The internet is eating your memory, but something better is taking its place
In the years since the world started going digital, one of the big changes has been that we don’t need to remember very much. Why risk forgetting a partner’s birthday or a dinner date with a close friend when you can commit the details to your computer, laptop, smartphone or tablet and get a reminder at the appropriate time?
Paul McCartney gave a useful insight into this in an interview over the summer. He claimed that back in the 1960s The Beatles may have written dozens of songs that were never released because he and John Lennon would forget the songs the following morning.
"We would write a song and just have to remember it. And there was always the risk that we’d just forget it. If the next morning you couldn’t remember it - it was gone."
How different to the way he records now then, when he can "form the thing, have it all finished, remember it all, go in pretty quickly and record it".
With technology now well ingratiated into our everyday life, researchers have been investigating the lasting impact that it is having on the way that we learn and remember information. Some research has suggested that our reliance on technology and the internet is leading to “digital amnesia”, where individuals are no longer able to retain information as a result of storing information on a digital device.
In one study, for example, 1,000 consumers aged 16 and over were asked about their use of technology. It found that 91 percent of them depended on the internet and digital devices as a tool for remembering. In another survey of 6000 people, the same study found that 71 percent of people could not remember their children’s phone numbers and 57 percent could not remember their work phone number. This suggests that relying on digital devices to remember information is impairing our own memory systems.
http://www.sciencealert.com/the-internet-is-eating-your-memory-but-something-better-is-taking-its-place
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Librarians honed skills and values that were incomplete in our classroom curriculum and were often missing at home. Improving our research skills was certainly important, but I think even simple things like appropriate care of a shared book carried over into respect for property, people and nature in adults. I look at today's throw-away, littering society and wonder how much time these people spent in libraries growing up.
I am way OT, but I do think librarians rock! 
[font color="navy" face="Verdana"]This, about "understanding patterns and how to apply that understanding," as well as being able to reason things out based on an underlying theme or principle - so very much more important than memorizing a load of facts for tests. Like you, I tested well as a result - I think because I was able to make accurate educated guesses when I hadn't actually memorized the answer to a question.
I lived in the library when I was young, too, always had my nose in one book or another - and my very first job was as a public library "aide," which was heaven on earth for me. 
[font color="navy" face="Verdana"]You're absolutely right that factual information is necessary and how to integrate/apply it is a critical skill. It's necessary in basic math, which is all most people ever use. Higher math beyond basic algebra and geometry is, in my view, more about learning logical thinking than memorizing a mathematical process of questionable use in everyday life.
Facts are also very necessary for learning one's own language or a foreign one - how to spell, conjugate, use proper grammar, etc. There are necessary facts that underlie the whole structure of a subject and need to be learned.
However, I think it can be very different in other subjects, like history and literature, for example. There, overall themes and interpretations are far more important than names and dates. Unless you're a history buff, who won which battle in what year is pretty useless, but the era, the part of the world, and why that particular war was fought are important for an overall understanding of history. The specific details can always be looked up if there's ever the need, but memorizing them just for a test is, imho, generally a waste of time and brain power.
Similarly, the overall theme and contextual interpretation of a great book are more important than the characters' names or specific plot twists. An understanding of literary devices is important for reading well, it's true ("I see what the author did there!"
, but not necessarily their names. (Thinking specifically of "The Jungle" here; I can't recall a single character's name or any particular literary devices used, but I vividly remember significant events, the reasons Sinclair wrote the novel, and the disappointingly selfish reaction from the public, most of whom completely missed the whole point of the book.)
So yes, facts are important, but critical thinking skills, powers of deduction, and, as you said, understanding patterns/relationships and the ability integrate information are more important.
That's what's lacking in this "teaching to the test" nonsense we're seeing so much of today. And that is why the internet is so useful - freeing up brain space for "what," "how," why," and patterns/trends/relationships, instead of just cluttering it up with details about "who," "when," and "where," which can always be accessed if needed.
