I wrote that. In all sincerity. On June 8, 2004. In an essay for my credentialing school entitled – of all things – “How Students Learn Math.”
This gobsmacked, gross-feeling moment is what I get for digitally cataloging every essay, handout, and lesson I have written since high school.
I am grateful, I suppose, that it only took me six years to go from “the best learning begins with a good worksheet” to the kind of instructional design that –Â for whatever good it does my students – has me excited to wake up in the morning, has me constantly double-checking my front pocket for a camera, has me excited to walk around and encounter math in my daily life. I’m grateful because I’m positive there exists another timeline, equally plausible to this one, where I’m still that enthusiastic about worksheets after six years, or ten years. Or an entire career. I hear that happens.
I’ll speculate twice here:
- I don’t think any of the other ten members of my UC Davis cohort ever wrote anything as stupid as “the best learning begins with a good worksheet.”
- I don’t think any of the other ten members of my UC Davis cohort has failed as fast, as often, or as productively as I have in the six years since we graduated.
My first post at dy/dan was four years ago today.
I am extremely grateful to a lot of different folks who have patronized my work over those four years, folks like Chris Lehmann, who threw some shine on my assessment writing in my first week of blogging; folks like Kathy Sierra, Tim O’Reilly, Nat Torkington, and my other patrons at O’Reilly Media, but especially Nat, whose promotion on the Radar got my grocery line post moving, whose invitation onto the terrifying Ignite stage at OSCON 2009 got me introduced to Brian Fitzpatrick who helped me score a job at Google where I met Maggie Johnson who helped me get into Stanford. And a lot of other folks. Especially those who stuck around during those first two years when I was basically angry all the time. All six of you.
I have blogged behind password encryption for an audience of zero and, more recently, for an audience of 6,000 subscribers. Both kinds of blogging have worked certain wonders on my teaching practice.
I’ll say this about the second kind – perhaps just as a reflection but perhaps also as a recommendation to those in the math edublogosphere who are working hard and picking up a lot of deserved press: use more readers as an excuse to fail faster, more often, and more productively.
The closer I track this blog to the theme “what I will do differently next time,” the more I draw readers who introduce me to new ideas, who offer me their time and energy to field-test my latest harebrained schemes, readers who have helped me pinball quickly from failure to success.
For the last four years.
There are worse forms of professional development than blogging.
DavidCSeptember 6, 2010 - 5:50 am -
There must have been forces at work outside of you that contributed to that mistake, right? It seems like a pretty common mistake. Are those forces still at work? What can we do about them?
AndySeptember 6, 2010 - 6:17 am -
*hides worksheets under desk*
Steve Da CatalystSeptember 6, 2010 - 9:18 am -
“What will I do differently next time is a good starting point,” as I am wondering what to do now. Start a blog.
Our 100-student public high school (call it alternative) has come under the watchful eye of Debra Gist and the state regulators for having low test scores. We now have to have math classes in order to lift scores. Previously all math was through projects. And while we are cramming our 11th graders in an effort to improve NECAP scores we are very much interested in, long term, elevating Mathematics as an art form so students are, as you say, are engulfed in the mysterious, captivating, perplexity of it all. Math doesn’t need to be relevant as long as it is inspiringly perplexing.
I operate under the premise that all humans are attracted to some for of problem. We want to puzzle, but we do not all gravitate toward the same puzzles. My work is also inspired by Paul Lockhart, author of A Mathematician’s Lament. The scathing indictment of education (especially Math) I’ve read.
Lockhart ran a 3-day symposium of sorts in Prospect Park in Brooklyn in mid-August. I brought four students from Rhode Island and our principal time and we had a blast doing math in the park. There were people of all ages drawing lines, rectangles, taking apart locking puzzles, working with shapes, basically immersing themselves in some dimension of inspiring perplexity.
This is the culture we are hoping to build in our small school in Newport, RI. Here are some of our questions:
What is Math? What is Mathematics? What should students study, Mathematically speaking, and be expected to know upon graduation from high school? Should students be required to pass a test in order to graduate?
