I’m working with a new tutoring client, and therefore starting at the beginning in training her to stay engaged with the math rather than getting frustrated or trying to read the answer from my reactions to her guesses. The other night, I came up with a new metaphor to help her with this as she was trying to calculate the area of a circle section. I can’t believe I never thought of it before, it’s so obvious.

[N is visibly struggling to unify the geometric and algebraic information. I love it, I feel like I can literally see her brain growing, but she’s getting frustrated.]

Me: You’re going to grow from this.

N [skeptical]: Really?

Me: Yeah. You’re going to figure this out, and then you’re going to understand that you already had everything you need to figure it out. Have you seen Star Wars?

N: No, but I know it.

Me: You’re Luke, this is Vader. You face Vader and then you become a Jedi.

[Long pause while N thinks about the problem, punctuated by occasional exchanges like, “if I divide the circle area by $\theta$, does that give me the area of the wedge?” “I don’t know, make up numbers.”]

N: Oh! 360 divided by $\theta$ will give me the fraction of the circle that’s the wedge.

[4 or 5 second pause]

N: Right?

[N has evidently been watching my face intently for the last 4 or 5 seconds, trying to get external confirmation of her insight. When it isn’t forthcoming, she begins to doubt.]

Me: The reason I’ve been looking out the window is so you won’t try to get a cue off of my face. [Stands up] I’m going to do the more radical version of this and get out of your visual field. [Starts to head out of the room.]

N: You’re not going to tell me if I’m right?

Me: You’re trying to get me to fight Vader for you.