Where I teach in New York, I know that other instructors commonly do the following -- Prior to the start of a class session, require a few (2 or 3) students to write the results of a homework problem on the chalkboard. From what I can tell, these problems are not assessed or discussed in any way (the instructor just starts the class with some other lecture topic). My impression is that students are checked off for meeting this requirement a few times through the semester (but it's not attendance; that's done separately). This is not something I ever encountered in my schooling, nor have I ever read about as a suggested technique in any report or study.
Can someone explain to me, or link for me, what the rationale of this practice is?