You get the drift. I have posted some thoughts in an effort to solicit wonderful ideas on what to do next.
Steve Da Catalyst
Tyler StubenhoferSeptember 6, 2010 - 10:26 am -
@Steve Da Catalyst
I’d never heard of Paul Lockhart nor his Lament paper… reading it now with jaw dropped and head nodding YES over and over.
Sam ShahSeptember 6, 2010 - 4:07 pm -
Four years is a HUGE milestone. I just realized that I’ve been going at it for three years, since I’ve started teaching. And that’s largely thanks to you. I read your blog when I was on the search for a teaching job, and it was from reading you that I started blogging. Because I wanted to join in the conversation too! The conversations you were starting.
(And some good larnin’ can start with a worksheet!)
Dan MeyerSeptember 6, 2010 - 7:44 pm -
@Andy, @Sam, nothing stupid at all about worksheets. What’s stupid is believing “the best learning begins with –Â I can’t even finish.”
Robert CosgraveSeptember 7, 2010 - 2:16 am -
If you take a worksheet as a placeholder concept for lesson design/instructional design, you were correct. It seems much of your ethos is around generating compelling and engaging problems, and working through them in an engaging way. It’s a way down the road from a good worksheet, but it is the same road.
Will RichardsonSeptember 7, 2010 - 3:33 am -
Sincere thanks for sharing your work here the last four years. (Said as I steel myself for another year of worksheet filled Friday folders coming home…)
KarimSeptember 7, 2010 - 4:55 am -
Congratulations on going strong for four years, and for all the accolades that you’ve deservedly received. I know that all of your readers appreciate your thoughts, and look forward to even more.
I agree with Sam’s parenthetical that worksheets can actually have a valuable role, insofar as they can provide structure to both students and teacher. I’ve often sensed from this blog a certain bias against scaffolding, or at least the explicit variety. Of course, even the most seemingly constructivist lesson is very structured; if it weren’t, things would quickly spiral into chaos, and “let’s see what we come up with” isn’t a viable practical strategy in a standards-based classroom. Still, when you taught linear equations, say, certainly you knew exactly where you were going, and how you planned to get there, which is why you were likely very successful as a teacher. Which is to say: there was a worksheet. You just didn’t print it.
It’s worth remembering, Dan, that not everyone is where you are. Yet. In the next few years, we’ll see more new and younger teachers than at any other time in recent history. Many of these teachers needs the structure of worksheets, of handouts, of the more “traditional” components of classroom instruction that are easy to bemoan retroactively.
Like many of your readers, I’m grateful for the role you’re playing in helping experienced teachers stretch their limits, and see you as a clear leader in instructional design: the “how” of teaching. At the same time, please don’t discount the efforts that others are making on the content side. People need different things, and I’m sure many of your readers–particularly the less experienced ones–need reminders from folks like you that, yes, it’s a process. That, no, it doesn’t happen all at once. And that there’s no singular, identifiable and *right* way to do this. If worksheets help, let’s just make sure that they’re actually good.
We need poets, who need poetry.
SarahKMSeptember 7, 2010 - 5:03 am -
Hey, we all have to start somewhere. I’m just glad you started your blog so all of us experiencing this paradigm shift (I think I’m using the correct terminology, I am just a math teacher here) can experience it together and share our ideas and experiences. I don’t know if this is what everyone else is experiencing but there are a lot of math teachers that are happy with what they’ve been doing in the classroom and don’t want to change their ways. By blogging together I’ve been able to find this wonderful open and willing to share group of people that makes me feel like we aren’t alone in our efforts to change how we assess and instruct students. Thanks so much for sharing your experiences with us all!
Dan MeyerSeptember 7, 2010 - 6:30 am -
Three points I wasn’t trying to make that I inadvertently made:
1. Four years is a long time.
2. 6,000 is a lot of subscribers.
3. Worksheets suck.
Longevity and readership numbers are relative. Someone has always been blogging longer and for more readers than you. (Unless you’re Will.) I’ve also gone to bat for worksheets (or at least against against worksheets) in the past.
