I gravitated toward those with exceptional academic backgrounds, which seemed like the right priority. They had stellar resumes, early career success (often in consulting, investment banking, or corporate America), and were driven to succeed. Yet such patently qualified people often proved hopeless in the world of innovation, and I couldn’t quite figure out why....So, there's your answer: education is to prepare you to excel at standardized tests. Unfortunately, or fortunately, life stops throwing standardized tests at you the minute you leave the schoolhouse.
When my son was in third grade, his science class was studying simple machines. With twenty bucks and a quick trip to Home Depot, we got everything needed to set up shop in the basement, and started playing around with boards, screws, and pulleys. One evening, we set out to design something that would let him lift a cinder block with his little finger. We came up with an approach that, I remarked in passing, he could use to lift his 250 lb. basketball coach. We laughed.
The next week, he came home from school discouraged: “I guess I’m not good at science.” He showed me his simple-machine test, which had blobs of red ink over the question “What simple machine would you use to lift a grown man?” His response was “a six-pulley system,” and included a sketch with pulleys, rope, and stick figures of a man and a child. While the design looked sound, there was a big red X across his answer with the terse note: “ -17. LEVER ! ! ”
After putting my Tiger Dad response behind me, I approached the teacher with a constructive suggestion: “Instead of asking which simple machine to use, why not ask students to come up with as many designs as possible?” The answer floored me. “Throughout school, these kids will need to take standardized tests. We need to prepare them properly. Open-ended questions can confuse them.”
If you want to learn to innovate, two excellent fields are history and philosophy, especially the history of philosophy. That's probably counter-intuitive: innovation is about the future, not what people did or thought in the past. However, while studying Medieval waterworks won't help you to innovate in the field of plumbing, it might be that you'll find there a concept they brought to bear that will prove to have an analogous application in the field in which you are innovating.
Likewise in the history of ideas generally, problems harmonize even when they are not strictly the same problem. As we were just discussing in the comments to this post about physics, one of the exciting new theories is really just an application of an ancient Greek concept -- atomism -- that was applied first to classical physics, and then to early Medieval theories about time.
They cite Aristotle as the origin point for his opponent's view, but Hogan’s instinct here is actually quite as old. He's arguing the atomist position, which comes up when you try to get a handle on the problems of how motion is possible in a continuum. This is Zeno stuff: if space is really infinitely divisible, then how can you traverse any distance given that you must first traverse an infinite series of divisions of that distance? It is impossible to get through an infinite sequence, so...This new atomism is really new, but it harmonizes with concepts that were deployed by both the Medievals and Ancients. It's an innovation, but a natural way to find it would be to read some very old thought. The problems aren't quite the same, but they're similar enough that the possible solutions align.
The atomist's position falls out of that naturally enough: well, what if there's not a continuum, but a structure made up of smallest-possible units? Then we just do them one at a time, and it's not an infinite number.
Aristotle's answer to Zeno wasn't that different, actually: he ends up arguing that there are no actual infinities, just potential ones. So, yes, theoretically (or even just conceptually) one could make all those divisions -- but they aren't actually made, so you don't have to traverse an infinite series.
The same thing came up years later when the Neoplatonists were trying to get a handle on the nature of time. It seems that time is also infinitely divisible, and it's most obvious unit -- now -- seems to be infinitely small. So one of the Neoplatonists -- Proclus, I think -- came up with the idea of 'time atoms' just as the earlier ancient Greek physicists had come up with the idea of atoms for space. It's a natural enough thing to think of, but that doesn't mean it's true.
Is education for that? So you can innovate better?
Well, no. Education finally isn't for anything. It's not instrumental: it's a realization of your basic nature as a human being. All men, Aristotle says at the opening of the Metaphysics, desire to know. We don't educate ourselves to pursue some goal. Education is the goal. We want to understand. We want it by nature.
I may pursue instrumental goals on the way toward that ultimate goal, but to learn and to understand is itself the goal. That's what education is, not what it's for. There are a few things in life that are the true ends: love, friendship, honor, and wisdom. Everything else is for them.