Michael, thank you for your response to my question (complaint?) that students do not seem to understand that having to work for something is normal. (On July 30 you wrote : I would propose that one difficulty in the issues you raise has to do with the mathematics is performed by teachers and professors (and I use the word 'performed' advisedly). Very few students at the K-12 level get to see mathematics done at the board. What they see is the cleaned-up results of a canned computation (and let's assume the case in which the instructor has actually worked the problem out him/herself). Things at the university level are not often better until possibly a few upper division courses, but even there it is likely that the problems and proofs done in class by the instructor are canned.) Aside: How do you put in those <s on each line?
I am quite sure that for the students who are not simply looking for an excuse this is very accurate and, frankly, I had never even thought of it. I can learn math and I think I can teach it, but I could not create new mathematics if my degree depended on it! When I look back, I have never seen anyone create and struggle with math since I did not go beyond a BA level in mathematics (and my BA is in economics anyway).
Does anyone out there have any suggestions on how to illustrate that work is a normal and expected process and that not being able to "get it" the firs time does not indicate that the task is impossible? In the "real world" courses like auto mechanics, the teacher actually does have to help students solve problems without an answer key!