[mapierce2]

You're right. It's hard to teach in schools though because of standardized (often multiple-choice) tests; teachers are incentivized to teach "skills" that have objective correct answers that can be easily tested.

Then by the time students hit college, they're resistant to any sort of mathematics that doesn't have a correct answer. I've been trying to sell it as a means of error-correction, or as a sanity check. If they've gotta answer a question "Joe is 6'4" tall and, at the suggestion of an ergonomist, wants to build a desk 40% of his height. How tall should the desk be?" I urge them to not immediately go into math-brain and just think for a minute, and estimate a reasonable answer to match their calculations against. This mental workflow sticks for a few of them by the end of the class.

[delecti]

Absolutely. The concept of a "sanity check" is so valuable. Thinking about what the answer should "look like", ignoring the precise value, always makes me much more confident in a precise value I've computed. It's the kind of thinking makes math so much more useful in the "real world" too.