The scene: yesterday at my 4:30 tutee session.
The topic: functions.
The set-up: To CFU (teacher term for "Check For Understanding," I ask a lot of seemingly obvious questions. Well, obvious to you and me, but not necessarily to the student.
Me: So, when y=10, and x is something else, y is still 10. What do you think y is when x is 1?
Student: ::pauses to think (another teacher term! "Wait Time!" and I give A LOT of wait time to this kid:: x is 1?
Me: Yes. If x is 1, what is y. Remember that our function is y=10 now.
Student: Y is....ten?
Me: Yes! Why is y ten?
Student: Because the function rule says y=10.
Me: Correct. Now, if x is 100, what is y?
Me: Yes! What about if x is 1000?
Me: You got it!
Student: And if x is a million, y is....ten!
Me: That's right.
Student: Oh! Y is ALWAYS ten because y=10! I get it! If x is ten million, y is ten! If x is a gajillzion, y is ten! If x is a hundred thousand light years trillzilion, y is ten!
Me: Um, sure!
Lightbulb moments are great, aren't they? And yes, my student did actually say "trillzilion."