It really feels like we're on the cusp of a textbook similar to the Primer in Neal Stephenson's 'The Diamond Age: Or, A Young Lady's Illustrated Primer'.
As in, something that learns your interests and customizes to your tastes while still teaching. A textbook that is able to diagnose common misunderstandings from a set of wrong answers to a problem set and evolve its teaching methods.
If advertising networks have effectively personalized propaganda on Facebook and whatnot and games like The Walking Dead are able to change script based on popular choices made by all players, we should be able to apply the same technology to personalized learning at scale.
Hey! this looks like something within my wheelhouse. Let me know if you need help with content/design/development. I'd love to be a part of this story.
If you are referring the course content creation. Well, I have thought about it.
In the initial stages, No.
You would want to have control over the content to
1. Update / Iterate it faster
2. Sense of continuity when switching from one course to successive one.
One of the problem, I have personally felt is the abundance of video based courses for a single topic. And none whatsoever for a deeper topic.
When you jump from one video-based course to another, then you either feel there is a bit of overlap or a bit of skip of content. This is due to different university teaching style and syllabus.
Self-learning online today, basically feels a bit disorganized. You need to scourge through the entire internet to find good resources. A lot of people have created wonderful platforms ("awesome" repos, Learn-anything.xyz etc) to curate those resources and my experience has been opposite when I encounter these resources.
I need one good resource, not 10+ resources to learn about a topic. And when I do complete a course, I feel I am missing out by not completing other good resource. This might be only a personal experience though.
The D.R.Y. Principle I wrote in the website, basically means, you don't need to waste effort studying something you have already covered. The teaching style will be uniform. And you can scale deeply. Kind of a like an endless book that keeps on adding new updated things for you to learn more. It is easier when you are in charge of course creation.
That being said, all the Course Notebooks, will be available free for everyone. Anyone can read what Primer is trying to teach without spending a penny.
Also, I don't have a fixed plan. Everything is based on this hypothesis that Conversational Learning is better for self-studying than video based courses. Given we are able to prove by putting Computer Science Resources by the end of the year, then we can discuss about what would be the best way forward.
> You would want to have control over the content ...
Ahhh. Personally, I tend to think of OSS as not really taking away control of stuff, as more enabling interested people to collaborate and get involved.
eg surajs below seems like a potential candidate
That being said, it's not the only way to enable such collaboration. :)
Right now, I am focusing on shipping as soon as possible. After that, I would definitely be spending time figuring out how can I involve people who are interested.
But I must confess, I don't really fully understand what I am trying to do and also didn't realize that many people would be interested in Primer, though.
It has been like a little side-project that took over my life. So, I have put these little milestones to keep on track.
Thanks for your insight, Justin.
I would be more than happy to understand how to enable such collaboration.
If you can mail me your thoughts at admin[at]primerlabs.io, I would be grateful.
Wow, I checked out primerlabs.io and I'm not sure about the competition, but if non-existent or small this could be the next Facebook. I would like to learn more, I work in venture capital. Emma Muhleman - please touch base u can find me on LinkedIn
If you check the parent comment, I posted in reply to this comment.
> It really feels like we're on the cusp of a textbook similar to the Primer in Neal Stephenson's 'The Diamond Age: Or, A Young Lady's Illustrated Primer'.
I think you meant sarcastically for the part I wrote in the documentation.
What I meant was giving an accessible path for college level physics for anyone who wants to learn on their own. Currently video based courses and textbooks don't do that.
I believe curiosity driven learning is more efficient when learner is excited and resources are there to aid the learner.
It really feels like we're on the cusp of a textbook similar to the Primer in Neal Stephenson's 'The Diamond Age: Or, A Young Lady's Illustrated Primer'.
Feels to me like we're about as close to that as we are close to regrowing limbs. We've made baby steps.
For one thing, the illustrated primer created content from scratch -- content especially suited to the reader. Mathigon and things like it can only present you with content pre-created by humans.
Secondly, the illustrated primer had an expert understanding of human development, human psychology, and human biology. It used this understanding, along with incredible sensor technology, dynamically to create complex pedagogical plans and follow them by presenting exactly the content the reader needs at the time. At the moment we have only extremely rudimentary planning capabilities (if any), extremely rudimentary sensor/input capabilities (basically limited to what to user types in), and extremely rudimentary algorithms capable of only low order logic (if the user does x they probably want why) with almost no understanding of human psychology.
