I've heard of classrooms with "fraction means divide!" as a mantra - wonder whether that might be the root of this mistake? Glad it's sorted, anyway!
Learning by epiphany, blocks - does this indicate too great a tolerance for not understanding the first time a mistake is made?
I suspect it did arise either in "fraction means divide" or in "to divide by a fraction, you multiply by the reciprocal." I originally thought the entire issue was that she was doing too much of the setup in her head, and confusing the original fraction with the reciprocal.
I think it's not a tolerance for not understanding. Erroneous belief that you are understanding, maybe, followed by a complete lack of insight into why that understanding was not producing the desired results.
DD as a preschooler was desperate to read, and begged me to use the "teach your child to read in 100 easy lessons" book. She got stuck on blending (an early step that the authors saw as so easy that they had no suggestions for what to do when your kid could not do it, which suggestions they did have for common sticking points), and no amount of effort on either of our parts would unstick her. So we gave up, and a few months later, with no effort at all, she could suddenly read anything.
She was the same way with walking - there was no incremental improvement, just bang, one day she stood up and walked without ever falling. Same with talking - she talked so little that she looked way behind, then suddenly she was way ahead.
From my own perspective, I completely thought I understood. I could have repeated back verbatim the usual explanation given in school for how to set the entries up. I'd carefully review it before I created an entry, look at each aspect and compare it to the rules, set up the entry, double-check against the rules. Everything looked right to me. And it was wrong every single time. I even thought about just reversing the entries I thought were right up front, rather than confirming they were wrong first, but I was reluctant to do that because I was sure I was right this time! (In my case, I think I was thrown off by the classroom mantra that "credit doesn't mean negative." As it happens, in my workpapers negatives are always credits, which makes setting up the entries trivial.)
