It sort of reminds me of Paperscape [1] but more on the style of wikipedia since it invites you to edit it.
Organizing knowledge is way harder than it seems.
Instead of for topics, I would personally like to see this implemented for courses and their prerequisites (and perhaps the topics in each course) in order to keep track of your own learning or plan out what you would like to learn in the future.
Thanks for your comments! :) We have plans to build on top of this to create a way for you to learn an entire "course" of topics. That's our next stage of development.
For now, we're happy to share the Topic Map as it is of independent interest. :) We hope that it might be helpful for people who are either already at a topic area within a course, or just like exploring maps.
This is a really good question! We don't think we're doing anything suspicious, and there aren't even any payment gateways anywhere on the site. To be honest, we weren't familiar with BlueCoat. Do you know what tends to make them rate a site as Suspicious?
We're just trying to create a valuable free resource, through crowd-sourcing. :)
I think the possibility of multiple explanations has a great value beyond just providing a "better" explanation. They also allow a different mental model to be expressed, which in my personal experience was very helpful in learning new concepts in mathematics.
In school, you are often taught a very strict mental model based directly on the books and then hammered with very similar examples hoping you will understand it after the n-th one. But what lead the concepts to "click" in my head were often somewhat different mental models (which I think are different for each person). That initial mental model can then be more refined and adjusted to be more in line with the textbook one.
I'd rather read 10 explanations that are a bit different and the understanding with 10 examples than to read 1 and hammer that in with 100 examples.
Once you actually get to an article, having to click "continue" after every paragraph is mildly annoying.
Edit: I am also not a huge fan of the choice to organize the topics by the "high school class" they were introduced in. There is absolutely no reason to break algebra up into "Algebra 1" and "Algebra 2"
In particular, this means you're putting "basics of matrices" arbitrarily with "Algebra 1" when knowing how to add and multiply matrices has literally nothing to do with the other topics in that group.
Thanks for your feedback! All feedback is really useful to us, as it helps us to continue to polish the product. The articles themselves are crowd-sourced, and they certainly show signs of being a community that is still growing. It's possible to create richer articles like this one: https://www.expii.com/t/gravity-weight-642
The main point of our post tonight was to share the current product of the Topic Map. As the rest of the site continues to grow, we hope that you will soon learn about it as a useful resource.
Regarding the split of Algebra 1 and Algebra 2: we fully agree that math should be more connected. We actually experimented with that here, in the "Theory" section of "Math". You can find that by clicking into "Algebra Revisited", which you can also find by first going here:
and then clicking on "Topic Map" to see a fully connected version of Algebra. This is much more theoretical though, and does not align so easily with standards used in mainstream schools. We chose to make the main sections of our maps align with standards so that they could be more immediately useful for the mainstream audience. However, we ourselves are a bunch of enthusiasts who love to think about how to push the envelope. :)
Nice. This is about 70% of the way there toward the fully visible conceptual graph I've wanted to make or find for years. I'd like to be able to see items from multiple zoom levels, for example. I want to be able to look at a bubble that says something like "addition of positive integers", and follow a sequence of arrows to every academic concept and career that makes use of addition.
Another thing I want software to do is highlight everything I think I know (maybe take some quizzes to prove it), ask me what I'd like to know, then show the graph and list of topics I need to learn in between. Based on another comment[0] it sounds like it would eventually be possible to use this data to do exactly that. So again, nice.
You are describing the projects that are on our roadmap. :) We felt that the initial conceptual map would be an essential backbone for data-driven guidance services that we could then build upon it. So, we invested a serious amount of effort into creating this first pass. The math and science maps were created through a collaboration led by our Education Director, who has taught in middle-school and high-school classrooms, and now teaches at the University of Pittsburgh down the street. The other partners in the collaboration were alumni of International Math Olympiad teams and scientists from the Hertz Foundation Fellowship program. :)
We're continuing to iterate on our concept maps, but in the meantime, our Engineering team is moving forward on more projects which successively build on our growing structure.
Your encouragement means a lot to us, and we'll keep on trucking!
I feel like physics and calculus has to be more intricately linked together. Due to how the recursive disjoint partitioning works, science and math gets disconnected right off the bat.
Also within each topic, having a directed acyclic graph of concepts is useful for modeling how one might encounter them in school. But outside of formal mathematical proofs (where something must be true before it can be used to prove something else), the way people learn things is a lot of more circular and definitely not a DAG. For example, I understand arithmetic which let's me understand the purpose of peano axioms which let's me "understand" arithmetic. If it is a DAG then it's only a DAG of the atomic units of knowledge. After forming clusters of these units, the edges between two cluster aren't uniformly in a single direction anymore (even if they are mostly going in one direction).
Sidenote: You guys don't seem to have anything on graph theory. Is this only aimed at highschool level?
Anyway, just thought the topic of how to model how people understand science/math topics can go beyond simple taxonomy by committee or traditional course syllabus prerequisites.
But what you have definitely works and is a very practical first step!
http://www.maa.org/press/periodicals/loci/joma/subject-taxon...
EDIT: Khan Academy has a very similar knowledge map that somewhat clusters in terms of layout, without explicitly partitioning or labeling the clusters of topics: https://www.khanacademy.org/exercisedashboard.
