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.
Great quote from Cantor. Thanks for sharing.
ReplyDelete"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."
Maybe I'm overly optimistic here, but doesn't Google on their phones just give us the opportunity to ask more meaningful questions? That's a challenge and an opportunity of course.
I love it when we can quote our math heroes back at the views so many people hold about what doing mathematics looks like. Now if we can only work on the "insane asylum" part ... :-)
ReplyDeleteGreat quote! Google may provide them with an answer but rarely will it give them the question! They need to know what to Google and therein lies the true beauty of the quote.
ReplyDeleteMost definitely--the internet is an amazing tool. I wouldn't have wanted to go through my own education without it.
ReplyDeleteHere's my hang-up/what I'm contemplating: how to we develop such curiosity in students that even when Google doesn't give them the answer, they continue to search for a solution to their question?
Hi Rebecka. It's so nice to see my favorite math quotes again and again as I peruse a few of this week's posts from NBI. Thank you for including Cantor's picture also. With Google, I'd have that open discussion with the kids, of how fast it is to access information (and Google is Google because a lot of math went into its search engine), but when the answer is given too quickly it robs us of thinking deeply, like you say, so our classroom culture is "never tell an answer," and I remind students often of this. I had a student just this morning sharing, but before he started, he asked, "Am I just sharing my thinking or the answer?"
ReplyDeleteThanks, Rebecka, and it's an honor for me to feature your post this week at http://fawnnguyen.com/2012/09/06/20120905.aspx
I didn't get that. Do you mean the question itself weights more than the answer? Like in political interviews sometimes posted on best writing websites?
ReplyDeleteHello. Thank you for your post.
ReplyDeleteI was recently asked: "can you do my homework for me?" devoted to famous mathematicians. So your post, you can say, is just in the subject ...
Georg Kantor is an authoritative mathematician who introduced the concepts of quantitative and ordinal numerals. About Cantor came a lot of publications, one of which was a publication in the book "The Creators of Mathematics" and a note in "The History of Mathematics." He founded the German Mathematical Society, and most of his scientific work is still used.
There is another famous statement by Georg Cantor on mathematics: "The essence of mathematics is in its freedom."
You are right when you want to develop children's curiosity. But the fact is that sometimes, not all the questions asked by them, you know the answer. And then, really, without the help of the Internet can not do ...
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