Light Blogging

I’ve got broadband now,

and I can’t say it’s doing anything positive for my productivity. I was content with dial-up, if I could have actually had dial-up, but the local mom-and-pop ISP’s service had deteriorated over the last six months. I’d get on, get disconnected, reconnect; It would work for ten minutes, then fail again. Then everything would be fine for several days. Finally, some doofus at “tech support” told me once too often to re-install the software. I dual-boot Linux and Windows. If it’s the software, why does it happen under both operating systems? “Sir, we don’t support ‘Lennox;’ Maybe if you reinstalled Windows?” Good idea; Then I’ll take everything out of my icebox, and put back just the milk. Then maybe the furnace will work better. I pay five cents per local call; Every time I connect, that’s a nickle. A nickle! Why, I remember when you could buy a good used car for a nickle; Of course, nobody had a nickle; And you tell that to kids today, and they don’t believe you! What was I saying?

Anyway, the local soulless corporation had a broadband deal, so here I am, cruising the infobahn at ninety gigawhats, accomplishing nothing much.

Right now I have an older box with two ethernet cards running as an NAT firewall/router. I thought setting that up would consume an evening and be an interesting exercise. Thanks(?) to Knoppix Hacks it took maybe five minutes and two commands. Three, if you count su. I hope I’m not unwittingly running a spam relay or anything. I haven’t figured out how to scan the log files like I should. I ordered a Linksys BEFSR41 from Amazon; As soon as it gets here, I’ll switch over to that. It may be a bigger drill getting the broadband provider to accept the new router. If I understand correctly, they authenticate the MAC address when you first hook up. They sent out a tech who did know about Linux (it works fine, but it’s not officially supported). He seemed kind of disappointed that I wasn’t running Fedora. But he assured me I could re-authenticate if I changed hardware. Authenticating the first time was kind of a pain; It worked after some trial and error.

Now that I think of it, I’ve got two modems, and a spare computer. I guess I could take one modem and a box out to the college and set them up in the math closet. I could dial in there, and have my own ISP for free. If anybody noticed, I could buy them off with a free account.


You are standing at the end of a road before a small brick building

Wow, that Doc Rampage does the best web pages ever.

Really, I mean it. Doc’s description of the webpage he didn’t make is better than the actual page would have been. Maybe this trend will catch on. Instead of a pop-up (which I wouldn’t see because I use Firefox) we could have an inoffensive text ad describing the pop-up that wasn’t. No more Javascript-encrusted monstrosities; No more blinking, flashing screen trash; Just good writing. Like the good writing you’ll find at the Thirteenth Storyblogging Carnival. Of course, you must imagine my segue was more artful.

Learning to Read, II

It was in first grade that Miss Bates started teaching us to read. She taught us to sound out our letters, and we sat in ability groups to practice. If you got good enough at it, you could go and read on your own. Early on, this became my Holy Grail, as far as school was concerned: To be left alone to read; left alone to go to the library; left alone to for Heaven’s sake stop cutting out snowflakes and get something done!

One winter day, Miss Bates read us a story. The children in the story built a snow fort, and had a fight with snow balls. Miss Bates paused in her reading and asked, “Now, children; What else could we make of snow?” And the answers began: snowmen, snowdogs, snowladies, snowcars, snowtrucks. And the answers went on and on, beyond all reason. Miss Bates smiling and nodding, “Yes, Johnny; Snowshovels? Very good. Who else? Melisa? Snow-windows? Oh for the snow house? Good! Sally? Snowshoes? Yes, good.” Everybody answered multiple times. Finally the answers came slower, and it began to stop. Then she said, “What about ice? What could we make out of ice?” And the litany of inanities began again. Sometime shortly after, I interrupted loudly, and suggested we continue the story. Then I got to go stand in the corner.