And here's another example that clusters, but don't hide or merge intercluster edges: http://math.stackexchange.com/a/127182
Minor formatting problem. I cropped out most of the screenshot, it's really on a 1920 width screen. http://imgur.com/uvZLELW
I like to think of these as a kind of hierarchy but I'm never quite sure where to put some things like philosophy, or how much overlap the titles have with each other (I guess it's not constant anyway).
Math -> Science -> Engineering -> Technology
I've tried to organize them with a mindmap before, but I am never satisfied with the results.
Hey there, I'm the lead developer at expii. Thanks for finding that bug! Would you mind telling me what browser you were using when you encountered it?
Hey, would you mind taking another look at the site to see if that bug is still an issue? Unfortunately, I wasn't able to reproduce it locally, but I put out a fix that I'm hoping should fix the issue you were seeing.
21 comments
[ 3.0 ms ] story [ 65.2 ms ] threadIt sort of reminds me of Paperscape [1] but more on the style of wikipedia since it invites you to edit it.
Organizing knowledge is way harder than it seems.
Instead of for topics, I would personally like to see this implemented for courses and their prerequisites (and perhaps the topics in each course) in order to keep track of your own learning or plan out what you would like to learn in the future.
[1] http://paperscape.org/
For now, we're happy to share the Topic Map as it is of independent interest. :) We hope that it might be helpful for people who are either already at a topic area within a course, or just like exploring maps.
We're just trying to create a valuable free resource, through crowd-sourcing. :)
I think the possibility of multiple explanations has a great value beyond just providing a "better" explanation. They also allow a different mental model to be expressed, which in my personal experience was very helpful in learning new concepts in mathematics.
In school, you are often taught a very strict mental model based directly on the books and then hammered with very similar examples hoping you will understand it after the n-th one. But what lead the concepts to "click" in my head were often somewhat different mental models (which I think are different for each person). That initial mental model can then be more refined and adjusted to be more in line with the textbook one.
I'd rather read 10 explanations that are a bit different and the understanding with 10 examples than to read 1 and hammer that in with 100 examples.
Edit: I am also not a huge fan of the choice to organize the topics by the "high school class" they were introduced in. There is absolutely no reason to break algebra up into "Algebra 1" and "Algebra 2"
In particular, this means you're putting "basics of matrices" arbitrarily with "Algebra 1" when knowing how to add and multiply matrices has literally nothing to do with the other topics in that group.
The main point of our post tonight was to share the current product of the Topic Map. As the rest of the site continues to grow, we hope that you will soon learn about it as a useful resource.
Regarding the split of Algebra 1 and Algebra 2: we fully agree that math should be more connected. We actually experimented with that here, in the "Theory" section of "Math". You can find that by clicking into "Algebra Revisited", which you can also find by first going here:
https://www.expii.com/t/2829
and then clicking on "Topic Map" to see a fully connected version of Algebra. This is much more theoretical though, and does not align so easily with standards used in mainstream schools. We chose to make the main sections of our maps align with standards so that they could be more immediately useful for the mainstream audience. However, we ourselves are a bunch of enthusiasts who love to think about how to push the envelope. :)
Another thing I want software to do is highlight everything I think I know (maybe take some quizzes to prove it), ask me what I'd like to know, then show the graph and list of topics I need to learn in between. Based on another comment[0] it sounds like it would eventually be possible to use this data to do exactly that. So again, nice.
You are describing the projects that are on our roadmap. :) We felt that the initial conceptual map would be an essential backbone for data-driven guidance services that we could then build upon it. So, we invested a serious amount of effort into creating this first pass. The math and science maps were created through a collaboration led by our Education Director, who has taught in middle-school and high-school classrooms, and now teaches at the University of Pittsburgh down the street. The other partners in the collaboration were alumni of International Math Olympiad teams and scientists from the Hertz Foundation Fellowship program. :)
We're continuing to iterate on our concept maps, but in the meantime, our Engineering team is moving forward on more projects which successively build on our growing structure.
Your encouragement means a lot to us, and we'll keep on trucking!
Also within each topic, having a directed acyclic graph of concepts is useful for modeling how one might encounter them in school. But outside of formal mathematical proofs (where something must be true before it can be used to prove something else), the way people learn things is a lot of more circular and definitely not a DAG. For example, I understand arithmetic which let's me understand the purpose of peano axioms which let's me "understand" arithmetic. If it is a DAG then it's only a DAG of the atomic units of knowledge. After forming clusters of these units, the edges between two cluster aren't uniformly in a single direction anymore (even if they are mostly going in one direction).
Sidenote: You guys don't seem to have anything on graph theory. Is this only aimed at highschool level?
Anyway, just thought the topic of how to model how people understand science/math topics can go beyond simple taxonomy by committee or traditional course syllabus prerequisites. But what you have definitely works and is a very practical first step! http://www.maa.org/press/periodicals/loci/joma/subject-taxon...
EDIT: Khan Academy has a very similar knowledge map that somewhat clusters in terms of layout, without explicitly partitioning or labeling the clusters of topics: https://www.khanacademy.org/exercisedashboard. And here's another example that clusters, but don't hide or merge intercluster edges: http://math.stackexchange.com/a/127182
I like to think of these as a kind of hierarchy but I'm never quite sure where to put some things like philosophy, or how much overlap the titles have with each other (I guess it's not constant anyway).
Math -> Science -> Engineering -> Technology
I've tried to organize them with a mindmap before, but I am never satisfied with the results.
Thanks
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