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.



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?

  • When you’re in class and the teacher is explaining A when you still don’t get, say A2 and A5.
  • When you’re in class and the teacher is explaining A, when she never thought to explain A2 and A5.
  • When you’re reading the textbook and you’re confused, but you don’t even know what child concepts you’re confused about.
  • When you memorize for the test/assignment instead of properly filling out your dependency tree.
  • When being too far ahead or behind the class leads to a lack of motivation.
  • When lack of interest in the material leads to lack of motivation.
  • When physical distractions divert your attention (tired, uncomfortable, hungry…).



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 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.



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 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.



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).



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.



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.

New Comment
88 comments, sorted by Click to highlight new comments since:
Some comments are truncated due to high volume. (⌘F to expand all)Change truncation settings

Excuse me if I'm misunderstanding your ideas here, but isn't this, almost bullet for bullet, exactly what Khan academy is doing?

2Adam Zerner
Khan Academy doesn't come close to executing the dependency tree thing thoroughly enough. There are a lot of concepts that are unexplained, and Khan Academy doesn't test to see what you know before teaching you. When I refer to the dependency tree, I mean for it to have concepts on a much smaller scale than the typical calculus, precalculus, algebra, trig etc. An even smaller scale than this. I apologize for not being able to effectively communicate the type of scale I'm trying to refer to. There are definitely some parallels with Sal's ideas though. For example, mastery based learning, learning from a web app, learning at your own pace and at your own convenience, and having smaller certificates. I'm not trying to "steal" his ideas or anything. I just see a huge bottleneck that is preventing progress (the absence of dependency tree driven education), and thought it'd be worth writing about.

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.

... (read more)
4Adam Zerner
Maybe, but consider how often in todays system a teacher or textbook doesn't explain something that they should. Even if the dependency tree wasn't perfect, it'd still be much much better than what we have today.
Possibly. But you were selling this as one of the most important things to focus on if we wish to improve education. Given the immense effort that this would require, it's massively unobvious that this would be the most cost-effective thing to concentrate on right now. I would put stuff like improving motivation by making the content of the teaching more relevant to people's daily lives, breaking down the artificial distinctions between subjects, applying the educational and motivational techniques that the makers of commercial videogames have developed, etc. etc. as things that were more useful to focus on at this moment. If the students are motivated enough, they can work out the problems themselves, even if not all of the inferential steps were completely explained.
It is one of the most important things and extremely cost effective Given enough data, the dependency tree can be inferred implicity from and we can also learn to accurately identify when a student doesn't understand a concept. I'm actually working on this exact problem right now
adamzerner said that he wanted a really fine-grained dependency map, at an even lower level than this. Are you also talking about such a level of fine-grainedness? I agree that dependency maps on the level of that map are likely to be cost-effective, it's the more fine-grained ones that I was skeptical of. If you are talking about an even lower level than the one displayed in that map, I'd love to hear more about it.
It is possible to detect correlations between questions (or even individual steps) and to implicitly determine skills at an even more fine grained level than that - given sufficient data. We aren't aiming to get that specific right at the moment - indeed, we mightn't have collected enough data yet to do that - but there's no reason why we shouldn't be able to do that Having tagged data is extremely useful for designing these kinds of algorithms, but we would only require a proportion of the data to be tagged. So it wouldn't be anywhere near as costly as you expect
Ohh, the Big Data approach. That makes sense, and also explains why it would be possible to do cost-effectively now when previous attempts haven't gotten very far. Not sure why I didn't think of that. Okay, formally retracting my skepticism.

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.

To add that keyword list: Adaptive learning, educational big data.
I am learning Math and Physics after a long break. I found putting together the sequence of things I need to learn has been quite difficult. Several times I found I had spent a lot of time on something that was not really needed. This is particularly the case with Math as a prerequisite for physics. The mathematicians seem to want you to learn a lot more Math than you need eg Rings, Category theory and Topology may be useful for physics at some stage. But not for me yet. Conversely I found that I was short on some unexpected topic once or twice eg Linear Algebra was in one case not listed as a prerequisite but would have been very useful. Others have commented on various difficulties in coming up with a single dependency graph. I do think you have underestimated the difficulties of this. Overall this post is a bunch of plausible ideas but in need of a) More research on the state of the art b) A test in a real learning situation. It is a cliche in the startup world that ideas are cheap, tested ideas with proof by execution are potentially far more valuable.
1Adam Zerner
Thanks a lot for the references!! I'll read up.
I've been thinking a lot about this topic as well. This comment is very helpful! Thank you!

