I haven't really seen that
In the districts I've worked in, kids (even Kindergartners and 1st graders) are always doing meaningful work. In fact, in the district I'm currently in, the Kinders' day is so jam-packed with academics that the choice time is down to about 30 minutes in the full-day program, I think.
I would be interested to know which districts Dr. Kozloff has visited. Perhaps he visited a lot of inner city classrooms with low expectations?