Wayne's response is predictable: that this isn't math and testing scores suffer. Likewise, a student good at math will scoff at how long it's taking her peers to grok the concept of "angle". You've gotta use a saw to remember? Yeah right.
However, if we take away the labels and look at hours in a day, learning to saw is productive, and has elements of being trusted more like an adult, allowed to use tools that may do inadvertent damage, especially to one's self. Cooking? Same thing. You're working with chemicals, substances, and using heat (the stove, fire).
Lets call that gross and fine motor skills training, or how about "scouting". We may scoff at a "math class" where they go to all the trouble to visit rugged terrain and then have the students geocache (treasure hunt) using instruments. Not only is it a long drive, it's physically demanding. What has this to do with math? Math isn't gym.
But we took the labels off, are just looking at handing on the culture. Mathematicians who aren't good with saws and don't have the physical stamina to climb out of a snowed in valley might be a dime a dozen, but thanks to "scouting" we don't plan to continue this level of neglect for the whole person.
However, I continue to share Wayne's concern they won't move quickly or lightly enough among concepts and fail to connect enough dots. If they hike 10 miles, "wasting" a day on fitness, I'll want some immersive astronomy teaching machine at the far end. dxyz/dt is in orbits. We keep the math high level but "impure" because, as believers in STEM, we're not believers in "pure". STEM is STEM.
God forbid that scouting get in the way of those wishing to learn quickly. Ten year olds are capable of doing some serious programming, we know that. STEM teachers who don't program will likewise be a thing of the past.
Mathematics in theater? Yes. The humanities are not unimportant all of a sudden. Yet I'm thinking a serious STEAM can cover them, adding that A, I say for Anthro- pology, they say for Art. Whatever. Anthropoids. Humans. We get the humanities back in through the A word.