Math class needs a makeover | Dan Meyer


Can I ask you to please recall a time when you really loved something — a movie, an album, a song or a book — and you recommended it wholeheartedly to someone you also really liked, and you anticipated that reaction, you waited for it, and it came back, and the person hated it? So, by way of introduction, that is the exact same state in which I spent every working day of the last six years. (Laughter) 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. I mean, it’s just a losing proposition. So there’s a useful stereotype about students that I see, a useful stereotype about you all. I could give you guys an algebra-two final exam, and I would expect no higher than a 25 percent pass rate. And both of these facts say less about you or my students than they do about what we call math education in the U.S. today. To start with, I’d like to break math down into two categories. One is computation; this is the stuff you’ve forgotten. For example, factoring quadratics with leading coefficients greater than one. This stuff is also really easy to relearn, provided you have a really strong grounding in reasoning. Math reasoning — we’ll call it the application of math processes to the 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 something that, the way we teach it in the U.S. all but ensures they won’t retain it. So, I’d like to talk about why that is, why that’s such a calamity for society, what we can do about it and, to close with, why this is an amazing time to be a math teacher. So first, five symptoms that you’re doing math reasoning wrong in your classroom. One is a lack of initiative; your students don’t self-start. You finish your lecture block and immediately you have five hands going up asking you to re-explain the entire thing at their desks. Students lack perseverance. They lack retention; you find yourself re-explaining concepts three months later, wholesale. There’s an aversion to word problems, which describes 99 percent of my students. And then the other one percent is eagerly looking for the formula to apply in that situation. 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, shows set in the present day, because he saw that when people fill their mind with four hours a day of, for example, “Two and a Half Men,” no disrespect, it shapes the neural pathways, he said, in such a way that they expect simple problems. He called it, “an impatience with irresolution.” You’re impatient with things that don’t resolve quickly. You expect sitcom-sized problems that wrap up in 22 minutes, three commercial breaks and a laugh track. And I’ll put it to all of you, what you already know, that no problem worth solving 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 our textbooks — particularly mass-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. (Laughter) In all seriousness. Here’s an example from a physics textbook. It applies equally to math. Notice, first of all here, that you have exactly three pieces of information there, each of which will figure into a formula somewhere, eventually, which the student will then compute. I believe in real life. And ask yourself, what problem have you solved, ever, that was worth solving where you knew all of the given information in advance; where you didn’t have a surplus of information and you had to filter it out, or you didn’t have sufficient information and had to go find some. I’m sure we all agree that no problem worth solving is like that. And the textbook, I think, knows how it’s hamstringing students because, watch this, this is the practice problem set. When it comes time to do the actual problem set, we have problems like this right here where we’re just swapping out numbers and tweaking the context a little bit. And if the student still doesn’t recognize the stamp this was molded from, it helpfully explains to you what sample problem you can return to to find the formula. You could literally, I mean this, pass this particular unit without knowing any physics, just knowing how to decode a textbook. That’s a shame. So I can diagnose the problem a little more specifically in math. Here’s a really cool problem. I like this. It’s about defining steepness and slope using a ski lift. But what you have here is actually four separate layers, and I’m curious which of you can see the four separate layers and, particularly, how when they’re compressed together and presented to the student all at once, how that creates this impatient problem solving. I’ll define them here: You have the visual. You also have the mathematical structure, talking about grids, measurements, labels, points, axes, that sort of thing. You have substeps, which all lead to what we really want to talk about: which section is the steepest. So I hope you can see. I really hope you can see how what we’re doing here is taking a compelling question, a compelling answer, but we’re 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’re doing here. So I want to put to you that if we can separate these in a different way and build them up with students, we can have everything we’re looking for in terms of patient problem solving. So right here I start with the visual, and I immediately ask the question: Which section is the steepest? And this starts conversation because the visual is created in such a way where you can defend two answers. So you get people arguing against each other, friend versus friend, in pairs, journaling, whatever. And then eventually we realize it’s getting annoying to talk about the skier in the lower left-hand side of the screen or the skier just above the mid line. And we realize