Worksheets aren’t stupid. The claim that “the best learning begins with a good worksheet” was stupid. (Again, “best.”)
As long as we’re here, though, I’ll admit that worksheets impose stronger order on learning than I prefer now. They necessarily foreclose on certain lines of inquiry I’d rather not lose. They give students the idea that “the outcome of this problem is foretold and my task is to fill in blanks pre-determined by a grown up.”
WCYDWT has it’s own ordering principles and, true, we aren’t leaving the floor open for just any line of inquiry. But the students are participating in the development of that order. (ie. “What question perplexes you here? What information do you need?”) We also leave room for the stray observations that worksheets foreclose on. Students feel like they are bringing something of themselves to the problem.
To Karim’s point that new teachers need a lot of different resources, I agree. Worksheets effectively narcotize a teacher, though. Enter quantity. Press print. Pass out. I speak from experience that it’s pretty easy to remain in that stupor, and that worries me. I’m grateful for blogging, and for how much good four years of blogging transparently about my practice in front of an audience cultivated of critics and boosters did for me. Which was the only point I was trying to make.
KarimSeptember 7, 2010 - 7:01 am -
Well put. It’s definitely a balance. Personally, I think you can write worksheets that respect students’ need to explore & come up with their own meaning, though invariably–and admittedly–there are always compromises. Likewise, I don’t think the absence of worksheets is a bad thing. (Indeed, in the spirit of WCYDWT, we recently added a third type of lesson on Mathalicious: Skills, Applications and Shorts, the last of which does not include a handout and is much less pre-determined).
Of course, even with structured lessons, you can always start with the Big Question, e.g. “how big is a 42″ TV, really?,” solicit questions, see how far you get…and then transition to the handout if & when things slow down. A friend used to say: “take as much time as you need in the next five minutes.” It’s your call how to set the timer.
That all said, Dan’s point about stupor is spot-on, and applies equally to the teacher who hews to the textbook letter-by-letter, as it does to the teacher who comes up with an idea on the ride to school and wings it through first period. Ultimately, I imagine the goal of anyone authentically interested in improving things (which is to say, NOT Houghton-Mifflin) would find resonance in the quote below. The NYTimes’ Sunday Magazine profiled Plumpy’Nut, a peanut paste hailed around the world as a sort-of silver bullet against starvation:
“We’re trying to put ourselves out of business,” said Salem, still brimming with optimism, after the trip. “That would be the best-case scenario.”
(PS – Dan, I just copied your most recent post and converted it into a Mad Libs. Totally different the second time around!)
Christian LongSeptember 7, 2010 - 8:10 am -
One of the finer posts (and follow-up comments by Dan himself) re: the life of a teacher + blogger I’ve read in a long time. Inspired by a 4-year anniversary, but inspiring much more. Thanks, Dan. For the mistake (I suppose), the ability to reflect, and the willingness (no, demand) to *fail* publicly. And to remind us to do the same.
Chris LehmannSeptember 7, 2010 - 8:20 am -
So happy to have been along for the ride. dy/dan is the first resource math teachers point out to new colleagues here at SLA. Your learning inspires ours. Thanks.
monika hardySeptember 7, 2010 - 7:07 pm -
i have to say… i’ve learned so much more from you here Dan – than the math. and i love the math.
but the class and tact and honesty and reflection and wisdom and push back and transparency you display with every post – is golden. that’s pd for everyone… and for life.
thank you for that.
and also for the very cool mathematical thinking..
Consumer ReviewsSeptember 8, 2010 - 4:52 pm -
Happy fourth Blogaversary! I think we all look back at various pieces of work, and wonder what we were thinking. It is all part of the learning / growing process.
ColleenSeptember 9, 2010 - 11:37 am -
I was a student of Paul’s at UCSC- he passed along A Mathematician’s Lament to me several years ago. It’s incredible. Thank you for this blog- it’s where I go when I need a kick in the butt. Unfortunately, after all the inspiration, I’m left trying to balance my own personal life on one side with this intense desire to come up with amazing problems like Dan. For now, I’ll plagiarize. :)
Kathy Clark CoueySeptember 9, 2010 - 8:40 pm -
“has failed as fast, as often, or as productively as I have” was my favorite part!!
