I once spent a long time trying to figure out, from first principles, what a perfect school should be. Then I went out to the library and researched the topic. Here's a summary:
Schools have some basic problems:
1.How to pay for the (perfect) school. 2. How to teach. 3. What to teach. 4. How to launch the (probably radical) institution in society.
The cost of reproducing information is nearly free, compared to the value of it. This indicates that theoretically. educations could cost nearly nothing.
Also, theoretically, a learning institution should be able to learn how to learn, in a virtuous circle that quickly optimizes the educational process.
As to what to teach: First teach how to learn, then teach how to do everything.
So, practically:
The major expense of schools are salaries. There is a solution. Students could be paid far lower amounts, by other students, to teach. This could be supplemented by a quality control system supervised by a certified teacher or two. However, the system should be stable even without certified watchdogs, because good students will only select and pay teachers that offer good service. Since they are on the spot, the students are the best judge of teachers, superior to parents or school-boards.
This automatically takes care of "how" because the extremely responsive market we just created will quickly research teaching techniques for each subject and optimize them to local conditions. Further, every junior student will be exposed to the best available teachers in the school- and imitate them to get a piece of the action, and then invest in better instruction. This is a powerful virtuous circle, because the incentives are running the right way, and selecting the right people, at high speed.
This structure is not only theoretical: It was pioneered for children by John Lancaster in the 1830's in his London poorhouse schools. The system was so effective at educating indigent students that it frightened the UK and New England states into producing public schools, to "prevent public nuisance." Lancaster's direct competition is what drove the initial creation of public schools in the English-speaking world, and arguably created the cheap human capital that kick-started the industrial revolution.
The fatal flaw of this system is that it cannot be used to warehouse children. If one tries to use it for this purpose, the incentives don't work properly, and the children learn nothing.
Of course, this is no surprise. Education has to be sought. However when I was 6, I was eager for school. The reality was a bitter disappointment.
J. Lancaster further made every appointed office of the school
(librarian, janitors, etc.) a student position, bid-for by students, paid
by fees from other students.
J. Lancaster also got to be very well off, because his system let a single adult run a school of up to a thousand children at a time.
This is also the original, traditional form of the University, before it was coopted by governments.
To economize on textbooks, lancaster schools kept textbooks in the library, which routinely rented sets of pages to students, who would share the pages by reading them from music stands.
Everyone agrees that a high teacher-to-student ratio is good. However, research in Kentucky by the state school board showed diminishing returns once class size got below 25 students. I interpret this as a decision to abandon some (admittedly small) percentage of students to maintain needed economies of scale.
Lancaster schools routinely achieved teacher-student ratios of 1 to 7, often as low as 1 to 3, while keeping tuition rates to about $240/year in 1991 dollars. Thus, they are _more_ humane than existing schools, as well as _less_ expensive (less than 10% of a church schools in my area, and less than 5% of the cost of public schools).
A related Kentucky study showed that self-paced mastery learning, in which one advances to the next unit only after mastering the present unit, is the single greatest improvement to conventional schools.
Lancaster schools automatically cause mastery learning. A student will not get students (gain income) until he or she has mastered a topic.
The average Lancaster graduate finished airthmetic, reading and writing courses (preparation for the high-paying, relatively healthy job of a clerk) in 3 years.
Uniforms are a traditional, inexpensive way of erasing social classes in school, and letting people concentrate more on their studies. One should use them.
Campuses are convenient but unnecessary, although meetings of some sort are essential. Many churches and public buildings have appropriate space that can be rented during week-days.
The only crucial item of furniture is a notebook. See below.
Now, that's how to pay for it, and how to do it.
What to teach? The least result we should accept are competent adults: No average person should be able to fail the instruction. If at all possible, we want polymaths, supremely competent people. So, first we want to teach people how to learn, right? After that, any following topical study will be immensely easier, so we can teach everything.
This is the theory of the traditional, ancient study of the liberal
arts. It started with the children's curriculum called the "trivium"
(yes, this is the root of the insult "trivial").
The trivium has three subjects, taught in sequence over several years: Grammar, then Logic, then Rhetoric.
Grammar studies how to understand languages, and includes reading, parsing and vocabulary. Once learned, it speeds up the next two stages. It should be learned intensively, so that the next two stages can be finished _quickly_.
In a more general sense, every subject has a grammar, and this must be learned before anything else. Human development seems to mirror this as well. Young children are very good at memorizing and repeating, and often delight in it.
An important part of grammar school is to learn terms: names of cities, geography, common plants and flowers, growing seasons, parts of mechanisms, etc. Another part is to learn counting.
Poverty schooling (including U.S. public schools) was traditionally limited to "Grammar" school, because (to paraphrase several founding documents) "Indigents have no need or use for higher learning, and their needs can best be met by the simplest education that will fit them to their work." (makes me mad just to think it!)
