I think we make this harder than it has to be, by not doing proof-based math earlier.
Real analysis is often the first class in a math bachelor's program where things really get far from intuition and much harder to wrap your head around than the material from earlier classes.
Making that the first proof-based class is just piling one hard thing on top of another.
I think we'd be better off if we made basic calculus proof-based, at least for people such as math majors who are going to need to learn to follow and do proof-based math at some point. For those going into fields where they will not need to read and do proves, have a separate "practical calculus" track.
You can start out with more informal proofs at the start of basic calculus, and slowly step up the level of rigor throughout the year.
Real analysis is often the first class in a math bachelor's program where things really get far from intuition and much harder to wrap your head around than the material from earlier classes.
Making that the first proof-based class is just piling one hard thing on top of another.
I think we'd be better off if we made basic calculus proof-based, at least for people such as math majors who are going to need to learn to follow and do proof-based math at some point. For those going into fields where they will not need to read and do proves, have a separate "practical calculus" track.
You can start out with more informal proofs at the start of basic calculus, and slowly step up the level of rigor throughout the year.