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Christopher Danielson:

Your quest for the perfect image that will get 100% of viewers on board with the same mathematical question may be a bit quixotic …

Avery Pickford:

In [my ideal] world, I imagine spending a greater amount of time talking about the aesthetics of what makes for an interesting math problem and much less time cajoling students to ask the “right” question.

John Scammell

It’s unfortunate that we are so curriculum driven that we have to trick them into inventing the question we want them to come up with.

Here's the thing: nobody watches Jaws and feels cajoled into wondering the question, "Won't anybody stop that shark?!" No one watches Star Wars and feels tricked into wondering, "Will the rebels defeat the Galactic Empire?!" Those questions are irresistible, not on account of any deception on the part of the cast or crew, but because the cast and crew evoked the central conflict of their story skillfully.

This isn't to say those questions are irresistible to everybody. Some people lack the cultural prerequisites to care about Star Wars. Some people possess the prerequisites and simply don't care. Not everyone is interested in every movie, however skillfully it creates a narrative.

The point of the #anyqs challenge is to evoke a perplexing situation so skillfully that the majority of your students will wonder the same question (whatever that is) and the rest of the class won't find that question unnatural or uninteresting, even if it wasn't the first question that struck them.

20 Responses to “Dissents Of The Day: Danielson, Pickford, Scammell”

  1. on 09 May 2011 at 5:20 amThomas Gaffey

    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.

  2. on 09 May 2011 at 5:52 amJohn Scammell

    I’m afraid I didn’t explain myself very well, if I ended up on this section of Dan’s blog. I’m buying what he’s selling, honest.

    I interpreted Avery’s longer comment as a plug for constructivism. In an ideal world, I’d let kids decide what perplexed them, and let them explore and head wherever they wanted with it. Unfortunately I teach in a system of rigid curricula and standardized tests. Rightly or wrongly, I feel that I have to cover my curriculum.

    The problem is that too many high school math teachers use the curriculum and standardized tests as an excuse to talk at kids for 80 minutes in an 85 minute class (the other 5 minutes is reserved for assigning 90 minutes worth of homework). This approach makes kids hate math.

    I see Dan’s stuff as a really good bridge between these two approaches. It’s way better than teacher lecture, and almost as good as pure constructivism. If I can use a WCYDWT approach tied into my curriculum, and engage students in math, then I’m doing a better job than if I lectured for 80 minutes.

    So to summarize, I will bring in multimedia artifacts at the appropriate places in my curriculum. I will have a question in mind that I want them to explore. They will most likely come up with that question, and go with it. They will be engaged because it feels like it came from them. This is a better way for me.

    Dan nailed it in his last paragraph above. “The point of the #anyqs challenge is to evoke a perplexing situation so skillfully that the majority of your students will wonder the same question (whatever that is) and the rest of the class won’t find that question unnatural or uninteresting, even if it wasn’t the first question that struck them.”

    All I’m trying to do is bring these perplexing situations in at logical places that fit my curriculum.

  3. on 09 May 2011 at 6:16 amDan Anderson

    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.

  4. on 09 May 2011 at 6:21 amDan Meyer
    Thomas Gaffey: 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.

    That’s exactly what I’m going for.

  5. [...] May 2011, seems to me, at least, to be a refinement of the #WCYDWT idea.  Dan’s follow-up post Dissents Of The Day: Danielson, Pickford, Scammell says: The point of the #anyqs challenge is to evoke a perplexing situation so skillfully that the [...]

  6. on 10 May 2011 at 5:56 pmCourtney

    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.

  7. on 10 May 2011 at 6:18 pmJoshua Schmidt

    What I’m finding about the #wcydwt is that the creation of the question is part of the skillset that the students are learning. Math is not just Math, it’s integrated into every topic are students are going to be learning. I remember I did an early lesson using the Daily Show and most questions were not Math based. Many in fact were aiming to get a laugh out of the classroom of students. However, now when we do these lessons, I find students asking questions that I even myself hadn’t thought about. We explore these with as much vigor as anything in my classroom, with a direct overflow to every other type of teaching I employ.

    In short, asking the “right” question is a skill, not a natural talent. I think it’s one that might be just as important as any other skill I teach to my students over the course of a year. Answering the right question is always the next step.

  8. on 10 May 2011 at 7:02 pmDan Meyer
    Joshua: In short, asking the “right” question is a skill, not a natural talent. I think it’s one that might be just as important as any other skill I teach to my students over the course of a year. Answering the right question is always the next step.

    Can I ask when you’ve ever had to ask the right question — by which I take you to mean, “the question the authority figure in the room would like you to ask?” — in your life outside the math classroom?

  9. on 10 May 2011 at 7:14 pmJoshua Schmidt

    Dan, I think that it “is” an important skill to put yourself into someone else’s shoes and wonder what they would want to know about a specific question. I always think of the private sector, where the goal is to make the customer happy. What questions would the customer be asking? I think that’s something that matters to the students lives. Sure, that will always change, and that’s not always the question that I would want to know. However, it is important to be able to answer more than just what you as an individual would want to know.

