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?

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.

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.

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.

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.

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.

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/

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.

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.)

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.

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.

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

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.

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.

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.

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.”

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.

> 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.

@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?

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.

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…