
Mathigon – an interactive, personalized mathematics textbook - mr_golyadkin
https://mathigon.org/
======
CoolGuySteve
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.

~~~
ai_ia
I am building Primer. :)

[https://www.primerlabs.io](https://www.primerlabs.io)

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.

[https://youtu.be/acTdwGV0s9I](https://youtu.be/acTdwGV0s9I)

P.S. The landing page is a horrible experience on mobile. My bad.

~~~
surajs
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.

~~~
ai_ia
Thank you Suraj.

Will definitely connect with you once I release the beta.

------
wcarey
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.

------
askvictor
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).

------
itissid
This looks awesome. But:

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/](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...](https://www.dropbox.com/s/0y545gn2withb5e/DuckworthPetersonMatthewsKelly_2007_PerseveranceandPassion.pdf?dl=0)
[2] [https://www.amazon.com/Make-Stick-Peter-C-Brown-
ebook/dp/B00...](https://www.amazon.com/Make-Stick-Peter-C-Brown-
ebook/dp/B00JQ3FN7M)

~~~
jacobolus
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...](https://mathigon.org/course/transformations-and-
symmetry/transformations)

~~~
robfitz
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.

------
gridspy
This is beautiful. I wanted more content like this, and supporting Kahn
Academy made me want to support this also.

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](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](https://mathigon.org/donate)

(When I posted this, Patreon had only 5 supporters - can you help too?)

------
anchpop
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"

~~~
LeonB
I'm also interested in the application of dependency graphs for knowledge.

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#...](https://metacademy.org/graphs/concepts/deep_belief_networks#focus=deep_belief_networks&mode=explore)

------
patel011393
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.

------
gubikmic
Source code is available:
[https://github.com/mathigon](https://github.com/mathigon)
[https://mathigon.io](https://mathigon.io)

~~~
lovemenot
there's no license file at the link above. I believe this software is mainly
intended for the use of educators to develop new content locally.

It seems there's a separate account for their MIT licensed software:
[https://github.com/mathigon/mathigon.github.io](https://github.com/mathigon/mathigon.github.io)

------
otabdeveloper2
"Edutainment" sucks donkey balls.

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.

~~~
qwerty456127
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.

------
octahedron42
I love the chapter on fibonacci numbers. So colourful!
[https://mathigon.org/course/sequences/fibonacci](https://mathigon.org/course/sequences/fibonacci)

~~~
neatcoder
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!

~~~
jonsen
Would you rather they showed mating between parents and offspring? I think
it’s quite normal for animal flocks to start off from a single pair.

------
mattlondon
Some feedback:

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...](https://mathigon.org/course/graphs-and-networks/eulers-formula) 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?)

------
saivan
I'm working on something somewhat similar, here's an example lesson:
[https://treena.org/#lesson/vector-
subtraction](https://treena.org/#lesson/vector-subtraction) There are more on
the home page.

It's not so mobile friendly yet. But the approach I'm taking is quite
different :) Great work Mathigon!

------
terrax99
It seems to be just one person working on this (!), but I can't wait until
they finish all the other topics.

------
Treegarden
I think this is great, but on first glance
[https://www.khanacademy.org/](https://www.khanacademy.org/) seems to be
significantly better. What makes mathigon different?

~~~
xacintosh
It's not just videos of someone going through the motions of solving problems.
These are interactive explorations of mathematics.

~~~
ehsankia
Hmm, you may have an outdated view of KhanAcademy. Sure, there's videos to
supplement, but there's also plenty of exercises and interactive content.

~~~
gallegojaime
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.

~~~
jacobolus
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.

~~~
gallegojaime
Those are all fair points.

------
onlyrealcuzzo
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.

------
jimhefferon
Can I ask who is behind this? For instance, I see that they take donations so
presumably not a for-profit.

~~~
turboturbo
See [https://mathigon.org/about#team](https://mathigon.org/about#team)

------
bibyte
Now this is an awesome way to learn math. I just tried the "Graphs and
Networks" course and it's so easy. I hope they release more courses soon.

------
saranglakare
Good effort! I have sent the link to my daughter (10th grade). Let's see what
she thinks. I think the chat to the bottom-right is a distraction.

------
qwerty456127
Wow! Looks insanely cool!