Given that I'm already involved in the creation of similar system (, 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.... (read more)

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.
One of the problems with traditional high stakes testing is that it incentivizes almost the opposite. It causes teachers to focus on what is traditionally considered 'learning", but ignores learning in a practical sense: Making sure students can use their knowledge in the real world, and are motivated to do so. I'd argue that using your knowledge to make money is in fact a good test for learning. Do you have a suggestion for fixing the problem I mentioned that minimizes bureaucracy and provides proper incentives?
5Adam Zerner
Hey Matt, It's nice to hear from someone interested in education! I understand that dependency trees get fuzzy outside of things like math. My thinking behind it was basically that whenever I'm failing to learn something, the things preventing me are prerequisite pieces of information; doing a better job making sure the learner has the prerequisites would make learning more effective. So I think I should have been clearer: I think that it's impractical to really come up with a perfect dependency tree. My point really is that instruction always happens in a certain order, and that we could do a better job of choosing the order (when you teach what) by coming up with a useful dependency tree. The downside of requirements is clear: the required lessons might not be what is best for you to learn. However, if you don't require things, students may mistakenly forego opportunities to learn things that would be most beneficial for them (probably out of inexperience/immaturity). To me, this is a tricky trade-off and I'm not sure what the best way to handle it would be. My loose intuition is that there should be much less requirements than there currently are, but still enough where you'd explore all the basic subject fields. What do you think the tradeoffs are, and why do you think they're in favor of not standardizing? (I agree with what you said about having credentials for more specific skills, but there's still the question of whether or not to require students to have certain skills.) That makes sense, but all of the individuals you're studying probably went through some sort of schooling that had some sort of requirements for them. So (presumably) your research shows that at a certain point, it's best to focus your education rather than be well rounded. And there's also the question of whether getting focused prevents you from exploring your interests. I love that portfolio approach! And I agree that people often "understand" something, but completely fail to ap
Just because you have identified a real problem doesn't mean that the first solution you can think of is good.
0Adam Zerner
It wasn't the first solution I thought of. I've thought through many others, and this is the best I've got.
Then why do you prefer that solution to the others you thought of? Articulating reasons why one alternative is better than another usually leads to a deeper understanding of the alternatives.
0Adam Zerner
Sorry, I don't have time to do such a comprehensive write up.
I think that the approach I mentioned of tagging resources with skill prerequisites effectively does this, but rather it ends up creating several different branching dependency trees, rather than just one. Consider that if your goal was to "create a nuclear reactor", and you didn't know basic math, the system would have to be smart enough to suggest a learning resource that teaches addition before suggesting a learning resource that teaches advanced nuclear physics. The issue of finding the most efficient/useful dependency true is a separate, but important one. I think it's probably best left to machine learning rather than human intuition. There are actually few organizations out there doing quite a bit of work on this already, Knewton is the one that first springs to mind. I suspect my tendency to go towards no standards is a values/emotions based decision. I dislike the idea of one institution choosing the standards for everyone, as there's too much opportunity to use that power to push a particular individual's or group's agenda. However, the real answer here is that this needs to be tested in a lean manner, using randomized controlled trials. I have write ups for several systems of incentive's or requiring liberal arts education, which I plan to test with Docademy, using different groups. I think you're right, that when the children are younger, they're less likely to be skilled enough to generate profit. However, if you're tracking exactly from whom they learn, and exactly what prerequisites they needed to learn their subjects, it's possible to create a trickle down effect, so that the teacher who taught you addition when you were 4 gets a small stake in your project to build a nuclear reactor when you're 24. I also agree that less planning would motivate teachers more. I've volunteered and worked in schools for years, and this is a common complaint. I ultimately think that you need to both raise the economic incentives, and lower the disincentives. The
Hmm. I'm not sure that this is such a good idea, given that the motivation that one has for teaching seems to be strongly based on social rather than market motives, and introducing market incentives to a situation governed by social incentives has been known to just screw things up. For example, my best friend has a daughter, and I've been giving her various books and games that either I used to enjoy, or which feel like they might be fun and useful for learning a mathematical mindset. I do this out of a general desire for her to have fun with them, learn useful things, and come to love science. Now if you told me that I'd get a cut out of her future earnings, it seems quite possible that that notion would start dominating my thoughts whenever I thought of giving something to her, and I'd start thinking stuff like "well, I could buy her this board game, but it's kinda expensive and any individual game is unlikely to have a big impact by itself, so would it be a good investment? Probably not." And she'd be worse off as a result. It seems easy to imagine similar failure modes that would start cropping up once you encouraged teachers to, in effect, start thinking in terms of "how could I profit from this kid" rather than "what would be the best for this kid". For instance, they might focus all of their efforts on the kids who showed the most talent and were already the most likely to succeed. They could even actively try to encourage the low-talent kids to drop out, so that they'd have more time to focus on the more promising ones. Or they could encourage their students towards careers that generally cause people to be unhappy but pay well, or teach the students attitudes towards life that promoted a focus on money above all else. Or, like those Israeli parents who started being more late once a fine was introduced and they could thus pay off their guilt for being late, some of the teachers might start thinking, "well if this kid doesn't do well in life later on, I'
