This is one issue that I'm passionate about. Research increasingly implies that homework is probably harmful in elementary; of dubious value in early middle school; and only valuable in high school and beyond.
> and objective performance assessments
I think some of these radical experiments are crazy. But, there's valid reasons to consider e.g. not grading missing absent assignments as a zero. A few of them:
A) If our goal is for grades to reflect demonstrated student mastery --- a missing assignment doesn't indicate that proportion of mastery "missing." Especially if it has been demonstrated satisfactorily on an exam or by other measures.
B) A couple zeroes on a gradebook can be an insurmountable hill to climb-- leaving no further grade incentive at all for students to work hard in the class.
C) Grades are strong motivation for already-strong students with the most involved parents, but can actually be demotivating for the bulk of your class. An effective teacher needs to find other ways to motivate students. For many students, grades are something that can make one feel bad about oneself but not provide an opportunity for positive differentiation.
The classes I teach are "easy A's" in the gradebook for most of my students... and are incredibly demanding compared to normal MS/HS fare. This requires buy-in from my students. I work to build genuine curiosity and in-class competition (on a variety of axes where all students can excel, not just the top couple dunking on everyone else).
A small (effectively zero) positive correlation was found between the amount of time a student says they spent on homework in elementary and achievement, but a slight negative (effectively zero) correlation was found when looking at the time parents reported students spending on it.
These measures don't show a causal relationship: "good students" are more likely to do homework. "poor students" are more likely to take a lot of time to complete the same amount of homework.
Elementary student reports of time spent on homework are not reliable. Parent reports are even worse.
The only causal evidence of a benefit in assigning homework in elementary comes from two short-term intervention studies: whether giving a homework take-home worksheet about vocabulary improves performance on the next vocabulary test (it seems so, very slightly). The longest term observational studies show a negative effect.