Let's then assume that we had unlimited funds, and could hire the best possible educational expert on a subject, perhaps the one who is best suited to write the textbook and lesson plans, to instead teach a single student directly, without any time or resource limits. What would the ideal course of study look like then?
Expanding upon this, here's my proposed research question: "If a curious, capable and motivated student has unlimited access to a kind, knowledgeable and motivated teacher, how should the relationship between the be structured to optimize the educational benefit?".
In particular, I'm interested in time allocation - how much time should the student spend studying per day? How much of that time should be spent with the teacher, how much on their own, how much with peers (with or without the teacher)? How much of the time with the teacher should be spent on the student listening to / watching the instructor, how much of that should be spent on the student asking questions, how much on the instructor watching the student tackle tasks and providing limited guidance? To what extent should the education be directed by the teacher, and to what extent by the student? And is there any framework that would guide both sides in this endeavor?
Are any of you familiar with studies on this and could perhaps direct me to some reading material? Any relevant research, or if possible, a suitable theoretical framework, or even just some good search keywords regarding this would be highly appreciated.
In particular, I'm interested in time allocation
When I homeschooled years ago, I read an article that indicated that a survey done by a parent of a typical school day at public school found that only one to two hours of the day were spent actually learning/studying. The rest was spent on roll call, lunch, recess, changing class rooms, etc.
At the same time, the state of California had several ways you could legally homeschool your children. One of those was "hire a tutor for three hours per say." Not eight. Just three.
Having homeschooled my sons for years, I can tell you that more than three hours a day of one-on-one instruction is not sustainable. It's too intense. It's too exhausting.
Eight hours a day of school only makes sense when you are splitting the time of the teacher between twenty or more students.
To what extent should the education be directed by the teacher, and to what extent by the student?
Homeschoolers often advocate for pursuing "child led learning." It generally works best to let the interests of the child direct things, if you really want to optimize for them soaking things up.
Though do be aware that you may need to place some limits and insist they learn certain things they don't really want to learn, especially if they have known disabilities. But it still is helpful to give them latitude, where possible, on how they learn those things.
Forced learning tends to not go over well.
No such thing. Perfection is the enemy of the good enough.
> assume that we had unlimited funds
No such thing. Lack of constraints hampers creativity and teaching is essentially a creative venture.
> some reading material?
Look under the subject of 'Pedagogy'.
You didn't mention the word so I assume you're not familiar with the discipline. No worries, that's why you're here. It's a technical subject, deep and wide.
All that said every student is different. And to answer your title question: IMHO Enthusiasm is the main key. I never learned anything from a teacher bored with their subject or just getting their paycheck.
Look at Adam Savage. That's the kind of patience, fluency with technicality in a subject, willingness to learn, and boundless naive enthusiasm you'll need to transmit with high bandwidth the lessons at hand.
The premise of the question is problematic. Most students aren't curious (in the absolute sense, maybe), capable, or motivated.
Those who are are hindered by the crurrent system because it is designed for students who are not, who are the majority.
One of the biggest challenges of teaching is precisely that. How do you make the student curious and motivated so they become capable.