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@mekkaokereke @longobord
When my brother was a math PhD student, he tutored undergrads, and his stories sound a lot like yours.

In one tutoring session, there was increasing mutual confusion until he finally wrote out:

x + y = y + x

…and the student said, “Why did nobody tell me this?!?”

Years of mechanical computation — learn process, repeat 50x — had left this student without the most basic mathematical intuitions. (Probably compounded by abusive teaching.) Of course they were lost.