This is not a ringing endorsement of the author's own problem-solving skills.
Why should his child care about how long America has existed unless it's on a test?
If you don't give someone a reason for why something is relevant, you won't get anywhere. If you don't try to make it interesting, to boot, you have no hope.
A good question might be: "Why did the Roman empire hold together that long and survived several serious crises, even though many other empires exploded and disintegrated in their first crisis ever, as the subjugated nations rushed for exits?"
That question has no definite answer, but boy (or girl), you learn a lot of fascinating history while trying to answer it.
The 21st century of public education does not seem capable of providing this experience. What the heck happened? Or was this a unique, one-time period?
Yes! The post WWII generation is what built the USA into the powerhouse it is today. There were two critical factors; 1) WWII left all of the competition in ruins 2) The "Cold War" forced the policymakers to focus on STEM education.
With success came hubris; the US has forgotten the factors which made it great and has lost itself in a miasma of Entertainment/Corruption/Finance/Management. It seems the "immigrants" are who are keeping the US flag flying high. I sincerely hope the US education system reforms itself and rediscovers its "lost" glory.
What if you paid the teacher through the school principal?
What if the invoice for your school fees were on the bottom of your kid's annual report card?
And you had to pay it, with a bank cheque, in person, to the teacher, on the Tuesday before Christmas, after waiting in the queue with all the other parents.
With your kid and the principal looking on, all minds focussed and incentives painfully exposed?
So, dean HNers, don't worry about STEM. No need to train engineering, look into physics, think over math - no hard subjects required to get successful in the world. Just kindness and good leadership. Onwards, Jameses Kirks... wait a minute, Kirk was able to reprogram the simulation. Never mind then.
You don't teach people to reason by giving them a step-by-step guide that they can mechanically follow without thinking.
You teach them to reason - to think - by giving them a problem and having them figure out how to solve it themselves.
Math shouldn't be about rote memorization and imitating a calculator. You can fit all the basic calculation skills people will need in everyday life in grade one to three, then teach them proper mathematics - which coincidentally means learning to reason in a precise manner.
If a curriculum is badly designed, it's going to dump one model on the students, and that's going to come to the detriment of some of them. Maybe you already learned your multiplication tables, and sitting around and drawing a 5x6 grid and counting the squares is going to frustrate and annoy. It's almost certainly going to drive parents wild, because they won't be raised with the jargon and rules, leaving them unable to help.
There's also the risk that any new material is poorly debugged or documented. When it's just about "a single right answer", we probably can get consensus that 5x6=30. But if we try to grade the reasoning tools used to get there, those are often not as universally standardized. One kid draws his 5x6 grid horizontally, and one draws it vertically. The teachers and grading rubrics have to have enough understanding and flexibility to recognize they're equivalent. In the worst case, you end up distracting students from the actual concepts by weighing them down with a bunch of unrelated rules unique to the teaching system.
I recall taking a maths class once which basically covered the same problems several times over, each time using a different model to solve them. I could see a case for a course like that. But that was a 400-level elective college course, so there's probably different constraints and expectations than when you're trying to teach 4th grade students multiplication.
The other worry I have is that we're doing a lot of window-dressing in the name of reducing "math anxiety". Every few years they try to dress up math concepts in a new way in the hopes students will find them less intimidating. Why does this seem to be unique to math? There seems to be no rush to replace Shakespeare in the schools with something students can more easily reason about.
Have you considered that different approaches to the same problem might indeed feel alien to you due to your lack of exposure, but aren't really that different?
Similarly I've seen Array questions marked wrong because they curriculum defines which order (row, column) lines up with the multiplicands and the student has them reversed...