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Some comments on my last post:

#1

I read stuff like this, and the first thought that goes through my mind is, “Man, I suck at teaching math.”

#2

I’m with Steve. I realize how far I am from where I should be.

#3

I’m with Steve and Craig- I can’t teach this way yet because my brain isn’t aware/smart/intuitive/mathematical enough to first notice these things, then develop a lesson, and actually deliver and make sense of it.

#4

I’ll echo Steve’s comment, I read this site and I feel like a fraud. I don’t know anything about teaching math.

I don’t teach to disempower students and I don’t blog to disempower teachers.

My largest point with these WCYDWT features, way above any other, has been that compelling, interesting math is everywhere. That you can capture it, mount it, and bring it into your class in such a way that students will also find math interesting and compelling and, in the process, become a little less intimidated by their own imaginations.

But I really suck at teaching that to teachers. Both off comments like those quoted above and off a recent, gruesome experience teaching online, it’s clear that I’m missing some key piece(s) of scaffolding.

Course Prerequisites

I’m trying to determine the prerequisites for this kind of coursework and — correct me here — I’m pretty sure there are only two:

  1. You like math. You weren’t forced into this job.
  2. You use math. You’re high on your own product. This isn’t a game to you. Math has made your personal life richer, easier, or more meaningful in the last week.

From there it’s a simpler matter of teaching:

  1. process — how to flip an interesting thing around into a challenging thing, detailed somewhat in my last post.
  2. technique — how to (i) capture photos / video, (ii) copy and paste images from the web, (iii) rip DVDs, (iv) download TV shows, (v) layer measurements on top of photos/videos, and (vi) post all of the above online.

Once the process becomes intuitive and once any three of those skills become easy, I think you fall quickly into this virtuous cycle of seeing interesting things > teaching interesting things > seeing more interesting things. The coefficient of friction falls to zero. It’s like skating on ice.

Case In Point

Kate Nowak, on the bite-sized opener clip I ripped from Parks and Recreation and posted two weeks ago:

This is cute, and totally slipped by me even though I watch this show.

I see little daylight between me and Kate as educators, which makes her comment all the more illustrative of the skills I’m talking about, skills which I use often enough that my antenna is on auto-scan for these passing mathematical moments. If I had to guess, Kate has never (iv) used BitTorrent to download a digital copy of a TV show and excerpt a clip in QuickTime, which means there is a certain degree of interference between her antenna and those moments.

Does That Make Sense?

If I allow myself any charity here it’s to acknowledge that this process is as much lifestyle as it is technique, and blogging — or any kind of asynchronous forum where dialogue plays out slowly — may be the wrong forum for teaching it. The right forum has proven pretty well elusive, though.

44 Responses to “This Blog Is Counterproductive”

  1. on 16 Jan 2010 at 10:14 amconcretekax

    I too, sometimes feel intimidated by your ideas. But the most crippling aspect of your technique is how do I fit it into my curriculum which is very structured. I have set pacing charts and district assessments to give. I even am told how to weight tests, quizzes, and homework.

    I feel as though every unit I teach to “the test” because I have no choice of how to assess my students. Do you have more freedom with your curriculum or do you make your “challenges” match the standards that you are teaching?

  2. on 16 Jan 2010 at 10:30 amDave

    I often feel like the commenters you quoted, but I think it’s a way of knowing you’re using the Internet the right way.

    In the past, you would evaluate yourself against the best teachers you knew — teachers in your school, and possibly one or two you read about in a magazine or met at a conference/PD.

    Now, we can compare ourselves to the best teachers from around the world. I think that’s the secret benefit that people who aren’t on the web, reading blogs, etc don’t even realize they are missing out on. (I freely admit that I don’t always take seriously people who aren’t at least reading blogs for exactly this reason — the bar that they measure success against is still set at at the local level, when the rest of the world is setting their bar much higher now.)

    Comparing ourselves to the best in the world, though, can be disheartening, and was as depressing as it was encouraging until I saw a blog post about that very topic. I’ve lost the post, but I wrote down a quote from it, which I keep prominently displayed on my desk: “Comparison leads to discontentment…Don’t let your self-comparison of yourself to others let you get down and quit.”

    The important thing is to acknowledge that I might not be the best in the world, but I can still be pretty awesome locally and make a stronger contribution than all the people who read their news in a magazine 6 months after the blogosphere has moved to new things.

  3. on 16 Jan 2010 at 10:47 amKate Nowak

    Hey, now. I’m getting better. But yeah it’s a process, just learning to notice.

    Did you catch THIS ONE? ^5!

    You didn’t mention the biggest obstacle I see – WCYDWT only lends itself to a subset of what I’m expected to teach. On dy/dan you provide multiple beautiful examples applying it to regressions, proportions, permutations, unit rate, volume (that’s off the top of my head, I’m sure I’m missing others).

    But when I’m like, ok, next week I have to get these kids to reliably add rational expressions with unlike denominators, I don’t think the picture or video clip exists to help me. I’d love to just punt that whole unit because, what the heck, gross, but the kids going on to calculus will need those skills, and my employers are making me anyway.

