I am OK with test retakes (one per test) if a student scored below 75% on a test, and the maximum possible retake score is 75%. It encourages students to do their best the first time rather than try to play the system (which is what they do), and it allows for some recovery for the good student who bombs one test.
I am very OK with zeros, particularly on homework that is not attempted. In my experience, completing homework is a very valuable part of learning math. Each day, I cruised the room and looked at everyone’s homework. Sometimes I was spot checking but mostly, I was looking for problems that students had with it. In precalculus honors, for example, there were usually three or four problems that gave many students problems, and I always addressed all questions. Occasionally, I assigned a problem that only a handful of students would/could do, and that was OK. It challenged the top students and I always made it clear that such problems wouldn’t be on any test.
I am also OK with zeros for tests or quizzes that were never taken.
One policy I didn’t see listed was the one about deadlines. The last year that I taught, we couldn’t impose deadlines on anything, so that, for example, a student could turn in a large stack of homework on the last day of the trimester and we were expected to accept it without penalty. I am very opposed to this because the idea of homework is that it facilitated learning as we moved toward a test. It was counted as zero points once we took the test over that chapter.
“fears of too many parents who worry that Madison’s public schools are not rigorous enough”