She agreed that hyphens and commas aren't mathematics. This is about "following directions." I mentioned that maybe too much of it can kill enthusiasm, but she didn't seem impressed. She admitted that she figures that at least half the fifth grade is afraid of her. She also said, "But I don't care. I'm here to teach them, not baby them and once they get to know me, they won't be afraid of me anymore." Uh-huh. I mentioned that there's a middle ground between babying and being too strict, but I didn't get the sense that that idea made much of an impression, either.
I have to call BS on this teacher and reiterated my earlier comment.
The rigidity is a cover for incompetence. She must be very insecure if she doesn't know how to grade a wide variety of methods and approaches to a problem.
Her approach just seems to be brazen bluster, without substance.
I did get through to her on one fairly big point, and the whole fifth grade will benefit. She gave them one of those beginning-of-the-year assessments and was APPALLED at how PATHETIC everyone's answers were. I asked to see the assessment. Turned out it was an end-of-year assessment. She had only looked at "the chapter titles of the fourth grade book" and written the test on what she assumed were the details. DD did the stuff we'd gone over already and didn't know the stuff we hadn't. Oh dear. Ms. T. actually looked surprised and said, "Maybe I better talk to the 4th grade teacher." I had to keep telling her "I went through this with DS last year; I remember what they learned and what DD learned."
So she's teaching fifth graders and clearly didn't even bother to look at the fifth grade math book.
This could be further evidence of incompetence. It also seems strange that such an extremely pedantic person is not thoroughly familiar with what material should be covered in what grade. (I suppose pedantic people can be lazy too.)
But you should check that all of the material that should have been covered in grade 4 was actually covered. It could be that the grade 4 teacher had inadequately prepared them. Also there is a huge amount of repetition over the years, so an end-of-year assessment could have a lot of overlap with a beginning-of-the-year assessment.