By the end, he understood all the different methods, except the funky one. He nailed them all, and was given an incomplete because he did not do it the "right" way.
That is a legitimate complaint, and if it's still going on, I'm pissed.
I attended elementary school through the 4th grade in a small town alongside the Platte River of Nebraska, where conventional teaching of arithmetic was used.
Beginning with the 5th grade, I was one of those
art-nouveau elementary schools in a small town in the heart of the Sandhills. There, even though the teachers were more ancient than those I'd had in the previous school, all these "new" things, these left-wing teaching methods, were applied.
Long division was my downfall. I'd learned it the standard old way in the old school, but the new school used a different way, probably some creation of the "childhood educator" the old terrorist William Ayers.
I tried, but I didn't get it. So I continued doing long division the old way.
My teacher in the 6th grade was a real witch about this. Even if my answer was correct, she'd still mark it as wrong, and keep me after school.
Whereas I'd been indifferent, or perhaps mildly enthusiastic, about arithmetic before, I got really antagonistic about it beginning at that time. I went all the way through high school without taking a single course in mathematics.
At the time, the University of Nebraska-Lincoln was compelled by law--it's not so any more, alas--to admit anyone who sought admission, who was a graduate of any high school in Nebraska, and so I got in there anyway.
But I had to take mathematics in college; there was no way out of it.
However, since I could now do the mathematics my way, it was a breeze, despite no high-school algebra, geometry, calculus, whatnot. I didn't get As--they were usually low Bs and high Cs--but I think that was pretty impressive, given my previous non-learnage.
Even though I was getting a liberal arts degree, I still had to take four courses (12 credit hours) in one of the "hard" sciences--chemistry, biology, zoology, botany, whatnot. I opted for what I figured was the easiest of the hard sciences, and took physics. I got As in all four of them.
Teaching "there's only one way, and it's the new way" is shit.