Sometime in second grade, we learned sight reading. In some circles today, this would be like saying we practiced reading from the Necronomicon. I found it pretty insignificant, for good or ill. It was a pink and blue workbook. There would be a selection of solid black outlines representing the shapes of words. We were to pick the one that fit the word. “Miss Bates, I’m done. Can I read from the story book?” I guess it did me no harm, nor much good either, but I didn’t do any sight reading until after learning to read with a big dose of phonics.

The big thing in early elementary school was SRA. This was a reading comprehension curriculum. There were color-coded boxes containing a dozen readings with questions to answer. You started with Red-1, read the paragraph, essay, story, whatever, and then answered a few questions. After you finished the Red box, you moved up to the harder Blue box, then to Green, and beyond.

Putting aside all modesty, I ruled SRA. I ran through those things like candy. I would happily sit and do SRA as long as the teacher would let me. I ripped through the rainbow in no time, and the teacher had to go to the closet for more. I mastered colors people had never heard of. Rose, Silver, Cerulean, Taupe. I went ‘on beyond zebra.’ Sadly, it ended in third grade.

In fourth grade, I finally got free access to the elementary school library. We’d gone there as a class, but that wasn’t the same as free browsing on your own. There was this brilliant series of books from a Chicago publisher, Children’s Press. They had a large format with wide margins, copious annotations, and an appendix. These were great. I got to read all the classics. I remember starting with The Call of the Wild.

Another book I remember well is David and the Phoenix This was fantasy, possibly the first I read. My initial exposure to science fiction was a novel called The Ant Men. I didn’t like it, and returned it unfinished. Besides these, there was Swiss Family Robinson, 20,000 Leagues Under the Sea, which was way better than The Ant Men, and of course all the stories and poems in my reading book.

Kids today seem to have a great variety of excellent books, some of which I read myself. A couple of years ago I did some substitute teaching. One day after lunch, I announced that I would be reading aloud from Holes. The class, a bunch of ill-favored delinquents whose behavior up to then had been barely acceptable, immediately became attentive. “Quiet! He’s gonna read Holes.” Amazing.

Nothing Ventured

James Harmon sat in the cafeteria eating soup. The translucent noodles, made from a starchy root native to the planet, were excellent. The broth was mediocre, with a slight chickeny flavor and a muddy aftertaste. James’ partner Ghraq came in, got a large mug of cocoa from the dispenser, and approached James’ table. “It will be warmer as the sun rises,” observed Ghraq in his native language.

James replied in kind. Ghraq knew a few English nouns, but like almost all of the Karriri was unable to learn another language without losing fluency in his own. Humanity’s skill with languages had interested the Karriri at first contact. James’ fluency, or most other species’ lack of it, made humans valuable as translators and got James his job with the trade mission. “Almost certainly it will be warmer. Good morning, Ghraq. Please sit down.”

Ghraq sat, and sipped his cocoa. He watched curiously as James spooned up the last of the noodles, and then raised the deep, cup-like plate to drink the remaining liquid. Of all his human friend’s peculiar habits, he found the idea of soup most odd. A food, and yet a drink. Still, he had helped James find the yellow leaves that flavored the broth. “Does the flavor please you?”

“Still needs work. Maybe some garlic. So, what’s up?”

“The drone reports a group of mixed gender traveling toward the village.”

“Yes; Another kin group is joining them for a celebration. The clan father told me about it, and suggested we might join them at mid-day.”

“The K’Brell will celebrate; We will join them, and learn what they might trade for the nuts. Let us meet at the gate half an hour before, and walk over together.”

“I’ll meet you at the gate at eleven-thirty.” After taking his tray to the kitchen, James spent the morning writing up his notes on K’Brell historical predicates, and got in twenty minutes on the ergometer. After a shower and a quick sandwich, he met Ghraq at the gate of the compound. The K’Brell had never shown any signs of hostility, but a defensive perimeter was Karriri policy. With centuries of experience on hundreds of planets, James supposed they knew what they were doing.

Ghraq was waiting at the gate and nodded in welcome as James approached. “Are you ready to go?”

“All set. What’re you packing?”

“I will carry a taser; And you?”

“I have some pepper spray, and a noise maker.”

