A quick (and painless) mathematics lesson

The library at the Cobalt Club is one of my favorite places on the planet.  One reason is that its shelves contain all the books that should be part of every secular library.

Such as Gray’s Anatomy.  Strunk & White’s The Elements of StyleJohnson’s Dictionary.  H.G. Wells’ The Outline of HistoryFollowing the Equator by Mark Twain.  Tales of the South Pacific by James Michener.  All My Best Friends by George Burns.  One Fish, Two Fish, Red Fish, Blue Fish by Dr. Seuss.

And The Books of the Elements.

On a recent evening, I’d taken a copy of Euclid’s greatest contribution to civilization from the shelf and gotten lost thumbing through it.  I’ve never enjoyed mathematics but have always been fascinated by the ancient geometric textbook.  Maybe that’s because Euclidean geometry is as much a study of logic as it is of integers.

That thought always reminds me of a conversation I had with Dr. Barry Spieler during his visit to the club.  At the time, he was professor of mathematics at Birmingham-Southern College, where he taught for 17 years before accepting a position at Montgomery College in Maryland.

Barry is anything but the stereotypical professor.  A personable man who dotes on his children, bakes his own bread, studies classical guitar, and has sung with the Birmingham Jewish Community Chorale, he’s a past Alabama Professor of the Year.  Seeming more comfortable to be “Barry” than “Dr. Spieler,” he’s the professor students hope they get or wish they’d had.  I learned more about mathematics during 10 minutes of conversation with him than I did during any math class I ever sat through.

“Did you always like math?” I asked him.

“I liked it a lot in elementary school and high school,” he said, sipping a latte as he settled into a comfortable chair.  “I was good at it, and it seemed to come easy.  My grandfather was good at math and puzzles and figuring things out.  He was a math major in college but left his last semester because of the Depression.  I got my math genes from him.”

“Mine must be on permanent holiday,” I replied.  “Math never came easily for me, and I’m sure that hoping to avoid it is one reason I chose to go into newspapers.”

“Well, a lot of people think of math as a field that is very specific, right or wrong. Those words carry a lot of emotional weight, as if it’s almost a moral issue. It’s something bigger than they are, so they’re afraid if they can’t get it right. But math is done by people. It’s all about ideas people have to understand quantitative things in the world. People who are afraid of math or shy away from it haven’t had the chance to see it that way. They see it as ‘always right or wrong, and I always get it wrong.’”

“Is math always scary?”

“The flip side is that some people take comfort in the right and wrong. It’s safe. It’s at least one thing that doesn’t waver. And that’s wrong, too. It isn’t just an answer to some question in a textbook.”

“So what is math really about?”

“Real mathematics is a combination of logic and reasoning and finding a precise language in which to describe your observations about things. You can think of it as a language that gives you an economy of thought. You make use of mathematical abstraction to process something efficiently.”

“Could you give me an example?”

“Sure,” he said, starting to look around as if he’d misplaced something.  “Actually, I wish I’d brought one of my visual aids.  That would make it easier.”

Emsworth suddenly appeared, proffering a multi-sided plastic object on his silver tray.  “Would this be helpful, sir?”

“Perfect.”  Barry took it and glanced up to smile at him, but Emsworth had already vanished.  He shrugged and pointed to the teaching tool.

“When you notice something that has a pretty symmetrical pattern to it, you can describe it in levels of precision. You could say it’s made up of shapes. Plastic pieces. Pentagons. Squares. Triangles. Equilateral triangles. How many there are of each. The more precise the description, the more mathematical it is. Mathematical abstractions, models, charts, graphs, and equations represent something that’s real and should be used to describe and understand things. There’s no need to make abstractions just to make abstractions.”

“So why do so many people – and I have to include myself — perceive mathematics as little more than pointless abstractions?” I asked.

“I think that, as teachers, we often underestimate people’s ability to have abstract mathematical ideas, while we over-expect them to be able to manipulate symbols.”

Then Barry told me about the math and music class he taught with voice professor David Smith at Birmingham-Southern. The Secret Life of Music and Mathematics explored how the two subjects are related.

“It’s really cool,” he said with the enthusiasm most people show when they’re speaking about anything other than math.  “They’re both abstract, they start with ideas in people’s heads, and they involve expressing complex ideas in a non-discursive language. We look at the role both play in society to find other connections between them, we look at the ways in which people make music (which, like math, has its own kind of logic and rules), the students write compositions without traditional instruments, and they learn some serious math and serious music in the process.”

That reminded him of how a guitar lesson prompted him to reevaluate his teaching methods.

“This is a good story,” he said as he finished his latte.  “When I’d go to a lesson, I’d watch the teacher play his guitar, he told me what to do, then told me to go home and practice, and I made no progress. Eventually I went to a new teacher, and he didn’t have a guitar. I sat down, and he said, ‘Barry, play something you like.’ I did, and he sat there and watched me. Then he moved my elbow about an inch and said, ‘Play it again.’ All he did was nudge my elbow, but I could feel a difference. It relaxed a tension in my hand I didn’t realize was there. The teacher was intently watching what I was doing and then suggested something to help me do it better.”

“And that was an epiphany?”

“It was. I went home thinking, ‘My gosh, instead of showing my students what to do and telling them to go home and mimic it, I want to be the teacher who says, ‘Show me what you do,’ and then nudge their elbows. That experience helped me realize what I was trying to do in my own classroom. Less lecturing, more listening. More showing them how to make things better for themselves, listening to their ideas and helping refine them.”

Ptolemy the First is reputed to have asked Euclid to identify the quickest and easiest way to study the postulates.  According to the account, Euclid’s answer was that there is no royal road to geometry.

There may not be, but I’m still rather glad I asked Barry Spieler for directions.

 For a full interview with Dr Spieler, conducted while he was still at Birmingham-Southern, click here.

 

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