Yeah, let me also add that my daughter would be having a MUCH easier time of things in college if someone had laid down the law with her re: showing her work in greater detail a lot sooner than, say, calculus.
She's internalized that she shouldn't HAVE to, see.
The real reason for showing your work is so that another human being can follow along using the same method of problem solving that you have chosen.
It's also grooming for higher levels of instruction where that is essential to helping students find and remediate problems with their own understanding and problem-solving process. Without being able to see exactly where a student's process derails, all you have is "this velocity question is wrong." That's not very helpful if the student's problem is that s/he wrote down the wrong mass, versus not differentiating correctly or something like that. KWIM?
It's about forming good habits young. And yeah, it's kind of excessive when we're talking about math facts that educators are also hoping that students will gain automaticity over-- because really, 'explain why 2 + 2 = 4' would be a pretty challenging thing for most adults, and ditto for a child who has one-to-one correspondence and math facts to 10 down.
But "explain" relative to simple geometry and algebraic problem solving lays the foundation for communicating more complex ideas, and proofs, etc.
How capable is the average 6 or 8yo of 'getting' that series of ideas? Probably not very-- not even if s/he is PG.
It's just a lack of perspective and life experience.
