Friday, February 20, 2015

The Boiling Point

There was clearly a disconnect between what I have been trying to get out of my History of Math class and what the instructor wants me to get out of the class.

I've never been much of a geometer.  I taught it for a year, several years ago, but haven't taken a geometry class since since the spring of 1981.  In other words, I was last enrolled in a geometry class when the embassy hostages were still being held in Tehran!  That's my way of saying I don't know much geometry.  So imagine my frustration when I'm thrust into a maelstron of Euclid, Archimedes, and Appolonius!  Compound that with a horribly written textbook--the author's explanations seem to assume that you already understand the mathematics and don't need much explanation--and I've quickly gotten lost.  And never having had an astronomy class I had no way of understanding so much of what was written, as much ancient mathematics was devoted to understand the movements of the heavenly bodies.

I thought I was supposed to be learning about how the ancients did math, and my inability to understand what they were doing, and why, and how, was truly frustrating.  And I don't handle frustration well.

The instructor offered to have me call him, which I did the next morning--a long distance office hours!  Before I knew it an hour had passed, and in that time he'd explained not only some of the "simpler" things that had been confusing me but also the expectation that the minutae in the textbook was more for background than it was a course requirement.  His goal is for us to understand how this math knowledge led to that math knowledge, and how this particular lack was satisfied by that mathematician who built on the work get the idea.  I was lost in the weeds, he's going for the bigger picture.

We also discussed the course research project, which he said is where we get to "get into the weeds".  I've long been interested in the development of logarithms so my research question will be "What types of calculations were being done that motivated John Napier to spend 20 years of his life developing logarithm tables in order to simplify them?"  I already have over a half-dozen excellent sources to go through but have no idea how I'll ever find the time to read them all, especially considering that I'm the world's slowest reader.  I think my first goal should be to learn what calculations Napier was trying to simplify, and then try to understand how his logarithms (which are quite different from what we use today) work--then I should be able to understand all my sources that discuss the logs.

So now, at least, I know what the instructor expects.  And I know I still have a mountain of work ahead of me.  And I jumped through hoops at the last minute to take this course--what was I thinking?!


maxutils said...

Geometry is an entirely different beast … I don't think it's any coincidence that I, with a very low-end math background, never had any trouble getting those classes … it's so spatial, and not at all partial to algorithms or set methods (there are almost always multiple ways to solve a problem) that I think it probably just drives better trained mathematicians nuts. But, I can't even count the number of times a student told me "I've never been good at math before … but this makes sense." It's a very different skill. Very cool of your Prof to spend that much time on the phone with you … that's what good teachers do (and yes, I know you would do the same.)

Anonymous said...

If you are going to write a paper on John Napier of logarithms fame, you *MUST* also somehow insert the quote on respecting other folks national customs. Wikipedia has it:

It is the bit that starts: "Be it so. This burning of widows is your custom; prepare the funeral pile. But my nation has also a custom..."

This isn't relevant at all, but the last names are the same and the story is cool!

-Mark Roulo

PeggyU said... is a site that might interest you.

EK said...

I teach history classes at a few community colleges, and I often see students try to do what I suspect you were doing in this history of math class—getting overly fixated on the minutiae. They start out trying to process and commit to memory every last piece of information they encounter—and the inevitable result is they wind up being totally overwhelmed by the sheer mass of data. The trick is to separate the wheat from the chaff, so to speak—sifting through the background information to grasp the elements of the “big picture” that are genuinely important. That’s easier to do in a face-to-face classroom setting, where I—the instructor—can tell you what the important stuff is that I want you to know. On-line classes have to rely much more on the textbook. Depending on the textbook, that’s not necessarily a good place to be.

It also occurs to me that your problem stems, at least in part, from a difference in perspective. You’re a mathematics teacher working on a math degree, and so, naturally, you went into this class and focused on the mathematics. But it’s not a math class. It’s a history of math class, which is not the same thing, and your instructor obviously wants to focus on the history at least as much as the math.

EK said...

As a young undergrad at the University of Texas at Austin, I took a math course that the instructor taught as a history of math class. I’ll never forget it. We spent the early part of the semester doing basic arithmetic problems in the ancient Sumerian base-60 number system, utilizing the cuneiform markings they would have used many thousands of years ago to represent the numerals. In fact, the instructor had us go out to local arts & craft stores, buy boxes of modeling clay, form the clay into tablets, and inscribe our homework problems in the clay.

I can’t begin to tell you how much of a mind-bender it was trying to get outside our comfortable, familiar base-10 number system with Arabic numerals and think instead in terms of base-60 rendered in cuneiform. It really messes with you. In fact, that was just about the hardest thing I’ve ever had to do in any math class I’ve ever taken in my life.

Darren said...

That's closer to what I was expecting!

Joshua Sasmor said...

Darren, I am also teaching a history of math course this semester. I think one of your issues with geometry comes from the perspective of a person trained in modern methods of algebra. We learn algebraic methods (even the rote arithmetic skills are algorithms) from the beginning and then are thrust into geometry in 9th or 10th grade. This makes most people _hate_ geometric methods.

However, historical records show that algebra and algebraic methods are much more recent - the last thousand years or so. Geometric methods are much older, so from a history perspective they are the foundational methods of problem solving.

Even with this point of view, there's yet another problem with written geometry - the lack of step-by-step diagrams! When I read a geometric construction, I have to draw each step in order to see if I end up with the _one_ diagram that the text provides! I think it is because parchment was expensive, so they only wrote down the last picture...