Cheers Dan, and may we all be inspired to do the same!
Darren DraperSeptember 9, 2010 - 9:32 pm -
Four years, Dan, great work.
Sorry for pissing you off so unexpectedly throughout the years. Sometimes when I speak (write) my mind, it doesn’t go over well in some crowds. I believe in your post here you call that “failing faster, more often, and more productively.”
I’ve been trying to call it “what I will do differently next time.”
As a result, I’m learning that I’ve also become much more reserved online, measured in my words, attempting a constant gut-check on all that I write. Being imperfect, like we all are, I fumble a lot. However, I hope you understand how impressed I’ve been with your writing style, your willingness to share, and your ability to keep technology in check while endlessly weaving it throughout your instruction.
I highly doubt your students really know how good they’ve got it.
David B. CohenSeptember 10, 2010 - 12:31 pm -
I think I’ve been lurking and popping in and out for at least two, maybe three of those years. Left a comment here and there, but benefitted from every read. Congratulations!
Scott McLeodSeptember 10, 2010 - 12:49 pm -
I remember that angry period. I had only been blogging about a month longer than you had. Was actually worried about you (not sure why!)…
So glad you’ve continued to write and share and provoke our thinking. Never thought I’d subscribe for so long to a guy who writes about teaching math but here I am years later…
Looking forward to much more from you in the years to come!
DinaSeptember 10, 2010 - 3:56 pm -
Ah. I get it now.
Dan MeyerSeptember 10, 2010 - 5:46 pm -
I knew you would.
Will EmenySeptember 12, 2010 - 12:15 pm -
Many congratulations on the 4th blogging anniversary. It’s plain to see what such a positive and large impact blogging has had on your own practice. To have your mistakes to learn from, in addition to our own is very valuable.
All the best for the next 4 years.
SeanSeptember 14, 2010 - 1:38 am -
You’re an enormous influence. Thank you. Used the ‘How I met Your Mother’ bit in my summer school section. It uplifted an otherwise dry five hours. Curiously, they didn’t need clarification that the data was made-up. Of course it is, one girl said, no way you had ten girlfriends.
I am interested in your vitriol towards textbooks. Textbooks are created by experts in the field- a panel comprised of dozens and dozens of committed, educated professionals- many at the forefront of math education. While their design and layout is troubling (see dog, handkerchief) there are often excellent activities that provide structure around important concepts.
In other words, it’s not all 3x + 12 = 9.
Dan MeyerSeptember 14, 2010 - 2:22 pm -
Sometimes textbooks present interesting problems in helpful ways. Too often, though, textbooks ask students to pseudo-solve pseudo-contexts. Which is to say, they present real-world problems where math only applies if you suspend your understanding of the real world and and students are supposed to solve them in this weird structured way that in no way resembles how real people (or real mathematicians) solve real problems.
If we were talking about one small-cap company, I’d probably lay off a little. But this a multi-billion dollar industry that defines pedagogy in the U.S. I don’t think there’s such a thing as too much scrutiny here.
SeanSeptember 14, 2010 - 2:51 pm -
Many textbooks present artificial (often comically bizarre) situations for systems . From your writings, I know this drives you mad. It does me, as well. Something like:
‘You sell 400 tickets to the school production of ‘My So Called Life.’ You made $1700. Student tickets cost $2 and adult tickets cost $5. How many adult tickets did you sell? How many student tickets did you sell?’
First, why is this data meaningful? The short answer: it is not. But to assume that the student is not engaged in or cannot learn something algebraically meaningful is not true.
Second, there are dozens more creative ways of figuring this out than setting up a system of linear equations.
Let the students explore them! Provide them with a highly structured problem like this. Have them solve it in three ways. In six ways. Have them solve it in a way that their little sister would understand. Have them solve it in a way that would impress a math teacher. Have them solve it as if they were trying to explain it to their past selves.
