Given that I'm already involved in the creation of similar system (Docademy.com), I figure I've finally found a thread on here where I have something to contribute :).
On the Dependency Tree
First some thoughts on your concept of a dependency tree. I started out thinking this would be the way to go, but I quickly ran into the problem others have mentioned on this thread: There's no one dependency tree. When looking at concepts like basic math, it's easy to think so, but the concept falls apart when you try to come up with a dependency tree for World History, the dependencies depend on the individual teacher.
The elegant solution to this is to tag individual learning resources (such as a video or chapter) with dependencies. The system will never give you a learning resource that requires B1 to learn B2 if you don't know B1, but will serve up other learning resources that teach B2 WITHOUT needing an understanding of B1. This solves all the problem of your dependency tree solution, but has none of the down sides inherent in the rigidity of it.
On The Standardization of Education
I am also in the camp that the standardization of education is a net negative to society and the individual. My research shows that the most effective individuals are those who specialize in the things that they are good at, rather than trying to be well rounded.
However, that doesn't change the fact that there might be certain skills which would be generally good to have. In that case, once you've solved the problem of being able to measure each skill individually, it's trivial for companies and organizations to simply not accept people who don't have these general skills. This would work similar to how modern Applicant Tracking Systems work, but it would allow you to get much more fine grained with the skills, and would have the benefit of being in a standardized format, rather than trying to parse variously formatted resumes.
After that, the free market would take care of the rest. If a group of skills truly allowed people to be generally more effective, the companies that screened for these skills would outcompete the companies that did not, and eventually they would be generally required for someone who wanted to function in society.
On Standardized Tests
You correctly assume that it's important to be able to quickly identify if someone is good at a subject. However, the type of standardized tests you mention, those that can be easily parsed by a computer, are only appropriate for a small subset of skills. Consider the following examples:
Ultimately, what these examples show is that for many skills, knowing how to do them in a way that can be easily measured by a computer is different then being able to actually use them in the real world. Rather, a more effective way to quickly measure someone's merit in a particular skill would take a portfolio approach. Under each skill it would list:
On Motivation
The final problem you mentioned is motivation. You mentioned two problems in motivation
1 . Kids don't know their prerequisites when trying to understand a subject.
This is fixed with the method above.
2 . Kids don't connect what they're learning with what they can do with it.
If you accept my premise above, that education shouldn't be standardized, I think you've actually got this backwards. If you look into the school models that are more self-directed, such as Waldorf, Montesorri, or Sudbury, you'll see that the students don't go looking for something to learn, then figure out how they can use it. Rather, they choose a goal, a project, or an experiment, then learn the skills they need in order to accomplish or create it.
Therefore this ideal school would have a list of goals, projects, and experiments to work on, which would be tied to skills. Students could choose the goal they wanted to accomplish (or create their own), and the system would suggest learning resources that would teach them the necessary skills.
I'd also like to add some of the other issues I see with motivation that you didn't mention.
3 . The lecture method of learning is low immersion and a poor way to keep students engaged.
To fix this, the main role of teachers would be helping students through completing their actual projects, and the teaching would happen more informally, as part of helping them complete the project. If it was a more in-depth subject for which the student needed a book or lecture, the student could request that, but it would never be FORCED on them.
4 . There's absolutely no incentive for good teachers that motivate students to use their skills; they get paid the same as the bad teachers, and can use the same skills for other jobs which are much higher paying.
If students are free to choose their own projects, one would assume that some of those projects will be profit generating. To solve this problem, you would allow teachers a small stake in every project for which a student used their skill, as a bonus on top of their regular salary. This would incentive them to motivate the students to use the skills they teach.
Anyways, I pretty much live and breath this stuff, and would love to discuss it more with anyone who's interested. If you're seriously interested in pursuing a venture that brings into reality the concepts I've discussed above, and see the implications for things like meritocratic voting, disrupting education, and disrupting hiring, feel free to PM on here and we'll talk.
If students are free to choose their own projects, one would assume that some of those projects will be profit generating. To solve this problem, you would allow teachers a small stake in every project for which a student used their skill, as a bonus on top of their regular salary. This would incentive them to motivate the students to use the skills they teach.
I don't think it sets a good incentive, as it makes the teacher focus on getting students to do money making projects instead of the project that maximizes learning. It also creates a lot of complicated bureaucracy.
Problems
Problems have bottlenecks. To solve problems, you need to overcome each bottleneck. If you fail to overcome just one bottleneck, the problem will go unsolved, and your effort will have been fruitless.
In reality, it’s a little bit more complicated than that. Some bottlenecks are tighter than others, and some progress might leak through, but it usually isn’t anything notable.
Education
There is a lot wrong with education. Attempts are being made to improve it, but they’re glossing over important bottlenecks. Consequently, progress is slowly dripping through. I think that it’d be a better use of our time to take the time to think through each bottleneck, and how it can be addressed.
I have a theory of how we can overcome enough bottlenecks such that progress will fall through, instead of drip through.
Consider how we learn. Say that you want to learn parent concept A. To do this, it’ll require you to understand a bunch of other things first
My groundbreaking idea: make sure that students know A1…An before teaching them A.
The bottlenecks to understanding A are A1…An. Some of these bottlenecks are tighter than others, and in reality, there are constraints on our ability to teach, so it’s probably best to focus on the tighter bottlenecks. Regardless, this is the approach we’ll need to take if we want to truly change education.
How would this work?
1) Create a dependency tree.
