Also, is that true that most trades can be learned on the job without prior training? I thought you needed a decent amount of training to be a plumber, electrician, etc.
"The modern use of the term liberal arts consists of four areas: the natural sciences, social sciences, arts, and humanities."
So no, math is not "generally thought" to be part of the liberal arts.
Interesting.
One was almost entirely conceptual and provided a fantastic base with which to reason about the world. Everything was explained completely without math and then a little bit of math (usually no higher than basic algebra) was used to describe what we had just developed to fulfill basic requirements of the curriculum. People had wonderful conversations about how things worked and understanding was developed from observation and intuition.
The other was almost completely the opposite direction and calculus based. I often found errors in the application of math and reasoning about the subject. There was a moment where the teacher couldn't be convinced that something he said was wrong because of the math he was looking at. Years later, in a college Physics course, a similar core concept was covered and I was internally vindicated.
Einstein/Feynman were known to be highly conceptual and the math was often worked out after a thought experiment. A famous quote by Einstein, "Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater."
It all depends on how it is taught.
All of that being said, Mathematics is an excellent tool to sharpen ones ability to reason.
Academic areas that are associated with the term liberal arts include:
Life sciences (biology, ecology, neuroscience)
Physical science (physics, astronomy, chemistry, physical geography)
Logic, mathematics, statistics, computer science
Philosophy
History
Social science (anthropology, economics, human geography, linguistics, political science, jurisprudence, psychology, and sociology)
Creative arts (fine arts, music, performing arts, literature)
is something lost when someone learns about propositional logic and set theory without learning about the vienna circle and logical positivism? yes. does it matter very much practically? probably not, and stem people who are interested in that kind of thing can probably pick it up on their own.
I hated my humanities courses all through middle and high school and college. I took as many advanced math/science courses as my high school had. I graduated from a well-regarded technical university.
My humanities courses have probably had more positive impact on my career earnings than my tech courses. I feel like I should find my old English teachers and apologize to them.
Students probably shouldn't be falling hard on one side or the other any earlier than they already do lest even more of them believe they are completely unrelated.
Be able to write well to communicate your ideas clearly and persuade people to your position.
Be able to apply math to a variety of practical problems.
I think that prepares you to specialize in any field later.
I think the complaint from the left is that minorities don't end up in the higher math offerings because they are either not offered at certain schools or, for whatever reason, unattractive to those students. That's the problem that needs to be fixed. Whether any public school can do that is questionable.
A neighboring district has a similar school geared towards Healthcare.
These schools obviously teach all necessary subjects but have more advanced classes geared towards those subjects than your average school would have.
We've got molten lava in our mouths that we can neither spit nor swallow.