Another teacher asked me an interesting question today. "What do you think about this idea of replacing calculus with statistics. After all statistics is more useful."
That's probably true on the surface, but I can't say I'm a huge fan of the "replace calc with stats" craze... even as I lament the poor understanding many people have of stats. It's obvious we need more education on interpreting datasets and visualizations.
But, there is a subtext to this argument I dislike. 1/
The subtext is that statistics is somehow "easier" than calculus since it's more connected to the "real world" --
But, nothing about real world problems is easy. Real world problems are harder, require more experience, more analysis, are less susceptible to canned techniques and strategies.
And more importantly it's hard to really understand much about statistics without knowing some calculus. Not a popular opinion. I know. 2/
@futurebird I'm sympathetic to the idea that statistics is a more practically useful thing to teach than calculus (for people not intending to go into STEM), but I would never claim that it's easier.
While I realize that calculus is needed to explain some concepts in probability and statistics, it seems like you could still teach a lot without needing it. For example, I have taught algebra-based physics, and while it limits what you can cover and prevents you from proving some things, it can still convey a lot of understanding of the topic. And it seems like calculus is more central to physics than to statistics. Moreover, couldn't one argue that concepts like measure theory or Stieltjes integration are needed to really understand probability? Yet I don't think most students taking statistics understand those.