Not to say we're not making great strides. We're just a really long way off.
Edit: thirdly, The illustrated primer had an expert understanding of every topic it taught Nell. I think we're a long way off from any computer system that has an expert understanding of anything. Our computers can do calculus a lot faster than we can, but they don't understand it at a higher order level.
Writing textbooks is extremely time consuming... Seeing 'Mathematics - May 2019' in the list of tracks for Primer strikes me as un-serious. Likewise the single animation for Hyperbolic geometry in the 'non-euclidean geometry' page on mathigon.
something that learns your interests and customizes to your tastes
I have grave misgivings about that sort of thing. This approach is what leads to the Google and Facebook "filter bubbles" [1]. What I need is something that exposes me to different viewpoints, opposing viewpoints, presented in convincing ways to challenge me and help me to grow as a person. What I want is to learn about new ideas that would never have occurred to me before.
Traditional schools, much maligned, try to expose kids to books and other media they never would've bothered with otherwise. Yeah, kids for the most part reject this stuff and slog through until graduation, but some don't! Some kids find a new passion for Mozart or Shakespeare or calculus for that matter. Maybe we can predict interest in those subjects before exposing people to them, but I'm not confident about it. There are outliers everywhere and it's not fair to leave them out in the cold.
My point is that society strictly benefits if we made a ‘filter bubble’ that teaches calculus instead of antivaxx theories or Shakespeare instead of polical radicalization.
We’ve seen many, many examples of people picking up new concepts from their filter bubble, stuff like pizza-gate, that they wouldn’t have thought up on their own.
The same click-reward feedback algorithm can be applied when teaching more virtuous knowledge. The algorithms that create filter bubbles are disturbingly good at teaching, as in really disturbing and really proficient.
(And besides, let’s not pretend western and Confucian education aren’t indoctrination processes to some extent in their own right. Western education is predicated on building ‘virtuous’ citizens according to what I remember from the Socratic/Platonic dialogs. Also I feel like a dickhead for saying “according to the classics”.)
> The algorithms that create filter bubbles are disturbingly good at teaching
Are they really though? I have found that when I start probing people’s weird conspiracy theories picked up from blogs/facebook (or even more mainstream partisan disinformation picked up from newspaper op-eds or think tank whitepapers), they are quite shallow and unsophisticated, typically papering over gaping holes in basic knowledge.
“Teaching” a bunch of made up bullshit has much lower standards and requires a lot less effort (for both teacher and pupil) than teaching about complex real-world structures even to a level of basic competence, let alone serious expertise.
Recommendation engines don't teach, they provide opportunities. That could be useful as a learning approach, if layer on to a tech-tree /leveling learning path.
The analogy with conspiracies is flawed, pretty sure Google and Facebook don't first link to the basics of conspiracies, and then move on from there.
I’m pretty sure you can make the same case about things taught in the US about vast swathes of American history like Christopher Columbus, the Louisiana purchase, the pilgrims, etc.
I’m not even American but I’ve noticed the bar’s pretty low after living here for years.
On one hand, we probably shouldn’t be making pedagogical policy based on the most gullible in our society, but on the other, everyone is gullible when they’re young and many continue to be so afterwards.
I see it more from the point of view of it giving extra attention to stuff you didn't learn the first go.
For example some language learning apps already do this, they will show you phrases you have learnt before and if you get them wrong it will show them more often, if you get it right, it will show it less as it knows you know.
I concur. While I appreciate that math education at the elementary and high school level is easier to author and has more data points, where I think this approach would really shine is at the college level.
The main problem in math is that the higher level you reach, the fewer experts who exist or are willing to sit down 1:1 and tutor students.
I think an automated teaching system for analysis, writing proofs, number theory, etc is the next step in democratizing mathematics and science and bringing what is now college-level education down to high school.
IMO most college level math isn't difficult, but not missing a step in your understanding along the way to that level and the 'math anxiety' that's introduced along the way is the real hurdle to teaching. It creates a situation where autodidacts are most rewarded, so why don't we use technology to enable more people to become autodidacts?
Don't make the mistake of assuming the entire world is like you. Plenty of people struggle with lower level math. What makes you think the concepts are not difficult for them, and to blame only the teaching?