  4. on 16 Jan 2010 at 11:07 amTom Hoffman

    So you’re saying teaching people to fish is harder than giving them fish?

  5. on 16 Jan 2010 at 11:37 amDean Shareski

    Three quick thoughts:

    1. If your ideas were so easy, everyone would implement them. While you do have some impressive design skills, the concepts you propose about seeing math all around you and bringing them into the mix is a mindset that creates some dissonance for everyone. Most of our math experience likely has never looked like that.

    2. While I know how much you value practical, “stuff I can do in my classroom tomorrow” ideas, I see it also as inspirational, a target to aim for. There’s nothing wrong with that either. I know that your intent is not to intimidate but anytime someone views an idea or approach they’ve never implemented, that’s going to be a natural reaction.

    3. I dig the fact that you care.

  6. on 16 Jan 2010 at 11:56 amDavid Cox

    I think the problem is that I’d like to do more of this in my classes, but “aesthetic”, “visceral” and “design” have never been part of my vocabulary and never had a place in my pedagogy.  However, you have shown that it’s possible to provoke a question with images.  I’m not sure how to get the rigor, iterations or differentiation out of images for concepts beyond “rates, we could use rates”, linear relationships, quadratics or combinatorics.  And once I have four image driven lessons that cover these concepts, what else is there?  I can use the tennis ball in the can, Mr. Meyer shooting hoops, me dropping a ball against a green screen or Travis Pastrana jumping Long Beach Harbor on New Year’s eve, but I still only have one lesson.  

    You raise a good point when it comes to technique.  BitTorrent, Photoshop and AfterEffects are not in my skill set.  Good questioning is.  Developing rapport with kids is.  I know what I’m good at as I’m sure most of us do. However, if I possessed the aforementioned skills or could fit learning them into an already tight schedule, I’m sure you’d see more production.  

    My problem is that I’m looking for a WCYDWT problem to fit my pacing guide and not the other way around.  I pass many opportunities for “cool lessons” because they don’t fit what I need to teach.

    But counterproductive?(really hopin’ I didn’t miss the sarcasm) Nah. You’re putting yourself out there, which really is the point. Teahers reflecting on their practice enough to say, “well I guess I suck at that,” isn’t a bad thing. It only becomes problematic if we all think we need to be another Mr. Meyer in order to be successful. And Lord knows there’s only one #6 slot in Real Simple’s life lessons.

    Keep doing what you’re doing. But if you want to mix in a link or two to tutorials on bittorrent, Photoshop or aftereffects, I wouldn’t be mad at you.

  7. on 16 Jan 2010 at 11:58 amNewteach

    I admit that I found your blog most inspirational when I wasn’t yet teaching and you still were!

    The one quote I remember from some point in the last year or so was about how your “low” class was less interested in the video clips, the ideas, the connections — I think you described them as not sitting forward in their seats like the other classes.

    Those are my classes. I have the “low” class at a “low” middle school. Most of what I learned in school or here or the usual places about teaching feels like it’s across a huge hole in the ground from where my kids are. Their basic skills are lacking, but more importantly, their ability to visualize and to think are greatly lacking. They guess all the time, they resist taking a minute to think or draw a picture or to reason something out. They greatly resist writing anything.

    Now, I’m working on it, and I try to not only cover the stuff they’ll need to know how to do for our state test (and really? for a high poverty, low achievement school? that’s the be all and end all). I’m starting at the point that math helps you to not get ripped off in life — money examples are the few that catch their attention. But, in general, school is the place they go to not get beaten, to get fed (even if it’s crap), and to resist learning, while having a good time with your friends. Even in rooms where discipline and behavior management are excellent, there is little rigorous work being done — it’s resisted. They’ll behave (or at least not go berserk) for a packet of worksheets or a class taught in the most traditional way, but be unable to have a discussion that doesn’t devolve into guessing, sleeping or worse. Tests that include questions beyond their abilities (as do many standardized tests that have a wide range of question levels) make them angry and then they shut down.

    Sigh. I want to be over that big hole in the ground. There are moments, there are glimmers, there have been stretches of classes where they catch onto an idea and can run with it for at least a little ways, but it feels very far from the point where it will happen more than occasionally.

  8. on 16 Jan 2010 at 12:00 pmBill Bradley

    I think that one of the best things that you do in your blog is show evolution, that these things don’t spring fully formed from your head. That’s an important thing both for other teachers to see, and to remember to teach our students (I often point out that if the laws of Physics and Chemistry were obvious, it wouldn’t have taken until the 17th Century to discover them). We’ve had a bunch of student teachers in the science department the last several years and I always make it a point to explain that for every one good lesson or lab that they see, we’d probably tried 4 or 5 and done many revisions to everything.
    It also makes me happy to see people actually trying new things. Even small changes can make a world of difference. at the last PCTM conference one of the presenters talked about doing a podcast based class. She had some examples, and they were nothing very flash, but just the fact that students in that section (and others) could go back at will and review the material, pause it, and work at their own pace made a huge impact. The recent AFT teachers study concluded that the most effective teachers are the ones always trying to improve things. You don’t become a marathon runner after one week of trying, but you sure can make improvement.

