Geez, I'm trying to figure out how to describe in a short paragraph or two what it would take a book to explain. Here's my best shot.
We've created an extensive knowledge graph representing all of mathematics (3,000 topics and counting) from 4th Grade Math up through our university-level material, and our algorithms traverse the graph to identify the optimal learning tasks to assign to the the student at any point based on their performance on previously completed learning tasks: diagnostics, lessons, reviews, quizzes, etc.
There are actually multiple graphs, including one that defines the direct prerequisite relationships between topics as well as one that describes encompassing relationships (e.g. the topic on Solving Two-step Linear Equations fully encompasses the topic on Solving One-step Linear Equations Using Multiplication), but there are other graphs as well.
In addition, the algorithms have to deal with spaced repetition, which is vastly more complicated to sort out within the context of a hierarchical knowledge structure with both full and partial encompassings. (Without encompassing relationships, the backlog of reviews would quickly slow progress to a crawl).
We actually have some deep-dive writeup in the works that attempt to explain how all of this works at a level that will be accessible to most people, but it's more than I can describe here, unfortunately.
We've created an extensive knowledge graph representing all of mathematics (3,000 topics and counting) from 4th Grade Math up through our university-level material, and our algorithms traverse the graph to identify the optimal learning tasks to assign to the the student at any point based on their performance on previously completed learning tasks: diagnostics, lessons, reviews, quizzes, etc.
There are actually multiple graphs, including one that defines the direct prerequisite relationships between topics as well as one that describes encompassing relationships (e.g. the topic on Solving Two-step Linear Equations fully encompasses the topic on Solving One-step Linear Equations Using Multiplication), but there are other graphs as well.
In addition, the algorithms have to deal with spaced repetition, which is vastly more complicated to sort out within the context of a hierarchical knowledge structure with both full and partial encompassings. (Without encompassing relationships, the backlog of reviews would quickly slow progress to a crawl).
We actually have some deep-dive writeup in the works that attempt to explain how all of this works at a level that will be accessible to most people, but it's more than I can describe here, unfortunately.
Anyway, I hope this helps a little.