“You do not expect fighting?”

“Well, it’s a party. If there’s trouble, we’ll walk away. If we can’t just walk, we pop the screamer, and shoot if we have to; Then walk. But no running,” he added with a significant look. They both remembered the unfortunate incident; It seemed that running upset the K’Brell. “Anyway, I’d much rather ride out any trouble. We need to be seen as part of their kin group.”

“I agree. More inclusion will remove their reluctance to trade.”

“I think our status as outsiders is part of the problem. They’ve been agreeable enough, if kind of distant. But there are still some elements of their language I don’t understand.”

“We will discover what they want and offer it. They will trade. As we trade, we will come to know each other better. Understanding will follow trade and reinforce it.” James hoped it was as straight-forward as it was logical.

The party began with arrhythmic drumming, which was clearly and annoyingly audible from a mile away. It became louder and more annoying as they approached and entered the cluster of hemispherical stone structures that made up the K’Brell village. The normally active villagers were sitting around a central bonfire talking quietly. Off to one side, the oldest males were drumming.

Approaching a vigorous black-maned male, James spoke aside to Ghraq, “Pretty quiet for a party.” And then to the chief of the K’Brell in their language, “I greet my friend Ahaing.”

Ahaing’s reply was civil, but he seemed distracted. “I greet my friend ‘ames.”

James continued, “We thank Ahaing for calling us to his celebration.”

Ahaing’s reply was a nod to both the partners, and a glance toward the road. Clearly he was expecting the group the drone had spotted. After a moment, James tried again; “Is all well with our friends the K’Brell?”

Turning away with a wave of his hand, the chief replied, “We shall both know soon. The L’Caust should be here in a moment.”


“He says the guests will be here any minute. He seems a little anxious about it.”

“Will there be violence?”

“Doesn’t look like it, but nobody seems very happy either.”

A group of maybe two dozen, both male and female, entered the camp. One approached the chief; Glum faces all ’round. Greetings were exchanged, and the guests took seats around the bonfire, intermingling with their hosts. At a wave from Ahaing, James and Ghraq joined the group. After a few quiet words here and there, nothing much happened. Hosts, guests, and aliens from two different planets sat and looked at the fire. The sense of gloom was palpable.

“Somebody tell a joke.”

The drumming, which had tapered off at the guests’ arrival, stuttered to a start and continued raggedly. After twenty minutes of increasing discomfort, James looked over at Ghraq. A few grimaces and raised eyebrows led James to take the bull by the horns. Clearing his throat, he spoke to the chief of the local group of natives. “My friend Ahaing, what of the day?”

Ahaing looked at his feet, looked at the L’Caust, and looked at James. After a few moments, he excused himself to his guests. Drawing aside, the tall and heavy chief bent down and spoke quietly. “My friend ‘ames, all is not well. There is great shame. The L’Caust are here, and they have no duro nuts.”

This got James’ attention. The duro nuts were what they were here for. The marketing director was eager to the point of mania for the duros. The fragrant oil pressed from them he hoped to trade for yet another product, and earn an immense profit. The K’Brell had been unwilling to part with more than a few, keeping all they had in a large building that seemed purpose-built to store the nuts. They didn’t eat them, didn’t press them for oil, didn’t wear them for decoration. So far, they had just cultivated them, packed them as they ripened, and stored them away. Anything involving duro nuts was of great interest. “So they have no duro nuts. Had you expected them to bring any?”

“No, of course not. How could they? They have none. They are deeply ashamed, as are we. There is no ciemittasae neshteyma. No good can come of this.”

James beckoned to Ghraq, who joined them. James explained the situation, as well as he understood it. “The guests didn’t bring any duros; everyone’s embarrassed about it. Something or someone can’t be attached to something else. He used a formal phrase I don’t understand. Interfering could be risky.”

“Risk generates profit. Their trouble is our opportunity. Ask if we can help.”

James spoke again to Ahaing. “My friend, please pardon my ignorance. We do not wish to give offense or cause embarrassment or discomfort. We do not know your ways, and yet as your friends we would like to help you if we can. May I ask you more of this matter?”

