More musing on the coaching relationship… I thought it might be worthwhile to imagine how I would assess myself and how I’d want observers to assess my classroom. Here’s what I’ve got so far. I hope that observers would see:
I’m about 2/3 of the way through Maggie Lampert’s remarkable book “Teaching Problems and the Problems of Teaching.” Why remarkable? Because she collected and analyzed massive amounts of data from an entire year of problem-based teaching, in order to figure out what kinds of decision-making and planning and work went into the art of teaching (at least for those kids, with that teacher, that year). It is both a teacher journal and an academic work, and it’s one of the best descriptions of the act of teaching I have ever read.
Meanwhile, I’m being a sort-of math coach this year (doing weekly visits to a small group of teachers at a public high school, helping them implement a problem-based curriculum). I’ve tried to hold onto Lampert’s descriptions of all of the decisions she’s balancing within every teaching act, and I’m really mindful of the complexity of teaching as I observe and debrief with my coach-ees. But there’s something more that I need to be doing as a coach, someone with long-term learning goals for the teachers I work with.
Thinking about the problems that Lampert lays out:
* Teaching to Establish a Classroom Culture
* Teaching While Preparing for a Lesson
* Teaching While Students Work Independently
* Teaching While Leading a Whole-Class Discussion
* Teaching to Deliberately Connect Content Across Lessons
* Teaching to Cover the Curriculum
* Teaching Students to be People Who Study in School
* Teaching the Nature of Accomplishment
* Teaching the Whole Class
* Teaching Closure
I wonder, in trying to change individual or school or district-wide teaching practices, do all of these levels need to be addressed? Is there an order? How are they interrelated? Are we better at addressing some than others? Is this a useful framework for organizing math coaching interactions?
Please think with me in the comments!
I wonder if part of the problem that northTOmom’s twins encounter in their math classes (http://northtomom.blogspot.com/2010/10/this-math-depresses-me.html?spref=tw) is that we don’t teach students how to learn and study math?
Here’s what I’m thinking about: to really understand and make use of something in math (like long division), you have to understand the CONCEPT, have METHODS for solving problems, and have a PROCEDURE that lets you effectively and efficiently solve any problem where division is useful. I wouldn’t expect students to discover the efficient long division algorithm. But I do expect that they can and will construct an understanding of long division concepts (like what division means — how many of these are in that, place value, etc.). I also expect that they are perfectly capable of finding ways to do meaningful division tasks (like figuring out how many 1 1/4 yard-long banners they can cut from 10 2/3 yards of cloth). Then I want them, once they have a concept and meaningful methods, to learn a procedure. That can be by teacher demonstration, by building up from student methods, by rote, whatever. Then, to do the exact task that northTOmom described in which students break down the procedure and connect it to their conceptual understanding and personal methods.
For some students, those concepts and methods are easy to come up with and the mathematical symbols are as sensible as the yards of material. For those kids, I’d be happy to show them a procedure and ask them to pick it apart. But for all kids I want to be sure that the have the trifecta of CONCEPT, METHOD, and PROCEDURE.
The various reform curricula are, I think, designed to be more explicit about focusing on concepts and methods. But too often in their implementation, students are expected to get to procedures very quickly without instruction, rather than being taught how to understand math problems, strategies to solve them, and learning strategies to help them move from solving one problem to developing a procedure. I’ve worked with too many teachers who see that the topic is “long division” and try to get students to do and understand long division procedures without actually teaching them. In good spiraling curricula, there is something to master at every level, but it might not always be the efficient algorithm. It might be getting good at reading and making sense of problem contexts that involve long division. Or getting good at recording the methods you used to solve long division problems. If those learning steps are noticed and celebrated, then the frustration element decreases, and the students’ understanding of what they are learning, and why, is increased.
I could go on, but I think I’ll wait to see what others might say in the comments…
Welcome to Max’s as-yet-unnamed blog! For the first post, I thought I’d do a preview of coming attractions (and that way when I don’t know what to write about, I can come back here and find out what I thought I was going to blog about!)
So, here are some things you could expect to see in this space:
Please leave a comment suggesting a cool name for a math-ed blog by a guy with the remarkably math-y name of Max Ray, and/or suggesting other topics you’d like me to blog about.