“No this is a valid mathematical technique. It appears silly in this example because the teacher is using single digit numbers. And yes the student should have been taught from rote memory that 9+6 = 15.”
But the way the teacher demonstrated it was nothing like this. She was either intentionally or unintentionally making it more complicated than necessary and ignored the meaning of base-10 numbers.
I maintain that this is deliberately done to bog down the smarter kids.
Maybe it's because the teacher is just as bad at math as her students.
She probably teaches them that the base ten numbering system is made of the digits 1-10.