- There is always a right answer
- There is only one way to do something
After a lot of work and practice, my kids are starting to see that math is not all about getting the answer and doing it the same way as everybody else. There are assumptions that are inherent in math, and estimating is a key skill. The importance is shifted from the answer and the method, to how well you can explain and justify your answer and method. It takes math out of the realm of numeracy, and puts in squarely in the linguistic realm. You have to explain, using math, why you think what you think. This also sits within a large circle of metacognitive understanding.
I would love to collect a large store of PDF Fermi problems to archive somewhere. If you have any, please send them along to firstname.lastname@example.org.