Dan Meyer, TEDxNYED.
Can I ask you to please recall time when you really loved something a movie, an album, a song, or a book? And you recommended it a whole heartedly to someone you also really liked and you anticipate that reaction you waited for it and it came back and the person hated it…
So by weight introduction does is the exact same state which I spent every working day of last 6 years.
I teach high school Math, I sell a product to a market that doesn’t want it but is forced by law of buy it I mean it's kind of it's just a losing proposition.
There is a useful stereotype about students that I see. A useful stereotype about you all I could give you guys Algebra 2 final exams and I expect no higher than a 25% pass rate and both of these facts say less about you or my students and they do about what we call Math education in the US today.
To start with I like to break Math down in a 2 categories.
One is computation this is the step that you have forgotten for example, factoring quadratics with leading coefficient greater than 1. This step is also really easy to relearn provided that you have a really strong grounding and reasoning, Math reasoning and we call it the application of Math process to world around us. This is hard to teach. This is what we would love students to retain even if they don’t go into mathematical fields. This is also submitted the way we teach it in the US all but insures they won’t retain it.
I like to talk about why that is? Why that such a cool calamity for society? What we can do about it and to close with why this is an amazing time to be a Math teacher.
First 5 symptoms that you are doing math reasoning wrong in your classroom.
This is really destructive. David Milch creator of Deadwood and other amazing TV shows has a really good description for this. He swore off creating contemporary drama and shows that in the present day because he saw when that people fill their mind with 4 hours days for example, 2-1/2 Man notice this back it shapes the neural pathways he said in such a way that they expect simple problems. He called that an “impatience with a resolution”. You are impatient with things that don’t resolve quickly. You expect sitcomsized problems that wrap up in 22 minutes with three commercial breaks and a laugh track, and I’ll put it to all of you what you already know that no problems were solved and is that simple. I am very concerned about this because I'm going to retire in a world that my students will run. I'm doing bad things to my own future and well-being when I teach this way. I'm here to tell you that the way are textbooks particularly Math adopted textbooks teach Math reasoning and patient problem solving it's functionally equivalent to turning on Two and a Half Men and calling it a day.
In all seriousness, here is an example from a Physic textbook and it applies equally to math. Notice first of all here that you have exactly 3 pieces of information there, each of which will figure into a formula somewhere eventually which the students will then compute. I believe in real life and ask yourselves what problems have you solved ever that that was worth solving where you knew all of the given information advanced or you didn’t have surplus of information and you have to filter it out or you didn’t have insufficient information and had to go find some.
I'm sure we all agree that no problem were solved in this life like that and the textbook I think knows how it's hamstringing students because watch this is the practice problem set when it comes time the actual problems set. We have problems like this here were we are just swapping out numbers and tweaking the context a little bit and the students still doesn’t recognized the stamp that this is molded from that it helpfully explains to you like what sample problem you can return to to find the formula and you get literally I mean just pass this particular unit without knowing any Physics and just knowing how to decode a textbook, that’s a shame.
I can diagnose the problem a little more specifically in Math. Here is a really cool problem and I like this it's about defining steepness and slope using a skillet but what you have here is actually 4 separate layers and I'm curious which of you can see the 4 separate layers and particularly how they compress together and present it to the students all at once and how that creates these impatient problem solving, I’ll define them here. You had the visual and you also have the mathematical structure talking about grids,measurements, labels, points, axis, and that sort of thing. You have sub steps which all lead to what we really want to talk about which section is the steepest.
I hope you can see, I really hope you can see that what we are doing here is taking a compelling question, and compelling answer but were paving a smooth straight path from one to the other and congratulating our students for how well they can step over the small cracks in the way, that’s all we are doing here. I want to put to you if we can separate this in a different way and build them up with students we can have everything we are looking for in terms of patient problem solving.
Right here, I start with a visual and I immediately ask the question which section is the steepest? And this starts the conversation because the visual is creating such a way where you can defend 2 answers. We get people arguing each other friend versus friend and pairs journaling whatever and then eventually we realize it's getting annoying to talk about the skier in the lower left hand of the screen or the skier just above the midline and we realized how great it would if we had some A, B, C & D labels. Let's talk about them more easily and then as we started to define like what is steepness mean we realize it’d be nice to have some measurements to really narrow it down specifically what that means and then and only then we throw down that mathematical structure. The math serves the conversation, the conversation doesn't serve the math.
