Today in class I overheard, "I tried it logically at first and then I tried it mathematically." It made me laugh a little, cry a little, and I had to force back the teachery knee jerk reaction, "But math is logical!"
The statement says so much about how our students view math and math class. If math isn't logical then we are doing something wrong, but I guess we already knew that.
While the statement made me sad, was this a case of actions speaking louder than words? The students were doing exactly what they should be doing, talking and working out how to solve a problem. Can a teacher ask for more?