Math: By intimidation . . . or not

“Change them signs, two at a time . . . Change them signs, two at a time,” Ms. Collins’ Georgia drawl echoed off the concrete walls as she walked up and down the isles of her algebra class.  She bent over James’ left shoulder as she squinted at his ciphering through her wire-rimmed glasses. Suddenly, she jumped back, pointed at his paper and said, “Boy, I told you.“ She began pounding rhythmically with both hands on his shoulders. “Change them signs, to at a time . . . Change them signs, two at a time.” The students behind them suppressed their snickers as James’ face turned beet red.

In 1966, Ms. Collins, a legendary spinster, was Marion High School’s most eccentric teacher.  No one crossed paths with Ms. Collins, nor failed to do her homework, nor willingly offered a solution to an algebra problem (except of Mason the Bully).

Her poundings on boys’ backs were more embarrassing than painful.  But then there was her ruler.  If the back-pounding didn’t get a boy’s attention, she might grab a hand, turn it palm up with fingers bent backwards and rap the exposed palm with her ruler.  That hurt.

One day she approached Wally Childers and raised her hands to commence pounding.  Wally was a big guy, one of the tallest in the class, head and shoulders taller than Ms. Collins. Just as she got to him, he jumped up, flew over his desk and jumped an empty desk between himself in the door.  He was gone in a split second, never again to attend Ms. Collins algebra class.

She was an intimidating teacher who knew the textbook forwards and backwards.  Rumor had it that she was math whiz, that she could calculate the cost of her groceries faster than the cash register, but her instruction was strict and un-inspiring – strictly limited to solving the equations and proofs by the book.  If the book’s instruction was not enough for a student, Ms. Collins could only resort to her chants and threats. Though I was an A/B algebra student, the point of the mathematical abstractions was missed.  The point of being in her class was simply to be correct and avoid getting embarrassed.

I would like to think that math instruction for high school students has changed over the past forty years. In all likelihood, few math teachers are physically beating algebra into their students; but they are still struggling to make math relevant and interesting to students, and few of them can offer much more than the explanations already present in the textbooks.

Fortunately, any modern day student with access to a computer has an alternative teacher.  His name is Sal Kahn.  Eight years ago, Kahn offered online math tutoring to his younger cousin.  His lessons were highly successful. When he got more requests for tutoring, he began posting them on YouTube.  Now, there are over 2000 of his lessons on-line, each of them getting at least 20,000 hits.  In 2009, Kahn quit his job as a hedge fund analyst and devoted himself full-time to developing his YouTube channel. With support from outside sources (including Bill Gates), Kahn and his high-tech employees are developing Kahn Academy as a web site that ties together his YouTube videos with practice activities and record keeping systems that allow any student or teacher to use the resources free of charge.

His use of technology is relatively simple – video screen capture of his desktop, a drawing program, and a microphone to capture his voice.  His explanations are systematic, clear and precise.  In terms of method, his explanations of a math concept and process are coupled with careful descriptions of the logic. But, since the lessons are on-line, the learner can listen to them repeatedly if necessary without risking teacher frustration or wrath.  With the additional use of the practice activities, the learner can check his accuracy and understanding. The record keeping system tracks performance and offers token rewards.

To get an idea of how Kahn applies his teaching method with the on-line technology, go to this link that shows his most basic lesson – simple addition: http://www.khanacademy.org/math/arithmetic/addition-subtraction/v/basic-addition

Now, compare the simple addition lesson above to one of Kahn’s basic algebra lesson, solving simple equations: http://www.khanacademy.org/math/algebra/solving-linear-equations/v/solving-one-step-equations

If you have read some of my previous blogs, you know how skeptical I am of the value of schooling.  There many reasons for that skepticism, most of which have to do with the inconsistent quality of the instruction, the difficulty of providing instruction that matches each student’s ability to learn, and the lack of support for schools from families and communities. 

There is a 20 year-old argument over how technology is going to change schooling.  The Kahn Academy is a good example of how it might.  Via the internet, the clear and inspiring instruction of one lone teacher can reach any student, any time. That’s not to suggest that millions of students suffer through poor teaching can simply walk away from school and get what they miss on-line.  After all, the face-to-face human element of good teaching cannot be easily duplicated on-line. I won’t live long enough to collect on this bet, but I will wager you that 50 years from now, thanks to technology, schooling probably won’t look anything like it does today.

Justice and the Road to Nowhere

How to define justice is problematic for philosophers.  For the non-philosophic, it is less of a problem.  Justice is fairness.  It is the application of the golden rule: treat others as we would like to be treated. In Plato’s Republic, Socrates kept challenging is friends to define justice.  Polemarchus said justice is giving to each what he is owed. Thrasymachus said justice is the advantage of the stronger. None of the definitions held up well to Socratic examination. Thrasymachus got frustrated when Socrates refused to offer his own definition, perhaps because, among groups of people, justice is illusive. Here is a good example from Southern Appalachian history.