I think this is true, and it's something I have a lot about. What behaviors would this reward system actually incentivize? I figured there would be two strategies teachers could use to maximize profit. One would involve as you said, focusing on the top students and taking them under your wing, making sure YOU are the one who teaches them as much as possible. The other would be to instead focus on motivating and effectively teaching as many kids as humanly possible, regardless of their perceived potential, and simply playing the odds. Other possible strategies would involve apprenticeship, in which your apprentice's work would effectively pay for your retirement, or company training, in which even if an employee was not loyal, you could still make money from them after they left you. I figured that these strategies were close enough to how I would desire teaching to work anyway, that it was worth a shot. One downside would be that it would cause teachers to compete to teach kids, instead of working together to get the best learning outcome. ---------------------------------------- That being said,, there's a lot being taken for granted above, not the least of which is that people won't figure out some way to game the system. I'm open to split testing this approach, like I am with everything in Docademy. Do you( or any other commenter) know of any ideas to substantially increase the social incentives for teaching such that it could measurably change the turnover rate? I haven't hit upon any yet, but I'm open to any suggestions thrown my way.
I would guess that being a teacher is a lot more fun if you don't have to give students grades. Especially for someone who tries to be really fair grading seems to produce a lot of unnecessary work. As far as the system goes in Germany, I think we just pay our teachers a higher salary and we have a low turnover rate. It might be that simply paying every teacher a decent salary is the way to go.
Filling your taxes is a nontrival skill in a country like Germany. It's not taught in most German schools at all. Still most people succeed in filling their tax returns.
Hi Christian, I'm not sure how this is relevant, it may be that I'm just missing your point here. One thing that is a useful distinction to make here is that "school" in the classic sense of the word doesn't apply to the system I'm talking about. If you learn something such as doing taxes, either through formal means, or through informal means, the goal of this system is to be able to track that you learned that, and show others that you can use it in meaningful ways. Moreover, if you haven't learned it, the system should suggest efficient ways for you to do so.
The general argument is that you shouldn't engage in what Nassim Taleb calls teaching birds to fly. If you take a bunch of young doves and try to teach them to fly, you may pat yourself on the back when they indeed start flying. You might think that you are a great teacher because the doves actually fly. I was once at a Barcamp where a teacher talks about her troubles of teaching young student how to use the technology of a Wiki. She made a good argument that every adult should be able to operate a Wiki. Editing Wiki's is something I learned on the side when I had the need to do so. People learn to fill their taxes when they have a a need to do so. I think you want two things in an education system. One is project based learning. The second is good learning of basics that you need for higher level skills.
Still trying to connect this to your original comment. Can you give an example of where you think my system would be insufficient, and what alternative you're suggesting?
I think the part that I quoted suggests that you get a list of what skills companies require and then work through that list teaching all those skills. I think that's a bad idea. Yes, companies might want their employees to be able to use a Wiki. On the other hand you don't have to go out and specifically teach the skill.
I think we're in agreement here. My point there was that companies decide what skills they require for a position, and that if they decide to screen for generally useful skills such as rationality or self-control, this may give them a leg up on the competition (which would ultimately lead to every competitor screening for these same skills.) It was a response to azerners arguments for a standardized curriculum. I tend to think that screening for a skill that someone can learn in an hour (like a Wiki) will limit your options and lead to less options for candidates, but who knows. Perhaps screening being very specific would cause you to only get candidates who had specifically groomed themselves for your position,and were therefore more motivated than the usual. My point being that the free market will ultimately make these decisions and weed out what skills are useful to screen for, this system merely enables the companies to screen those skills n a more objective way than the traditional hiring process.
The interesting thing is that learning to use a Wiki isn't the kind of skill that a school teacher considers to be easily teachable in an hour to her average student. Seeing the plight of a teacher who tries to be modern and tech the kids to use modern technology has made me question the extend to which schools teach anything useful. Okay, I'm in agreement with letting the market decide which skills employers want to hire for.
I think that both of you are assuming an average computer-proficient person when making estimates of how hard it is for someone to learn to use a wiki. An average person in general, or an average computer-phobic person, could have a much harder time. E.g. one of my friends, who's definitely quite intelligent but has issues with computers, did eventually learn to use wikis, but not before three or four different people had tried to teach them to her. (Or possibly she did learn them on each occasion but then completely forgot about them in the intervening time - I'm fuzzy on the details.)

