This is pretty interesting. The paper basically starts by talking about "Concept maps", or graphs of concepts and relations. These concept maps correspond to an SQL schema, and instances of concepts and relations correspond to table rows.
Then they go one level meta and discuss how to create "alignment mappings" between the concepts generated by different people. This makes me think about how math standards for different countries/school systems could be aligned. For example, using an "alignment mapping" between math topics taught in US and math topics taught in UK, you could repurpose a high-quality educational content source (e.g. Khan Academy) to be used in UK schools.
But wait, there is more! The space of mappings between concept maps can also be represented as a graph also a category, and somehow there is interesting structure that can be used to categorize and link the alignment mappings (15+ pages that I didn't understand). I wish they had continued the SQL analogy. What would a functor be? Is it a migration? Or an ETL script? And what is a flow?
Then they go one level meta and discuss how to create "alignment mappings" between the concepts generated by different people. This makes me think about how math standards for different countries/school systems could be aligned. For example, using an "alignment mapping" between math topics taught in US and math topics taught in UK, you could repurpose a high-quality educational content source (e.g. Khan Academy) to be used in UK schools.
But wait, there is more! The space of mappings between concept maps can also be represented as a graph also a category, and somehow there is interesting structure that can be used to categorize and link the alignment mappings (15+ pages that I didn't understand). I wish they had continued the SQL analogy. What would a functor be? Is it a migration? Or an ETL script? And what is a flow?