Somewhat by accident, I decided I was going to make this year's batch of Pre-Cal students write their little fingers off. Mechanics are great and all, but can you reason? Can you explain? Can you defend an argument?
First, something rare on most math tests, some paragraph writing on the differences between the main trigonometric parent functions:
Not everyone wrote me quite the essay I was looking for, but lots of good things. I find these questions are a good way to see who pays attention to what. A lot of students will mirror your explanations (the ones citing infinity/negative infinity got that specifically from a discussion we had), or offer a new spin (vertical vs horizontal flow in the last one).
Some are more reluctant to play my game:
While it wasn't in a paragraph structure, I liked this one for the attention to detail in the diagram and the talking points breakdown. Bonus points for the use of the word "squiggly."
Earlier in the same assessment, I made them agree or disagree with some conclusions about the output of some inverse trig functions:
Let me validate your suspicions and tell you that no, not everyone churned such long discussions. Some were a little short and to the point. Others generalized a bit too much. When it comes to writing tasks, think about what you'd like the minimum to be, and add 3 sentences. There's always that subset that's going to undershoot. Providing a stretch goal will prevent you from getting frustrated when someone writes two words when you wanted a few sentences. No one was penalized for missing the 7-10 mark. I just wanted 5.
Any rumblings about having to write have disappeared. They expect it. One student even remarked after Test 1 "ok, now that I know you expect a lot of explaining, I'm going to adjust how I study."