how great would it be if we just had some A, B, C and D labels to talk about them more easily. And then as we start to define what does steepness mean, we realize it would 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 at that point, I’ll put it to you that nine out of 10 classes are good to go on the whole slope, steepness thing. But if you need to, your students can then develop those substeps 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. And I’ll yield the floor here for a second to Einstein, who, I believe, has paid his dues. He talked about the formulation of a problem being so incredibly important, and yet in my practice, in the U.S. here, we just give problems to students; we don’t involve them in the formulation of the problem. So 90 percent of what I do with my five hours of prep time per week is to take fairly compelling elements of problems like this from my textbook and rebuild them in a way that supports math reasoning and patient problem solving. And here’s 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? First things first, we eliminate all the substeps. Students have to develop those, they have to formulate those. And then notice that all the information written on there is stuff you’ll need. None of it’s a distractor, so we lose that. Students need to decide, “All right, well, does the height matter? Does the side of it matter? Does the color of the valve matter? What matters here?” Such an underrepresented question in math curriculum. So 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 so often see in textbooks, we go out and we take a picture of it. So now we have the real deal. How long will it take it to fill it up? And then even better is we take a video, a video of someone filling it up. And it’s filling up slowly, agonizingly slowly. It’s tedious. Students are looking at their watches, rolling their eyes, and they’re all wondering at some point or another, “Man, how long is it going to take to fill up?” (Laughter) That’s how you know you’ve baited the hook, right? And that question, off 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, all right? And I’ve got kids who will not join a conversation about math because someone else has the formula; someone else knows how to work the formula better than me, so I won’t talk about it. But here, every student is on a level playing field of intuition. Everyone’s filled something up with water before, so I get kids answering the question, “How long will it take?” I’ve got kids who are mathematically and conversationally intimidated joining the conversation. We put names on the board, attach them to guesses, and kids have bought in here. And then we follow the process I’ve described. 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. (Laughter) And that’s terrifying, because the theoretical models that always work out in the answer key in the back of a 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 the most valuable. So I’m here to report some really fun games with students who come pre-installed with these viruses day one of the class. These are the kids who now, one semester in, I can put something on the board, totally new, totally foreign, and they’ll have a conversation about it for three or four minutes more than they would have at the start of the year, which is just so fun. We’re no longer averse to word problems, because we’ve redefined what a word problem is. We’re no longer intimidated by math, because we’re slowly redefining what math is. This has been a lot of fun. I encourage math teachers I talk to to use multimedia, because it brings the real world into your classroom in high resolution and full color; to encourage student intuition for that level playing field; to ask the shortest question you possibly can and let those more specific questions come out in conversation; to let students build the problem, because Einstein said so; and to finally, in total, just 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. And why this is an amazing time to be a math teacher right now is because we have the tools to create this high-quality curriculum in our front pocket. It’s ubiquitous and fairly cheap, and the tools to distribute it freely under open licenses has also never been cheaper or more ubiquitous. I put a video series on my blog not so long ago and it got 6,000 views in two weeks. I get emails still from teachers in countries I’ve never visited saying, “Wow, yeah. We had a good conversation about that. Oh, and by the way, here’s how I made your stuff better,” which, wow. I put this problem on my blog recently: In a grocery store, which line do you get into, the one that has one cart and 19 items or the line with four carts and three, five, two and one items. And the linear modeling involved in that was some good stuff for my classroom, but it eventually got me on “Good Morning America” a few weeks later, which is just bizarre, right? And from all of this, 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 just really encourage you, whatever your stake is in education — whether you’re a student, parent, teacher, policy maker, whatever — insist on better math curriculum. We need more patient problem solvers. Thank you. (Applause)

100 thoughts on “Math class needs a makeover | Dan Meyer”

  1. I only discovered I liked math when I started helping kids with theirs. The way they were supposed to do the problems was stupid and I couldn't make any sense of it, so I ended up having to figure out the answer from the bottom up. Turns out it was actually fun. Sad thing is, the kids insisted they had to solve it the stupid way or it was wrong. WTF?