And that point I'll put it to that 9 out of 10 classes are good to go on the whole slope steepness thing but if you need to, you stood as can then develop those sub-steps together. Do you guys see how this right here compared to that which one creates that patient problem solving that math reasoning it's been obvious in my practice to me. In all year before here for a second Einstein who had believe has paid his dues, he talked out the formulation of problem so incredibly important and yet in my practice in the U.S. here we just give prompt to student we don't involve them in the formulation of the problem.
90% of what I do with my 5 hours of prep time for a week, is it take fairly compelling elements of prompt like dish my textbook and rebuild them in a way that supports math reasoning and patient problem solving and here is how it works.
I like this question, it's about a water tank. The question is how long will it take you to fill it up, okay? First things first, we eliminate all the sub-steps. Students have to develop this. They have to formulate this. And then notice all the information written on there is stuff you'll need. None of it's a distracter, so we lose that. Students need to decide does the height matter? Does the side length matter? Does the color of the valve matter? What matters here is such an under representing question math curriculum, for now we have a water tank. How long will it take you to fill it up and that's it and because this is the 21st century and we would love to talk about the real world on its own terms, not in terms of line art or clip art that you often see in textbooks we go out and take a picture of it. Now we have the real deal, how long will it take to fill it up? And then even better as we take a video. A video of someone filling it up and it's filling it up slowly, agonizing slowly. It's tedious, students are looking at their watches, rolling their eyes, and they're all wondering it in some point or another. How long is going to take to fill up.
That's now you know you baited the hook, right?
And that question of this right here is really fun for me because like the intro, I teach kids because of my inexperience. I teach the kids that are the most remedial. I got kids who will not join a conversation about math because like someone else has the formula, someone else doesn't have to work the formula better than me so I won't talk about it but here every student is on the level playing field of intuition like everyone spilled something up with water before so I get kids answering the question, how long will it take? And kids who are mathematically and conversationally intimidated join the conversation and we put names on the board, attached them to guesses and kids have bought in here and then we fall the process of describe and the best part here or one of the better parts is that we don't get our answer from the answer key in the back of the teacher's edition.
We instead just watch the end of the movie.
And that's terrifying because the theoretical models that always work out in the answer key at the back of the teacher's edition. That's great, but it's scary to talk about sources of error when the theoretical does not match up with the practical but those conversations have been so valuable among them most valuable.
I'm here to report some really fun games that students who come pre-install these viruses day 1 of the class, okay? These are kids who now want to master I can put something on the board totally new, totally foreign and do have a conversation about it but 3 or 4 minutes more than it would have started the year which is just so fun. We're no longer adverse to worry problems because we've re-defined what a word problem is.
We're no longer intimidated by math because we slowly redefining what math is. This has been a lot of fun.
I encourage math teachers I talked to, to use multimedia because it brings the real world into your classroom in high resolution in full color to encourage student intuition about level playing field to ask the shortest question you possibly can and let those more specific questions come out in conversation.
Let students build the problem because Einstein said so and to finally in total this be less helpful because the textbook is helping you in all the wrong ways. It's buying you out of your obligation for patient problem solving and math reasoning to be less helpful.
Why this is an amazing time to get your math teacher right now is because we have the tools to create this high quality curriculum and are from our pocket and it's ubiquitous and fairly cheap and the tools that should be it, freely under open licenses has also never been cheaper or more ubiquitous. I put videos here in my blog not so long ago and I got 6,000 views in 2 weeks. I get e-mails still from teachers and countries that I've never visited saying, wow, yes we had a good conversation about that. Oh by the way here's how I made your stuff better which is wow!
I put this problem on my blog recently. In a grocery store which line do you get into the one that has 1 cart and 99 items or a line with 4 carts in 3, 5, 2 & 1 items? In linear modeling, involving that was some good stuff for my classroom, but it eventually got me in Good Morning America a few weeks later, which is just bizarre, right? And from all of these I can only conclude that people not just students are really hungry for this. Math makes sense of the world. Math is the vocabulary for your own intuition.
So I really encourage you whatever your stake is in education would be your student parent, teacher, policy maker whatever just insist on better math curriculum we need more patient problem solvers. Thank you.
About Dan Meyer
Dan Meyer asks, "How can we design the ideal learning experience for students?" As a part-time Googler, a provocative blogger and a full-time high-school math teacher, his perspective on curriculum design, teacher education and teacher retention is informed by tech trends and online discourse as much as front-line experience with students.
Meyer has spun off his enlightening message -- that teachers "be less helpful" and push their students to formulate the steps to solve math problems -- into a nationwide tour-of-duty on the speaking circuit.