And we turn him into an anecdote, to dine out on, like we're doing right now. But it was an experience. I will not turn him into an anecdote. How do we keep what happens to us? How do we fit it into life without turning it into an anecdote, with no teeth, and a punch line you'll mouth over and over, years to come: "Oh, that reminds me of the time that impostor came into our lives. Oh, tell the one about that boy." And we become these human jukeboxes, spilling out these anecdotes. But it was an experience. How do we keep the experience?
John Guare, Six Degrees of SeparationWhen I was a starting teacher, it was as much as I could do to articulate what I wanted my kids to know at the end of the day, much less at the end of the week or month. A key development for teachers in transitioning from that beginner level to something like "proficient" is learning to anticipate what's needed for instruction over the next week, month, and year: for example, knowing that you have to teach a bunch of chunking in Algebra II and Precalculus so that students can do integration by substitution in Calculus.
That's where standards come in: they tell you what you have to do in each year so that kids can go on and do what they need to do the next year. Whether you're using the Common Core standards, Next Generation Science Standards, or an in-house list, this shift in perspective -- from "What am I going to do today?" to "What do kids need to learn?" is crucial if you're going to accomplish anything--and if your students are going to make any genuine progress.
But I've noticed that master teachers--like my co-blogger John, or my friend Doug O'Roark--ask a different question, not necessarily first, but early in the planning process. This question is: "What experience do I want kids to have?" I find that this question more than any other has changed my perspective about planning for classes.
What experience do I want kids to have? Is the goal to give them the experience of discovering something? Of exploring in a rich "sandbox" of cool math ideas, regardless of what they wind up conjecturing and proving? Of solving involved numerical problems? Of developing a set of ideas to describe a new situation? Of applying old ideas to solve a new problem? Or ... ?
Attending to the quality of my students' experience rather than simply on what I want them to learn leads me to new ideas--that, even in a mostly-remedial algebra class, it's important to have fun. (The way Doug and I did this was to do magic tricks with Algebra.) And it puts common teaching pitfalls into perspective. I mean, who would answer the question "What experience do you want the kids to have today?" with "I want them to watch a powerpoint for 30 minutes"? And who would want kids to have the exact same experience, every day, for 180 days?
I think that one way to understand the Standards for Mathematical Practice section of the CCSS is very much in this vein: they describe and, to a certain extent, prescribe the kinds of experiences we want kids to have while they are learning the content in the other standards. For example, take SMP-1, "Make sense of problems and persevere in solving them." The "standard" doesn't describe a set level of perseverance that kids are supposed to attain, or even clearly define what "making sense" of a problem is. But it suggests that kids ought to be experiencing problems that are ill-defined, or at least initially resistant to mathematical analysis, and that these experiences should include trying more than one approach before being successful. Thinking of the SMP in this "experience" way helps me reconcile the essentially-fuzzy nature of those standards to the others, and also helps me think about how to mesh the two: the point isn't to do one kind of standard and then the other, but to approach one (content) standard in the mode of one or more of the others.
And that "or more" leads my musings to a caveat. At its best, mathematical experience is rich: a great class is one in which kids are spotting patterns, making conjectures, trying things out, having fruitful errors, using various technologies (from compasses to computers), all woven together into great mathematics. It's a rich story. What the CC-SMP provide us is more like a set of anecdotes. Their list isn't exhaustive, and it isn't supposed to be exhaustive--but that's not my problem. My problem is rather that boiling down one of these terrific class days into a set of three or four practice standards is, as Guare's character Ouisa warns us, turning an experience into a set of anecdotes. When we do that, we lose--the math loses--something essential: by being just explorers, or cross-examiners, or number-crunchers, we stop being the rich, mathematical people we were when the class was going on--and the math stops being, well, mathematics.