  2. @simbeau
    Tell me about it! My math teacher was mostly a gym teacher who did a bit of math on the side, and a dyslexic.

  3. omg hes so great, young and idealistic. it took me to till my second, third, or mayve even…fourth? year of college (as a math major) to not totally fear the basic shitty model of learning I picked up in highschool. I thought I was great at math.. i was very good at math, and awesome at reading textbook code. I remember the teachers I've had that taught me this skill (which I have still yet to master) and they were the rare reasons that I became a math major!

  4. He definitely found the key to the problem: that kids are only looking for an exact formula to copy, either from a text book or from another student. However, in a real job, you won't have an encyclopedia of formulas for every possible situation. The problem with his solution is that he needs to find a way to get individual students thinking on their own, outside of a class discussion where the smart kids do all the work.

  5. @shiftyjake The problem solving algorithms in math are the result of proofs worked out by past math geniuses. There is only one right way to solve a math prob, and students are expected to show the steps – how else can a teacher know that they "get it"? A real prob with math is that it is usually taught as a game of algorithms without providing the insights which led to the algorithms in the first place. Few learn what the quadratic equation is about, but may be able to solve algorithmicly.

  6. @rh001YT I'm not sure how interesting math history would be to the 3rd and 4th graders I was dealing with, but it wouldn't address the main problem. By all means, the kids should show their work, but my issue was that they were more concerned with the baffling and redundant instructions given them than with actually solving the problem in whatever way got the job done. Also, there were several ways to solve the problems given to the kids as homework.

  7. @shiftyjake See David Bernstein's books: Infinite Ascent, A Brief Tour of the Calculus and History of the Algorithm. These books are great at explaining the fundamentals of math and how math progressed throughout history. The books are very inexpensive new and used at Amazon. Regarding History of the Algorithm, I got lost at the halfway point, where things get very abstract – after that the material is for math majors only. For a super mental workout: Critique of Pure Reason (free on internet)

  8. @shiftyjake BTW, when teaching or tutoring math fundamental #1 is that the child has memorized the axioms & can repeat them on demand. The child must be advised that the axioms are unprovable & merely obvious. Theorems are proved w/ the axioms. Theorems can be memorized & used without necessarily knowing the proofs. Most word probs are to be graphed or visualized on the Cartesian coordinate system. Time, distance/volume, & gravity(weight/mass) are usually denominators due to how the mind works.

  9. @rh001YT That's a little advanced for kids who are just getting their heads around negative numbers. They aren't introduced to graphs til 5th or 6th grade and they generally don't know words like "axiom" and "theorem". They're still memorizing their times tables. Okay, some of them are memorizing their times tables. Most of them are just using the multiplication chart in the book because apparently they're allowed to.

  10. @shiftyjake Well, that speaks to the prob with math education. The axioms are the rules of the game, like the rules of a card game or sport. Aristotle is said to have coaxed a 6 yr old slave boy into figuring out how to "double the (area of a) square", illustrating that the axioms are built into the mind. Kids can leard the rules to a card game, board game or sport, so they can learn/memorize the axioms (algebra & geom). Multiplication table up to 12 should be in memory by end of grade 4.

  11. @shiftyjake Negative numbers: it ought to be explaned early on (grade 1 emphasized thru grade 5) that negative numbers are value statements about "bad", negative=negro=black=dark&scary=crime undercover of darkness=dead&rotting=debt=loss=bad. So the Hindus it is said invented negative nums to keep track of debts. "0", from the Hindus = debt paid. Also, as to quantities (and energy), there never is actual loss, but the quantities move, say from person 2 person, thus total quantitiy remains same.

