## Dan Anderson’s Mathematical Story

Frameworks are inherently limiting. The more guidelines you specify, the more material you exclude, some of which can be very good. Frameworks are great, though, because they make implementation easy. I know what happens in the first, second, and third acts of a mathematical story, so it'd be a simple matter to use Dan Anderson's lesson in the classroom — no lesson plan or handout required.

### 9 Responses to “Dan Anderson’s Mathematical Story”

1. on 24 May 2011 at 7:20 amChristopher Danielson

Happy to dissent here.

Dan M.:

I know what happens in the first, second, and third acts of a mathematical story, so it’d be a simple matter to use Dan Anderson’s lesson in the classroom — no lesson plan or handout required

Spoken like a man at the beginning of his formal career in teacher education. No dig intended here, Dan. It’s just that the knowledge you have (and possibly many of your readers-I don’t honestly know) that allows you to take the candle video, plug into the framework and run with it-that knowledge does not come for free.

You (Dan Meyer) have written that you were a crummy teacher for the first couple of years of your career. That’s a very common story. You took a lot of risks, learned from the failures and became the teacher you are today over time. That’s my story too. But in mastering your framework, you gave very careful attention to the details of your lessons. That’s a lesson plan.

I’ve learned a lot from working with teachers around Connected Math. Launch, explore, summary is a framework too, and I can report from the field that a solid framework does not a cohesive lesson make.

Consider Griffy counts. It’s fun and there’s some real math to do with the video. But what happens after I show it? I have a rough idea. But I’d need to sit down and plan my lesson if I want it to go in a productive direction. I know my audience (e.g. College Algebra students) quite well, so I have some decent guesses about the strategies they’ll use (to wit: most will assume proportionality between time and count, but few or none will use the term; a few will draw on their knowledge of young children and guess that he doesn’t ever get to 120; a really sophisticated College Algebra student might notice that Griffy is getting the syllables out as quickly as he can and try some sort of proportionality between time and syllables-and therefore no proportionality between time and count).

And what do I do to turn all of that into a productive lesson? I plan.

I have a thought experiment I apply to my problem-based lessons (and to those I observe). The thought experiment serves as a kind of assessment: If someone asked my students on their way out the door, “What was today’s lesson about?” what would my students say? If they say it was about a little boy counting, I’ve not nailed it, I don’t think. They would need to say it was about proportionality, or linearity, or rate of change, or function. The framework doesn’t make that happen; the lesson plan does.

Now, I don’t write the kind of formal lesson plans I make my methods students write, nor the kind that it’s fashionable for principals to require these days. But you’d better believe I’m not just relying on a set up and a framework to make the math fall into place.

No, there is lesson-specific work to do.

Now, it can certainly be argued that Dan Anderson has done that work with the stuff he has put together in his second and third acts. But that’s the lesson-specific work I’m talking about. That’s not just the framework (a general tool for describing the flow of a certain class of lessons). That’s a lesson plan (a specialized tool with details pertaining only to a specific lesson).

But if Dan is my methods student, or if he’s a new teacher and I’m his mentor, or if he’s a colleague trying this framework out for the first time, I’m going to want to know more. I’m going to want to know how he expects students to generate the linear regression; I’m going to want to know what he’s going to do with the student who just can’t get past the different colors/shapes/fragrances, etc. I’m going to want to know how he’s going to get students to learn from their process; how he’s going to help them generalize these ideas to other situations.

In short, unless Dan is experienced at this sort of teaching, he’s got some more planning to do. And if he is experienced at this sort of teaching, I bet he’s done that planning-whether on paper or in his head.

2. on 24 May 2011 at 8:38 amjosh g.

As a still-newish teacher who has more ideas and theory crammed into his head than he has practical classroom planning experience, I think I’d agree with Christopher.

The three-act framework, SBG, and my own pet theory of porting game design principles to teaching, are fantastic tools to guide my work. But until I actually *do* them, I don’t achieve mastery.

Wait, that’s just like learning math.

Theory -> understanding
Practice -> mastery of skills

Metacognition, oh snap!

3. on 24 May 2011 at 8:53 amjosh g.

ps. But that doesn’t change that this is an awesome video.

Although I’ll admit I was sure the question would be, when will the melted wax run over the edge? Except *it doesn’t unless there’s a breeze* oh snap on me! (And the long form video that Vimeo reveals shows that he’s onto the total burn time and the wax is just happily contained at least halfway through)

4. on 24 May 2011 at 1:57 pmKristjan

So, how long does it take?

5. on 25 May 2011 at 6:52 amgasstationwithoutpumps

Why isn’t there a clock in the video?

6. on 25 May 2011 at 2:21 pmDan Anderson

@Kristjan
Information for final answer found here: http://dandersod.wordpress.com/2011/05/23/candle-burn-wcydwt/
I’m too much of a teacher to just give you the answer :)

@gasstation
Because I’m a complete Adobe After Effects newbie. Still need to learn the ins and outs before attempting a timer.
Also there is good math to be done in figuring out the burn-time using the time-lapse settings. No?

7. on 26 May 2011 at 12:37 amGilbert Bernstein

Maybe it’s just me, but the fascinating things about the candle burning (for me at least) were not how long it takes to burn. Rather…

* Wait! The candle seems to be disappearing. Do candles evaporate?

* The candle seems to change shape in funny ways. Those are some cool shapes.

This isn’t to say the “How long…” question isn’t a good one, but it seems like the candles could be used to get at some much more meaty questions that might not have nice mathematical solutions. For instance “How does the candle’s shape change over time?” You could probably do that by melting other things too.

Also, while it’s on my mind, perhaps there’s some danger in using too many videos that are all designed to prompt the same kinds of quantitative questions. Is there also a place for occasionally interjecting videos that resolve into natural questions that the students won’t be able to answer? (and not just as a “that’s why we’re going to learn about…” kind of moment)

8. on 26 May 2011 at 1:51 amDan Meyer

I just wanted to check in here and say, yeah, Christopher has me by the throat. Only by degrees, though. I overreached but I still stand by storytelling as the framework that nails the rule of least power better than anything I’ve encountered yet, a happy marriage of flexibility and utility.

9. on 26 May 2011 at 5:28 amChristopher Danielson

Dan:

Only by degrees, though.

So to speak. Well, only one technically. And it won’t be long.

I still stand by storytelling as the framework that nails the rule of least power better than anything I’ve encountered yet, a happy marriage of flexibility and utility.

No argument there.

Say, not sure whether these comments are the place, but I’d love to start a conversation about the roles of context and culture in the framework.

I posted a flaming turd of an #anyqs video this week. Ruminating on the no-longer flaming revision (possibly still a turd, though), it occurs to me that my interest in the mathematical question here is due to my particular interests in (1) the mathematical thinking of children; (2) the tools of mathematics instruction in elementary school; and (3) the interactions between these.

I teach a course in which these three topics are central. I conjecture that a few weeks into the course next fall, after having analyzed a number of instances (mostly video-based) of children’s mathematical thinking, and having spent some time with the Dienes blocks Griffy is discussing, that my students will have very different questions from those surfacing from the population of Twitter-savvy math teachers. That context will be different; my elementary licensure students will bring a very different mathematical lens to the party.

A dear teaching friend of mine challenged you and me on a related issue recently. You sort of left at the existence-proof-that-#anyqs-can-be-done-well phase. No argument there.

But it seems reasonable to probe a bit deeper on issues of classroom context and culture-especially in light of your contention (which I support, by the way) that WCYDWT is a potential boon to ELL students.

Thoughts?