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.

And the rest of being rational is making sure that the future likelihood of making the same kind of mistake is as low as possible!
Yes, just because one recognizes a mistake doesn't mean that one has already updated.

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.

Mu: (I agree with both of you). 1. Make a dependency Map of topics. 2. Have students tackle projects and learn what they need along the way. 3. Teach students A1 before teaching them A. 3 requires 1. 3 is not necessarily optimal, since it still implies a set curriculum. IOW, teachers teaching to students instead of students learning what they need. 2 is made more efficient by 1. If I'm trying to learn how to do a high-level thing like build a machine learning algorithm, normally, schools would require me to take calculus and statistics courses beforehand, however, I could just learn what a gradient is (and all the pre-reqs for that like partial derivatives).

moved to Discussion (writing quality insufficient for Main)

4Adam Zerner
Meaning the ideas, or my ability to communicate them? Tell culture - hit me hard.

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... (read more)

Seeing a visual representation of that "tech tree" probably would. One thing lacking in school is a clear communication of the intended skills to master and progress towards that mastery. The tree would need to be able to be displayed at multiple levels of hierarchical composition. Anyone know what Khan Academy already has in this regard? Or other educational software? That really should have been his starting point - study what's already been done.
I am not doubting that seeing the visual representation of the "tech tree" would make some students somewhat more motivated. But I am thinking about many other things which make students unmotivated (such as: the student's parents are preparing for a divorce right now, and the student cannot focus on learning at school), so I doubt how many % of the total "unmotivation" can be fixed specifically by showing the students the "tech tree". 5%? I'm probably being too optimistic here. This. I don't know if they have other subjects than math processed in this way.
That Khan Academy tree is pretty demotivating for me, and it's actually less math than I know (it looks like it only goes up through derivatives in a more traditionally structured series of classes). Now imagine that there are similar, more comprehensive trees for every major field of knowledge. To truly face the fact that you will only ever be able to learn a tiny fraction of any given field is pretty depressing. Of course, this is partially a reflection of the scale at which the tree is made and the way it's presented, but motivation is not at all a sure thing.
First, if that reality depresses you, you need an attitude adjustment. I got a PhD in EE which taught me that neither I nor anyone else knows squat. That's just the way reality is. Second, the graph isn't enough without identifying levels of competency against some standard, which could be population statistics, or grade level. That's what's needed for education - realistic goals, and a way to track progress toward completing them. That should be sufficient for schooling. After that, experts could recommend material based on desired specialties.
In tough times, the advantage of habits of achievement and monitoring developed in good times should provide significant help, if not a guarantee of success, which I don't think anyone promises or expects.
Well, yes and no. There are methods (usually called within-class groups) that allow students to progress at different paces while being in the same classroom. These methods usually depend a lot on small-group instruction and peer helping. So no, they won't be simply listening to the teacher, at least not all at the same time.
-2Adam Zerner
Maybe, but probably at level 1, maybe level 2, but surely not level 3. I don't see anyone else emphasizing the importance of the dependency tree and of making sure that at a small enough level, students know the prerequisite information. At a small enough level, yes. But I don't think we'll really be able to understand this level well enough to use it. So I think that the idea is just something to keep in mind when thinking about how to motivate students. Not at all! If I thought that this could be done with 10 volunteers I'd be trying to do it right now. I think that this would need hundreds, probably thousands of people. Consequently, I think that the best thing I could be doing is making enough money to (help) pay for all of this, so I'm starting a startup:
When I was a student, teaching other students privately math, I automatically started explaining any topic by testing whether they understand the prerequisites. -- I started one step before the new topic, and if they failed the test, I backtracked another step before the failed test. I didn't have a complete map in my mind, but at each moment I simply thought: "what are the immediate prerequisities for this?". I doubt I was the first person to think about this. Does the fact that I don't remember anyone explaining this to me explicitly (before I came to university) make it somewhere between the levels 2 and 3? You know what all teachers do in summer, before the school year starts? They prepare the sequence in which they will explain the topics during the year. (At least if they teach for the first time, because later they usually reuse the stuff from the previous year.) As I said, they probably don't think about this as a "directed acyclic graph", but rather as a "linear sequence where some parts can be reordered" (because most of them are not computer science people). The idea that the topics have some prerequisites, and you need to explain them in the proper order, is out there at least for decades.
Let's just say American education isn't as good as Slovak.
I agree with Eliezer that this shouldn't be in Main, but I think your "ability to communicate" is fine.

