The Pure/Applied distinction is one that I loathe. It is the creative/mindless distinction that I care about. –Paul Lockhart
Many of my friends and family have asked me about today’s Op-Ed by Garfunkel and Mumford. I couldn’t get really excited about agreeing or disagreeing with it. In my very short experience, coming up with rich and engaging applications for teenagers isn’t any easier or harder than coming up with rich and engaging “pure” problems. MBP discussed part of the reason for this in his comment (“Let’s partition the world of course-spanning questions into the purely mathematical and applied mathematical questions…”). But to me, in the end, whether or not a student genuinely goes after a question comes down to whether or not the student makes the question her own. And I’m finding it slow going, as a beginner, to do what Lockhart describes in the same article cited above:
Look. A child will have only one real teacher in her life: herself! I see my role as not to train, but to inspire and to expose my students to a wide range of ideas and possibilities; to open up new windows. It is up to each of us to be students – to have zeal and interest, to practice, and to set and reach our own personal artistic and scientific goals. Children already know how to learn: you play around and have fun and struggle and figure it out for yourself. Grownups don’t need to hold infants up and move their legs for them to teach them to walk; kids walk when there is something interesting in the room that they want to get to. So a good teacher is someone who “puts interesting things in the room,” so to speak.
Whether the interesting things are mortgages or matrices doesn’t matter, if they are actually interesting.