In my experience teachers tend to only give examples of typical members of a category. I wish they’d also give examples along the category border, both positive and negative. Something like: “this seems to have nothing to do with quadratic equations, but it actually does, this is why” and “this problem looks like it can be solved using quadratic equations but this is misleading because XYZ”. This is obvious in subjects like geography, (when you want to describe where China is, don’t give a bunch of points around Beijing as examples, but instead draw the border and maybe tell about ongoing territorial conflicts) but for some reason less obvious in concept-heavy subjects like mathematics.
Another point on my wishlist: create sufficient room for ambition. Give bonus points for optional but hard exercises. Tell about some problems that even world’s top experts don’t know how to solve.
In my experience teachers tend to only give examples of typical members of a category. I wish they’d also give examples along the category border, both positive and negative. Something like: “this seems to have nothing to do with quadratic equations, but it actually does, this is why” and “this problem looks like it can be solved using quadratic equations but this is misleading because XYZ”. This is obvious in subjects like geography, (when you want to describe where China is, don’t give a bunch of points around Beijing as examples, but instead draw the border and maybe tell about ongoing territorial conflicts) but for some reason less obvious in concept-heavy subjects like mathematics.
Another point on my wishlist: create sufficient room for ambition. Give bonus points for optional but hard exercises. Tell about some problems that even world’s top experts don’t know how to solve.