The upshot for this is that the benefit is as much for the student doing the teaching as the one doing the learning. Teaching has a much greater effect on _retention_ than listening reading or even doing, which is the majority determinant underlying the primary school curriculum.
There are a whole host of secondary benefits to this (as well as lots of logistical challenges): the students are doing something useful, teaching, and we pay teachers if you wanted to expend budget there I suspect it would have great effect, as would any other form of ~~bribery~~, I mean, incentivisation; socialising, especially if you have the teaching being done across different classes (which you would want to do because you want the teacher to know more than the student).
Projectors, videos, computers, tablets, calculators, are all completely useless in teaching math.
I have a great deal of respect for you. Your math skills are much greater than my own. But you have stretched your statement too far. Flash cards can be very helpful in teaching math. Timed tests for math facts can be very helpful. Both of these can be facilitated with computers or tablets. Animations can be a very useful instructional tool. Even taking a picture of the chalk on the blackboard and putting it online can help students (and possibly helpful parents) review the in-class lecture from home while they do their homework.
I don't dismiss your overall point, but don't be too flippant. A video of the lecture can be very helpful.
What works:
1. having a lecture on a chalkboard
2. taking notes by hand. Yes, by hand. Something about the act of writing it by hand fixes it in my brain
3. using pencil and paper to do the problems.
4. and what really works is giving an in-person lecture on how to do it
What doesn't work:
1. everything else
I've watched many instructional videos. Poof, none of it sticks. I've audited classes. Poof, none of it sticks, because I didn't do the homework.
I've never known anyone who learned arithmetic from a calculator.
It's like wanting to be strong. You have to do the work to get strong. There is no substitute.
There are visual learners out there. Being a visual learner doesn't mean you don't need to do the work, it means you typically need some visualization for things to click, and then you practice applying it like everyone else. Some people can even manage with just lectures.
This causes some students trouble in school because their needs may not be met by every teacher. It's especially worse if the student hasn't learned what their learning style is yet.
Learning Styles: VAK Doesn't Exist (Here's What Research Actually Shows)
https://www.structural-learning.com/post/learning-styles-myt...
Belief in Learning Styles Myth May Be Detrimental (by American Psychological Association)
https://www.apa.org/news/press/releases/2019/05/learning-sty...
I have difficulty believing that my learning style is uncommon. Consider trying to build muscle. There are techniques that are proven to work best. There are no individual "muscle building styles" that work better, unless the person has a disability.
And I don't believe that in general the kids in classes are mentally disabled.
Yes, I know about ADHD, autism, and dyslexia.
I think it's more of a motivation problem. Not all students are eager to learn. They may not be interested in the subject for whatever reason. It's hard to teach someone who isn't open to it. Learning styles can help bring some of those barriers down by shifting the material into a form that they are more open to.
The same applies to building muscle. Not everyone is self-motivated to do it. There are different ways to motivate people to work out. But in the end they all need to do the work/practice.
You have to do the exercises. But it might be beyond your ability to start doing them straight from the textbook. Crafted didactic material can walk you through initial exercises to the point where you have a theory of where to begin on another one. Or it can let you investigate a structure until you have an idea.
In your analogy, if you want to be able to bench 150 pounds, at some point you'll have to bench 150 pounds. But a nonconfigurable 150 pound weight isn't the best way to get there. You can have a set of weights that let you start with easier tasks. You can have a set of exercises that aren't bench pressing. Those things are helpful, and generally required.
The real problem beyond all this is that the educational spending goes to the wrong spots. If you ask me, teachers should be empowered to select their own curriculum using a budget and most of the rest of the money should go towards paid tutors, better teacher-student ratios, etc (and probably way fewer administrators). I am firmly convinced that a lot of kids act out because they can’t grasp the material, not in spite of it.
In the USA there are approximately 50 million students aged 5-18. If you paid for each student to get 1:1 attention one day a week, you would need one teacher per five students in schools that meet five days a week. Let's use that number because it reduces 50 million students nicely to 10 million teachers. Let's pay each teacher $70K/year. That would cost $700 billion per year.
The USA military spent $100 billion per year in Afghanistan.
If the USA provided the 1:1 attention only in 1st Grade and 3rd Grade, they could fund it with the same commitment they made in Afghanistan with a lot fewer deaths. The USA persisted in Afghanistan for 20 years. Shall we experiment with education for 10 years and see if we get a better result than we did in Afghanistan?
That 100 billion goes to a bunch of extremely well-connected businesses who fund lobbyists to make sure the USA continues expending munitions in a series of utterly pointless, futile, wars.