A reflection from the submitter:
I think this 10th grader is saying .174>.34>.5. I wonder what she would have concluded if she’d followed the directions and rounded to 3 decimal places? Many kids were tripped up by the .5, maybe she’d say they were increasing except the .5?
Do you agree with the submitter’s assessment? How do you help a student learning trigonometry nail this down?
I think it’s important to say something more subtle than “this kid doesn’t understand decimals.” One thing that this site has documented is that kids can understand something at 1:00 and then do something entirely different at 1:01. It’s best to see this not as a failure of decimal knowledge, but maybe a failure to use decimal knowledge in this situation. (Some people would say this kid’s knowledge of decimals in a certain context failed to transfer to this problem.) The difference is in how we respond. This kid probably doesn’t need the “basics” of decimals. We just need to make a connection to somewhere where she knows about decimals, I’m speculating.