  9. on 16 Jan 2010 at 12:08 pmAndrew

    The realization that what I’m doing is not good enough, driven by reading your and a couple other blogs, was a powerful motivator for me this year. The feeling of inadequacy can push you to become a better teacher, heightening your senses to the teaching opportunities around you. I wouldn’t stay up late lining up a grid just perfectly over a video still if I didn’t feel compelled to at least see if this will work for my students. On the other hand, that feeling of inadequacy is at least partly responsible for me taking a non-teaching job at a new school for next year. But that has more to do with management than instructional design. I’m not sure what your role is as the author to guide your readers towards the productive rather than the dejected, but it’s certainly not to avoid provoking the feeling in the first place.

    And the blog is a great tool for spreading these ideas. Sure it takes some basic skills to be able to create compelling images. But just as important is the constant awareness of opportunities for math. Reading the blog forces (gives an opportunity to?) us to think about this every time we read a post. Just as the mindset begins to fade, there’s another great example to remind and challenge.

    Keep it up. I, for one, welcome the challenge.

  10. on 16 Jan 2010 at 12:12 pmGlenn

    Dan,
    I don’t think this blog is counterproductive in the least. I really like Tim’s comment above. It is truly harder to teach someone how to fish. You are trying to TEACH us what you do, not tell us what you do.

    I, for one, am thankful of that. Not that I am anyway near being capable of doing it yet, but I can reach, jump, claw and drag myself out of the framework given to me by the district and try to accomplish small things every day that will make be a better teacher.

    And that is why this blog is not counterproductive. It is productive because it is helping many teachers become better teachers for our learners.

  11. on 16 Jan 2010 at 12:15 pmAndrew

    Newteach:

    I also teach in a low performing urban school, where the students are well behind and resistant to anything that doesn’t have a neat tidy set of steps to follow.

    Some of my WCWDWT lessons have fallen flat on their face. Others have pretty much worked. All of them have at least exposed my students to another way of thinking. I work them in when I can, and their response (and my design) has gotten better and better. Keep with it.

  12. on 16 Jan 2010 at 12:23 pmMr. K

    I’m on both sides of this.

    I sometimes wonder at how you come up with this stuff. But, I’m capable of learning (as my 12 month apart entries into your design contests show). I’m not going to be like you as I mature as a teacher, but I sure as hell am stealing a lot of your tools, and using you as one of my role models for getting to wherever the hell I’m going.

    The flip side is that I work with a lot of other teachers. Teachers who may have been teaching for 1 year, or 4, or a dozen. And they complain that they can’t make kids learn. And when I try to show them how it works for me, they act all amazed, and then go back to doing what they were doing before.

    Finally, I’ll echo Kate’s sentiment. This projects smack of our district concept tasks – they’re useful, and they provide a lot of context for kids to hang other knowledge onto. They’re good, but they only cover about 30% of what I have to teach.

    How do I use popular culture to explain the differences and similarities between the different ways of writing an equation for a line? Or rational expressions?

  13. on 16 Jan 2010 at 12:36 pmsylvia martinez

    Dan,
    It’s fascinating to watch/listen to you grapple with these things out loud.

    Seems to me like a step in your journey would be to find other teacher educators who focus on math (and the kind of math education that interests you). One I’d suggest is Constance Kamii out of the University of Alabama. I wrote a post last year about watching her teach a group of new teachers about her math education methods. You might find her interesting and benefit from her large and respected body of work, both scholarly and classroom-practical.

    http://blog.genyes.com/index.php/2008/08/20/questioning-assumptions-with-constance-kamii/

  14. on 16 Jan 2010 at 12:45 pmJeff

    Comparing kids to kids results in someone’s self concept taking a battering. The same goes for teachers. Comparing yourself with others is very counter productive.

    A much better approach: take small steps, improve at one thing, then another. Reflect on what you have done, then try to improve.

    Another necessary pre-requisite is liking kids. Sometimes it is necessary (especially at the start of a new class) to build repore. Much better learning follows and time wasted on the “forced” curriculum is soon made up.

    Finally, I would highly recommend that you subscribe to a RSS Reader and add all the great Math blogs out there. Then, check it regularly and you will learn heaps and have a bank of creative lessons from the likes of Dan and Kate!

  15. on 16 Jan 2010 at 12:59 pmjosh g.

    I wonder how many people are intimidated by the “technique” / technical, vs intimidated by the “process”. I ran into WCYDWT at the same time as I was taking a math-ed course with a fantastic teacher who followed a very similar process but used absolutely zero digital media. Many students had the same reactions as the comments above, just from the perceived gap between the teaching process they were used to and the challenge/inquiry-based process this prof demonstrated.

