I just got done with Open House at our school, and I shared a slide with the following to my parents:
In mathematics, the art of proposing a question must be held of higher value than solving it.
Georg Cantor, 1867
I asked them if they were ok with a brief math history lesson. They said yes as long as there wouldn't be a test afterwards (I like this group). I gave them a few tidbits that I find really fascinating about Mr. Cantor: he was one of the forerunners to formalize the rigorous definitions we use in calculus; he classified the levels of infinity (WHOA); people thought he was so crazy, he got thrown into an insane asylum.
So a genius beyond genius, if you ask me.
But one of the things I love most about Cantor is the quote from above. Because it summarizes my thoughts not just on mathematics but on teaching mathematics so beautifully.
I told the parents, as a teacher, I'm much more interested in developing students who can ask deep questions, than students who know how to take a multiple-choice test. I'm interested in helping students learn when to ask, "Mrs. Peterson...why do we do it this way?" or "What if we considered this case instead?" I want to help develop curious students; and central to curiosity is the desire to ask good questions.
One challenge that I face, however, is that my students are used to their curiosity being satiated so quickly and easily. If they want to know the answer to something, they can just Google it. On their phone. Right there.
Don't get me wrong, I love that we have access to so much knowledge. The downside is...many of us are not used to really, truly working hard to find a satisfying answer.
And the downside to that? We never experience the joy of a hard-fought discovery.
And that's one of the coolest things in life.
Hence, my love of this quote.