Here’s a mistake from a trig class. Would the question be easier in a Geometry class?

Here’s my theory: teachers underestimate how weak most of our students’ knowledge is, and how weakly in transfers. In particular, this problem became twice as difficult as soon as it was offered in the context of a trig class, without carefully writing the right angle in there with the lil’ square.

Am I right? Wrong?

Thanks to the Uncanny Tina Cardone for the submission.

There’s a ton to comment on here. I doubt you’ll need much in the way of a prompt, but here goes: what mistakes are missing? You grade this test on Sunday; what does Monday’s class look like?

Thanks to Tina Cardone, who is not-so-slowly taking over this blog, for the submission.

What other mistakes would you expect to see from this problem? How do you teach so as to help students avoid these pitfalls?

Thanks to Tina Cardone for the submission.

What’s the fastest way to help this student?

Thanks to Nico for the submission.

Say something smart in the comments about why kids forget “little” things on problems.  Or, alternatively, disagree with the premise of my first question. (How’s that for a lousy prompt?)

Thanks to Mark Kingsbury for the submission!

What made this question hard for the student? How come they got it wrong? Why did the student get it wrong in this particular way?

Today’s submission comes from Tina Cardone, who blogs at Drawing On Math.

The proof above isn’t great. In the comments, take on any of the following questions (or any others):

1. Sometimes kids slap stuff together when they’re confused, and other times they’re substantively mistaken. Which is this, and what evidence supports your position?
2. How would you help this student recognize that the logic in his proof doesn’t flow?
3. What would your next steps be in working with this student? What sorts of problems would you ask him/her to solve?
4. From the picture above, what evidence of knowledge do we have?

This one is a little bit hard to read, so I’ve transcribed the student’s writing below the image.

What’s going on, and how could you help?