I spent an hour last night in the company of 8-year-old boys. (My oldest son had a Cub Scout meeting.) The discussion topic: safety, including fire safety, and what to do in case of an emergency.
One of the boys in the group got in a “mood”, and every question that was posed to him, he’d twist around into a more extreme predicament:
Leader: What should you do if your clothes catch on fire?
Scout: What if your FACE is on FIRE?!?!?
Leader: What if you and your friend are walking across a frozen pond, the ice breaks, and your friend falls in? What should you do first?
Scout: What if there’s a giant glacier, and they fall in, but they’re too deep down to reach? And you’re in the middle of no where, and you can’t go get help?
Leader: What should you do if your house is on fire?
Scout: What if part of the roof falls down, and you’re stuck underneath, and you’re UNCONSCIOUS! Then what do you do???
My reaction was “Hey, he’s thinking like a mathematician!” He knows the stock answer that is expected, and he’s asking what happens if we change the hypotheses, considering a related problem where the conclusion doesn’t follow. HE’S DOING MATH!!!!!!!!!!!!!!!
And then I realized that no, he isn’t, he’s just being an eight year old at a cub scout meeting.
I’d love if my students responded to my questions with phrases like “But what if we use fractions instead?”, or “But what if the coefficients are matricies? Can we still complete the square?” etc….
So the challenge, as we prep for our classes: find a way to ask questions with obvious answers, that will get students motivated to say “yeah yeah, but what about THIS situation?”, and aim to “lead them” (pushing rope comes to mind) toward the actual course content we want to explore.
If anyone has insights in designing lessons that exploit this inate human cussedness, I’d love to learn more.