What’s going on here? What’s the misconception? What is there to build on?
Thanks to Nathan Kraft for the submission. Click on the blue words to check out his blog and this blue word to follow his tweets.
This one is really interesting. We’ve got both a sample of student work, and on the left the student has crossed out 
Kid: [Raises hand.]
Teacher: “What’s up?”
Kid: “Are you looking for a 1 or, like, the number 1?”
What is the student’s question, and what does it reflect about what he knows and thinks? How would you help?
[The submission also comes with an answer, yielded by the teacher through further questioning, revealed in the comments.]
What’s something that interests you about this student’s work?
Another quality submission from John Weisenfeld.
How would you help this student become sensitive to this language?
Another quality submission from John Weisenfeld.
Would the student have made this mistake if she were just given 
Oh, and go check out Chris Robinson’s stuff, and go follow him on twitter.
What does the kid think the distributive property is?
It’s easy to say: “Well, I’d avoid this mistake in my class by teaching the distributive property correctly.” Well, what’s the wrong way to teach this thing, then? What’s the smartest possible way to teach this, and still end up with your kids making that mistake?
After you’re done writing an awesome comment to this post, go check out Josh Weisenfeld’s blog. He spotted and submitted this gem of a mistake.
Categories
Function Notation
How do you teach function notation? How would you help your students avoid this sort of mistake?
Categories
Lines Tangent to a Point
What does the student know? What doesn’t the student know yet?
How did this happen? How might you help?
Say something intelligent about this bit of student work.