Just to reinforce things: we are talking about kids very early in their math career. And math is drill; Khan academy, all that. It's an investment.
You can do drill in 8th grade, or you can do it in your freshman year of college.
The point is:
1) I thought it annoying and pointless in the 8th grade. Oh clever me, I knew so much better.
2) People who sucked it up and did it, with whom I shared classes, blew my doors off in college math courses for a couple of years. A teacher made this the central fact of the algebra class they took.
3) Then I took the discrete math course, and stopped having trouble.
There is something to this. Rigor is not natural. Learning rigor is essential to being able to operate your life well.
You can do drill in 8th grade, or you can do it in your freshman year of college.
The point is:
1) I thought it annoying and pointless in the 8th grade. Oh clever me, I knew so much better.
2) People who sucked it up and did it, with whom I shared classes, blew my doors off in college math courses for a couple of years. A teacher made this the central fact of the algebra class they took.
3) Then I took the discrete math course, and stopped having trouble.
There is something to this. Rigor is not natural. Learning rigor is essential to being able to operate your life well.