“You are my friend. Ask what you will.”

“The L’Caust have no duro nuts, yet you have many. Would the shame be less if they had some duro nuts?”

“Yes, of course. What of it? They have none! Ciemittaset’eshteyma. If things were otherwise, they would be different.”

“Is it inconceivable that you could give them some duro nuts?”

“We could do no such thing. Vaghentaa cuidshi. That would be worse yet.”

“And yet, a few weeks ago you gave Ghraq a basket full of nuts, and others of your people have given me nuts on two occasions.”

“Yes; What of it? You are not L’Caust; You are not K’Brell. You sopeliashest’balisha.”

“Could we then, Ghraq and I, give duro nuts to the L’Caust?”

“That would be very kind of you. But you have few. At most two baskets, is it not? I appreciate your good will, but our store house has hundreds of baskets.”

Actually, the traders only had a double handful of the nuts left. The marketing director had sent out samples, and laboratory analysis had used up most of the rest. James again withdrew and spoke to Ghraq. “If I understand correctly, we might be able to act as middle-men and at least help the situation.” Again Ghraq urged him to be aggressive. He pointed out that both of them were growing older, and neither wished to do so on this backwater planet. James continued to Ahaing, “My friend, if you gave us the nuts, could we give them to the L’Caust?”

“My friend, I know not what to say! You offer hybchsea’tartuba? You will help us?”

“Yes, my friend, just as you would certainly help us if we needed something.”

That afternoon, James and Ghraq moved baskets of duro nuts from the storehouse to the side of the trail. It was unclear how this would get them any of the nuts, since James and Ghraq assumed that the L’Caust would take the nuts home with them. The work was tiring, but at least the drummers had found a beat. Both L’Caust and K’Brell watched the traders with contented expressions. Ghraq was enthusiastic. “We’ve helped them; They’ll help us. Maybe not today or tomorrow, but soon. You’ve often spoken of their commitment to equity,” he reminded James.

“That’s true, and I think it’ll work out. But I didn’t completely understand everything Ahaing said. He used some formal constructions I hadn’t heard before. Okay, that’s the last basket. Here comes Ahaing, and the L’Caust female.

“Grach, ‘ames, we are very grateful for your help. Cyitoksha istabalishta. Vrexni is our guest from the L’Caust.”

“Greetings and thanks, ‘ames and Grach; Cyitokshi istabalishtat. You have helped us very much. Ahaing tells me your friends value the duro nut. Would you like these?”

“Uh… Yes, thank you. That’s very generous of you; But don’t you need them?”

“Oh no, not at all, not now. Please take them. We are shaculynat now; Baymami’yeis.

Ghraq was thrilled, and his enthusiasm was undimmed even after he learned that he and James must personally carry away the baskets, at least as far as the compound. After that, Ahaing assured them, they could do as they liked.

Maybe it’s an operative future concessive

After a week of hard labor hauling baskets of nuts, James had come to regard duro oil as stinking rather than fragrant. Still, he and Ghraq enjoyed the enthusiastic congratulations of both the marketing director and the head of mission himself. Commissions to both the young traders would be generous. Ghraq came into the cafeteria one morning to get his cocoa. James sat reading, with a spoon held over his bowl. Soup again, this time one of the cream variety, served cold. “Good morning James; How is the soup?”

“Uh, fine thanks.”

“Are you troubled?”

“Well, there may be a problem. You know I told you the K’Brell had fourteen different declensions? Don’t glaze over on me, this is important. Their thing-names end differently depending on what they mean. Well, I’ve found at least two more, and, uh, another kind of action word as well.”

“James, I am sure this is very interesting, but honestly it gives me a toothache. How is any of this a problem?”

“Well, you know how I thought the K’Brell and L’Caust had given us a monopoly on nut trading?”


“Well, the thing is, I may have misunderstood. We may have given them the monopoly.”

“We gave them nothing. On what could they have a monopoly?”

