Random thought...actually I was reading a blog on someone who I wish I knew better's site. Research in Practice - Ben Blum-Smith If you've not seen it, take a look. Just come back here when you're done.
I've seen some D. Ball videos. I was forced to watch the same one 4-5 times and the little kids are cute, but they're not high school students. My kids are a little more, um, real. I've taught from 5th grade right through 12th. Elementary school kids are much easier, molded. (I sometimes wonder why I moved up) She's still a master.
I live in Michigan, and though D. Ball is at Michigan State I still think she rocks, but my wife doesn't (really, just on general principle. If you lived in Mi you'd understand)
I'm calling this the "Case for Co-teaching"
Its so frustrating being the only person, in most classes, asking the questions. Lets face it, at times we're like chess masters playing high-school neophytes. I hate this. I've once, in the past 5 years, had a student really surprise me, mathematically. If only we did a better job modelling having a good mathematical discussion, then maybe they would know what one looks like (and how much fun it can be).
Our choices are to model this behavior in some way... Or, hope that mathematical discussions will just spontaneously begin and allow us to be witnesses of it. (or you can become known as the weird math teacher with all the puppets and strange voices..)
I've done the "special-ed" co-teaching thing. Generally with a teacher who is also teaching history and another math class as well. I love the Special Education Dept at my school, so let me get that out into the open and honestly had I done things differently then I'd be one of them as well. That being said, they are either stretched too thin, pulled from the class or honestly ill-prepared and sadly the kids get an opinion about them that unfortunately is true.
I want a teacher, someone who the kids know is in the classroom to come by and visit. I want 5, maybe 10 minutes of their time. Just to come by and have a mathematical discussion. It doesn't need to be scripted out, the visiting teacher would get to choose the topic (and would pre-warn me...seriously, if I've got to talk about the economic theories of Malthus or something I want a little notice). I want to model a mathematical discussion. I want the students to see two people work their way through a problem involving mathematics. Imaging me coming to your class (for sake of argument, my part in any movies will be played by Johnny Depp as he is the teacher I most often get told I look like) and asking you to help me with proving Heron's formula the week before you start teaching proofs to Geometry students. (I promise I won't try and make you change all the "s"'s to "arrrrrrghs".)
I've contemplated the idea of doing this virtually. Timezone issues make this problematic, though not necessarily too bad as I live in the Eastern Standard Zone. For teachers in the West, sorry it is not fair. (math teachers will get that, probably no one else). It does require two teachers willing to follow the same general curriculum timeline (hello CCSS... you've given us the same topics lets see what we do with it). Although in all honesty, it really doesn't. Better yet imagine Skyping with my class; as students in my class help you introduce Logarithms. In this way we first model the discussion, then we show students having the discussion with a teacher and perhaps, finally our kids could discuss mathematics with each other. Either IRL or virtually.