When I think about WCYDWT problems and what [I think] you are trying to accomplish, I think about situations where I find myself absorbed in a brain-teaser toy or when I am troubleshooting a computer problem. I get a feeling of total immersion; I have tunnel vision and nothing else matters until I solve the problem. For that moment, I am obsessed with finding a solution and sometimes after finding it I want it to be more elegant.

Building this capacity is what I see in your approach. The artifacts you present make it easy for many learners to think to themselves, “alright, I am stuck here in this math class …this seems interesting to me…I might was well have fun with it.” The more this thought occurs the more it becomes habitual and a part of their personality.

The trick to #wcydwt is getting the students to stumble down the mathematical path by accident. It’d be nice if they stumbled down the *correct* mathematical path (what you want to teach), but I often settle for any significant mathematical path. The best #wcydwt problems do this without the teacher being too heavy handed.

One nice thing is that, with practice, even the less confident students in class get better at seeking the more interesting questions, instead of asking “why does princess leia’s wear her hair like that?” The increase in their “wcydwt literacy” allows them to see the media (and the world?) in a different light.

I have been following this conversation about the #anyqs challenge and can’t help but comment that I think this is actually more than a possible form of student engagement as some may suggest. Methods such as this should be the goal of classroom instruction in general.

This approach to teaching is essentially student directed despite being orchestrated by the teacher. A teacher would gain the buy-in so important for working with authority-challenging adolescents. It also promotes an active higher order thinking where students practice become more curious about their world and knowledgeable about how to explore it.

Really Dan? A qualified “quixotic” merits dissent of the day?

Don’t get me wrong; I’ve got no problem being labeled dissenter. I’ll wear the badge proudly, in fact. But I do think the context of the dissent is important. Namely that I think you’ve developed a fabulous exercise.

But I want to return to a phrase you’ve used multiple times in the #anyqs discussions-so skillfully. An important lesson to be learned from these discussions and the various entries in the game is that this is really, really hard to do well.

Really hard.

And done poorly, we’re no better off than with the original bad clip art in the textbook. And we may have added the dynamic of the frustration of the teacher who invested his/her time in the image watching the experiment go down the tubes. Now, you and I have the resilience to fail dramatically, learn and make it better next time.

I’m sure this sounds like only so much more dissent. It’s not intended that way at all. It is intended as a reminder that this is a challenging and high-level task. Dan Meyer appears to do it with ease, and may in fact be uniquely qualified to do it with ease.

I, too, spend a fair amount of time teaching teachers to do really challenging things. My “dissent” comes from those experiences; the questions I raise here are closely related to the questions I ask myself in my own professional development work. What is reasonable to expect from a well-written problem in a curriculum? What is reasonable to expect a typical math teacher to execute in his/her classroom? What will be reasonable to expect this teacher to be able to do five years from now? What support does a teacher need to get better at these things?

And finally, in reading your Twitter feed over the last week, you’ve been providing fabulous professional development in giving feedback to those who have posted (including my own marshmallows 1.0). Thank you for that. I’d be interested to read your reflections on the madness when you have time to write them up.

Dan:

In terms of curriculum design, I think we know what comes next but I’m less certain what the exercise looks like. How do we add more weight to the stack?

I have absolutely no idea what it means to “add more weight to the stack”.

But I think one important aspect of what comes next is this question: What are all the ways you imagine students might solve this problem?

There is an extremely important distinction between this question and How would you solve this problem? or even How would a mathematically sophisticated person solve this problem?

And of course it’s different from How do you wish your students would solve it?

Then the next question is, Which of these ways will be mathematically productive in the future? I.e. which are generalizable to other things, and which are dead ends?

After the hook, it’s got to be about the strategies.

Ref Peggy Smith’s research group at Pittsburgh on Orchestrating mathematical discussions.

Dan:

My higher-order question is this: what mechanisms can we offer
teachers for exercising that practice online, availing themselves of all the great teachers just hanging around on Twitter?

As someone who has been active on Twitter for precisely one week (as a result of a certain #anyqs challenge with which your readers may be familiar), I’m not yet equipped to answer that question from a Twitter-mechanics perspective.

I do observe that the blog may not be the best venue for this. Consider the Coke v. Sprite example of a few months back. Lots of solving, not a lot of discussing. I’m not sure anyone learned much about possible student solution strategies.

Here’s a high-concept starting place. Once the problem is posed, the poser solves it in as many ways as he/she can think of and posts these solutions online, tweeting out the problem and the link to posted solutions. Readers solve, then look at solutions and tweet either (1) the solution number that was closest to their own, or (2) their own, new solution. You can probably think of a way to grease the social media wheels here.

To that end, here are my five solutions to Russian stacking dolls. Surely you’ve done the math, Dan-which of mine is closest to yours?

Dan, there question in the title of the article was interesting for me: “What If There Weren’t So Many White People?”

The most interesting part inside the article was the “Supposing” interactive. It asks a more particular version of the same question: “How would people approach others for dating if we removed racial bias from preferences and/or racial distribution inequality from the population?”

The totally open question to ask is the one in the title.

The intermediately open question is the one I asked above. It becomes even less open if you actually provide the interactive, rather than data behind it. I think reading the interactive is challenging enough that there is some openness left, though – it’s not a rote exercise. At least I found the task fun enough, for myself.