[rjtobin]

I interpret the article quite differently. The triangle example (which as the author writes is actually an example from “Lockhart’s Lament” on American math education) isn’t about whether triangle-area-formula was ever justified to students. It’s that students aren’t given the chance to really ask the question themselves - a chance to approach math, or biology, in the way that a mathematician or biologist does in reality: trying to work it out for themselves, and being invited to wonder at just how improbable textbook biological facts are etc.

I agree with your point that some students will be more inquisitive, and will need less prompting to do the above thinking themselves. But many (most?) students are not like this, and it’s a shame that many of these students could enjoy a subject that they instead come to loathe.