There’s a new post at my new blog.
Another example of something powerful in mathematics that seems at first meaningless to the students is the name of properties (distributive, associative, etc.) However, the full payoff only comes in abstract algebra (which most students will never take!) so it wasn’t as good as an example as functions.
This is being updated weekly now so unless I need to make a supplemental post I don’t plan to update here each time there’s a new post. (I do plan to still update here. I have a magic trick I tried with my students last week I’d like to write about.)