It's not either or. It's difficult to understand concepts (well) and it is also difficult to EXPLAIN concepts (well).
The better the explanation the easier it is to understand for more people. Whereas a bad explanation is something that assumes students understand something most of them don't.
It's really not a blame-game but more an impedance mismatch between the teacher and the students. IF you can have your own tutor the tutor can adjust their level of explanation just to you, but that is not economically feasible for most students. Therefore if automated AI-learning text-books can make progress in this direction it is great.
It may be that the biggest impact of AI will be not by having something smarter than us, but something that can teach more people to understand difficult concepts. In other words biggest impact of AI may be in education.
A thought: Most people who learn to play piano do so by having a piano-teacher whom they privately meet with once a week or so. Whereas this is not the convention for learning math. Maybe it could apply equally well for math as it does for learning to play piano.
Note that hiring a private piano teacher for every child in the country would also be a difficult proposition, politically / economically. Especially if we expected every person to reach the level of competence at music that we expect with numeracy/mathematics.
If we wanted to switch from the current classroom model to a private tutorial model, with the amount we currently spend per student on teachers, we could hire 1:1 tutors for only a few hours per week for each student, which would (a) not really be enough time to cover everything students are expected to learn in school, and (b) would then also leave huge amounts of time where the school wasn’t providing childcare service, which is one of its primary purposes.
However, just as upper middle class families can currently afford weekly private piano lessons or 1:1 sport coaching, you are right that they could likewise afford private math tutorials, and get better results than classroom instruction.
Right. It is impractical and probably wasteful for everybody to have their own private (human) tutor. But therefore I find the prospect of AI-based personal tutors intriguing. The concept of Artificial Intelligence making humans more intelligent in general. Even AI teaching itself.
For most people I'm certain the problem is to translate it into logic expressions they understand naturally.
It's the same as how most people fail to correctly apply basic logic when presented with arbitary problems and immediately succeed when presented with a human context of person A did X.
All these low level problems needs ways to help people to generalize their existing intuition.
So true. I recently began taking college math courses online for fun and the ALEKS system was great up to Pre-calc, but once I hit calculus, and only found video lecture-based courses, things became frustrating, half-clear and confusing.
Suddenly textbooks and multiple other sources became necessary to combat what you so cleverly called "math anxiety."
As a nerdy programmer and human computer interaction researcher, the fact that we are getting incredibly close to having all of the bits required (multitouch, extremely high pixel density screens, batteries/processors that merely add millimeters of thickness to it, recent advances in neural networks, fast enough wireless connectivity to stream high resolution interactive content, etc.) to build this technology is extremely exciting.
As someone who has been doing their best over the past ~10 years to understand how technology has interfaced with societies, cultures, political & business interests, etc. over human history - and all the ways that it has gone wrong - the first thing that I can think of is: who will make this "Young Lady's Primer", and what are their incentives for making it?
A Young Lady's Primer built by the Chinese Communist Party, or Facebook, or American evangelical Christians would be an extremely scary thing.
How can we nerd out on building the former while actively working against the latter?
> As someone who has been doing their best over the past ~10 years to understand how technology has interfaced with societies, cultures, political & business interests, etc. over human history - and all the ways that it has gone wrong
What a fascinating subject to look into! Any books you would recommend?
"Figuring out your interests" isn't the hard or useful part. The hard part is changing your default (usually harmful) interests into something useful and productive.
That involves lots of psychology and (yes) manipulation and coercion.
Some years ago I worked at a technology-oriented summer camp where I personally taught several bright young children to program. Minecraft mods were an incredibly popular project and a big driver of interest for many of the kids. Many of my counselor colleagues got into programming themselves modding Warcraft III and other games of that era. The absolute conversion rate may be low because the playerbase is so huge, but I think something like Minecraft is definitely the first (or zero-th) step in the journey of a lot of kids these days who become interested in technology and will later develop into the next generation of programmers & technologists.
I detected a pattern in an arithmetic sequence I was working on (we were adding six each time), so I went from 28 to 28+6. Apparently that was incorrect. When I protested that it was definitely another way of writing 34, the animated tutor then linked me to a video of a man suggesting that I always bubble C on multiple choice exams or something. When I noted that that wasn't really a response to my question, it linked me a youtube video about Einstein.
Kafka would be proud. Heaven forfend actual students encounter such teachers who don't know how addition works!