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 ... (read more)

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.

1Adam Zerner
Good to hear!

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... (read more)

-1Adam Zerner
Absolutely. I think that it'll take hundreds, maybe thousands of people. And lots of money. So I'm starting a startup in order to make enough money to get this going. I thought about this, and I agree that it'd make more sense if there were only a few people working on the project. But I think that there'd be too much overlap in content, and it'd be too tough to create the system from what is currently available. So I think that execution would require producing content to avoid all of the bottlenecks. Yes, but that's separate from the web app (sorry, I should have made that more clear). Yes, bureaucracy sucks, but I think that if this web app was made, it'd be so clear that it's better that schools would have to adopt. I could start off by providing it to people to use for free, and showing results. It might be tougher to get things like rationality, social atmosphere, tutoring etc. implemented. I think that they're really important, so I'll have to brainstorm hard about how I could make that happen.
You plan to earn enough money to pay hundreds of people? It's not possible to do with high probability, and you have to be good enough to have even the small chance. A normal career may give better expected outcome, even though it won't give that rather small chance of getting rich. (Read Graham's essays, for example these two.)
-1Adam Zerner
1) I don't necessarily have to make enough money to pay for the whole thing. Just enough to do enough to get other people interested enough to do the same. 2) I think I've got a solid chance at getting rich. This is my specific argument, and this is the general one.
This is not particularly convincing. You should take into account the a priori improbability of this event, so that getting to a "solid chance" would require much more than evidence that merely improves the estimate. See also base rate fallacy and attribute substitution (e.g. the question you need to answer is "What is the probability of success?", but the question you end up answering might be "How good is my startup's pitch?").

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 think part of the reason is the reputation adamzerner has. I'm thinking in particular of this earlier post, that convinced me that adamzerner is a very irrational person. This initial bad impression probably influenced what people thought of this article.
Fundamental Attribution Error? The heuristic of being mindful of the word "is" seems useful here. Also, I read a lot of my old posts and cringe. If I saw a similar post by somebody other than myself, I would dismiss them as hopelessly irrational. Thus, I'm less quick about dismissing people as irrational. But, I do agree that his reputation probably has contributed to how well received his posts are.

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... (read more)

IMO, having a road map ahead, even if it is blurry, helps to organize the immediate details. The map ahead will be blurry of necessity, as you don't understand the details yet. What probably would help for motivation is to see what people can do with the knowledge you're trying to master - see what problems the knowledge will allow you to solve.

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.

These aren't necessarily mutually exclusive. You might be curious about something, but also e.g. constantly distracted by video games, with the deadline helping you to actually focus your effort and get started on the thing you're curious about.
I'm not aware of any research that says that intrinsic motivation is stronger than extrinsic motivation, so I would question your second sentence. However, your first sentence pretty much sums it up... why have the extrinsic motivation when the intrinsic works fine already?
I haven't said anything about strength of motivation. I have said something about learning. Learning is about finding meaning in patterns. That works much better when you are curious. Even if being curious doesn't increase the amount of time spent learning or the amount of focus you have during that time, it still builds a better fundament for learning in a way that produces lasting knowledge that you won't forget.
Makes sense, will have to think about it more.

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... (read more)

Link to "Good writing" is 410, deleted now.

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.

