It is humbling to have a PhD in Engineering, and not be able to understand Grade 6 math homework. If I can't understand the lessons they are trying to teach with regards to digits and digit placement, then what chance do the Grade 6 kids have?
Knowing plenty of PhDs myself, and having one... indeed...
On another occasion, while in first year Algebra, I vividly remember suddenly understanding key concepts from Grade 7 math. For instance, why does one care that numbers have the distributive, associative, and commutative properties? that can be named and explained?
Perhaps you weren't very good at maths as a kid? When I was in grade four, I distinctly remember puzzling over questions like "how does long division actually work?" I found the answers in things like associativity, distributivity, etc., though I expressed them differently in my mind. And when I got to final year high school, I was the only person in the class (top class, academically selective school) who could still do long division. I bet that now, 12 years on, I am again the only member of that class who can still do a long division.
The point wasn't that I am very smart... but that I was no doubt absorbing some long-forgotten lesson on associativity. There are kids who really do get the point of these patterns very early, and remember them, and use them in their secondary and tertiary educations, and who use the same skills in the workplace.
I'm just not sure what is the point of introducing concepts to children, without the ability to explain the reasons for the concepts.
Nope. Many people can speak English well, and teach it, without understanding the first thing about linguistics. Nor do you need to learn grammar to learn a language---it may help but it is obviously not necessary for children. Maths is just another language, though it is possibly not a language everyone is capable of speaking.
Why focus so much on obscure terminology, to the point that no one understands why you are even asking a question? Math is about understanding why things happen. Not wrote answers to naming conventions.
Interestingly misconceived. Physics and engineering is about understanding why things happen. Maths is about refining abstract notions and identifying patterns among them. Naming and denoting abstract concepts is what a lot of maths is about. They are very different skills: you can be an excellent physicist or engineer without being good at maths, and you can be excellent at maths and just not get physics or engineering.