I once had an assignment quite like this when I was still in college. For psychology (child development), we were tasked to observe a toddler, record his behaviors, speech, etc and compare those to existing studies to determine developmental delays and advances. I have to put emphasis on the word OBSERVE; we were strictly told not to interact with the kid, and not be obvious that I was doing an observation.
Lot's of school have a "take care of a kid" project. We had to take care of baby dolls that cried all the damn time (like real babies) when we were in high school. The baby recorded whether you fed it, changed it, how long you let it cry, etc. It was part of a Personal Planning course. So probably something like that, I guess?

Okay but why is that a school assignement to begin with ? Is it something that happens in real life ? Baby-sitting a kid as group work ? I very much doubt it.