Excuse me if I'm misunderstanding your ideas here, but isn't this, almost bullet for bullet, exactly what Khan academy is doing?
Your inability to effectively communicate the kind of scale you had in mind might be because we don't actually know what the prerequisite tree looks like at that scale, and just finding out would be a major step forward for educational science.
It's also not clear that any unique dependency tree even exists at such a fine-grained scale, because there exist multiple different ways of accomplishing a goal. Feynman talked about this, when recounting the episode where he learned that he counted time by mental speech, whereas his friend counted time by watching a visualization of a tape with flowing numbers:
...By that experience Tukey and I discovered that what goes on in different people's heads when they think they're doing the same thing - something as simple as counting - is different for different people. And we discovered that you can externally and objectively test how the brain works: you don't have to ask a person how he counts and rely on his own observations of himself; instead, you observe what he can and can't do while he counts. The test is absolute. There's no way to beat it; no way to fake it.
It's natural to explain an idea in terms of what you already have in your head.
This is the beginning of a very good idea. Happily, many, many highly-competent educational researchers have had it already, and some have pursued it to a fair degree of success, particularly in constrained domain fields (think science, technology, engineering, maths, medicine). It certainly seems to be blooming as a field again these last 5-10 years.
Potentially-useful search terms include: intelligent tutoring systems, AI in Education, educational data mining.
One particularly-nifty system is the Pittsburgh Science of Learning Centre's Datashop, which is a shared, open repository of learner interactions with systems designed to teach along these lines. The mass of data there helps get evidence of what sequence of concepts actual learners find helpful, rather than what sequence teachers think they will.
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....
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.
A lot of being rational is about being able to admit that you made a mistake. Rationality is not about being good at shooting down the mistakes other people make.
My groundbreaking idea: make sure that students know A1…An before teaching them A.
I disagree.
Just getting a personal pet project is frequent advice for people who want to start to learn to program. Working on the project leads you to learn the things that are necessary to solve the problem.
You also should explain how this interacts with what you say about essay writing. To me it seems like you advocate two distinct ideas that sound reasonable on the surface without having thought deeply about how they interact with each other.
Uhm, both.
The main ideas of the article -- (1) you must teach the prerequisites first; (2) it could be useful to make an explicit "knowledge tree"; (3) you should test whether the knowledge was properly understood -- are good. But the ideas (1) and (3) are what almost every teacher already knows and does. So you're kinda reinventing the wheel here. It's worth mentioning it explicitly to people who already don't know. But those who teach, already do (which doesn't mean they always follow it; people compartmentalize).
Even the idea (2) is known on an intuitive level; most teachers would probably think about it as a linear sequence, not a directed acyclic graph; or at best case a very simple graph consiting of long linear parts. But that's because in a typical school, you teach linearly. To use the graph structure fully, you would have to allow each student to progress individually... but then you can't have in the same classroom, listening to the teacher. So the full use of the graph requires individual learning, which could be achieved by a web application, as you say. (And the Khan Academy already does this.)
So, the ideas are good, but you are trying to sell them as someth...
I read the first 1/3 of the post and then skimmed the rest, because I think that you yourself are "glossing over important bottlenecks".
As I see it, for you the main problem with education is that students don't learn effectively in schools and you try to treat this problem. However, you should be asking: how did this problem appear? What could be done to solve the real problems? And those are in fact more difficult questions and require much deeper changes than creating a dependency tree and applying it to the students.
Creating and following a ...
I work for an educational maths company and we are working on implementing a fine-grained Knowledge Graph as are a number of our competitors.
I can't see a government successfully implementing all of this by itself. Fortunately, intelligent online tutoring software has really taken off because of Khan Academy. Charter schools will be the first to structure their lessons to take advantage of the flexibility this software provides in terms of having students working at their own rates. Eventually, I imagine that educational departments will notice that this works and restructure themselves around this model too, but this will be a slow process.
I propose that we pool all of our resources and make a perfect educational web app.
Bad idea. Putting all resources in a single project is stupid. We want diversity.
It's especially bad because it means a single person can't focus on solving part of the problem in a way that actually pays his bills when all his efforts are focused on contributing to the one perfect educational web app.
A few weeks ago a somewhat similar idea came into my mind while thinking through resources I'd have liked to have and ways to improve education (I think what started me off was the way that many concepts taught in early parts of school turn out to be incorrect simplifications?). I dumped some extremely rough notes into my ideas file (at the end of this post), and mostly concluded that it was an immense project which would require many years of focus to become really useful, and unless it got a lot of momentum would easily stall. On the other hand, this kin...
These ideas are not exactly new but they aren't exactly trivial either. Why are there so many downvotes then? This community confuses me sometimes in their voting behaviour.
I agree with others that the Big Idea here is less exciting than adamzerner appears to think it is.
It seems plausible that learning prerequisites solidly first is a good technique. But it isn't obviously best and I don't see any evidence here that it is actually best. Another possibility is that actually it's best to be exposed informally to ideas before you have all the background to understand them completely, so that (a) they will be more familiar when you see them "properly" and (b) they will give a bit more context when learning the prerequi...
Metacademy already implements a dependency tree that starts at basic statistics and reaches to academic papers in machine learning.
However, if they don’t exist, students probably won’t have the incentive to learn.
Sudbury Valley student manage to learn without any deadlines. If you don't learn because you are curious and motivated to know something but because there's a deadline, you probably won't learn well.
I think that there are likely some problematic aspects to this idea. One is that the general "I learned X, therefore I can learn Y" seems really strongly applicable to all STEM-types of classes, but I think it would likely falter in English, History, and related subjects to some extent - for example, in history, there's a lot of problems trying to organize how and what to learn that mean making a simple graphlike structure seems problematic. All events have preceding events and resulting events necessary to place them in their proper context. You...
There is a saying that education is what remains after you forget almost everything you have been taught. Point is, you sort of described a process without stating what end goal you want to achieve.
I think the whole idea of having a centralized curriculum is flawed and holds education back from developing. Schools should be free to teach whatever they consider to be useful for students.
Diversity is good and if children in different schools learn different useful skills that benefits society as a whole as every student can go on to apply their skills.
If you get rid of the whole idea of a curriculum teachers are suddenly free to innovate.
Given the way the post is written I don't understand why you don't list the social aspect under the section "Where does our system fail us?"
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.