The Road to Nowhere begins in Bryson City and winds across the lower ridges of the Smoky Mountains.  Just past Swain County High School, it enters the Great Smoky Mountain National Park, traverses forested slopes overlooking Fontana Lake, crosses Nolan Creek and ends at a tunnel.  Barricades block motor traffic from the tunnel, but not hikers, horseback riders or teenage graffiti artists. Hikers enter into a fading light that slides away until footsteps and trickling water echo through darkness. The motionless air smells of mold and horse manure. Guided by a frame of daylight at the far end, hikers slowly regain decades of graffiti accumulated at the exit and emerge into the forest.

The tunnel is a threshold between the man-made and the nature-made.  At the exit of the tunnel, the Road to Nowhere ends.  Travelers must walk or ride horseback into a vast region of mountains and streams.  Hardy travelers pass each other, their cross-purposes subdued by the harmonic sounds of a modern wilderness. The forest at the end of the Road to Nowhere has not always been a wilderness and will never be what it once was. Scarred by the rusted remains of conflicts, the Smoky Mountains is a classroom and a laboratory for human culture and science.  Nature lost control centuries ago.

The history goes way back. In 1776, the mountains now encompassing a national park existed within a vast Cherokee homeland. After the Declaration of Independence, colonial militia in western Virginia, North Carolina and South Carolina attacked and burned every Cherokee village in the Little Tennessee valley.

For 50 years, Cherokee territory shrunk as white settlers encroached from every direction. By 1838, when U.S. army troops rounded up 16,000 Cherokee, they were a tired and defeated people.  They marched compliantly along the Trail of Tears, an 800-mile walk to Oklahoma. Disease, exposure and starvation killed 4000 Cherokee.  Four hundred Cherokee hid out in the remote mountains and another 600 Cherokee, who had gained state citizenship through intermarriage with white settlers, remained behind.  These 1000 Cherokee became the Eastern Band of Cherokee Indians. They now live along the southern edge of the Great Smoky Mountain National Park.

A hundred years after displacing the Cherokee from their native lands, in order to create the national park and Fontana Lake, the federal government displaced several thousand white citizens who had lived in the Smokies since the Cherokee removal. Fontana Lake displaced 1300 families and cut off road access to upstream farms, churches and 33 family cemeteries.  In 1943 the federal government promised to build a road around the north shore of the lake to provide access to the cemeteries.  By 1969 six miles of the road were built, including the tunnel, but funds for the continuation of the road dried up.  For the next 40 years, the displaced families fought with the federal government and environmentalist over the completion of the road.  Environmentalist wanted to preserve the backcountry of the new park.  Families demanded the deliverance of the road and access to their cemeteries. 

Both white and Cherokee people who live around the boundary of the national park see little purpose in government. Money does not buy justice. Victims are nameless and faceless. They are citizens subsumed by the larger citizenry.  

I had an intimate encounter with the cultural conflicts of the Smokies when two fishing buddies and I hired a couple of Cherokee Indians to pack our camping and fishing gear into the backcountry. After fishing for three days in an area where the horses couldn’t go, we met our Cherokee friends in a campsite where horses were allowed. They had a big tent and a tarp that covered a portable table, a two burner stove and a campfire. They had beer chilling in the creek, liquor, jars of moonshine and marijuana. A big pot of chili was cooking on the stove and cornbread baked in a Dutch oven on bed of coals. The Cherokee shared their riches with the less than successful fishermen.

We spent a rowdy night swapping tales and jokes about day hikers in expensive clothes carrying binoculars and bird books. The white boys’ stories fell far short of Cherokee bravado and contempt for regulations. They carried an axe and chainsaw to keep the trails clear for their horses and to provide firewood. One claimed to be a chronic poacher, once paying a $1200 fine for a bag of ginseng – a dollar per plant. “F____g judge, it’s our woods.  We were here first,” he said. The other once paid a fine for cruelty to animals.  His horse had broken a leg in the backcountry.  Lacking a gun, he put the horse down by slitting his neck. A passer-by reported him to the warden. “F_____g judge, what was I supposed to do – leave the horse there to be mauled by bears?”

When the Cherokee got us back to the other side of the tunnel, two Harley Davidson motorcycles roared through the parking lot and stopped in front of the barricade. The motorcycles shut down.  Two guys and a girl got off the Harleys. The girl pulled a video camera out of bag and walked past the trailer where the horses were tethered and toward the entrance to the tunnel. 

In a few minutes, she returned. “I didn’t see nobody in the tunnel,” she said.

“Did you walk to the other end?” the older man asked.

