In my famous Circle Of Power post, I described a strategy I used to teach some trigonometry that involved students doing a lot of measuring by hand. They had a ruler, a protractor, and a circle physically printed on some physical paper.
What if they had used a Geogebra applet instead? I could have whipped up a “drag the angle and measure the x- and y-coordinates” applet in 5 minutes, and saved the students 20 minutes each. The data in class would have been accurate to three decimal places instead of (generously) one. By a lot of objective measures, the computer would have been better.
When do you have students do work by hand?