From: Joerg Arndt <arndt@jjj.de>
As for the test in general, I strongly believe that these things are part of education in the broader sense. Thinking about ill-posed problems is an important skill,
... it is considered part of intelligence ...
especially in math.
erm, of all things, shouldn't math (more so school math) rather be a shining example of clarity and unambiguity?
So many things should be shining examples! But no, I don't think that an education that represents math solely in that manner is beneficial. Students must learn to question problem statements, to look for ambiguity, to seek the clarity where it seems to be missing. If they believe that mathematics emanates flawlessly from oracles, then they will be reluctant to sully it with their own flawed intellects.
Actually, in written exams I detest ambiguity in questions, no matter what the topic is, at the very least in those "exact" sciences.
Written exams have too much tension associated with them to be useful to anyone but the instructor. I read today about a teacher's complaint that a textbook recommended giving elementary school students the assignment to "draw nobody". Personally, I think it is a terrific concept.
It appears to me that students silently assuming questions are unclear and have to be reinterpreted is a positive obstacle when it comes to math. Would you agree?
But so many questions are unclear that if a student does not realize that early on, success is impossible. Many seemingly fundamental questions are unclear. Of course, a large dose of contradictions and errors in instruction would be simply frustrating, and I am not advocating bad instruction as a goal. But, I think that some amount of "think about what this might mean" is a good thing, I recommend embracing the occasional error in homework assignments with intellectual gusto rather than contempt. In 7th grade our math teacher was irritated with the class for complaining about a math problem that involved the cost of a "night letter." We didn't know what it was, couldn't even guess. He told us to find the actual cost of such a thing by the next day. Our Western Union office got 35 calls about it, and they were as confused as the students, "night letters" having been eliminated years before. We all learned a valuable lesson. Mine was an eye-opening revelation about the kind of people who wrote our textbooks. They were probably ... OLD!! Hilarie