“No, I ain’t walking through that tunnel.”

“It don’t matter,” the younger guy said, “I’m going.” He cranked the Harley and started rolling toward the barricade.

One of the Cherokee yelled, “Hey . . . hey, you can’t drive that cycle through that tunnel.

The motorcycle stopped and the driver looked back.

“What’s your problem?” the older man asked.

“He can’t drive that god-damned motorcycle through the tunnel.  You see that barricade.  It’s there for a reason.  The U.S. Park Service don’t allow it.”

“I don’t see anybody from the park service around here,” the older man said.

“You can’t drive that motorcycle through the tunnel,” he yelled again.

The girl with the camera walked up. “People do it all the time.  I saw the videos on You Tube.  You should hear the roar of the engine in the tunnel.”

“You can’t drive that motorcycle through the tunnel,” the Cherokee yelled as he looked at his horses.

“We rode all the way up here from South Carolina, just to ride through that tunnel.”

“Well you ain’t riding through that tunnel today.”

The older man looked at the Cherokee, then looked at the horses.  He walked over to his friend with the motorcycle still idling.  They talked for a moment. The girl got on the bike. The younger guy looked at the Cherokee and then roared away from the barricade back toward Bryson City. The girl gave the Cherokee the finger.

“We’ll come back later,” the older man said as he pulled away on his cycle. 

“Dumb ass bikers,” the Cherokee said.  “Those horses would never ’ve gone near that tunnel again.”

I don’t think much of the needs of those three Harley folks. But in the long history of the Smoky Mountains lies a problem for justice – whatever it is. How do we provide it for the groups that comprise the larger group? Who makes the laws?  Who appoints the judge? To provide for white settlers, we displaced the Indians. To preserve a scenic view and memory of nature, we displaced their ancestors. I am certainly a beneficiary of that displacement. We required a few thousand to sacrifice for millions – the greatest good for the greatest number. Justice aspires to work that way. But in some events and from some points of view, Thrasymachus was right. Justice is the advantage of the stronger.

Old Age and Wealth

Most days I don’t think of myself as particularly old, but it helps not to look in the mirror. Okay, I’ll be honest.  I think about old age more than I should.  And I fear it.

I recently started rereading Plato’s Republic and, low and behold, one the first conversations between Socrates and his friends is about old age, and about the whether or not wealth eases the difficulties of growing old. For a conversation that occurred about 400 years before Jesus conversed with his disciples, this conversation seems remarkably modern.  Here it is, presented as a script for a radio play. For ease of reading, I’ve made a few minor changes to the wording and omitted a few lines that required footnotes to be fully understand.

__________BEGIN SOCRATIC CONVERSATION__________

Old age and wealth: A conversation in which Socrates talks with Cephalus, an elderly friend, about how it feels to grow old.

Clephalus:  Socrates, you don’t come down to see me as often as you should. If it were still easy for me to walk to town, you wouldn’t have to come here; I’d come to you. But, as it is, you ought to come here more often, for you should know that as the physical pleasures wither away, my desire for conversation and its pleasure grows.

Socrates:  Indeed, I enjoy talking with the very old, for we should ask them how the road of old age travels, what kind of road it is and whether it is rough and difficult or smooth and easy. I’d gladly find out from you what you think about this, as you have reached the point in life the poets call “the threshold of old age”. Is it a difficult time? What is your report?

Cephalus: By god, Socrates, I’ll tell you exactly what I think. A number of us, who are more or less the same age, often get together and talk about it. The majority complain about the lost pleasures they remember from their youth, those of sex, drinking parties, feasts, and the other things that go along with them, and my friends get angry as if they had been deprived of important things and as if they had lived well then but are now hardly living at all. Some others moan about the abuse heaped on old people by their relatives, and because of this they repeat over and over that old age is the cause of many evils. But I don’t think they blame the real cause, Socrates, for if old age were really the cause, I should have suffered in the same way and so should everyone else of my age. But as it is, I’ve met some who don’t feel like that in the least.

Indeed, I was once present when someone asked the poet Sophocles: “How are you as far as sex goes? Can you still make love with a woman?”

“Quiet man,” Sophocles replied. “I am very glad to have escaped from all that, like a slave who has escaped from a savage master.”

I thought at the time that Sophocles was right, for old age brings peace and freedom from such things. When the appetites relax and cease to solicit us, everything Sophocles said comes to pass and we escape from many mad masters.  In these matters and in those concerning relatives, the real problem is not old age, but the way people live. If they are moderate and contented, old age, too, is only moderately onerous; if they aren’t moderate and contented, both old age and youth are hard to bear.

Socrates: When you say things like that, Cephalus, I suppose that the majority of people don’t agree. They think you bear old age more easily, not because of the way you live, but because you are wealthy. For the wealthy, they say, have many consolations.