  16. on 16 Jan 2010 at 6:27 pmMatthew Bardoe

    What I have realized, is that often teachers don’t want to teach what they don’t know by heart and head. Lots of “good” teachers are using “perfected” lesson plans. They are not looking for the new thing. And they generally fear learning new mathematics. They say how can I teach it if I don’t know everything about it, and I think that the math you are exposing here is math that few math teachers are expert at.

  17. on 16 Jan 2010 at 8:39 pmJason Dyer

    In two weeks I am going to be (for 2/3 of my session at a conference) teaching how to use WCYDYT-style teaching, so any pointers how to make it clearer would be appreciated.

    (The other 1/3 will be hint tokens, which works mind-bogglingly well but I haven’t evangelized because there’s not much to say past that one small post.)

  18. on 16 Jan 2010 at 9:06 pmCramer

    My comment was meant to be a complement to Dan and the amazing amounts of imformation I have gleaned just in the one month I have been reading this blog.

    I was an engineer for 15 years and used a layoff this summer to do some soul-searching and became a high school math teacher. The “I realize how far I am from where I need to be” references the learning process I am undergoing as a first-year-non-teaching-degree-newbie. I am constantly experimenting with ideas I have and ideas I have seen other people use and I know that one day I will develop “my” system that works for me and my personality just the way Dan, Kate, Steve, Mr. K. and everyone else have developed theirs. But even that system (and those I referenced) will be an ever-changing progression to something better as the years go on.

    I had this grand plan of coming in and showing my students how a production line has a cost equation and a profit equation and the intersection of the two is the break-even point until I realized my standard Algebra II students DON’T CARE about that. I realize that eventually I might be able to incorporate that with some foundational work and they might understand it – but the way to their hearts is to find math as it exists on their terms (more along the lines of WCYDWT). That leads me to a whole different argument that I sometimes get frustrated that I have to entertain them when they could at least have the decency to show a little bit of initiative and get out a pencil and a piece of paper during my class. Sigh.

    Dan – thanks to you I scrapped my old-school method of assessment on a whim and I gave my first assessment to my classes yesterday. They didn’t do well (I had some students score a 0 on all four concepts) – but the looks on their faces and the looks they gave each other while I explained how the grading system worked assured me that – if nothing else – it’s a whole new ballgame with me and them. Your blogging is not counterproductive. Don’t get exasperated with our self-criticisms. Take heart in knowing that seeds are being planted in school districts throughout the country thanks to your willingness to share.

  19. on 17 Jan 2010 at 1:32 amElizabeth

    Dan — FWIW, I don’t feel discouraged at all when I read your blog. In fact, I feel actively *encouraged* to try the many new ideas you have no discernible trouble pounding out.

    I view you as an amazing, generous, and inspiring conduit of ideas and more importantly, a deeper encouragement to think and talk about this stuff in fresh new ways.

    I sometimes have to remind myself that I am me and you are you, and that I need to allow *your* ideas and methods to seep into my unconscious so they can find authentic expression in *my* own practice. The one thing kids can smell from a thousand miles away is inauthenticity. I will never be the video expert you are, and no one would be fooled for a second if I were to try to imitate your video/new media methods.

    However, I have my own strengths, including my storytelling skills and myth-making process, each of which has its own benefits.

    What’s most important in all of this, is for each of us to find her or his own authentic voice in teaching this material.

    I can’t just become a cinematographer or a Final Cut Pro expert quickly, but I can certainly adopt your ideas about layering in a set-up and pay-off by starting with a non-threatening, topical, and accessible discussion gem (like your which liquid is most expensive topix) that can turn into A Big Question which we can use as a group to work out some methods and procedures to which math is a major payoff.

    And your idea about having them use texting to get actual conversions—? Positively brilliant, in my opinion.

    We each need to take care with ourselves not to beat ourselves up just because we didn’t think of someone else’s approach. Isn’t this what we’re trying to help our students *stop* doing?

    Reach for the deeper, structural lesson in what Dan is discovering, then see if it makes sense to implement in your own practice. Then remember to step back and drop expectations about what’s “supposed” to happen.

    The magic in teaching comes from the fact that no two super-teachers are alike, which is what opens doors for students of all different kinds of intelligences. You are finding your path. I’m finding mine. And on blogs like this, we are all just sharing our experiences in a non-judgmental, reflective capacity.

    Let’s please start giving ourselves credit for having a reflective teaching practice in the first place. And let’s remember to celebrate the fact that in spite of all the negative chatter in the media that filters down into our communities, we are out there every day, making positive effort for the good.

  20. on 17 Jan 2010 at 6:13 amSue VanHattum

    I agree with Elizabeth. I’m never going to become skilled at all the technology that you use to create your lessons, Dan. But I can use the “Which is more expensive?” lesson without the high tech pretty well.

    I’m inspired by your blog, and will transform things here into my own dialect, which is more like Elizabeth’s, story-telling and community building. Elizabeth, I’d like to hear more about myth-making. Do you blog? Have you written about that?

