What constitutes a story?
"The first C is Causality. Events in stories are related because one event causes or initiates another. For example, "The King died and then the Queen died" presents two events chronologically, but "The King died and the Queen died of grief" links the events with causal information. The second C is Conflict. In every story, a central character has a goal and obstacles that prevent the goal from being met. "Scarlett O'Hara loved Ashley Wilkes, so she married him" has causality, but it's not much of story (and would make a five-minute movie). A story moves forward as the character takes action to remove the obstacle. In Gone With the Wind, the first obstacle Scarlett faces is that Ashley doesn't love her. The third C is Complications. If a story were just a series of episodes in which the character hammers away at her goal, it would be dull. Rather, the character's efforts to remove the obstacle typically create complications—new problems that she must try to solve. When Scarlett learns that Ashley doesn't love her, she tries to make him jealous by agreeing to marry Charles Hamilton, an action that, indeed, poses new complications for her. The fourth C is Character."
At the end, Willingham challenges us to incorporate these C's into lessons. In particular, the most important C, Conflict. "Teachers might consider using 10 or 15 minutes of class time to generate interest in a problem (i.e., conflict), the solution of which is the material to be learned."
I think this is compatible with several MTBoS approaches, in particular & obviouly, 3-Act lessons.
Character - my biggest question after my first read was who are the characters? Not in a heavy handed Life of Fred way, but in the story. I think it must be teacher and students for us. We resolve the conflict, after all. Probably one of the inherent advantages of inquiry teaching is making the students the central characters. Not that we teachers can't be involved - I think we have to be ready to jump in, too. But we can't be Deus Ex Machina everytime, and let the students know there's always an out.
Math lessons are well set up for storytelling otherwise, I think.
Causality - why does this work is a great basis for an investigation. Add up the digits - if that's divisible by three the original number was, too. What? How could that work? Look - these three centers of a triangle are always on the same line. Why on earth...? Of course, if we make it out that knowing the fact is more important, we're killing the story. This is historically a great spark for mathematical developments as well. While I was writing this Sam Shah posted this image which got my mind wandering, making me go off and do some GeoGebra.
Conflict - I have no idea if this is unusual, but I try to get good math arguments going every chance I get. I usually refuse to be the authority. ("Is this right?" What do you think? "I think so..." Well, let's ask the class!) Plus anytime I ask for an answer, I always ask if there are any other answers. And when the students propose answers, there's a chance for a math argument. It also makes me think of Chris Luzniak and his Math Debates. Even whether a particular topic is math can be a great argument. There's a course I start with Sudoku, and the last question is, were we doing mathematics? I have never had a class agree on this answer.
Complications - is there anything more mathematical than this? Oh, that worked. What if we added this? Could we do it still if we didn't know that? Messing around with conditions is prime mathematical behavior. And if the problem is problematic enough, this happens by itself. I could solve it if I knew that, now how do I find that out? Or you're trying all the cases and get to one where the freak out lives. Or you're practicing the very mathematical habit of mind of trying to find counter-examples to your own idea.
Where I think these C's might be helpful to me is in being more intentional about the type of math the students are working on, and using this structure to help design how I'm going to try to get my lead characters to find the problem.
progression of multiplication, so I'm going to try to use that in contrast with their native ideas about teaching multiplication. (Also such a nice synthesis of understanding to model for them.) In the past I've mirrored mathematics development in children and schools, starting with number concept and building up. This will essentially be going in reverse, but will hopefully be a more obvious need to know that will motivate the deconstruction on supposedly simpler topics to follow. Wish me luck!