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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 disconn
by rawnlq 11y ago
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-taxonomy 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 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 http://math.stackexchange.com/a/127182