“Well, that’s just it. We may have incurred a perpetual obligation to haul these duro nuts around every six weeks. I’m afraid we’ve given them a monopoly on ourselves.”

Tom Harrison, 2005

Learning to Read


There was some discussion a few weeks ago about a Principal in Rockford, Illinois who was fired for teaching phonics. Of course, that’s hyperbolic language. I suspect there’s more to it than that, and something to be said on the other side.

I used to read the Rockford Register Star, and gape in horror at the continuous train wreck that was the Rockford public schools. At last, I got tired of the constant litany of disaster, and the inability of the Rockford Register Star to deliver a newspaper three days in a row. I cancelled the paper, and tried to forget about the Rockford public schools. Beyond a certain point, the people who choose to live there have the schools they choose to have.

So having already written one hundred twenty-five words on something I know nothing about, let me tell you about my childhood.

The Early Years

My parents had read to me, and let me read along, for a couple of years before I started school. I remember my mother read me Little Britches and Man of the Family, both by Ralph Moody. My father read or recited lots of Doctor Seuss, and stuff like “The Walrus and the Carpenter,” or “The Owl and the Pussycat.” Also, for my moral edification I suppose, he read me “The Death of Socrates.” For reasons known only to him, he also taught me the correct medical/Latin names for half a dozen of the more obscure sexually transmitted diseases.

Kindergarten was a new thing; A little half-day program to prepare kids for first grade; Something to get them acclimated; Think ‘slippery slope,’ and ‘Mozart in utero.’ We came to school and took off our snowsuits. Then the teacher read us a story, and we had a snack. Then we took a nap on our special mats. Then we put on our snowsuits and went outside for recess. We came in, took off snowsuits, sang a song or colored a picture, put on snowsuits and went home. Unless it was Halloween, Easter, Christmas, Washington’s birthday, Columbus day, or a classmate’s birthday. Then we had a party, with treats.

Twenty years later in Officer Candidate School we did something called ‘Uniform Drills.’ Put on class B’s, have inspection, run upstairs, put on class A’s, run back down for inspection, change to BDU’s with tactical camo paint, then back to class A’s, then bdu’s with helmet liner and poncho, etc. Like the man said, everything I really needed to know I learned in kindergarten. It was more fun with snowsuits.

I think at some point during kindergarten, it must have been early fall or late spring, we learned our colors, and to say the alphabet in unison. I remember we learned to tie our shoes, but not to tell time. The first graders had a special clock they used, with movable hands. I was really excited about learning to tell time. Again, parallels with Basic training come to mind.

We didn’t get letter grades in Kindergarten. We got marks for unsatisfactory and satisfactory. I got all S’s, except in skipping. I got a U in skipping. I did eventually master it, but I rarely skip anymore.

Okay, everybody back in the box

In my class today, I presented a mixture problem as two equations and two unknowns. You’re to mix some forty-percent acid with some sixty-five percent acid to get twenty liters of fifty percent acid. After working out the problem on the board, I took the opportunity to talk about inconsistent systems of equations. I said, “What if a customer wanted seventy percent acid? Could you mix some up?” Someone noticed the difficulty and spoke up, and I drew a graph of two parallel lines, and all was well. Then another student asked, “Couldn’t you label the jug ‘seventy percent, plus or minus five percent,’ and give the customer that?”

UPDATE: The alert reader will have noticed that this type of problem does not in general graph as two parallel lines. The problem has no solution because it would require a negative amount of one component, not because the lines don’t intersect.



I’ve made a couple of changes to my blog roll, removing Brian’s education blog (I hope temporarily – he seems to be having technical difficulties), and adding Wesleyblog, which I’ve been reading for a few months.

I’ve removed the “To Be Read” list, because it was just embarrassing. I don’t really read to a plan, and it was foolish to try. I still keep a list of books I’d like to take a look at, but I’m going to keep it to myself.

