My new favorite game is trying to classify math mistakes. (See: Classifying Math Mistakes)

Right now, I see three big categories of mistakes:

- Mistakes Due To Limited Applicability of Models
- Mistakes Due To Applying Properties of a Familiar Model in an Less Familiar Situation
- Mistakes Due to Quickly Associating Something In Place Of Another

I think this is pretty clearly an example of the third category. The student’s brain was working hard, and they swapped the 10 and the x.

These sorts of mistakes are interesting to me because I think a lot of teachers see these and say, “*Oy, this student thinks that you can just swap out the x with the angle.*” Or others would say, “*Oy, this student has no conceptual understanding of trigonometry*.”

Nah. This kid needs more practice with the Law of Sines so that you’ve got enough brain power available to pay attention to all the moving parts while you’re trying to solve the problem.

There’s something else that’s interesting about these associational errors, and it’s about the associations that students make. Isn’t it interesting that the x*sin(10) is more familiar to this student than 10*sin(x)? Maybe this also points to the need for more practice that mixes up missing angle and missing sides Law of Sines problems?