Quote Originally Posted by HoreTore View Post
Well, a problem can be diagnostic without it being a "problem solver"-question. Ie. the problem 0.4x0.3 will not show whether the student understands anything, while the problem 0.4x0.2 will show it.
When I want to see if someone can do a little practical mathematical thinking I usually ask them to calculate a simple square root. For exampl what is the square root of 2025? People who can do more than just use a calculator all go like well that has to end with 5 then. Hmmm...it's between 1600 and 2500, so if it is a natural number it should be 45. But it's scaring how few people come up with that easy solution. Some panic already by hearing the square root and a number higher than 100 in the same sentence.

It's quite sad if I look back to see how little I learned in high school, that I either didn't know already or was completely useless. Sadly I don't have the feeling I'm getting much smarter at college either. Well not from the classes I take. Thank god for it's library!