Two things that are better than in the “good old days”

A local ‘antique’ shop had a used book sale to get rid of a lot of books they’d accumulated: ‘twenty-five cents a piece, or five for a dollar.’ I rummaged around and came up with four that I wanted, and went up to pay. The clerk said, “You can have another one for free.” I said, “I’ll take a whole box full if you give me a dollar.” She got a little snippy about it, and I haven’t been back.

At the actual used book store, they sell comics, trick cards, and D&D paraphernalia, besides the books. I stop in every month or so, and maybe twice a year I buy a couple of volumes of classic SF or fantasy. I give the guy maybe seven dollars a year gross. Clearly he’s not getting rich off me, or anyone else; Yet he’s always pleasant and friendly.

Across the street is a more upscale place. Nominally a book store, but really a coffee shop with lots of (new) books for sale. Not large, but they have a well-chosen selection of books. They make good coffee, which is clearly the main source of revenue. I stop in every month or so, buy a cup, and browse around.

Every library I’ve ever been to has had a monthly rummage sale, or a sale rack of books for a dime or a quarter. Occasionally I’ll find something good there.

The local mall has a B. Dalton; Going there used to be a waste of time, but they’re doing better. They have a nice selection of SF and fantasy, the usual best-sellers, a lot of Japanese stuff, for want of the correct term. (Is this the Manga people are always on about? It looks about as interesting to me as a Mary Worth comic strip.) If I need something to read I could go to the mall and find something, but it would still be a ways down on my list though.

Someone had the idea a few years ago of a kind of ‘Media Play lite’ for smaller markets. I don’t think they had anything to do with the real Media Play, but they had a similar strategy: A selection of books, movies, and computer software, but all in a much smaller store to serve markets too small to support a big-box retailer. It started off fine, with a nice if limited selection of stuff. The books were the first thing to go, and in a year or so they were closed.

In the nearest city, there’s a Borders and a Barnes & Noble. I always enjoy visiting. I usually buy a cup of coffee, more rarely a book or magazine. The ‘problem’ is the libraries. You can get (almost) any book in the world through interlibrary loan. At the bookstore I might a reference book, but I usually get those from Amazon. Other than the occasional gift, I buy books that are going to take me a long time to read, like ‘The System of the World.’ I get most of my books from the library. It’s not free, because my taxes go to support it. But I have to pay the taxes any way. My book habit is subsidized by the taxpayers who don’t even know where the library is, poor fellows.

UPDATE: More good fiction; Bring your own coffee:

The twelfth Storyblogging Carnival is up at Back of the Envelope.

Nunc mihi, cras tibi

From liberal to conservative

I remember a college class whose name stuck with me. I didn’t even take the class, I just noticed it in a course catalogue twenty-five years ago. It was “The Avant Garde Tradition in the Visual Arts.” Maybe the terminology had some specific technical meaning, but I understood it as one of those “perpetual revolution” things. I always wondered how that was supposed to work out in the long run.

“But my son, we are people of the Avant Garde tradition.”

“No longer, old man! Oh, wait…”

What ultimately happens if we make constant change our permanent goal? Do we evolve into beings of pure energy? Third-stage guild navigators? Kleptocrats?

Having been each among the other, I’m prepared to say that it was more agreeable to be a liberal among conservatives. But then everything is more agreeable when you’re young, at least in retrospect. So there’s youth, and the happy fallibility of memory; and everyone is more tolerant of the young, because they see themselves, or they see what they wish they had been. The rest of it, though, is that conservatives are more tolerant of the things that one ought to tolerate; The folly of youth, for one.

To take it out of politics, it would be more fun to be a liberal among Baptists than a conservative among Episcopals. Who wouldn’t rather be the witty insurgent, pushing the envelope, demanding, “Why not?” and “What’s this button do?” That’s way more exciting than droning on, “Stop that; Put that down; Don’t mess with that, you don’t know how it works.”

But as tiresome as riding the brake is, pushing the envelope is a job for Sisyphus. There’s always another guideline to be ignored, another “arbitrary convention” to be mocked. Someone said that it only takes twenty years to make a liberal into a conservative, and you don’t even have to change any of your opinions. To stay liberal, you have to keep raising the bar. They want to be known as “Progressives,” but modern liberals act on an ideology of motion, not progress.