Cephalus: That’s true; they don’t agree. And there is something in what they say, though not as much as they think.  A rich person might find old age hard to bear. But a bad person would not be at peace with himself in old age, even if he were wealthy.

Socrates: Did you inherit most of your wealth, Cephalus, or did you make it for yourself?

Cephalus: What did I make for myself, you asked! As a money-maker I am sort of between my grandfather and my father. My grandfather inherited about the same amount of wealth as I possess, but multiplied it many times. My father diminished that amount to even less than I have now. As for me, I am satisfied to leave my sons not less, but a little more than I inherited.

Socrates: The reason I asked is that you don’t seem to love money too much. And those who haven’t made their own money are usually like you. But those who have made it for themselves are twice as fond of it as those who haven’t. Just as poets love their poems and fathers love their children, those who have made their own money don’t just care about it because it’s useful, but because it’s something they’ve made themselves. This makes them poor company, for they haven’t a good word to say about anything except money.

Cephalus: That’s true.

Socrates: It certainly is.  But tell me something else. What’s the greatest good you’ve received from being wealthy?

Cephalus: What I have to say probably wouldn’t persuade most people.  But you know, Socrates, that when someone thinks his end is near, he becomes frightened and concerned about things he didn’t fear before. It’s then that the stories we’re told about Hades, about how people who’ve been unjust here must pay the penalty there – stories he used to make fun of – twist his soul this way and that for fear they’re true. Whether because of the weakness of old age or because he is now closer to what happens in Hades and has a clearer view of it, he examines himself to see whether he has been unjust to anyone.

If he finds many injustices in his life, he awakes from sleep in terror and lives in anticipation of bad things to come. But someone who knows that he hasn’t been unjust has sweet good hope as his constant companion – a nurse in his old age, as Pindar says.

It is in this connection that wealth is most valuable, I’d say, not for every man but for a decent and orderly one. Wealth can do a lot to save us from having to cheat or deceive someone against our will and from having to depart for that other place in fear because we owe sacrifice to a god or money to a person. Wealth has many other uses, but, benefit for benefit, I’d say that this is how it is most useful.

_________END OF SOCRATIC CONVERSATION___________

So, if I, John Max Jr., am worried about old age, perhaps rather than looking in the mirror or into the state of my bank account, I’d best look into the state of my soul. Now that is a tough one – counting my acts of justice and injustice and worrying about the balance of my words, deeds and decisions.  Will there be enough time left?

Coming later – Socrates on justice.

Here is a link to an on-line copy of Plato’s Republic: http://www.literaturepage.com/read/therepublic.html

The conversation in this blog occurred near the beginning of Book I.

Your Next Contribution to a Covered Dish Dinner

            It’s Saturday afternoon in July and a brain-frying 95 degrees in the shade – which is why I’m inside and looking for something fun to think about.  So I picked poke salad - because of Tony Joe White’s Poke Salad Annie.  In case you don’t remember it, here’s a link to a YouTube cut of White’s performance on the Johnny Cash show, circa 1970: http://www.youtube.com/watch?v=gRPO9qXCyyg.

            You won’t have any trouble finding pokeweed.  It’s all over the southern United States. Probably along the edges of your yard or sunny road ditches leading to Grandma's house.         

Mature pokeweed (from http://bulletin.ipm.illinois.edu)

           I’ve tried branch lettuce and rabbit tobacco, but can’t say I’ve eaten  poke salad, so I started wondering how to prepare it.  What I found were a few recipes and lots of cautions, e.g. – it’s poisonous, will kill you, even starving animals won’t eat it.

Immature pokeweed

            In spite of all the cautions from a variety of agricultural/scientific agencies, there are plenty of web sites that explain how to cook pokeweed.  If you like it, you should plan to attend the Poke Salad Festival in Blanchard, Louisiana. Though I’m not going to try it, here’s a recipe (from: http://www.trippyfood.com/tag/poke/) that sounds like how Poke Salad Annie might’ve prepared her pokeweed:

·      Pick enough young, tender pokeweed leaves to fill about two paper grocery bags full.

·      Boil them in water and rinse.

·      Boil and rinse.

·      Boil and rinse.

·      In a well seasoned iron skillet, fry several chunks of bacon and cook down for the fat.

·      Add the pokeweed, scrambled eggs, onions, salt and pepper.

·      Remove the bacon, unless you really like something bitter and foul-tasting.

What remains is, according to the web site, delicious.

By the way, Indians used pokeweed berries to make dye and smoked dried pokeweed roots for medicinal purposes.

THIS INFORMATION IS FOR EDUCATIONAL PURPOSES ONLY. 

 EAT, SMOKE, TATTOO OR MEDICATE AT YOUR OWN RISK.