Fundamental Theorem

A student told me I make being pregnant look easy.

I’m holding on to that one for a while.

*****

While I thought (and hoped) my little boy would be here by now, staying a bit longer meant I got to teach my calculus kids the Fundamental Theorem of Calculus today!  It’s a favorite of mine.  I still don’t do a great job of explaining why it’s such a big deal.  I mean, it took the human race about two thousand years post Archimedes to figure this out (and to think…Archimedes was SO close!).  Despite my inability to make those jaws drop as wide as I’d like, I still love this lesson.

When I finished the lesson, I took out a stack of one hundred and fifty note cards, each of which had a theorem and its proof that I had written on it.  I explained that when I was studying for my comprehensive exams in grad school, I had each of these one hundred and fifty proofs memorized (the things we do to ourselves)…and somewhere in the vast stack was the Fundamental Theorem of Calculus.

I passed the stack around and the kids oohed and awed (rightfully so, if I do say so myself).  But what I really wanted to get across were these points:

  1. I understand what it’s like to have to work your tail off to get what you want.
  2. Anything worth achieving is going to take a great amount of effort.
  3. What they’re studying right now is some very cool–and fairly advanced–stuff!

I love the moments that I get to share pieces of my life that have made me who I am today. The math that we teach is important, yes; but there are other lessons infinitely more so.

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4 thoughts on “Fundamental Theorem

  1. Do they see the indefinite integral symbol before the Fundamental Theorem? If so, I think that interferes with understanding the big deal – because definite integral looks like anti-derivative to them too, then.

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