Experiment in my algebra classes: I work with a small group on new content and my co-teacher works with another group on independent practice. So far it’s going awesome. My kids aren’t able to work in groups independently (YET) but I can facilitate conversation between them when I have a group all within arms reach. I do a bit of elbowing when kids don’t respond to each other and they’re all “oh! I could answer his question!” One kid was in the bathroom when we started so the group started catching him up. Then a kid went to get a drink of water during that time. When he got back from his drink he asked, “are you still explaining?” And we were, but it was great, because in the group kids here and say the ideas so. many. times. And what better way to internalize an idea?
I gave PreCalc a couple complicated functions and asked if they were inverses. They know several ways of determining that and there was quite the debate over which (if any) method they should use (some kids were convinced they weren’t inverses and wanted to just write that). Finally a kid said to graph them so I pulled up desmos. The whole class gasped when they saw the perfect reflection. Now they were hooked and wanted to compose the functions to see how it could possibly simplify. A student came up to the board and tried things and the class cheered and yelled and clapped when they finally figured it out!