> If there's one complaint I have against Math education it's that all my educators actively encouraged eliding the units even for problems based on physics. I'm not sure if this was just to try to trip students up on tests, but it was absolutely horrible from an educational perspective. ALWAYS keep the goddamn units so you can at least minimally sanity check your result!
For what it's worth, as a mathematics teacher, I do my best to encourage my students always to keep their units (though I do bow to tradition by not requiring it). This started in helping to guide them through setting up differential equations [0], but, when I saw what a good tool it was for organising thought, I exported it to my other classes as well.
(It's just occurred to me to compare dimensional analysis with Haskell's if-it-compiles-it-works property: it doesn't guarantee correctness, but at least it ensures only interesting errors. I try to give a lot of partial credit when grading, but these days I am ruthless if a proposed differential equation involves adding, say, a distance and a time!)
[0] To the extent that I am pretty confident that, if any of my students reads this, then he or she will know who I am.
For what it's worth, as a mathematics teacher, I do my best to encourage my students always to keep their units (though I do bow to tradition by not requiring it). This started in helping to guide them through setting up differential equations [0], but, when I saw what a good tool it was for organising thought, I exported it to my other classes as well.
(It's just occurred to me to compare dimensional analysis with Haskell's if-it-compiles-it-works property: it doesn't guarantee correctness, but at least it ensures only interesting errors. I try to give a lot of partial credit when grading, but these days I am ruthless if a proposed differential equation involves adding, say, a distance and a time!)
[0] To the extent that I am pretty confident that, if any of my students reads this, then he or she will know who I am.