Another kafkaesque move: On the traveling salesman problem, I can choose 2 for the number of cities the truck must visit, making the complete graph bipartite. When I fill in the blank that the graph is thus bipartite, I'm told that's not quite right. The fundamental (unfixable?) problem here is that the software doesn't really understand graph theory. It's just a series of syntactic prompts to guess what the software is thinking. That's no way to teach.
I'm a maths teacher in Australia, and have been using a system over the past couple of years call "Maths Pathways" (it's only designed for the Australian Curriculum at this stage). I think of it as a personalised electronic text book, and after a bunch of diagnostic assessment, it provides the learner a choice of worksheets they are ready to learn next. Solves the problem of the massive disparity of ability levels that you get in a typical high school maths class. It totally doesn't replace the teacher in the classroom, but rather replaces the textbook (it's mostly worksheet-based, and not particularly interactive).
But one key point, both from using Maths Pathways, and as a teacher in general, is that a lot of learners need a human to guide them through some of the problems. This is usually for confidence reasons rather than anything else, and ideally we move to students who can take more control of their own learning and solve their own problems, but in reality, a lot of students (for a lot of reasons) will take a lot longer to get there. I'd be fascinated if a chatbot interaction could pull this off if it were 'human' enough, but I suspect not (though that's probably my own bias).
1. Grain of salt: contemporary research shows how learning has other facets that are also important like grit[1]
(i.e. repetitive application of hard work that has the right direction).
2. Contemporary research suggests that when learning a new concept is made "easier" using such methods its more efficient. On the contrary this is only the first step. Learning is better when its harder, but harder in a very specific sense: recall and mixing different concepts in tests spaced appropriately is really the hard work[2]
3. Contemporary research is also very much against bucketing learning as just only about "Learning Styles", like learning with music, play and pictures for the very same reason as above.
I also love the WWC: https://ies.ed.gov/ncee/wwc/ Its a much standardize way look at what educational techniques pass muster in the real world. I wonder what similar to mathigon is present in WWC's list.
Yes, this format makes it hard to ask very difficult questions, and the little chat bot rewarding the students with animated gifs of cartoon characters is a gimmick.
This is okay for teaching basic vocabulary and concepts, but seems to go no further than a pretty superficial exploration. Not much ingenuity or thinking is required from the students. Everything is pre-digested.
If a high school student were trying to learn about transformation geometry, working through Yaglom’s books of hard problems (Geometric Transformations, 4 thin volumes) would yield a much deeper understanding than going through https://mathigon.org/course/transformations-and-symmetry/tra...
I think you're focused on making good learners great (which I assume is the journey you experienced in school), but there's also a fairly large opportunity in helping every student get up to a certain baseline of "pretty good". A student who can't grasp how to plot a point isn't going to benefit from Geometric Transformations.
This is excellent. I'm not sure if this functionality is present, but one thing that would be cool would be some kind of dependency graph for knowledge. For example I can get through the euclidean geometry section without much knowledge of algebra and vice versa, but to understand trig I expect I would need to have taken both. It would be cool to be able to select trig and say "I already know euclidean geometry" and have it say "Then you need to take Algebra as a prerequisite"
Check out just about any large textbook company now. They are doing something similar (Carnegie Learning: Mathia). That said, I think Mathigon has a more user friendly, open, and engaging approach that I'd like to see take off.
One of the things I'm forever resentful for is the way my life was ruined by not learning things in a structured and rigorous way in childhood. Re-learning (and learning to learn) in adulthood is a pain and is never quite as good as doing it right the first time around.
Thankfully, my own kids are spared of this horror.
So you mean you've learnt the things the "edutainment" way when you were a child and are resentful for that? I just didn't learn the things in any way in childhood. There was no edutainment, the way teachers taught most of the things were next to impossible to actually understand (I had near-zero understanding of anything in math by the end of high school, only capable to use some formulae substituting) and all the practice was debilitatingly boring.
If Mathigon, BetterExplained, Ivan Savov's no-bullshit books and things like that existed when I was a child that would be a totally different story. I'm so glad my children are going to study with these and better things given.
I think the primary gain here is the examples. When learning the eps-delta or eps-N def of limits as a child in high school (15 or so yrs old) it took quite a few examples before I grokked it, despite the concept being quite simple.
