those arithmetic drill books, endless columns of 3 + 6 and 12 – 5 and every other possible combination? I loved paging my way through them, filling up all of the blank spots. My grandmother’s living room had a big bay window with a flat base I could crawl onto (I don’t think it was intended as a seat), behind the curtains, and I loved to hole up there with that book. Even *better* was when I encountered those drills in elementary school, and they were *timed*! Hooray, a race!

But even before those memories glows a beautiful eureka moment I hope I’ll never forget. I was in daycare, somewhere between 4 and 5 years old, musing about multiplication (for no reason I can recall), when suddenly I Got It. I jumped up and ran around trying to share the shining vision that I’d had. The best I could do then was, “But it’s so simple! Two times two is just 2, two times!”

I still remember those words, and I remember the lack of a similarly excited response from the other kids. Was it incomprehension? Disinterest? I couldn’t seem to put my revelation into words that made sense to anyone else, and I was buzzing with commingled frustration and joy. At that moment, the “x” sign had ceased being an arbitrary symbol specifying a relation to be memorized. Instead, it had *meaning*. I was swimming in triumph at the feeling of having *cracked the code*, seeing yet another pattern but also the whys behind the pattern. (Of course, when I reached elementary school, I then got to memorize the multiplication tables, like everyone else. So much for eureka…)

I have a handful of other memories from that daycare. Conspiring with a friend to stash our pears from lunch, which we hated, in our pockets for later disposal. Sprawling on threadbare green carpet in front of the TV and goggling at afternoon cartoons. Singing “This Old Man, he played one, he played knick-knack on his thumb…” Discovering awe and predation on finding a black widow spider out back. Discovering how surprisingly hard other kids can pinch if you don’t wear green on St. Patrick’s Day. Shivering at horror stories about loose baby teeth being tied to a door and extracted with a slam, then rushing to the bathroom to inspect my own teeth for any worrisome looseness. But these have all faded in a way that my “2, two times” moment has not. And it left me with an appetite for that feeling of “Oh wow, I get it!” that is what makes the study of anything new so very delicious. More learndorphins, anyone?

## Simple English wikipedia

An xkcd comic led me to the Simple English Wikipedia. This wikipedia aims to provide simplified versions of articles from the Ordinary English Wikipedia by limiting the vocabulary used, grammar complexity, and sentence length. I admire the motivation behind this resource: to make general knowledge accessible to non-native speakers, youthful readers, or those with disabilities. Yet to an adult native English speaker, the language of these articles can be gratingly unaesthetic (and imprecise). For example, consider this excerpt from the page on Mars:

The planet Mars is made of rock. The ground there is red because of iron oxide (rust) in the rocks and dust. The planet has a small carbon dioxide atmosphere. The temperatures on Mars are colder than on Earth, because it is farther away from the Sun. There is some ice at the north and south poles of Mars, and also frozen carbon dioxide.

This is all factually accurate, but achingly simplistic (especially the “because it is farther away from the Sun” statement — the atmospheric composition is also a critical player). On the other hand, if I had to read wikipedia in, say, French, I would no doubt appreciate the simplicity!

But I experienced even more wincing when reading pages about topics from Computer Science, such as the neural network page, half of which consists of:

What is important in the idea of neural networks is that they are able to learn by themselves, an ability which makes them remarkably distinctive in comparison to normal computers, which cannot do anything for which they are not programmed.

(Technically, they don’t learn by themselves — they require supervision in the form of labeled examples — and any machine learning method exhibits the learning property, not just neural networks, and what is a “normal computer” anyway? A neural network is an algorithm for learning a model, not a special-purpose computer. Finally, even neural networks cannot do anything for which they are not programmed! More accurate: “Neural networks can learn from examples, allowing them to make predictions about objects they may never have seen before (generalize).”)

Or consider this part of the page on Computer Science itself:

A computer is a device which takes orders as fast as you can give them to it and works as fast as it can to solve the orders.

(makes a computer sound like an active agent (e.g., waiter), which it isn’t) or from Computer programming:

The instructions in “machine form” are usually in a .EXE file (which is called an executable, because it can be executed). These machine-instructions will by default open a black “command-prompt” window, but can open games as well as other things.

(Well, am I really surprised that “simple” computer programming has such a strong Windows bias? ;) )

There’s an interesting issue at the heart of this project: how do you talk simply without talking down? (Or worse, misleading the reader!) Clear, simple language has real value even outside of this venue. However, translating all value judgments into the simple words “good” or “bad” not only gives the text a childlike sound but also gives its meaning a childlike interpretation, and important distinctions may be lost.

I actually find this wikipedia harder to read, not easier; the stilted sequences of simple sentences dominate my attention with their awkward rhythms and unanticipated gaps (likewise, you may have found my alliteration distracting :) ). Good writing blends its details in to the background and leaves you room to think about the ideas being presented. But yes, I know: I’m not the target audience for this product. I expect that many people are benefiting from much of the information in the Simple English Wikipedia. Hopefully they also get a chance to dig deeper for the real details on their subjects of most interest or need.

## Progressive acquisition of foreign characters

I love YesJapan!

