Most children were expected to go to school--unless they were farmers, and sometimes they were needed by their fathers in the fields. So many farmers lost their land (750,000) during the depression, so their land meant everything to them if they still owned it.
For those who lived in "town"--they went to school every day. The girls did wear dresses--most of them dressed up, really. When at school, they were not to speak unless they were called on--and once called on, they were to stand up next to their seats and speak.
When not in school, kids could pretty much run around within "earshot" or so that they could hear when their parents called for them to come in. They were usually called home once it got dark. When parents spoke--kids did as they were told for the most part. Kids didn't "mouth off" to their parents like we see today, either. That would get a lashing from a belt or something like that. There were NO "time outs" back then--just spankings--but usually a lot scarier than what we think of today.
They didn't have a lot to do in the 30's--they had no money, NO technology like we have today, and there was nothing to do. Most kids made up their own games and made forts--like we see in the novel.