Current high schooler in the US here. I feel that today the trend is definitely more towards looking things up as opposed to memorizing them. For example, in my chemistry class, we always got a periodic table (with weights) and were given things like Planck's constant. We did, however, have to memorize some of the more basic ones such as speed of light and Avogadro's number. With regards to math, all tests involving more than trivial amounts of math you get a calculator, so I have never even thought of memorizing logs or exponents.
"I don't know the answers because I do not need to clutter my head with the answers you seek. I hire smart young people from your schools who have memorized information(like the indians) that you think is intelligence. My job is to keep my head clear of such clutter and trivial facts so that I can think" Henry Ford
Or at least, it's attributed to Einstein. It's a common enough sentiment, though, I'm sure I've independently said similar things myself.
On the other hand, it can easily be taken too far. Sometimes a random factoid isn't just a random factoid, it's part of the scaffolding on which you hang your knowledge. If you have to go to your periodic table to look up things like "Carbon" and "Hydrogen" you're never gonna have an intuitive understanding of chemistry.