  12. @rh001YT I care less about whether they've memorized the times table (I never memorized the 7's) than if they get the concept of multiplication so that they can figure it out by adding if they needed to. My point is that problem solving is why math as we know it exists, and problem solving is its practical application. Unfortunately, that's not how it's being taught.

  13. @shiftyjake I agree that in too many settings math is not taught as concretely as it could be, but at the same time the students do get a lot of word problems which are "problem solvings". The prob with the array of world probs is that they are too scattered so the students puzzle it together, such as noting that time, space & gravity are usually the denominator, & that quite often a value judgement is implicit. Note however that math exists in the mind regardless of problem solving.

  14. In my school the best math teachers were only teaching the best students.The rest of us were lumped into shit classes run by the weakest teachers.I guess it was the schools way of deciding who the factory workers would be.

    I can honestly say I have learned more new things in the last seven years on my own, then in my twelve years of public school.I spent my entire childhood thinking I was stupid, and lo and behold it turned out it was the education system itself that sucked.

  15. @rh001YT But generally, axioms in maths (at least at the level we are discussing) are so intuitive, that stating them outright isnt necessary…in fact, it might just confuse the kids.

  16. @divicool72 I disagree. When the axioms are not spelled out, and the students informed that they are intuitive and not provable, a great deal is cleared up for the student. And a few of the axioms are not very intuitive, such as closure. When the axioms are memorized, then as more maths are learned the student will, hopefully, identify which axioms are in play as the basis for each new learning. As with the axioms of chess, a move is or is not allowable according to the axioms.

  17. Why every lecture that is given, is always to the ones who already understand the subject.What happens to the numerous students and adults that don't understand.

  18. This was never a problem for me, because I've always, by some nature, been interested and intuitive with numbers, shapes, and generally, math. However, this also made it very confusing for me to watch many of my fellow classmates struggle to grasp what were very intuitive concepts for me. This video does an excellent job of clearing up that confusion. I applaud his quote of Einstein. Discovering the origin of a useful formula is always more interesting than learning to use the formula.

  19. I recognized this when I was little. Turns out it makes me just as angry thinking about it as it did when I was drudging through it. I am predisposed to forgetting (with lightning speed) anything that I can't be convinced is useful to me. It made school so hard for me. (angry still)

  20. This is great, better than the other math teacher one because he starts tackling the problem of making maths relevant rather than avoiding it.

  21. I'd respectfully disagree with that last statement, bje, and say that as you get to more advanced math, the closer your maths approximates reality.

  22. Can we really separate the phenomenon that Meyer talks about from the issue of assessment – where students are tested almost exclusively on the relationship between data and information? Quite understandably this ultimately becomes the objective of the teaching profession. Most of those forced to study maths never need to solve an equation. What they need to do is to be able to model real life uncertainty in mathematical terms. Mathcad, R etc. can do the computation for them.

  23. I've had a few good math teachers in my lifetime but none of them were as creative as this guy. Wish more teachers thought like him

  24. This video was pretty interesting. I liked his analogy at the beginning about how students are like consumers who are forced to buy something they don't want to buy. He had a lot of valid points and the ones at the end seem like they might be very helpful for many teachers.

  25. Im going through the exact same thing you did. Its difficult because you are right they do put the best teachers into the more advanced classes. Everyday in my math class all we do is look at a board and watch my teacher do math exercises, not once does she ever really explain the problem. Am i really learning?

  26. Id say 19. Although the one with the 4 people has less items, they'll each have to say hello, get their check, give the lady their money, etc.

  27. Well, maybe you can learn the basics of drawing or playing instruments, but you won't be able to perfect the art unless you are gifted or talented.

