Occasionally I’ve noticed I’m handicapping myself. I don’t let knowledge I know from different contexts seep in. I’ve got to solve the assignment problem the “proper way”.
If this was a problem I’d stumbled upon in the wild I would throw any tool I had at it. I’m not trying to solve this math question instead I’m performing a social ritual. I need to discharge obligation so I can say “I’ve tried” which then lets me read some fiction guilt free.
To compartmentalise is to keep different bits of knowledge from influencing each other.
Common sense contains a lot of knowledge. Couple that with some rough guesses and a bit of reasoning can get you really far.  Enrico Fermi was jokingly considered a magician because of the kinds of inferences he could make.
A back of the envelope calculation or fermi-question is great for cutting through some of these types of errors. What is the mass of the moon? 
I've also noticed this pattern when I'm talking about the results of a recent study.
Me: "a study showed facebook causes low mood".
friend: "how did they get that".
friend: "well if I was trying to show this, I'd try and find people who don't use facebook and give them happiness quizzes, maybe that's hard because most people use facebook. Hmm, maybe I'd get 1000 people and get half of them to stop using facebook for a month."
me: "... how did you do that?"
There's a little learned helplessness on my part here. It's as if "the conclusions" have been given to me by the authority that is scientists. eg: Turns out Science says facebook is bad.
It was nice for me to realise that studies are essays written by people who looked at some phenomena for a while. The smarter the person and the longer they looked the better, but people nonetheless.
 Carl Schulman has complained that people do not do enough fermi's coupled with wiki-look ups and googling. Research advice here.
 The mass of the moon is 7 x 10^22 kg. how'd you do it? can you get it from a different angle?
Street fighting mathematics is a wonderful course about generalised-fermi's. It has a beautifully silly introductory video. A promo reads: "No epsilons or deltas are harmed by taking this course"
The title is taken from a Feynman anecdote about Brazilian students guessing the teachers passwords