  10. on 10 May 2011 at 7:49 pmDan Meyer
    Joshua: I think that it “is” an important skill to put yourself into someone else’s shoes and wonder what they would want to know about a specific question.

    This gets tricky. It is an important skill to put yourself into someone else’s shoes and wonder what they wonder. It is a useless skill to wonder what someone else wants you to wonder, in spite of how unnatural it is to wonder that thing. That skill, for students, is commonly known as “guess what the teacher is thinking” and it is the result of a teacher who doesn’t care to put herself in her students’ shoes.

    The point of #anyqs is not for me to put up some drab mathematical imagery about which no one is wondering much of anything and then tell my kids it’s important for them to learn to figure out what is my question, or the right question, or the next question.

    The point of #anyqs is for me to put up some mathematical imagery that evokes a perplexing situation so skillfully that I know what question my students are going to ask because I’ve put myself in their shoes.

  11. on 11 May 2011 at 5:10 amJoshua Schmidt

    And I think that is fantastic, but I think there becomes a certain point where the students are not going to be able to make that question. Especially for me in my school system where my students have never had to ask questions in a classroom before. The beginning of the year next year will be tough, the beginning is a struggle. I think they need to be coaxed into this skill. I hope that it takes very little time before i need to help with the questioning.

    Don’t get me wrong. I want my students to ask good mathematical questions, stuff like “what is your favorite movie?” – a real question I got during the Italian job WCYDWT – is not helpful in many contexts, the goal is to get off track. #anyqs is great, I love the goal. However, I think that there will always be a point to where no matter how much work we do, the students need help in coaxing them them to a good question. It doesn’t have to be the question I want, just one that is valuable. However, creating activities takes plactice, which is exactly with #anyqs does.

  12. on 11 May 2011 at 11:35 amChristopher Danielson

    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.

  13. on 11 May 2011 at 12:53 pmMaria Droujkova

    Here is the best ratio and proportion collection of stories I’ve seen in a while. Check out the interactive “what if” box. From a dating site, at that.

    http://blog.okcupid.com/index.php/what-if-there-were-not-so-many-white-people/

  14. on 11 May 2011 at 2:12 pmDan Meyer
    Christopher: 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?

    Yeah, those are the questions. Support is a crucial issue in both math ed (obviously) and in math teacher ed. How do you offer help that doesn’t downgrade the cognitive demand of the task, whether that’s adding fractions for the student or designing curricula for the teacher? What is the right kind of help to offer here? Can we offer teachers some generative exercises to help them develop as designers of curricula?

    The early results of #anyqs are promising. It’s low-risk for everyone, whether you’re posting an image / video or responding to it. For some people it appears to be generative, also. (Check out Lisa Henry’s phenomenal improvement over three protoypes.) To whatever extent I’m a professional developer here (on Twitter *snort*) it’s also easy for me to offer brief, targeted feedback on a just-in-time basis.

    We’ll see where it goes. A lot of folks clearly haven’t given the first thought to what happens after you’ve captured a sufficiently rich and perplexing scenario. 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?

  15. on 11 May 2011 at 2:19 pmDan Meyer

    @Maria, this is actually the kind of curriculum design I’m trying to push us past. We have these moments were we find math on the Internet (and OK Cupid offers those moments in abundance — the whole blog is great). Often what happens next is we post the link on Twitter and tag it “wcydwt.”

    But what are the implications for the classroom? What do I do with that link?

    So the question I’m asking in this particular thread is this:

    What interests you, Maria, about that article? Then what is the concise question that would lead to that interesting thing? And then, what is the image that would lead many students to wonder the same concise question, without you having to ask it?

    That’s the #anyqs challenge. I’m trying to push us past posting links and on to something more useful.

  16. on 12 May 2011 at 5:50 pmChristopher Danielson

    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.

  17. on 13 May 2011 at 2:46 pmDan Meyer
    Christopher: After the hook, it’s got to be about the strategies.

    Great. Yes. Solid set of questions up there.

    Check this out: I’m in the audience of a panel discussion with Pam Grossman and DL Ball yesterday. Ball is talking about the importance of core practices when Grossman notes, “Classrooms are somewhat unforgiving places for new teachers to learn.”

    Posing a problem is only one core practice out of a zillion. But #anyqs might be — might be — a useful exercise for that practice, one that doesn’t require a classroom.

    So if the next core practice is, per your suggestion, anticipating student solutions, is there an exercise
    for that practice that doesn’t require a classroom? Obviously there is:

    You have your #anyqs. You know which questions your students are likely to ask. Now how many ways can you think to solve those questions.

    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?

  18. on 13 May 2011 at 4:56 pmChristopher Danielson

    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?

  19. on 13 May 2011 at 5:00 pmDan Meyer
    Christopher: 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.

    I’m excited about this.

  20. on 17 May 2011 at 5:52 pmMaria Droujkova

    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.