precalc 7


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.

geom26 question


geom 26 4 geom 26 geom 26 3 (640x422) geom 26 2 (742x800)


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.

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?