What does the student know? What’s the mistake? How would you help?

Here are two classic mistakes:

Whenever I see a mistake that recurs at all different levels, and with all different students, I wonder: what makes this mistake so attractive? What’s the misconception? And what can we do about it?

Say something smart in the comments, and then go check out this post from Fawn Nguyen.

What makes this idea so attractive to students? Why should it be true that $2^0=0$? How do you help them see the light?

What is going through this student’s brain? What would you say to the kid to help out?

Let me know if you’re having trouble reading today’s submission. If image quality continues to be a problem then I’ll experiment with typing the student work up.