[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.