And if you much teach systems, and you must use this problem, dig deeper into it. Do not make your students robots so that they recognize a problem-type, rather than a context. Persistently- annoyingly even- make them think about what each component of the problem represents. Engage the process and not the answer.
I do not like this problem. There is not a sillier, more contrived context. But, in fairness to you, how different is that from seconds gained or lost taking the stairs?
Dan MeyerSeptember 14, 2010 - 3:16 pm -
Good comments here, Sean.
Sure. But whatever algebra the student learns must be balanced against the cost of using unreality to try to prove to students that math is used in reality. The cognitive dissonance is so dangerous I’d so much rather tell my students, “I have two numbers sealed in this envelope. They add up to 400. And when you double one number and add it to seven times the second, you get 1700.”
If we really can’t find a natural context for systems of equations, it does us no good to force an unnatural context.
I’m trying to figure out if you’re talking about my escalator problem. I’m happy to explain the difference but only if I’m not misreading you here.
KevinSeptember 14, 2010 - 6:14 pm -
Your original statement was correct, but let me translate it:
“The best learning occurs through solving the right problems.”
Problems are the fundamental unit of measurement from which all organization flows for math instruction. If you research top scoring countries, its not their method of instruction that has commonalities, its their problem design.
SeanSeptember 15, 2010 - 12:46 pm -
‘I teach high school math. I sell a product to a market that doesn’t want it but is forced by law to buy it.’
Your crowd is with you. You slay them with patient problem solving and minimalist digital design.
I know it was for comedy. But I’d like to deeper look at that statement, knowing full well that devil’s advocate is just…ungrateful. I have literally pillaged your site for material and deeply admire your thoughtfulness.
But what you said about the students- It’s not really true, is it? And neither is this propagated misconception that weepy films like ‘Waiting for Superman’ try to sell. It’s either a) students are disengaged and hate math or b) students are heros tragically let down by unwise, avaricious adults.
Taught math for five years in NYC and Chicago. Never once would I describe my occasionally challenging populations as a market ‘not wanting’ the product I was selling but ‘forced to buy it.’
I would even go so far as to label them ‘desperate for a really good product but doubtful any teacher can provide it.’
It’s these ideas that make people tilt their head and look at you teary-eyed when you tell them you teach math in the city. ‘That’s just so nice of you’ or ‘How do you do it? Isn’t it dangerous?’
WCYDWT is creative and engaging. It is unlike anything I’ve taught. It is- and I love this- fascinating.
Your Feltron project write-up, though, troubled me. How much time was wasted while doing that if just over half even completed the assignment? How much time is wasted in WCYDWT in general? And don’t come back with something like,’ Ah, but the gains were ineffable. My precious students learned how to think…’
I don’t want student gains best expressed through poetry. I want my students to know the difference between quadratic, exponential, and linear functions.
How do we do this? Simple strategies. Show them two different approaches to the same problem simultaneously. Spiral homework every night. Do not rely on discredited research like ‘learning styles.’
I would like you to meet us in the middle, man.
Dan MeyerSeptember 15, 2010 - 7:39 pm -
It’s true. Not of every student in the entire world, of course, but certainly true of the majority of my (as I noted in that presentation) remedial Algebra students.
Why are they “desperate?” Do your two different approaches and spiraled homework make them desperate to know more about mathematics?
My students out-performed and out-paced my department. Not the departmental average. The entire department.
It’s this revolutionary: if a problem claims to be an application of math to the real world, let’s make sure both the real world and the problem solving process of real people are accurately portrayed.
No one’s winning any comparisons to John Dewey with that kind of pedagogy.
If I don’t blog about assigning twenty problems of classwork or teaching trinomials with the box method, it’s because that stuff is easy. Making them desperate for math, though, that’s the real trick, innit?
dkzodySeptember 20, 2010 - 9:22 am -
Yes, that is the real trick, Dan, and I’m glad you’re out there trying to make it a different world. Keep writing.