Me: You’ve seen hermit crabs, right? They move from shell to shell throughout their lives. And it’s scary for them to leave their warm, safe shells behind. It makes them feel anxious and vulnerable, because their pink little crab bellies are exposed.
Student #1: Poor crabs!
Me: But they keep on moving. And do you know why?
Student #2: Because life is pain!
Me: It’s because that old shell could only take you so far. It may have felt like home, but the new shell is going to feel even better.
Student #1: It is?
Me: Yes! And that’s the way it is with you guys. You have this old way of thinking about graphs – as shapes, or curves. And it worked great before, but now it’s holding you back. You’ve got to start thinking about graphs as relationships between inputs and outputs. And for a while, while you’re making that change, you’re going to feel scared and vulnerable, just like the hermit crabs. But trust me, it’s worth it.
Student #3: Can we still go back to the old shell sometimes?
Me: Sure. But you’re going to love the new shell once you get used to it. You might not even want to go back.
Student #2: But it’s so safe here!
Student #3: I don’t want to leave, Mr. Orlin.
Me: Be brave, hermit crabs. Be brave!
All students: We’re just crabs! We’ll be helpless! Don’t make us do it!