Why (she asked, rhetorically) is it okay for me to use guess-and-check when I’m solving a problem, but I hate to see my kids use it? I could make an argument that when I use guess-and-check, it’s at a much higher level, but they’re just grabbing numbers out of thin air (yeah, right).
I think my prejudice against guess-and-check comes from its being used too early in the process. It can too easily become just guess; if you don’t know the process, you can’t check your answer. That being said, I’m realizing that one of my most-often used problem-solving techniques is a form of guess-and-check.
This hit me the other day when I was working through some of the Discovering Geometry problems [I have got to see if Anita has the TE!]: I wanted to get some idea of how the problem worked, so I set up the problem with certain parameters, and the answer became obvious. Why am I not teaching this to my students?!?