  21. on 17 Jan 2010 at 7:54 amLeslie Healey

    So…..Dan, I am a high school English teacher and read you religiously. I get ideas every time. Could I teach math? Not in a million years–but I do know someone who practices the ART of teaching and you are it. Doesn’t matter what subject we teach. Love of the subject, love of life, love of kids, that’s what it takes. Keep blogging. We all need you.

  22. on 17 Jan 2010 at 8:27 amChuck

    Dan – Your blog challenges me, it frustrates me, and it makes me feel insecure about my own teaching practice. And it does so routinely. And I’m a better teacher because of that. So thanks.

  23. on 17 Jan 2010 at 9:17 amZeno

    Are the other teachers using the “Which is more expensive?” lesson in their own classes using the same (incorrect) conversion factor that Dan used?

  24. on 17 Jan 2010 at 10:55 amElizabeth

    @Sue – I have not started blogging yet. I’m still more of a lurker (and a desperate scrambler to keep up with my daily obligations so far).

    The best analysis I’ve read on myth-making was from Mr K’s blog:

    http://blog.mathsage.com/?s=vampire

    He hits the nail on the head about one of my pet peeves — the distractingly false and frequently insulting “real world” scenarios thrown at kids in word problems in a misguided effort to bring things into the so-called real world.

    Mr K suggests using irrefutable mythologies (such as vampire hunters, versus babysitters) both to engage the kids and to keep them from veering off-track into arguments about how clueless the protagonist of the “real world” is.

    This was a light bulb moment for me.

    So when I need a word problem, I use vampires, treasure hunters, assorted monsters, astronauts, aliens, extraterrestrials, or other oddball examples. It engages them with the material and it builds community, as you were saying, because we have a shared mythology.

  25. on 17 Jan 2010 at 3:16 pmSteve Phelps

    I guess instead of “Man, I suck at teaching math” I should have wrote, “Man, I suck at seeing the math that is all around me everyday and finding ways to bring it into my classroom.”

    I think that is what I meant write.

    Man, I suck at writing what I mean to write.

  26. on 17 Jan 2010 at 4:26 pmDan Meyer

    It seems like there are, broadly speaking, two kinds of insecurity discussed here.

    #1

    The sort that spurs a teacher to action, to self-improvement, or even to the thought expressed by many here, “Look, I can’t do all of this. I can do parts of this and, in the rest, I’m content with the differences between me and Dan as educators.”

    That’s productive.

    #2

    The kind of insecurity I’m worried about is the kind that derives from a post which intimidates other teachers without also equipping them with useful tools for resolving that intimidation.

    There is a lot of well-meant encouragement here and I appreciate it but very little can convince me I have done a sufficient job equipping willing educators with those tools.

    A useful counterpoint here is my testing strategy. I have blogged about students who are satisfied with and involved in their own assessment, about classes transformed, etc, etc, but I don’t see the same intimidated, insecure reaction to those posts as I have with WCYDWT. I believe this is because I have defined and provided tools (procedural and technical) in such a way that they are accessible to interested educators.

    I see this as a really serious deficiency in my blogging — no false modesty — though perhaps this also reveals a fundamental deficiency of blogging as a vehicle for professional development.

    Tom: So you’re saying teaching people to fish is harder than giving them fish?

    With WCYDWT I post a photo or a video and nothing more. How is that giving away fish?

    David: And once I have four image driven lessons that cover these concepts, what else is there? I can use the tennis ball in the can, Mr. Meyer shooting hoops, me dropping a ball against a green screen or Travis Pastrana jumping Long Beach Harbor on New Year’s eve, but I still only have one lesson.

    I’ll go on record with this: 90% of the time that your textbook associates an illustration with an application problem, we could recreate that problem under WCYDWT constraints and walk away with more imaginative students better equipped to solve problems in the world outside your classroom.

    Kate: WCYDWT only lends itself to a subset of what I’m expected to teach. [snip] But when I’m like, ok, next week I have to get these kids to reliably add rational expressions with unlike denominators, I don’t think the picture or video clip exists to help me.

    None of this is to say that all math is visual or should be visual. Or that the only math that matters are the application problems. But like I’ve said somewhere before, the mediocre problem-solving promoted by my textbook in its section for visual application problems tends to make the pure math a lot harder.

    [Incidentally, it appears I mischaracterized Kate in my post. She later accepted my challenge to find and crop an antique media artifact (an older episode of The Office) and completed it within 27 hours. Goes to show me.

    Bill: I think that one of the best things that you do in your blog is show evolution, that these things don’t spring fully formed from your head.

    This is useful. I thought a bit about this. I may need to begin a WCYDWT post a lot farther back in the development cycle, at the moment I first notice something mathematically interesting, to illustrate the evolution you describe.

    sylvia: Seems to me like a step in your journey would be to find other teacher educators who focus on math (and the kind of math education that interests you). One I’d suggest is Constance Kamii out of the University of Alabama.

    Thanks for passing along the name. I'll follow up.

