July 27, 2016--Midcoast: Rhumb Line

It was a hot morning and George took a break from mowing our lawn.

"I hear from you missus that you're looking for a new place to have lunch on Wednesday."

"Yes, a cousin is going to be in the area. In Rockland."

"I know you like the Slipway in Thomaston. The same owner now has a place on the harbor in Camden, the Rhumb Line."

"That's exciting," I said, "He had one of our favorite places in Port Clyde. Until Linda Bean of the LL family bought the property. He couldn't stand her because of her homophobic politics and refused to remain as chef. That's when he opened the place in Thomaston."

"The one in Port Clyde was called the Dip Net."

"In addition to being such a good restauranteur," I said, "he comes up with great names for his places."

"What do you think about Rhumb Line?" George asked.

"We haven't been there yet," Rona said.

"I mean the name."

"I know what a dip net is--a long-handled net used to land fish--and a slipway is a boat launching ramp. But a rhumb line? That's a new one for me. It sounds nautical."

"It's a navigation term," George said, "If you don't know what it is I think you'll like it."

"I'm eager to hear."

He let go of his lawnmower and with a sweeping gesture, using both hands, created in the air the shape of a large sphere. "Make believe this is the earth," he said, "In three dimensions."

"I got you. I loved solid geometry in high school. Especially how to think about and understand how lines on a solid three-dimensional globe work. Arcs and such."

"Exactly. So if you, for example, head east from here across the Atlantic and don't change course--in effect, go straight--the shortest distance from point to point is not a straight line, as it is in two-dimensional plain geometry, but an arc, a circle. Thus ships or airplanes follow the great circle route to get to England most directly."

"And a rhumb line?" I asked.

"I'm getting to it." George likes to take his time when explaining concepts to be sure you're following him. He is exceptionally good at this. Particularly if the concept is complex or full of ambiguity. His favorite type. He also likes telling stories of all sorts. The shaggier the better.

And so, again with a gesture, maintaining the outline of the globe with one hand while with the other, where the Equator would be, he traced a spiral in the air, up from the Equator toward the North Pole.

"A rhumb line is a line on a globe that as it moves forward crosses all lines of longitudes at the same angle. That's the key--the same angle. Longitude, as you know, being the way on a globe that we map north-south slices of space and location."

"I think I'm beginning to get it," I said, "To trace a great circle on a sphere one moves along in a three-dimensional arced line, not changing course because the distance between lines of latitude are constant."

"Exactly."

"But with a rhumb line, to cross longitudes at the same angle one has to constantly change one's course."

"And thus a spiral is traced on the globe because as you head north--or south for that matter--as one approaches a pole the separation between the lines of longitude get narrower and narrower. If you will, compressed closer and closer together so it's necessary to constantly adjust your heading."

Rhumb Line

"And?" I said.

"And what?" George said.

"Whenever you get into these kind of things you always have another meaning or two to offer."

"Me?" he said with a shrug, trying to hide a smile.

"Please proceed."

"I know how you like to go round in circles. I mean," he quickly added, "not in a bad way, but metaphorically to see what you might stumble onto that's interesting."

"Could be true," I conceded. "And so?"

"With great circles and now rhumb lines you have more circles and spirals within which to go round." George winked.

"But is it a good restaurant?" I thought I had cleverly circled around to where we began.

He smiled and said, "According to the theory, no matter what course you set we all end at the same place."

As I pondered that, he said, "Be sure not to forget to order the fried oysters."

December 4, 2013--Requiring Math

There was a report in yesterday's New York Times about how American school children in mathematics continue to slip behind students in other countries.

At one time our kids scored at the highest levels on international tests. Last year they slipped behind students in Ireland and Poland and in previous years saw themselves coming in well behind those in China, Japan, South Korea, and Finland.

The United States came in 36th while Latvia was 28th, Slovenia 21st, and Liechtenstein 8th.

While worrying about this, I recalled a board meeting I went to some years ago of one of America's leading education reform organizations. It was a bluechip board and included, among others, two former Secretaries of Education.

The discussion turned to ways to improve math instruction, especially for low-income students. There was a promising approach being developed in Houston called Move It Math. An educator from there made a presentation about what made this approach promising and how there was gathering evidence that students befitted from its methods.

I didn't have much to say, not knowing all that much about math instruction. But after a time, I requested the floor and asked why we require all children to take math in elementary, middle, and high schools and often in college. "Why must everyone take algebra?" I wondered, acknowledging this was a heretical thought since years and years of math had been a universal requirement for decades.

"Why geometry and trigonometry? What's the case for that?" I asked. "Particularly when this seems to be so difficult for so many students and that struggle--frequently unsuccessful--turns them off to other parts of the curriculum."

There was more than a moment of silence. I thought because the others in the room were wondering how to metaphorically pat me on the head without offending me so they could get back to a serious discussion about ways in which to improve math instruction.

Finally, surprising me since I had not until that moment had such a thought, the dean of a noted school of education said, perhaps surprising herself as well, "This is worth considering." All heads around the table swung in her direction.

"How much of this makes education sense as opposed to giving in to the math industry."

"Math industry?" a nationally-known professor of educational history asked with considerable sarcasm.

"You should know all about that," the dean replied. "How years ago organized groups of math instructors and advocates from organizations such as the National Council of Teachers of Mathematics, founded, I think, in about 1920, how they fought hard to get as much math as possible included in the core curriculum. And how, among other things, by having such a central place in what was required of students more power and jobs accrued to those in what I just called the math industry. And I'll stand my that."

Around the table a few heads began to nod.

"And let's not forget that this focus on math--and science--swelled, in reality became  a nation obsession after 1957 when Russia launched Sputnik. As part of our effort to win the Cold War."

"If we didn't require so much math, how much should be required?" a midwestern university president asked. "I'm assuming that no one here is saying that no arithmetic or mathematics should be required. If we want to talk about this seriously we need to address that. Also, we need to discuss national needs. How important is math to the viability of the American economy because, let's be frank, to justify public support for education (and not just for mathematics) we need to be able to make the case that what we are now seditiously considering," he smiled at that, "among other things, must be in the best economic interest of America in a globalizing world."

"I can see," I jumped back in, "requiring basic arithmetic and computational skills--those proven to be necessary to functioning as a citizen: how to keep track of one's finances, be an informed citizen and voter, things of that sort. And I can see introducing everyone to mathematical reasoning and elementary algebra so, among other things, those with math talent will be challenged and interested and also to let educators know the math capacities and gifts of their students so that those with mathematical inclinations can be discovered and encouraged to pursue more math more seriously."

I continued, "This are very preliminary thoughts. Admittedly I do not really know what I am talking about when it comes to the details of mathematics education and methodologies," there was considerable playful nodding when I acknowledged that, "but rather step-back questions to see if what we are requiring makes sense and is not just being driven by tradition and, in some cases," I looked toward the dean, "organizational self-interest."

"We need to come back to that," the board chair was eager to move on, and we did.

Some years later, contemplating the full meaning of the Program for International Student Assessment scores, I wonder if it might be time to get back to that discussion.