Can confirm - While I was decent at math up to a point, fractions and long division in 4th Grade sent me down a hole that took me years to get out of...until Algebra II as a junior in HS crushed me.
I blame this on my Chemistry teacher - a class which I was also taking at the time - who spoke little English and had never taught in the United States until the year I landed in her class. I actually did reasonably well in Algebra for the first quarter or so until it all fell apart.
I re-invented what turned out to be short division (no joke! I wouldn’t learn it had a name until I was in my late 20s) because I hated long division so much, same year we started doing long division in school (4th grade? 3rd? IDK).
Fits in about the same space as the original problem unless it’s printed so small that you have to rewrite it, and way less room for transcription errors. I also find it clearer but that may just be me (fwiw I’m “bad at math”—I find it incredibly boring and basically can’t follow proof- and equation/identity-based stuff, I have to turn it all into algorithmic thinking to have a prayer of understanding it; i.e. my opinion on the superiority of short division is that of a mathematical imbecile, so, grain of salt)
> I blame this on my Chemistry teacher - a class which I was also taking at the time - who spoke little English and had never taught in the United States until the year I landed in her class.
It doesn’t help that in chemistry, 1 + 1 may be 1. Or 3. :-)
Under the “example” section, the little superscripts are what you write in by hand on the problem as you work it, at least as I did it. 9/4 in the hundreds place is 2 with 1 remainder, so write 2 up above as part of the solution and a 1 superscript next to the 5 in the problem itself (tens place), now that’s 15, divide that, 3 goes in the tens place of the solution, write the remainder (3) next to the digit in the ones place as a superscript and do it again, if you need to keep going just add a decimal point and zeroes as required.
Way faster than working long division, takes up less space, and less error prone (imo). What’s actually going on is clearer (again, imo)
I blame this on my Chemistry teacher - a class which I was also taking at the time - who spoke little English and had never taught in the United States until the year I landed in her class. I actually did reasonably well in Algebra for the first quarter or so until it all fell apart.