[zamfi]

I think this is actually proof that students are treating math as a set of rules applied to a process, and not having any real understanding of how the variables and equations they’re mechanistically applying rules to have any connection to the real world.

If they did, it would be a lot easier to talk about trains speeding through the night!

[jimhefferon]

Trains are how the courses try to help folks move from blind processes to understanding.

A person can wonder if it would be better to start with understanding. (Personally, I only briefly taught that age but my oracle for how to teach it, Mr Barton, does say that experience shows you have to have down the class's ability to mechanically solve before you introduce the trains. The other order, apparently, doesn't work when you try it with actual students in practice.)