So I was listening to Hamilton when this struck me the other day. They make references to going to college and getting their degrees, and it for me thinking how would college from then compare to now. As well as lower grades like secondary and elementary schools, to what extent were they around? Or was it mostly private home tutors. I haven’t been able to find that much info saying that far back so I thought maybe the fine people of reddit could enlighten me.
I would be delighted and honored to enlighten you! I've written about this topic in response to a number of other questions, so I'll be pulling from, and linking out, to those answers.
Frst things first. The modern structure of 8 years of elementary/grammar + 4 years of high school + 2, 4, or 6 years of college for most young people is relatively new - we're talking 1960's new. Two hundreds years previously, in the 1760s and 1770s when many of the founders were young, the entire system looked and functioned very differently.
The colleges referenced in Hamilton are known as the Colonial Colleges. They were:
One of the most important things to know about the colleges is that the average age at most of the schools was 15 or 16. In other words, they functioned very much like an exclusive private boy's boarding school of today. (It's not an exact parallel but it works as a loose analogy.)
In order to get in, a young man had to do a lot of memorizing. Girls simply didn't attend - it wasn't they they applied and were turned away, but rather, the things society felt girls needed to know couldn't be found in a college. Instead, college was a place for the sons of men in power (which is to say white) what they needed to learn to in order to become men in power. Answers to What was the college admission process like in colonial America provides more context around the specifics of the admissions process. All students and professors (sometimes called tutors) were white. Many of the colleges used enslaved people to keep things running for the young men, all benefited in one way or another from chattel slavery.
One similarity between then and now is what's known as the liberal arts curriculum. In effect, a liberal arts curriculum is about exposing the learner to a broad range of topics and content in order to develop their critical thinking skills. The main difference is back then, students followed a course of study known as "classical." From a question about history class in America:
Until the mid-1800's or so, the purpose of formal education in these United States was mostly about providing the sons of those with access to power (which is to say white men) the knowledge base common among those with access to power. The curriculum, known as Classical, focused on Greek, Latin, logic, rhetoric, some math, and some sciences. They learned Latin, not because it was useful [in a practical sense], but because smart men knew Greek, Latin, etc. Studying history, English literature, and modern languages like French and Spanish were seen as less necessary and usually not a part of formal education. This isn't to say the boys wouldn't learn about history or read literature, rather that, in the hierarchy of what teachers and tutors were responsible for teaching, they were low priority. In effect, history was taught with broad strokes, focusing on Great Men and the things they did.
Since a shift in the late 1800's or so, schools have provided a modern liberal arts curriculum (English, Social Studies, Math, Science, PE, etc.) Another shift is around how adults frame the purpose of education. Back in the Colonial era, the prevailing belief was that learning hard things made one smart. Which is why Latin and Greek were so popular - learning a dead language is hard work. So, the goal was basically to build one's brain muscles and make social connections.
In this answer to a question about the evolution of America education, I get into the system for younger children in that era. Suffice to say, it was a hodge podge messy system.
Over time, American adults came to see school as a place every tax payer should support so children could learn to be a critical thinker and an American. What content they studied was important, but not as important as what they did while they were learning. A consequence of this is that American schools don't focus on career preparation - that's what college or trade school is for. This framework of a liberal arts education K-12 is stepped in the notion of meritocracy - that anyone in American can become anything if they just work hard enough.
In the Colonial era, the ones expected to become anything of note were white men. So, in effect the greatest difference between then and now is that for the Founders, formal education was for the few. In the modern era, it's about every child.