Understand

School is an enemy of understanding, nothing is more pointless, unless the point is to foster mindlessness. It is pointless because even and especially the clever and curious kids are disinterested in the worthless thin watered down stew of standardized empirical knowledge they're filled with. It is pointless because kids are bored and feel repressed in many many classrooms. It is pointless because the bland information that is beaten into them as a reflex too rarely corroborates their individuality. Students might enjoy a school topic but any real interest is almost always investigated outside of the classroom. Which is the first problem.
The fucking Internet exists-- feeding kids standardized facts and not asking them to digest it but to poop out bullshit for a grade isn't worthwhile. An alternative:

Education NEEDS to put it on developing students to figure out every "fundamental" procedure they are taught and to figure it out for their selves. Giving kids times tables and theories and grammar as definites is an unimaginably stifling practice and near exclusively an American one. In my experience the U.S. teaching methods are almost across the board formatted like this: describe a procedure, provide examples, and have the kids practice it. And, in My experience, that seems to become the framework for how too many educated Americans live. Think about how much time you spent in school pointlessly repeating addition problems and carrying the one and borrowing the one -cheater tricks- ... And compare it to how much time you were encouraged to think about what that really represented, or told the real meaning. An alternative:

Personalization goddamit. No kids want to learn anything from school nearly as much as they want to learn things from the rest of their environment and they are completely justified. Because school classifies kids instead of letting them classify it. From the beginning a kid is called gate, seminar, proficient, above grade level, A,B,C......... But, what? is it AT ALL possible to quantify the learning experience? To call anything improvement when it should all be called development? Black and white is the imposition we assign to students. Good and bad. Instead, each learner should comprehensively personalize his/her intake and application-- this alone is the purpose of school.  Motivating kids with extrinsic rewards and grades has been seamlessly proven to decrease long-term interest in a topic and we need to stop it. So the most important thing (also trying to answer how to pique desire for learning/using logic and intuition) is to replace imposed ranks, imposed grades, with connections. Every kid is brought into a functioning, excelling state -lit on fire- by at least one activity. So whats important is to show students how connected and analogous everything is, find each kid's passion and transform the classroom into NOTHING MORE than a resource for furthering their connection with that passion. Only after doing this does a teacher have any right to impose ideas/books/theories that he thinks are important. And the way to add what a teacher deems important to what the kids deem important: customize it- make analogies between the reason that kid's passion exists and the reason that math,science,literature,specificbooks,specificequations,specificcschoolsofthought exist. If kids saw equality in this light, then passion for learning about their interest would translate to passion to learn more about anything. Followed ideally by critical thinking and metacognition development and ultimately understanding.