When we go from 2 pairs of rabbits to 3 pairs of rabbits, we see a brother and sister rabbit mating to produce a pair of offsprings. This does not sound realistic and could also be disturbing to kids.
But for some reason, I have seen this example cited in many places. Why is this example so popular despite the implication of siblings mating while going from 2 to 3? Surely, we can come up with better illustrations if we try!
There is no help if I get something wrong. E.g. on the last question on https://mathigon.org/course/graphs-and-networks/eulers-formu... I did not understand the final section's explanation (I have no idea what "the topmost face of the polyhedra becomes the “outside”" is supposed to mean!). I tried entering a number into the last box and it was wrong. I entered another - wrong again. The "chat" thing just said "try 2" and it was right.
So why was it 2? There was no explanation or more help to explain that to me. I was just told to enter 2 and I did without anything to help me understand more, and then it let me continue.
It would be useful if, when someone gets the answers wrong once or twice, that some extra material appears, perhaps with more examples or more step-by-step explanation to help explain why. No need to show this to everyone - only show it if people are struggling or click on a "tell me more" type expandy thing.
As it was, I still do not know why the answer was 2 and I leave mystified and frustrated.
Otherwise its very nice - one or two weird moments where I had to click on "reveal all" on Firefox (appears to have not realised I scrolled?)
I used Khan Academy to complement my math and econ learning. While the concept of KA is good, with quality practical exercises, I found the videos very inefficient to learn most things.
I understand that it's step by step for the general audience, but KA applies this very slow, remedial structure to everything. The throughput was so bad I quit many series because of desperation.
Some MIT OCW recitation videos are examples of how to do this right. The lesson-giver has surgical precision and gets right to the point. Here's this problem/subject, and here's the relevant knowledge nugget. They'll mention what built up to this problem, which is amazing for discovering prerequisites - but never discuss those in depth. (I believe videos are not the most optimal way to learn in general, but in review and understanding they are very good.)
KA, on the other hand, goes into needless detail and redundance. (It's fine if you mention how demand graphs are relevant, but don't explain the basics of demand graphs again! I'm watching a more specific topic!).
That's how you end up with a long series of videos with sparse knowledge where, after six videos of ten minutes each, you have learned squat and the words "oh, let me use this pen color..." resonate in your head.
You should think of Khan Academy as an average high school lecture course, aimed at an audience of typical students, and with an approach and exercises closely aligned to the standard (frankly, quite uninspiring) USA school curriculum. It isn’t the best possible quality, but it does have 2 big advantages: (1) it is self-paced and available to anyone anytime, and (2) it is consistently okay, setting a quality floor. Human teachers are more variable in quality.
As a society, we could definitely aspire to producing much better materials, but even though I myself would never use it, I’m glad that Khan Academy exists.
I also used kahn academy for similar reason and I think their quality changes depending on the subjects. For me the real value came from their exercises. You get a problem, you don't know the answer, you open all the hints, after a couple of exercises of doing that you see the pattern, and then you have learned that specific thing. When I got stuck was when I watched the videos. It also helps the watch them at 1.5 and 2x respectively, depending on your need.
You can’t compare KA to MIT OCW. Khan Academy is for a general audience and OCW is for an audience of MIT students, who are highly preselected for aptitude to learn this material.
For specialized subjects there is a need for some MIT mettle, but I find many freshman courses are very clear and easy to understand, even more so than their equivalent Khan Academy materials.
Before his controversies, Lewin's Course 8 classes/recitations were a gold standard in Physics learning. He combined intuition and rigour masterfully - along with some brilliant practical experiences.
The recurring theme in many courses (not only Lewin's, but Calculus, Economics, or even Strang's linear algebra) is the great care and preparation of the materials to get the point across. I think this, more often than not, is very successful.
I didn't look into this yet as much as I'd like to -- especially before commenting -- but I did want to give you the feedback that I've been DYING for an entertaining, informative, and quick way to learn stats. YouTube videos are nice, especially Open Courseware, but I don't think it's enough. I like your story telling angle -- think that's really important.
As in, something that learns your interests and customizes to your tastes while still teaching. A textbook that is able to diagnose common misunderstandings from a set of wrong answers to a problem set and evolve its teaching methods.
If advertising networks have effectively personalized propaganda on Facebook and whatnot and games like The Walking Dead are able to change script based on popular choices made by all players, we should be able to apply the same technology to personalized learning at scale.