A smell of petroleum prevails throughout

  • Note to searchers: “Just before Christmas a piece appeared in the Guardian discussing cases where people had dreamed that they had uncovered the secret of the universe, only to waken next morning and find they could not remember it. One classic instance, reported by the psychologist William James, was that of a man who repeatedly had this dream and finally managed to write the formula down before he went back to sleep. Next morning he found he had written: “A smell of petroleum prevails throughout.” Another involved an opium addict who jotted the secret down, only to read when he came to full consciousness: “The banana is great, but the skin is greater.” — Downhill to Mandalay

Illuminating but unsound ideas on pedagogy

In my algebra class, I harp a lot on the associative, distributive and commutative laws. I started doing this because it seemed to me that most of the students’ systemic errors came from misunderstanding these basics. I suppose that’s almost a tautology. When I took linear algebra in college, we did a systematic development of algebra from first principles. I found this tremendously helpful. Much that had been confusing to me became clear, and I hoped that at least some of my students would experience a similar epiphany.

Anyway I wonder if what I’m doing, with my students and the commutative law, is trying to get them adopt a better ontology. The discussion about taxonomy at Faith in Fiction; something I read on Slashdot about folk taxonomies on the web; something my uncle told me; These all came together to make me wonder: How would my students classify algebraic expressions? I read about an exercise in website usability where you give to a few of your users index cards with all your web pages on them, one web page to a card. Ask your users to sort them into categories. Look at what they’ve done, and organize your site accordingly. How would my students classify equations? Expressions? Word problems? (“Johnny has a pie… So divide? Or square it, because it’s a pie…”)

At Faith in Fiction, a weblog by a fiction acquisitions editor, Dave is trying to construct a taxonomy of writing that doesn’t lead to the same old genres. In an off-hand comment, I suggested that maybe you could divide novels up as character-centered (Great Expectations) vs. plot-centered (Jurassic Park or The Hunt for Red October). Thinking about it, I’m not sure this is a good idea. You might end up putting the readers into categories, instead of the books. But that discussion put the idea in my mind.

In my senior year of high school, my uncle told me that “the purpose of college is to make you conform.” He meant this in the sense of adopting the outlook of the ruling classes, i.e. the college graduates who ran things from his point of view. He advised me to cooperate in the process. If he’d been less plain-spoken, he might have said, “Go to college to learn and adopt our society’s dominant ontology.” (I ignored his advice, and would have no matter how he phrased it. Like the scorpion said, It’s my nature.)

Well, Somebody has a skull full of mush anyway…

So all this stuff was in my mind, and I thought of my math students. Of course, they’re never far from my mind. That’s just the kind of guy I am. Conscientious to a fault, and self-effacing to boot. I wondered how my students see algebra. (Through a glass darkly, in some cases.) How do students categorize expressions? What taxonomy do they use? For some, a poor one that leads them into error. I want to replace theirs with a better one. I want them to adopt the outlook of the people who can do algebra; To leave thinking like a lawyer.

Could I do this more effectively if I set out purposely to do so? And how did the students acquire this bad ontology, the one that I’m trying to replace with a better? Have there been any studies of early math education and how students develop their ontology? Something backed up with solid diagnostic testing? If we could use that research and get to them in the early grades…

Then I realized: This is how we end up with stuff like new math, or whole-language learning, or outcomes-based education.

Maybe in the course of a good education students do adopt the outlook of other well-educated people. Certainly math education could be done better, especially for those who aren’t going to go on to be mathematicians or engineers. But there’s no royal road to geometry, to algebra, or to anywhere worth going.

It’s not rocket science, nor yet philosophy. It takes practice. To learn algebra, students need to show up to class, ask questions, think about what they’re doing; They need to read the text book, work through the examples, and do their homework.

And I need to stop blogging and write up the next test. There will be a question on the distributive law.