I think that the ancients tried to teach logic and rhetoric too young, because most people do not become able to reason until they are 13 or so. Therefore, the teachers would burn out, or become very harsh and try to teach reasoning by rote, a doomed process. However, they probably did this because parents could not afford extended schooling.
On the other hand, children learn languages _better_ than older people. So, we should start language instruction in kindergarten, using immersion, without formal grammar. Basically, fluent teachers speak simple, but real foreign language with our impressionable yound children.
The reading, grammar and arithmetic should start later, at 9 or even 10. 10 year-olds learn reading, writing and arithmetic ten or more times as fast as 6-year-olds. I also know that educators don't expect real literacy before a child is 9 or 10.
Logic teaches one how to think about facts, and also how to evaluate which facts are important. Aristotelian logic is _not_ repeat _not_ the same or even comparable to symbolic logic. Aristotelian logic teaches a large, memorizable set of valid forms of argument. This leads in an absolutely natural way from Grammar into Rhetoric, without a confusing detour into the foundations of mathematics. I also am aware of the technical defects of Aristotelian logic. At some point these should be explained.
After logic, Rhetoric would be taught. Rhetoric is the study of how to actually do things, gracefully. It cannot be started until one has mastered the grammar and logic of a field of study. Communication is a prerequisite for learning any other field. so traditionally Rhetoric is first taught as literary composition, poetry, oration and debate
There are general principles of rhetoric, now almost lost to modern people. The basic trick is to pick a good (or _best_) standard form for the subject at hand, then use it for the particular topic or activity at hand. This trick assures both a minimally competent treatment, and easy comprehension and constructive criticism by fellow practitioners.
The scholastically-accepted forms of any particular subject were chosen to maximize comprehension. completeness and accuracy, while minimizing the total amount of work for both the composer and audience of a work.
Good teachers applied rhetorical principles to _everything_. Not merely to written composition, oration or debate, but also to mathematical proof, business arrangements, art, music, architecture and engineering of all sorts, agronomy, gardening, and even management of servants (think about the subtle differences between butlers and bailifs). However, the details of these fields were left to "high school."
Just befor ethey graduate, after the primary school students have learned basic grammar, logic and rhetoric, then we teach them how to find and study each phase of a subject. This brief course should be repeated when people are 14, because some people won't have sufficiently developed reasoning abilities at the end of primary school.
In a subject's grammar, the basic skill is to use a library and social groups to get information, locating good sources, and eliminating poor ones. Also, one has no choice except to memorize new terms and their definitions. It's not hard to teach this.
In a subject's logic, most subjects have one or a few key pieces of logic. Once these are llearned, the rest of the subject can be understood as a hierarchal tree of proofs, information and examples. The right way to study a subject's logic is to take notes in both lectures and books, and then unify the notes in a hierarchy. One then fills in the logical holes in the tree by asking questions of an instructor or other social resource.
In a subject's rhetoric, one must actually do things, by memorizing and mastering the standard forms that a subject produces. Criticism from peers and the instructor is critical to improving one's form.
A modern grammar school also has to include prophylactic health education
(wash the germs off your hands, and drugs_can_ ruin_your_ life),
prophylactic moral education (it's _bad_ to steal, kill and destroy), and
physical education (Be strong!).
Why do I think it only takes two years to learn the trivium, and not the
3 of Lancaster?
1. We start later, with more mature kids. 2. The kids get modern food
and medicine, and 3. Summer vacations? No way! We don't live on farms
anymore.
Now, you're 12. You have decide: Do I want to bother with this education stuff, or cut to the chase, grow up and make money? _You_ should decide, because an education cannot be forced. It must be sought.
If you decide to get on with your life, then you start at trade-school, and in a couple years, at 14, you become an apprentice earning money in a _real_ job. Just before you're 14, you get the "how to study" course again, with an admonition to apply it to learning your trade for your whole life. In 4 more years, at 18, a motivated apprentice can become a skilled journeyman, well able to start a family. Best of all, you''ve only wasted 6 years of your life on a general education, and hey, everyone needs to read, write, figure, and talk to tourists, right?
Also, if the high school is private enterprise, at any age a late-bloomer like me could go back, risk the laughter, and get the education.
But, _you're_ 12, and say you don't feel done. You feel the intellectual adventure ahead. . . (oh 12-year olds can be so earnest, and cute, don't you think?)
Medieval high schools were customarily started by 10, and completed by 16. I think 12 and 18 make more sense because people become able to reason hypothetically (Piaget's term was "formal operational reasoning") at about 12.
Sociologists affirm that in mixed classes, young women talk and learn less than men. Therefore, I think high schools should be segregated by sex, so that people can do school, not sex, and so that even the most deferent and shy women can learn to be more than decorations and brood mares. I've met several shy women from segregated catholic high schools, and I was much more impressed with them than with shy women from coeducational schools. They were both more themselves, and more skilled. I also think that in the long term, they were happier.
Schools of course could sponsor social events, but I would even teach social graces in segregated classes, so a mistake could not be a social disaster.
