Mathigon – an interactive, personalized mathematics textbook
mathigon.org
mathigon.org
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.
You can checkout the documentation part for images/gifs to learn how it works.
Bit late on schedule, but working hard to release soon.
Made a video about the same explaining the interface.
P.S. The landing page is a horrible experience on mobile. My bad.
Will definitely connect with you once I release the beta.
I have taken reference from here https://teachyourselfcs.com
:o
I will be contacting. Thanks for taking time to go through the web site. :)
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.
Hope it makes sense.
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.
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'.
TBH, I have been full-time working on it alone since last year Jan. Left job and moved back to parents place.
Cannot afford hiring anyone as I am basically broke.
Planning to bootstrap. Thank you once again.
Will check it out. Thanks.
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.
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.
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.
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”.)
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.
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 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.
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.
That'd be extremely useful to have.
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?
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.
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.
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.
In this vein, there is the Incredible Proof Machine‡, an interactive visual proof assistant designed for introducing beginners to mathematical proofs.
Suddenly textbooks and multiple other sources became necessary to combat what you so cleverly called "math anxiety."
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?
What a fascinating subject to look into! Any books you would recommend?
It's not rocket science, a mole rat could figure out that kids want to play video games and eat candy all day long.
Putting a rocket into space is just a lot of maths; we're not close to having anything like that in regards to human outcomes.
"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.
The cognitive nihilist in me shudders at the thought of a technocrat deciding what my own best interests are.
"Your best interests are the games I like to play, not the games you like to play."
Which is a fine position and all that. The objectionable part of it is the pretense of objectivity.
It's better than Candy Crush (no overt addicting psychological tricks) but ultimately the same kind of waste of time.
No child ever grew up and said "gee, how great it is that I spent 10000 hours in Minecraft instead of doing sports or learning a useful skill".
I grew up on video games myself; trust me, it sucks.
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.
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.
[1] https://www.dropbox.com/s/0y545gn2withb5e/DuckworthPetersonM... [2] https://www.amazon.com/Make-Stick-Peter-C-Brown-ebook/dp/B00...
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...
They have a Patreon page. If you like what's here already and want it to grow - you should donate too!
https://www.patreon.com/mathigon
Just a couple of dollars from each of us is likely to make a huge difference to such a volunteer effort!
There are more options here : https://mathigon.org/donate
(When I posted this, Patreon had only 5 supporters - can you help too?)
Metacademy is an open source/CC site that is based around this idea. For example here's the dependency graph for learning about deep belief networks. https://metacademy.org/graphs/concepts/deep_belief_networks#...
It seems there's a separate account for their MIT licensed software: https://github.com/mathigon/mathigon.github.io
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.
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.
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?)
It's not so mobile friendly yet. But the approach I'm taking is quite different :) Great work Mathigon!
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.
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.
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.