    Jason: In two weeks I am going to be (for 2/3 of my session at a conference) teaching how to use WCYDYT-style teaching, so any pointers how to make it clearer would be appreciated.

    I'm not sure if you saw the presentation I ran in December at Asilomar. If any of those slides would be useful to you in advance of your own talk, let me know. (There is one entirely new, un-blogged bit of business at [15:00].)

  27. on 17 Jan 2010 at 5:15 pmTom Hoffman

    I think you could easily just keep cranking out WCYDWT posts for about five years before you’d need to start worrying about teaching other people how to do it. And even then, most people won’t be very good at creating these things on their own.

    It is just the nature of reality.

    I’m just saying you don’t need to rush into the next stage.

  28. on 17 Jan 2010 at 8:17 pmElissa

    You’re right about the difference between the assessment post and WCYDWT. I need the step-by-step breakdown of how you do it so I can figure out how it will work for me.

  29. on 17 Jan 2010 at 8:19 pmElizabeth

    Dan – I think you’re being a bit hard on yourself given the scope of this blog and the finite number of hours in each day.

    I think the job of “equipping willing educators with th[e]se tools” is the goal of a life’s work — not a simple objective for one teacher’s blog.

    I consider myself both inspired and fortunate to participate in this conversation and to witness (and learn from) your own process with your own tools.

    So please lighten up a bit on yourself, man. And please keep thinking out loud.

  30. on 17 Jan 2010 at 9:14 pmmonika hardy

    I’m wondering if part of the problem is thinking we have to be in control … have all the answers…. know where the conversation is heading..? Is it our impatience with irresolution?

    We’re so used to the edge of the box. (the box being the standardized math topics)

    I’m wondering if we step out of the way and out of the box (perhaps the real fear) and let kids own it… take over… I’m wondering what would happen…?
    Would they like math? … like school?…

    I’m guessing most will say… we’d never be ready for tests on boxed math.
    After a semester of experimenting with 30 kids… we’re thinking….be very efficient with the boxed math.. self automate it.. [as we're trying to do here http://tinyurl.com/yeejs2x - unit 5 is where we started getting the hang of it].. so that most of our “together in a room” time is for rich conversations/activities like WCYDWT.

    I’m wondering if we had that freedom (of more time) and were brave enough to send the kids straight to your stuff (or whatever stuff) without trying to box it up (or resolve it) first… well… I’m thinking we’d be highly invigorated by the learning that would take place. We would become colleagues with the kids… a very cool place to be.

    I absolutely love this presentation http://blog.mrmeyer.com/?p=5368 … a great “how to” video for those wanting to see more of how you do it. I’m planning to show pieces of it to my kids… like the 4 layer capability of digital media… just to see where they go with it. If I try to box it for them first… I’d certainly be blocking some creative sparks.

    David Warlick just did a keynote for our district. He recommended always taking kids to pd. I see your out of the box questioning and creations in much the same way Dan. Just take them straight to it. Intimidating for us – maybe..but getting the kids off the drug of resolution ..certainly begins with us.

  31. on 18 Jan 2010 at 12:17 pmBurt

    Good discussion. I went through 30 comments and came up with these 6 issues:
    1) Judge myself as inadequate, impatient with irresolution, vs make small improvements, knowing that if I keep at it they will add up to better teaching, adapt your ideas into my own style at my pace; learn from one another.

    2) Notice the math around you that has potential for a lesson

    3) Transition to the Challenge/Inquiry based process. Requires better grasp of the math concepts than the Demonstrate-Practice approach

    4) Can’t fit into a structured curriculum. no graphic or video for many math topics

    5) Learning multimedia techniques

    6) Low, remedial kids not connecting to any of it

    Dan: Once the process becomes intuitive
    I may need to begin a WCYDWT post a lot farther back in the development cycle, at the moment I first notice something mathematically interesting, to illustrate the evolution you describe.

    Dan, my sense is the teachers’ feelings of inadequacy that concern you stem from the process in points 2 and 3. I see two parts to the process rather than a single process: first noticing the math around you and, second actually teaching the lesson. Not having a WCYDWT graphic for a topic that needs to be taught (#4) can be addressed to a large degree by using the challenge/inquiry layered process (#3) with the illustration in the book (Dan), or maybe without any graphic at all (Sue, Josh).

    Sharing your thinking from when you first notice something interesting will help with noticing the math. I agree with Josh about teaching the lesson:

    >blockquote> I ran into WCYDWT at the same time as I was taking a math-ed course with a fantastic teacher who followed a very similar process but used absolutely zero digital media. Many students had the same reactions as the comments above, just from the perceived gap between the teaching process they were used to and the challenge/inquiry-based process this prof demonstrated.>/blockquote>

    Maybe this is where you need to provide more structure. Maybe you know the process too well; it is intuitive and you don’t recognize the need to explain “the obvious.” For example, your summary points on the process may be too general:

    1. Find an interesting thing.
    2. Transform that interesting thing into a classroom challenge.
    3. Help your students develop tools to resolve that interesting challenge.
    4. [Optional] Blog about it.
    5. Repeat.

