An important question

I've often wondered if my bombastic, loose, witty lessons combined with my adult ADD (easily distracte---boy is it a beautiful day for a run today, if only my knees would cooperate), and minor Turret's (I have a difficult time having unspoken thoughts) help or hinder my ability to teach. In fact, my proclivity to wander off subject, take time out to explore a good joke, or interject random bits of trivia in no particular language is the main reason I entitle my blog "Off On A Tangent," that and that it was a great math pun (oh, yeah, I often say things in class that are punny).

My digressions tend to get worse throughout the day as I get tired, hungry, or begin thinking about what I'll do after school. They even get worse throughout the year, as my educational endurance reaches into its reserves. This year's been even worse having to adjust from a block schedule. I'm pretty much slap happy and sometimes ridiculously delirious by 2:00pm. Compound all that with the fact that I don't eat breakfast nor do I eat lunch (13 years now), relying instead on my morning dose of caffeine via 12 cups of dark, black coffee. By mid-afternoon, I'm not only hungry, my body is crashing. None of this is necessarily any good for my last period class of the day, a class that, more than any other of my classes, requires me to be focused, explicitly clear, and cognitively cogent. That class is BC calculus.

This time of year, in BC, we're getting into some pretty high-powered math, abstruse concepts and often paradoxical results (see Torricelli's Trumpet for an example), but the concepts become even more difficult to understand when they're not presented well. Granted, the students I'm expecting to just "pick up" on the ideas and their implications are among the top math students in the world, which means they'll probably understand in spite of any dereliction of duty on the didactical dictator's part. Everything has always worked out in the end, meaning all have gone on to do well on the AP exam in May, a successful, well-adjusted university career, and beyond. As a result, I've never tried to temper my enthusiasm or ballistic approach, but lately I've noticed that, left unchecked, I've progressed further and further, becoming what might seem more like incompetent lunatic, rather than eccentric math teacher.

I'm beginning to feel the judgmental eyes of the BC class as they wonder if their mathematical future is in good hands. What they don't realize is that I'm trying to come up with wonderful, meaningful examples on my feet, to try to make the lesson "fresher," more "relevant," and "customized," but it's very hard to come up with such examples from the hip. It's even more difficult when your exhausted, hungry, and "crazy." While my intentions are good, many of my impromptu examples have been dead ends, and while I can extract a valuable lesson from each of them (.... soooo this series actually diverges, ......sooooo we should never assume lest we make one of ourselves, .....soooooo here's why you should get plenty of sleep and plan all your extemporaneous speeches in advance), it's hard to save face in the eyes of our society's future top scientists, engineers, doctors, lawyers, teachers, clothing designers, and stay-at-home-parents.

So I'm contemplating the question: should I teach on the straight-and-narrow and lose all the interesting, memorable follies, foibles, and fallacies that go along with learning and teaching a great group of students, or should I continue to teach like I do, running the risk of a few moments where I look like an unprepared, incompetent, mathematician gone bonkers?

Or perhaps . . .

I could just start eating lunch?