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Mathigon – an interactive, personalized mathematics textbook
- jimhefferon 8y agoCan I ask who is behind this? For instance, I see that they take donations so presumably not a for-profit.
- turboturbo 8y agoSee https://mathigon.org/about#team https://mathigon.org/about#team
- anchpop 8y agoThis 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 8y agoI'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#focus=deep_belief_networks&mode=explore https://metacademy.org/graphs/concepts/deep_belief_networks#...
- Treegarden 8y agoI 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 8y agoIt's not just videos of someone going through the motions of solving problems. These are interactive explorations of mathematics.
- ehsankia 8y agoHmm, you may have an outdated view of KhanAcademy.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 8y agoI 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.
- Treegarden 8y agoI 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.
- CoolGuySteve 8y agoIt 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.
- hanniabu 8y ago> A textbook that is able to diagnose common misunderstandings from a set of wrong answers to a problem set and evolve its teaching methods. That'd be extremely useful to have.
- CoolGuySteve 8y agoI 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?
- solipsism 8y agoIMO most college level math isn't difficult 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?
- patel011393 8y agoCheck 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.
- wcarey 8y agoI 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.
- otabdeveloper2 8y ago"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.
- bastih 8y agoOut of curiosity, which topics would you have liked to be taught in a more structured way?
- scarejunba 8y agoI 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.
- qwerty456127 8y agoSo 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 8y agoI love the chapter on fibonacci numbers. So colourful! https://mathigon.org/course/sequences/fibonacci https://mathigon.org/course/sequences/fibonacci
- neatcoder 8y agoWhen 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 8y agoWould 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.
- Grue3 8y agoBecause the growth of a population of rabbits is the exact problem Fibonacci studied to come up with his sequence! It has historical appeal.
- itissid 8y agoThis 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/DuckworthPetersonMatthewsKelly_2007_PerseveranceandPassion.pdf?dl=0 https://www.dropbox.com/s/0y545gn2withb5e/DuckworthPetersonM... [2] https://www.amazon.com/Make-Stick-Peter-C-Brown-ebook/dp/B00JQ3FN7M https://www.amazon.com/Make-Stick-Peter-C-Brown-ebook/dp/B00...
- jacobolus 8y agoYes, 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/transformations https://mathigon.org/course/transformations-and-symmetry/tra...
- robfitz 8y agoI 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.
- terrax99 8y agoIt seems to be just one person working on this (!), but I can't wait until they finish all the other topics.
- gubikmic 8y agoSource code is available: https://github.com/mathigon https://github.com/mathigon https://mathigon.io https://mathigon.io
- deleted 8y ago[deleted]
- lovemenot 8y agothere'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
- askvictor 8y agoI'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).
- gridspy 8y agoThis 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?)
- qwerty456127 8y agoWow! Looks insanely cool!
- bibyte 8y agoNow 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.
- saivan 8y agoI'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!
- saranglakare 8y agoGood 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.
- wriclan 8y agoA bit lame. Founder Looks like a loser but that aside, the idea isn’t new. Conrad wolfram on board and wolfram screams for trouble and I can safely write this endeavour off
- onlyrealcuzzo 8y agoI 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.
- mattlondon 8y agoSome 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-formula 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?)