When I buy a dictionary (I'm talking about back in the day here...) I don't feel like I wasted money because I didn't use every entry. You buy a dictionary because you want to cover all the words you might need and you don't know what they are in advance.
Isn't education like this? We have no idea how our lives are going to turn out in the future so the smart thing to do is get some broad coverage because most skills are too difficult to learn the day you suddenly need them.
Anyway, I don't buy all that "learning how to transform a matrix into Smith normal form will make you better at reasoning about other things in life" stuff. Learn stuff for pleasure, or for the possibility it'll be useful or bring you an income, but not because of some mythological side effects.
I feel like when people justify learning a subject by using the "it'll make you reason better" story, the actual message they are sending their listeners is that the speaker is unable to think of a good reason.
Do you think there's a reason to learn planar geometry? I ask because the standard reason given is that it is a good way to learn about semi-rigorous proofs, auch seems similar to "makes one reason better".
@robryk Some course has to be the one to introduce the concept of proofs and I think planar geometry is for many students the one to do this. Though it has to be added I use planar geometry on a daily basis.
But I think this is entirely different from teaching people to reason generally. And teaching the *entire body of mathematics that is typically taught*, in order to teach general reasoning, which is the case I'm criticising, seems very wrong to me.
(I'm pretty sure that when Aristotle wrote down the rules of syllogism he was making observations about the way people were already reasoning successfully.)