The purpose of school is to equip students on how to teach themselves, not to spoon feed them facts. For that reason, philosophy, rhetoric, logic, music, literature, and mathematics should be the priorities. Students who are well-versed in those areas WILL figure out the rest of it a million times faster than some kid who drilled on history, science, or other facts. Teach the kids how to study history, don't feed them names and dates. Teach the kids how to research, don't make them regurgitate someone else's results. Teach kids how to comprehend and analyze a text, don't make them read Homer and then regurgitate the events. Modern education is bullshit.
'Science' is also a method - one that took a long time to develop - and is fundamental in understanding the universe. It should also be included in your list of essentials...
I believe science as method would be included with philosophy, given the direct relationship between the two. I imagine in a proper school, there would be a "philosophy of science" course of some sort, but it wouldn't look like the science courses we have today. Instead, it would be focused on allowing students to pursue research projects, letting them learn a baseline of information on a topic, propose a project, and then do their own research and analysis. The problem is that today, they are given textbooks and told to memorize data they won't use and that they can find on Google in five minutes. It isn't teaching them science the process or asking them to engage in questioning the validity of one study over another, which is the true-to-life test of a person's understanding of science.
How great would it be for a kid to ask "why does rain slide off of leaves?" rather than be told all the different leaf shapes and tree types? How excellent would it be to have a kid spend time documenting all the different types of clouds and offer a hypothesis on their purposes rather than just telling them the formal names and descriptions? Teach them the process, don't make them memorize. No one ever said, "wow, I really am glad they taught me the difference between cumulus and cirrus clouds in middle school science."
You're kidding yourself if you think that this purpose doesn't also extend to the Universities. High School graduates don't design missile guidance systems, nor do they work with FBI to break TOR, etc.
This was probably the biggest demotivating factor in school. Trying to force feed me a bunch of biology terms for every species isn't going to help me learn biology. There is little purpose in memorizing a bunch of random subjective names that people named things.
>We are students of words: we are shut up in schools, and colleges, and recitation -rooms, for ten or fifteen years, and come out at last with a bag of wind, a memory of words, and do not know a thing.