They are also free to teach e.g. young-Earth creationism. At least some degree of standardisation is beneficial, since it creates boundaries against worst excesses. Also, curriculum makes it easier for a beginning teacher to organise her classes, although this could also be arranged by having loose guidelines instead of strict curriculum.
There are many textbooks out there that are easily available for a teacher who wants to use them. A teacher doesn't need a central authority to tell him what to teach to be able to find resources. Not having the central authority even makes it easier for market participants to create textbooks that teacher want to use.
I actually agree with you on all points, but I think you are underestimating how overwhelming things can be for a teacher just beginning her career. Without any central curriculum a teacher has to inspect textbooks much more carefully in order to find a book that would suit her needs. It's a lot of extra work. This is a smaller problem in math and science teaching and a larger one at humanities and social sciences. This problem could be alleviated by having teacher education include classes where you get familiarised with different textbooks and different approaches to teaching your subject.
Teaching a teacher about different approaches of teaching his subject seems fairly straightforward for teacher education for myself. I once tried to learn something about reading by looking at what an academic journal has to say. It spoke about fancy terms like Heideggers notion of meaning. I'm well educated despite having spent a lot of time in school and do have an idea of what Heideggers notion of meaning happens to be. On the other hand it's useless for a teacher who wants to teach his students to read. Teachers education could simply switch to teach the actual practice of teaching instead of trying to teach fancy educational theories and the problem would be solved. I think that getting rid of curriculum provides a lot more benefits in the humanities and social sciences than it does in mathematics. To me it would make a lot of sense to teach students during humanities or social science classes nonviolent communication (NVC). It a fairly straightforward framework with decades of history. On the other hand I do know that your average high school teacher doesn't have the skills for teaching it, so it's impossible to just write it into a centralized curriculum. Berlin has 12 districts. Each of those has a democratic representation. While my sister was in school there was a political change that lead to the voting age for that particular democratic representation be lowered from 18 to 16 years. There were a lot of people in her class that could vote because they were 16 but not 18. A good political science teacher would have addressed that opportunity to actually teach how this kind democratic representation works. I use the term democratic representation because it's not a parliament because it can't make laws and I don't know whether there a term in English that directly translates the German word. Her teacher didn't because she was too busy teaching to the curriculum. Most of the stuff she taught the student will probably be forgotten after 5 years. She miss
Yes, there are costs to standardization. But there are also benefits. Standardizing the curriculum means that the work of preparing educational materials (such as textbooks) can be shared across many teachers. Students move between schools pretty often, and certainly they move between teachers within schools. Standardization makes it easier for students to move without getting completely lost. Standardization also allows easier assessment, which some people think is important. You might be right that we should give up on the idea of a standardized curriculum, but it's not the least bit obvious to me which way the cost-benefit tradeoff goes. It's not even obvious to me how we could test this. You'd have to have some curriculum-agnostic way to know how well the education system was working, and I don't know how to do that. Thoughts on how this could be tested?
You are right that I'm calling to a revolution that's not immediately obvious. Thank you for pointing that out. It might make sense for me to start a deeper project for making that case on a deeper level that mind produce an article.
Getting rid of a central curriculum would stop two teachers from using the same textbook. On the other hand it would make it easier for the people who write the textbook. The could simple write the textbook that they consider to be optimal for learning instead of having to focus on covering exactly what the specific curriculum of a school district or a particular state's education policy lays out. The people who write the textbook should decide what goes in it. Not a politician or bureaucrat that draws up a curriculum. If the textbook is good teachers are going to use it.
In the US, at the k-12 level, the school buys the textbook, not the teacher. The books are owned by the school, rented to the student, and used by several students over several years. Teachers turn over quickly, however, and so it would be quite costly if each time a new teacher starts teaching a course, the school has to buy a new set of books. The increased costs of producing textbooks for every preference show up as acquisition costs, and the schools are reluctant to pay those costs simply to satisfy the preferences of teachers who might not be there next year or who might change their minds.
A student can choose whether to go to school A or B. I'm not opposed to schools making decisions about what to teach at school level. It might be even good if it's general knowledge that students who go to school A get taught from the Bayesian statistics handbook while school B rather teaches math like calculus. Schools should be free to develop profiles of what they want to teach because of what they consider to be useful for students to learn. How much freedom a specific school gives individual teachers can be up to the school. I think that when a school makes a decision to buy a particular textbook it has a lot to do with what kind of textbook the teachers at that school find helpful. I think that if a school buys textbooks based on what a bureaucrat thinks instead of based on what the teachers who interact with the students on a direct basis think, that's bad for education.

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?"

I think the dependency tree should at least in part be derivable from the data in Cyc.