    Your headings in the actual lesson description could be included in the summary. I like to tie the “why” to the “how” as much as possible. I don’t mind restating central points, even if they seem obvious. I get reinforced for doing so when I hear a student say, “Oh, I get it,” after I thought everyone had already gotten it.

    2a. Calm down with the math for a moment. Invite their intuition. Pull everyone in. Everyone can process it at this level and attempt a solution.

    3a. Slowly lower mathematical structure onto their intuition. Keep it meaningful so students can refine their solution at each step.

    I am almost through reading Mindsets by Carol Dweck, after I was inspired by this post at Ben’s blog. The way I worded the first point about feeling inadequate versus working to improve, is consistent with Dweck’s description of two mindsets. People with the fixed mindset believe qualities like intelligence are fixed, you have it or you don’t. Struggling with irresolution, and worse yet, failure show that you don’t have it; and there is nothing you can do about it. The result is you’re always judging yourself and others. People with the growth mindset believe that we can grow and improve. When struggling, feelings of inadequacy may be strong, but the self-judgment is not there. It’s not that you lack the ability; you just haven’t learned yet, so you make the effort to learn. Elizabeth’s comment #19 is a good example of the growth mindset.

    It is amazing how wide ranging and strong an influence our mindset has. For example, in an fMRI study, people pay attention to feedback about whether they are right or wrong on the experimental task, but those of the fixed mindset don’t attend as much to feedback that can help them improve, as those in the growth mindset do. Who do you think will do better over time? People can change their mindset: stop judging; realize that everyone makes mistakes; it is a natural part of the growth process.

    Dweck developed a program to change student’s mindset, called Brainology. In the book, Dweck wrote about a “hard-core turned off student…. In our very first workshop, we were amazed to hear him say with tears in his eyes: ‘You mean I don’t have to be dumb?’” Dweck said, “You may think these students are turned off, but I say that they never stop caring. Nobody gets used to being dumb.”

  32. on 19 Jan 2010 at 9:19 amLynn Rasmussen

    Yes, Dan. To make a difference with teachers you’ll have to teach them the way you teach kids.
    In the classroom you’ve moved from book/lecture to real life visuals.
    Show not tell.
    Responding directly to kids’ needs, to their feedback, to what they need to get it.
    Can it be done for teachers, in a blog? Can it be done when your primary job is kids? Or is that your primary job?
    I think that the blog is enough. A view of what’s possible leads people to new ways of thinking and doing.
    I would like to see actual examples of what you’re doing in class in math.

  33. on 19 Jan 2010 at 3:28 pmDavid Cox

    Hey, if we’re talking about taking a problem and deconstructing it in such a way that we can withhold information until students are ready for it or, better yet, ask for it, then I’m right there with you. I thought you were after more with WCYDWT. I thought this was about the higher fruit. I am not sure that I’m going to get the rigor or iteration or ability to throw a curveball at the advanced kids by taking problem #37 and re-creating it.

  34. on 22 Jan 2010 at 12:57 amBurt

    At the risk of belaboring this tread, I’ll offer one more comment.

    Dan, I think you pointed to the core skill of WCYDWT when you said:

    I’ll go on record with this: 90% of the time that your textbook associates an illustration with an application problem, we could recreate that problem under WCYDWT constraints and walk away with more imaginative students better equipped to solve problems in the world outside your classroom.

    You demonstrated how to do it in your conference presentation with the ski lift textbook problem, then elaborated on it with the other examples in that presentation, and generally in your blog. A textbook exercise is accessible and clearly defined, so it is a good way to get hands-on practice creating and delivering lessons to develop the skill, and gain confidence and build intuition. I would guess it would then be easier to see interesting things in the environment that could be turned into a math lesson. Maybe the most important thing about using the WCYDWT model, even with a reworked textbook exercise, is that it would produce dissatisfaction with just telling the class about the topic and seeing students process the information in a way that is disconnected from their general working knowledge. Once confidence develops, teachers facing varying situations could create their own variations and innovations that produce engaging lessons and meaningful learning.

    What’s preventing people from reworking a textbook exercise and getting this hands-on practice? Is it lack of multimedia skills? Do you think it is practical to teach us how to create the kind of slides you used in your ski lift presentation? Once people got started, they might want to expand their knowledge of multimedia techniques, but first they have to get started.

  35. on 22 Jan 2010 at 2:16 pmBreetai

    > But I really suck at teaching that to teachers.

    No, you don’t. I get what you’re trying to do in your classroom. I feel like a fraud because I should be doing it more, too.

    I enjoy reading your blog, and it has made me work to become a better teacher.

  36. on 24 Jan 2010 at 7:52 amDan Meyer
    Burt: What’s preventing people from reworking a textbook exercise and getting this hands-on practice? Is it lack of multimedia skills? Do you think it is practical to teach us how to create the kind of slides you used in your ski lift presentation? Once people got started, they might want to expand their knowledge of multimedia techniques, but first they have to get started.

