[batman-farts]

It's a bit sad that calculus remains the stereotypical example of difficulty in most curriculums. Throughout childhood, I remember it seeming like some sort of complex, inscrutable, untouchable phantom hanging in the distance at the far end of the high school math course progression.

If somebody had told me that calculus is how you transition between dimensions, or that techniques of integration would enable me to generate 3D shapes from 2D lines, I think I would have been much more motivated to progress rapidly in math, and much less discouraged when I hit the "hard parts." Those are the answers I tend to give today when somebody asks me, "why take calculus?" Demystifying it doesn't even have to be a wholly practical explanation, like deriving acceleration from velocity.

Segregating out the "hard stuff" doesn't even necessarily lead to great learning outcomes, either. At my high school, and it seems many others, the honors kids were put on the track leading to calculus while everyone else ended up in a dedicated statistics class. The honors kids were expected to pick up statistics through supplementary assignments in their laboratory science classes, and this same approach carried over into lower-division undergrad. As an adult, I feel like that approach has only given me cause to go back and seek out a firmer grounding in statistics.

[sanderjd]

Motivating topics for students is so important and underrated. It's also super hard I think. For one thing, everyone responds to different motivation. Some people are motivated to learn basic algebra more by the possibility of extending it into applied math so they can get a good job as an engineer. Others don't have any interest in that, but rather would be motivated by the beauty of pure math. And students themselves have no idea what they like.

But yeah, I can think of so many examples of things that I would have been way more into in school if I understood how they mapped onto the adult world. Statistics is probably at the top of that list though.