In high school in the middle ages, people learned the "upper four" of the seven liberal arts, the quadrivium. In modern terms, these are "commerce", "mathematics", "science" and "art and artifice."
In each of these fields, one should theoretically learn the grammar, logic and rhetoric (literally the "trivia"), of _each field_, in _that_ order. There's no sense in learning how to learn, and then sabotaging the process, right? Well, medieval schools tended to leave carpentry out of their architecture classes, but we shouldn't.
For example, in commerce one would learn about the different types of products (commodities, manufactures, dry goods, perishables, real estate, services, etc) and businesses (producers, manufacturers, wholsalers, retailers, providers, and investors), that is, the grammar, and then learn the logic to making each combination profitable. Finally one would write business plans, and implement small businesses, the Rhetoric of commerce. (This sounds dry until you have to make payroll!)
It was traditional to teach the logic of a field by the socratic method, in which the teacher asks carefully considered questions to guide the students through the field's logic. In other words, the teacher would stand people in front of class until they actually thought accurately about the topic.
The socratic method seems to be the _only_ known method that reliably teaches people to reason. Read that again, because I looked very hard in my library research. The teacher cannot give facts, and a good teacher can quickly expose foolish thinking to a withering storm of questions, which of course helps people to avoid being fools in public, after graduation.
Generalists should not be crippled by ignorance about artifice. Our study should cover the science (grammar), design (logic) and practical construction and utlimate form (rhetoric) (the _trivia_) of every type of artifact, from personal belongings up to cities. I'd include architecture, industrial, mechanical, electronic and software design with hands-on courses in primal industrial arts like construction, foundry, metal shop, electronics, and programming, leading up to a mandatory course in systems engineering. All generalists assemble and diagnose systems.
Retired master craftsmen and engineers can often be recruited to teach the hands-on classes. They also know the most.
Of course, with the practical arts, come the fine arts. This is not an optional part of the program. A person that cannot draw, sing, dance, accompany themselves on an instrument, or write poetry is socially crippled when it is time to court or pursuade.
The science and math, well. It's scary. The real need is to get nontrivial physics ASAP. I would do two radical things: Teach a simple programming language in the first term. Then teach real physics using finite approximation in place of calculus.
Second, in the math I'd teach calculus using inifnitesimals, an approach that is now mathematically rigorous, and accessible to anyone with algebra. I _have_ (somewhere) a text book "Infinitesimal Calculus", and it's a slender amusing book, only 150 pages, and more complete than my door-stop from the university.
For learning purposes, my favorite programming language is an object-oriented FORTH with floating-point math and data structures. FORTH is an extensible language with a simple grammar, and a very simple internal structure. It leads one to the foundations of computing machinery by natural baby steps, something that no other programming language does. (It's also _terrible_ for commercial projects. I know this already. Please don't flame me! Engineering specialists can learn something commercial!)
Also, there _has_ to be physical education. Strong bodies make smart minds.
We also need specialties. The military/government courses need trivia
comprising history & geography (grammar). strategy (logic) and tactics
(rhetoric). Legal courses need trivia of history, philosophy and
oratory. Religious courses need hermeneutics, philosophy and homiletics.
In these days, we might also add medical and engineering courses, with
appropriate trivia.
It was also customary in a medieval high school to learn at least two languages, usually a scholastic or religious language and a commercial language. By starting languages with immersion in the primary school, in high school we can concentrate on Rhetoric, that is, accent, fluency, literature, composition and oratory. After 12 years of instruction, people ought to be fluent.
So the curricula has Art & artifice, 2 languages, math, science, business, a specialty, and PE. This seems intensive, but possible.
Ok, you're 18. You're a polymath: a physically-fit mathematician, scientist, artist and practical engineer, with a specialty, with the ability to run any type of business, and sell in a couple of languages, because you've been selling your skills for 10 years to a brutally practical market (other students in a Lancaster school). Now what?
Now you
1. Get apprenticed at a much higher level, the fast track to an executive
suite. Or
2. Go to university and get a specialized doctorate (no BA, MA, etc.
you've done that).
3. Marry and raise children (a high calling, I think, and not one to put
off)
4. Decompress for a year, traveling and fine-tuning your accents, then
reconsider 1..3
So, you just saved 6-10 years from a scholastic education in the U.S., and you're a better person for it.
And, you have a certified _liberal education_, at least as good as the finest education available.
Now, is this purely theoretical? No.
At personal (you want to get the education). You can pursue the references in a good library.
For your kids, homeschooling is legal in every U.S. state except Nebraska, and also in most countries that permit private schools. Many homeschoolers are pursuing programs as ambitious as this.
If you're more ambitious, and want to help others, start a private school. This will get almost every possible social cooperation if you can pursude an accreditation committee that students can teach. The first step is to get yourself accredited, and then to figure a plan that scales from the low-overhead home-schooling approach up to a university. Don't forget to develop a recruiting plan for teachers, and advertising for students.