When I first started flipping my math classes, class time was agony for me. I could hear the crickets chirping, and I knew there had to be better things to get my students to do than the usual text book questions. But now, about two years in, I'm having a hard time fitting things into my class time.
What am I trying to fit in you ask?
I don't mean lecturing, of course, and I don't mean necessarily me talking, but I do mean a whole-class discussion. I want to create some sense of group cohesion, that we are a team, on a journey, and that part of the journey is getting to know each other in this math context. I don't want to go through a whole year with a bunch of people who feel no connection to each other. And yes, it's fine if all they have in common is that they worship their math teacher, I suppose I can live with that. But if, once they're done this course, they never speak to each other again, or never think fondly of the things that they did here, I have failed them in some way.
So at the very least, we spend a few minutes chatting, maybe about math, or maybe not. I like to start the class talking about something that they have done, like their comments from the most recent voicethread, or about some of their recent blogposts. Recently we laughed about some of the words we're using in our log studies, like logalicious, smooshing, de-logging, and they came up with a new one: to "Lion King" a logarithm. More about that in another post. But in coming up with our own funny language, we all said, without words, "We are us."
This might be just a quick checkup on the basics, for example, I often have them all work something out on the eboard at the same time. This isn't only so that I can see if they're getting it, it's also a nice combo of individual work and group work - they're working on their own but they're checking out everyone else's work at the same time. And they love it! If they don't know what to do, they watch a peer's work unfold, and I can just get someone else to answer questions or explain as they're working. It's a great opportunity to get them talking about math in their own language. Here's how one group's work looked at the end, and by the way, not everyone started out knowing what to do, and we talked about scientific notation to boot:
The goal of this time is to deepen their understanding, often doing group work. I'm not a huge fan of group work just for the sake of group work, but if it arises organically, as a result of a need to discuss, compare, gather info, then I'm all for it. There are a lot of people out there who are creating wonderful activities like this, for example, Dan Meyer, Kate Nowak, John Golden, or any of the people in the geogebratube.org community.
When I create my own, I use Malcolm Swan's great document as a guideline. Last week, I wanted to open their eyes to some details that they may have easily overlooked, for example, that log ab² is not the same as log (ab)². Here's the activity, complete with answers, which, by the way, I did NOT make available to them until they had struggled and suffered to my satisfaction:
Individual help time:
During this time, they are working on the items I've assigned via a weekly checklist, which means this is when they are likely to need help. My goal is to speak to every single person. This is the greatest time-hog of all. I cannot honestly say that I am reaching every student everyday, à la Jon Bergmann/Aaron Sams, but I do aim for that. I try to set things up so that if I'm not available, they can ask a peer for help. (So far, in the online environment, that hasn't really happened to my satisfaction. I think that is one thing that happens more organically in the brick and mortar class. That's another post.)
Just like in any class, there are some students who always initiate a conversation with me (Mrs. I need help with...), and some who never do. For those kids, I have my checklists (info that they send me during the week via a google form) at the ready. So if I see that Susie hasn't checked off the geogebra activity.....Susie, have you uploaded your geogebra? No? You need help? Or, Tommy, you haven't checked anything off for this week, what's up? Get it together man! (I don't actually speak to my students that way. Yes I do.)
The Big Picture
I'm not saying that I can fit all of these into every single class! Most of the time, I manage to fit in the talking and the individual help, with something else sandwiched in between. And that something else is constantly evolving. My hope is for that part of the class to live up to the goal set in this brilliant post by Robert Talbert, that is, to "focus class time on the stuff where they are most likely to get stuck and need their social network and a professor to help."
But that evolution can only happen with collaboration, unless you are immortal, or don't have anything else to do in your life like, say, take care of a family or watch movies and go for walks. It takes a boatload of time to create, try out, reflect on, and improve our classroom activities, and when we share, or better yet, create things together, or EVEN BETTER YET, COFLIP, we divide and conquer that time!