    This is good. I’m at my wit’s end so I’ll take any kind of life preserver but this looks particularly buoyant. I need to formally blog about the exploded view of a textbook application problem (those layers from my presentation) and then perhaps we’ll host a show-and-tell where teachers can submit their own revised examples.

  37. on 24 Jan 2010 at 10:55 amElizabeth

    @Dan – I want to echo Burt’s suggestion of a step-by-step exploded view of layering a textbook application problem in the way you suggested in your ski lift presentation.

    Also, FWIW, I want to express my worry that very of us will be able to achieve your level of competence at digital filmmaking and editing. Given my time and talent constraints, it just feels out of reach.

    And if that’s going to become the new baseline for being considered a good math teacher, our whole society may be doomed.

    I can definitely take other people’s multimedia materials and turn them into effective classroom experiences. But I’d have to become a different person to develop a filmmaker’s orientation.

    Is there room in your view for a distinction between our becoming skilled *users* of sophisticated, targeted digital media in the classroom and the need to become an army of Steven Spielberg-level *producers* of professional-quality math films and snippets?

  38. on 24 Jan 2010 at 10:00 pmDan Meyer
    Elizabeth: Is there room in your view for a distinction between our becoming skilled *users* of sophisticated, targeted digital media in the classroom and the need to become an army of Steven Spielberg-level *producers* of professional-quality math films and snippets?

    Yeah, absolutely. I’ll go one farther and throw out the digital media altogether. If you see something interesting in a newspaper or in a magazine, an interesting fact or analysis, do you know how to flip that around, how to obscure parts of the analysis or certain crucial facts and challenge your students to recreate them?

    WCYDWT has been about bringing my own learning struggle into my classroom in a way that my students wouldn’t just observe passively but also participate in.

    So at a certain point you get sick of just bringing in news clippings and you start copying/pasting interesting things from the web into your slide software. And then eventually you get sick of those constraints and you start snapping digital photos of interesting things on the way to work. And perhaps at that point you start to seek out stronger tools and so it goes. But we can definitely start with non-technical constraints.

  39. on 29 Jan 2010 at 1:19 pmMaria Droujkova

    I’ve ran into the problem before in my work, and I think I figured it out somewhat. Your writing isn’t messy enough. Process vs. product: the blog posts are polished and the process may not be visible for the novices. Someone experienced would know and see what it takes to arrive, and you do give enough info to approximate that – but not enough for everybody, I guess.

  40. on 16 Feb 2010 at 6:47 pmbmc456

    I like your style. The way you pull math from just about any where. My mind is not wired to think like that, which is one reason, I like visiting your site to gain some new ideas and perspectives. I am trying to retrain my mind so that I can see the math around me and share that passion with my students. I feel that I am too stuck in the traditional way of teaching with the same non-engaging problems from the book. Keep on doing great things and inspiring us other math teachers to attain to bettering ourselves and teaching methods.

    when i first started reading your blog, I didn’t think i could use many of your ideas b/c i teach the low level, basic math classes but I see you teach remedial algebra so probably teach about the same skill level of kids. I need to have more confidence in their ability.

  41. on 24 Feb 2010 at 2:44 pmNeil Stephenson

    Dan – while I highly value both the openness and the thoughtfulness in which you share your teaching resources, I do feel that there’s something missing for me – student work.

    Your approach to designing work is commendable. I’ve sent your blog to countless math teachers asking how they can embed authentic, real world situations into their math curriculums.

    What I would love to see is what your students are doing.

    I think in education, and in the blogosphere in particular, we focus most of our time and energy to what teachers are doing. And you are a master of both creating and sharing your end of the learning experience. However, I’ve often thought I’d love to see what happening on the other end.

    What do students create in your class? What forms do their mathematic thinking take? Do they model like you? What do you count as evidence of deep understanding from your students? How many kids get it? What do you do when they don’t?

    I’d love to see you collect and share your students work – since this is what matters the most.

    Some of the greatest lessons I’ve had have flopped in the classroom – and I learn this from examining the student work…

  42. on 24 Feb 2010 at 3:03 pmmonika hardy

    nice Neil. That goes for all of us. We can flap about all we do – but we need to share and listen to what the kids are doing and saying about it.

    :)

  43. on 25 Feb 2010 at 9:27 amDan Meyer

    @Neil, good suggestion. I will keep it in mind.

  44. on 20 Jun 2010 at 9:07 pmhillby

    I’ve been going through this blog and some of the others for a few weeks now, and I can emphatically say that this is what I’ve been looking for. I feel like I get it – and I know that no small part of that is because I majored in physics, not math.

    But understanding it myself, and being able to teach are two completely different things. So what I’m saying is that you’re dead on about the prerequisites. If you’re only interested in the “purity” of math, these lesson ideas aren’t going to make sense to you. But if you’re interested in USING math to accomplish something else, then it all falls into place.