2) Explain each cell in the tree.
3) Devise a test of understanding for each cell in the tree.
4) Teach accordingly.
Where does our system fail us?
My proposal
I propose that we pool all of our resources and make a perfect educational web app. It would have the dependency trees, have explanations for each cell in each tree, and have a test of understanding for each cell in each tree. It would test the user to establish what it is that he does and doesn’t know, and would proceed with lessons accordingly.
In other words, usage of this web app would be mastery-based: you’d only proceed to a parent concept when you’ve mastered the child concepts.
Motivation
Motivation would be another thing to optimize.
One way to do this would be to teach things to students at the right times. Lack of interest is often due to lack of understanding of child concepts, and thus lack of appreciation for the beauty and significance of a parent concept. By teaching things to students when they’re able to appreciate them, we could increase students’ motivation.
Another way to optimize motivation would be to do a better job of teaching students things that are useful to them (or things that are likely to be useful to them). In todays system, students are often times forced to memorize lots of details that are unlikely to ever be useful to them.
By making teaching more effective, I think motivation will naturally increase as well (it’ll eliminate the lack of motivation that comes with the frustration of bad teaching).
Pooling of resources
The pooling of resources to create this web app is analogous to how resources were pooled for Christopher Nolan to make a really cool movie. When you pool resources, a lot more becomes possible. When you don’t pool resources, the product often sucks. Imagine what would happen if you tried to reproduce Batman at a local high school. This is analogous to what we’re trying to do with education now.
How would this look?
I’m not quite sure. Technically, kids could just sit at home on their computers and work through the lessons that the web app gives them… but I sense that that wouldn’t be such a good idea. It’d probably be best to require kids to go to a “school-like institution”. Kids could work through the lessons by themselves, ask each other for help, work together on projects, compete with each other on projects etc.
Certificates
I envision that credentials would be certificate-based. You’d get smaller certificates that indicate that you have mastered a certain subject. Today, the credentials you get are for passing a grade, or passing a class, or getting a degree. They’re too big and inflexible. For example, maybe the plant unit in intro to biology isn’t necessary for you. Smaller certificates allow for more flexibility.
Deadlines
Deadlines are a tough issue. If they exist, there’s a possibility that you have to cram to meet the deadline, and cramming isn’t optimal for learning. However, if they don’t exist, students probably won’t have the incentive to learn. For this reason, I think that they probably do have to exist.
My first thought is that deadlines should be personalized. For example, if I moved 50 steps and the deadline was at 100 steps, the next deadline should be based on where I am now (step 50), not where the deadline was (step 100).
My second thought is that deadlines should be rather loose, because I think that flexibility and personalization are important, and that deadlines sacrifice those things.
My third thought, is that students should be given credit for going faster. In our one-size-fits-all system now, you can’t get credit for moving faster than your class. I think that if you want to work harder and make faster progress, you should be able to and you should be given credentials for the knowledge that you’ve acquired. Given the chance, I think that many students would do this. I think this would allow students to really thrive and pursue their interests.
Tutoring
I think that it’d be a good idea to require tutoring. Say, in order to get a certificate, after passing the tests, you’d have to tutor for x hours.
Tutoring helps you to master the concept, because having to explain something will expose the holes in your understanding. See The Feynman Technique.
Tutoring allows for social interaction, which is important.
Social Atmosphere
The social atmosphere in these “schools” would also be something to optimize. It's not something that people think too much about, but it has a huge impact on how people develop, and thus on how society develops.
I’m not sure exactly what would be best, but I have a few thoughts:
The idea of social value is horrible. In schools today, you grow up caring way too much about how you look, who you’re friends with, how athletic you are, how smart you are, how much success you have with the opposite sex… how “good” you are. This bleeds into our society, and does a lot to cause unhappiness. It should be avoided, if possible.
Relationships are based largely on repeated, unplanned interactions + an environment that encourages you to let your guard down. I think that schools should actively provide these situations to students, and should allow you to experience these situations with a variety of types of people (right now you only get these repeated, unplanned interactions with the cohort of students you happen to be with, which limits you in a lot of ways).
Rationality
I propose that rationality be a core part of the curriculum (the benefits of making people better at reasoning would trickle down into many aspects of life). I think that this should be done in two ways: the first is by teaching the ideas of rationality, and the second is by using them.
The ideas of rationality can be found right here. Some examples:
After the ideas are taught, they should be practiced. The best way that I could think of to do this is to have kids write and critique essays (writing is just thought on paper, and it’s often easier to argue in writing than it is in verbal conversation). Students could pick a topic that they want to talk about, make claims, and argue for them. And then they could read each others’ essays, and point out what they think are mistakes in each others’ reasoning (this should all be supervised by a teacher, who should probably be more of a benevolent dictator, and who should also contribute points to the discussions).
I think that some competition and social pressure could be useful too; maybe it’d be a good idea to divide students into classes, where the most insightful points are voted upon, and the number of mistakes committed would be tallied and posted.
Writing
Right now, essays in schools are a joke. No one takes them seriously. Students b.s. them, and teachers barely read them, and hardly give any feedback. And they’re also always on english literature, which sends a bad message to kids about what an essay really is. Good writing isn’t taught or practiced, and it should be.
Levels of Action
Certain levels of action have impacts that are orders of magnitude bigger than others. I think that improving education this much would be a high level action, and have many positive effects that’ll trickle down into many aspects of society. I’ll let you speculate on what they are.