I never really understood what showing your work meant in my schooling before college. I'd solve the problem through whatever I had memorized and would occasionally jot down the more complex parts like long division or large multiplications, at least until I was allowed to use a calculator. In high school we started getting to more complex things like algebra and inequalities and I was able to power through with intuition and a solid proficiency with my TI-83 and some Basic.

I don't know exactly what my teachers were doing but it all came to a screeching halt in college when I encountered severe gaps in my knowledge that made Calculus my hardest class. I had missed some very important lessons from earlier on that were huge hangups. It's hard to differentiate an equation if you aren't solid on how to factor the variables.

I had the same reaction as you. I think MOOCs are lacking in more than just this area. I'll use myself as an example:

I used MOOCs to learn various programming languages, simple database queries (insert, update, select with join, etc.) and how to use APIs with JSON. Lots of fun stuff. But when I came to university I started being taught all kinds of math and CS stuff through difficult assignments and tight deadlines that I never would have done on my own.

Yes, you technically can learn a lot of math and other things through MOOCs but it's not always as fun. The advantage of university is that they give you a set of required courses for a major and you have to take them, whether they're fun or not. Sometimes the courses which are the least fun turn out to be extremely valuable later on.

Data from an external source is usually fuzzy and requires some communication to reduce the fuzziness so that it can be properly interpreted. That involves communicating to understand why it's represented a specific way or negotiating to change the representation to better fit your needs.

The same is true for the output of your work.

That's a part of it, which doesn't come up in MOOCs at all (specifically, collaboration in a corporate environment within the software development lifecycle, and negotiating with project stakeholders about specs, requirements, and results).

I also didn't learn anything about that in school, but I did from my coding bootcamp, so if anything I think that is a general criticism of the education system.