In engineering, they have a term called "reinventing the wheel", which means wasting time re-engineering a problem that has already been solved. An addendum to that is "reinventing the wheel wrong" or "reinventing the wheel poorly", which is that not only are you wasting time working on a problem that has already been solved, you are also doing it poorly and coming up with a solution that is worse than what already exists.
I think the very concept of having "teachers", that is, a person in the same room as you who explains stuff to you that is already contained in a textbook, is inherently "reinventing the wheel".
Furthermore, it is also "reinventing the wheel poorly" for every teacher except for the very best teacher, or the top 1% or so of teachers, of a given topic. Another way to look at it is taking teaching material in a textbook or teacher's manual that is reviewed and vetted for mistakes and replacing it with mistake-prone improvisation.
My idea is to have an online-based teaching system of videos and interactive web pages based on competition. The concept is called "Teach or Die" which is similar to the web site "Funny or Die" in that the teaching materials that are not successful will be discarded, leaving only the most successful teaching materials.
Each class, such as Algebra 1, will be split into standardized lessons, which will be taught in a standardized period of time, from 1 day to a couple weeks, depending on what is appropriate for the subject matter. There will be a standardized test for each lesson. Multiple "teaching teams" will develop competing videos and/or interactive web pages for a particular lesson. These lessons will be shown to a random set of students spanning multiple schools and races and income levels. Some classes could have separate tracks (normal and advanced, for example) split into different standardized lessons with different standardized tests.
The standardized test results will be analyzed to see which lesson(s) are the most successful. "Success" of a lesson can be determined in multiple ways. The simplest method would be the mean standardized test result. It can also be fine-tuned to see which lesson(s) are the most successful for different categories of student, such as race, income level, learning style, etc. Or, rather than just looking at the mean, it could try to minimize the number of students that fail.
The test results can be used to fine-tune future iterations of a lesson developed by a specific "teaching team". For example, if one lesson did very well overall but had a particular weakness like a particular question that most of the students missed, they could attempt to correct this weakness and re-enter the lesson into the never-ending competition.
Teaching teams would be paid based on the standardized test results of the lesson and how much the lesson is used. They would continue to be paid as long as the lesson survives the never-ending competition. There would be some sort of pre-filtering by experts before showing the lesson to actual students, and "teaching teams" would not get paid unless the lesson passes this pre-filtering process. Ultimately, if this becomes a national program, some of the most successful "teaching teams" will become millionaires.
Some of the "teaching teams" will actually be individuals, such as hobbyists or professionals in the field of study (i.e. not necessarily teachers) that will maintain a small set of lessons. Some of them will be small or mid-sized companies that employ full-time computer animators and human psychology experts and entertainers (comedians, journalists, famous scientists, etc.), and will work on continuously improving their active lessons, finding new lessons to work on that they consider weak and that they can defeat in competition, creating new lessons for new classes, etc.
The "teach or die" lessons would be taught either via home schooling or in actual physical schools (public or private). The physical schools would not employ teachers in the traditional sense for the "teach or die" classes (which wouldn't have to be ALL of the classes), but instead would employ non-skilled "organizers" who would make sure the kids pay attention and take attendance and stuff like that. The school could also hire skilled tutors that would be available during a "study hall" period or could pay for an online tutoring service. The sum total of "organizers" and tutors would probably be less than the current number of teachers, since the "organizers" could watch multiple classrooms via cameras or larger classrooms, at least for older and calmer groups of kids.
If successful, the "teach or die" system could drastically improve the quality of education and provide equal opportunity to education, and at the same time drastically reduce the cost of education. This reduction of cost could be so immense (literally cut in half or more) that large supplementary projects could be implemented, such as round-the-clock free child care and recreational activities on school premises, universal free access to child psychologists, etc.
* Classes could be taught to different sets of students at different times, that way there is always a fresh set of test results to use as feedback for continuously improving the lessons. So, for example, there could be 12 sets of students each taught one month apart, thus allowing the "teaching teams" the remainder of the month to improve the lesson for the next set of students. This could also allow the students to be separated by birthday, thus eliminating the unfair advantage some students receive by being older compared to the other students in their grade due to the time of year of their birthday
* I think there is an unfair bias against using videos for teaching. I think this is due to propaganda fed to us as children by teachers who were trying to get disinterested students to do their schoolwork instead of watching TV for entertainment purposes. It is also based on cable TV historical or scientifically branded channels not really being educational, and containing cheap reality shows and conspiracy shows instead. Also, many videos shown in school were shown only because the regular teacher was absent thus reducing the likelihood of getting in trouble for not paying attention, often didn't have relevance to the class or weight on the student's grade, and often weren't always created with the goal of being shown in a classroom, all of which reduced their effectiveness. I think kids would quickly get used to learning effectively from videos rather than in-person teachers, and wouldn't screw around and refuse to pay attention like previous generations of students did when watching videos.
* The video lessons wouldn't have to be documentary-style, rather they could be video of a teacher writing on a chalkboard. Also, competing lessons could be of different formats, for example, a chalkboard lecture video vs. a video with animations and whiz-bang visual effects vs. an interactive web page vs. a combination of all of the above.
* Some of the lessons could involve homework
* Some of the standardized tests and homework could be turned in to the unskilled caretaker, who could digitize it to be graded remotely
* Some classes would be less amenable to this system and may still be taught by regular teachers as decided by the school.
* Some interactive learning, such as science experiments, could be done by part-time employees (similar to substitute teachers) or by employees that are full-time and normally serve as study-hall tutors
* The students wouldn't be able to ask questions during the lesson. This might superficially appear to be a large downside in the "teach or die" methodology, but if you think about the nature of a student asking a question in a class, it can either signify a) that particular student didn't understand, but most or all of the other students did, in which case you are wasting the other students time (to some degree, since they may gain some value from repetition, although that same repetition could be built into the lesson); or b) most or all of the students didn't understand, because maybe the teacher made a mistake or went too fast or something, which can be gradually eliminated in the iterative improvements of the "teach or die" methodology.
* Maybe the students could submit questions electronically to be used by the "teaching teams" to improve the lectures. And the tutors could provide feedback to the "teaching teams" as well.