This website, designed to teach you “Japanese from Zero”, has a lot going for it. It has a simple, clean design, five courses of increasing complexity, and a free 7-day trial period (after which the monthly subscription fee is \$14.95). But beyond the mechanics, I really like the pedagogy. One of the things I find most challenging about learning written Japanese is the kana (and kanji). If a book is written purely in Japanese script, I find it tiring and tedious to slog through; I’m just not fast enough at decoding the symbols (yet). But if it’s all in romaji (“our” characters), then it’s easy to be lazy and not learn how to read actual Japanese. Given my upcoming trip to Japan, I’m guessing that being able to read signs will come in particularly handy.

YesJapan to the rescue! They use a “progressive” solution to this problem in which they teach you a handful of new kana at a time, and from then on, the new ones are replaced in all subsequent lessons. For example, by lesson two you’ll encounter words like “あre” (“are”, “over there”) because you’ve already learned the hiragana for “a” (あ). You end up being able to read the kana without exerting much incremental effort at all, since there are only a few new foreign things to remember at each time. Brilliant!

Another great thing about the site is the copious use of pronunciation links. There’s nothing like being able to play (and re-play) native speakers’ versions of what you’re trying to say, so that you can emulate your way to perfection.

There are quizzes to test your retention, vocabulary lists for writing practice (using only the kana you’ve learned to date, of course), and interactive games like Kana Attack to let you “fire” at incoming kana by correctly guessing their romaji — flash cards on steroids!

Course 1 has this motivational phrase at the top of the page:

Chiri mo tsumoreba yama to naru

Piled up specks of dust become a mountain

So here I am, piling up specks of Japanese dust to build a my own little mountain. Yesterday, after four hours of teaching and five hours of work on my thesis, it was great fun to indulge in a couple of hours working through the first two lessons in Course 1.

## “O let not Time deceive you”

Last semester, I joked that I’d somehow gotten ahold of a virtual Time-Turner, since I was taking a class at USC that occurred at the same time I was teaching at Cal State LA, on Thursday evenings. This was possible since I was taking the class through the Distance Education Network, and therefore could view the 2.5-hour lecture on my computer at a later date (usually the weekend).

Santa sometimes has a funny sense of humor, and this Christmas he brought me (among many other wonderful things) an actual Time-Turner. And yet — while it was pretty cool to be able to turn time last semester, unlike Hermione I didn’t actually end up with any more hours in the week. By the end of the term, I was aching for a break. So I held my Time-Turner and realized that, rather than a symbol of incentive for double-booking, really it was more of a warning — a caution against that kind of stacked-up crazy schedule.

But did I heed the warning of the Time-Turner? No. By the time January rolled around, I’d already committed to an even crazier term: working, teaching an entirely new class at Cal State LA, taking yet another class at USC, all the while trying to write a Master’s thesis so I can graduate this spring. None of them are technically overlapping in time, but (just as when the Time-Turner let me spread things out) all together it’s still a gradually suffocating weight.

Thank goodness my teaching duties end with the winter quarter at Cal State LA. As of March 15, I’ll have one less thing to occupy my energies. And if I ever propose this sort of schedule again in the future, someone kindly strangle me with the Time-Turner’s chain.

## Programming by Platonic Ideal

I am teaching a programming class on Data Structures: lists, arrays, trees, heaps, stacks, queues, and other fun things. This is my first time teaching at this particular university, and I’ve had to successively ratchet down my expectations of the students as it became clear that their preparation was not, well, adequate for the topics this course covers. Or rather, they do well catching on to the concepts, but struggle mightily when it comes to implementing them in code. I’ve been somewhat puzzled by this, since even students who have the prerequisite course under their belts seem to be having trouble.

Today, I got my first glimpse into why.

I scheduled a brief post-midterm conference with each student, to give them feedback on their current progress and to answer privately any concerns they might have about the course. One student today launched into a description of what that prerequisite course was like.

“I don’t want to say anything bad about the professor, but I don’t think I learned much. He just showed PowerPoint slides, and never ran any of the code, and we never had to write any code. He said it was more important to know the concepts, and he didn’t want us to write code because then we might get too used to the syntax of one language. You know, each language is different.”

I was flabbergasted, but tried to hide it. Sure, programming languages differ. And it’s great to get to a point where you have a solid grasp of the abstract ideal of an iterative loop, or a recursive method, or, heck, a list or an array or a tree or… all the stuff we’re covering–without being tied to one language’s syntax. But it’s staggeringly unfair to expect a student to get to that point without having worked in any languages at all.

It’s possible that this student’s view of his professor’s pedagogical opinions has been filtered or changed from what the professor actually intended; we don’t always communicate effectively. But the sad fact is that many of these students lack basic programming skills in the language in which these courses are taught, and that leaves them handicapped when facing all of the rest of the courses in the department. I can hope that they’ve gained some skill from the battery of assignments I’ve given them (and knowing what I know now, if I started the course over, I’d reduce the volume of that battery significantly), but any skills have been gained at quite a cost. I continue to be impressed at the amazing amount of energy and hours these students invest to keep up with what I give them.

Interestingly enough, six students (one from my current class) have already signed up for the class I will teach starting in January (Machine Learning!). You’d think they’d be sick of me by now. :)

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