  28. Way more than the basics. You won't become a composer or an artist, but you will be able to draw great portraits or play very difficult and nice songs.
    Sure, obviously we can't have all teachers being great educators like Feynman, but we don't even need so.
    Quite right that you can't be the greatest without talent (which mostly comes from childhood education, not from genetics, in my opinion), but you can get to very high levels, well above the basics.

  29. You may be able to play a very difficult song if you're trying very very hard, but it would be much easier if you had the talent. I mean by hard work you may be able to be good at something, but the problem is most teachers thinks that teaching is an easy job so they don't work really hard to be good at it.

  30. Google lockhart's lament. Read about how this, what is shown in the video, the idea that math is about solving problems. Useful problems, useless problems, fun facetious nugatory problems, with the mind alone (and a touch of pen and paper). It is what math education should be about.

  31. This is exactly what i was thinking my math teacher has to just fly through everythin and just barly teach us because she has so much fucking ground to cover and then she just drills the steps in our head with mass amounts of hw.

  32. I've observed this myself, but there is something else I have observed. There are usually several students who struggle at just the basics. There are students who still struggle to plot points or subtract negative numbers. I think, even with a lot of material to cover, teachers should slow down and focus on the core ideas. Whizzing through 50 topics where 25% of your class didn't even master the basics sounds pointless to me. They clearly aren't learning it in that way.

  33. Of course, what about the more mathematically mature students? I think that's where in-class open-ended exercises come in. I'm in a college math class where we work on problems during class. We don't all make the same amount of progress on the problem. Weak and strong students alike find themselves struggling at some stage, but everyone learns something. The point is the problem is appropriate for a very wide range of mathematical maturity. Stronger students just go deeper, but everyone learns.

  34. Last thing…it's also a ton of fun. Now I know I chose to study math, but I still find math lectures boring most of the time. It's a lot of just cramming information into your brain, and if any questions arise then they are resolved in a matter of seconds. I actually struggle to stay awake sometimes, and that never happens in the class where we work on problems. I'm full of energy when I work on the problems, even when I'm really tired.

  35. This TED talk made me think. I love that! This actually makes me want to take a math class… From Dan! 🙂

  36. Tell me about it. I barely scraped a C in school, after being thrown in the lowest classes throughout. Got forced into doing it at college(In Britain, that is ages 16-18 before university). and now I am achieving decent A grades in all my maths qualifications, and I am starting my mathematics degree in October.

  37. "I'm gonna retire in a world that my students will run" that should enough for anyone who educates or trains others to care about their subjects and the material they teach

  38. The education system is a joke. I LOVE this video and it's going to help me take my teaching to the next level. I LoVe teaching math and I'm quite good at it, but now I can really start to master it. Thanks!

  39. I always got good grade for effort in all subjects. In math. At first I was OK, but the algeabra I really stuggle a lot. I failed the state examination but still got a D in the class, I did all the homework and the teacher new I put a lot of effort. But the geometry teacher next year failed me in the class. I failed the big exam but still did well in class and much effort and I even brought her homemade cookies once in a while. She should have given me at least a D. All that effort and an F

  40. Kids need math and science education that engages real, exciting topics.  Often, the concepts and problems are too abstract, and don't engage their interest.  With that said, limits in intelligence due to the inherent nature of the bell curve (the natural distribution of intelligence in the population) prohibits many from learning either math or science as well as might be hoped.

  41. @ 2:00.
    Score in my classroom : 5/5.

    And that's the second best teacher I had in my life.
    My school must suck by international standards…

    Competing with students having a teacher like Dan Meyer just isn't fair :/

  42. I think computer science and "computational thinking" could help solve this. In computer science, we are forced to create the formula to solve the problem, sometimes even before we begin the problem. If we teach math alongside these concepts, we may be able to better preserve and connect with math the computational and abstract thinking that Dan Meyer hopes we will retain.

  43. The problem with this is that it takes much more time. It would be plausible in high school, but in college, the professor has to move fast and just teach the base material due to time restrictions. If teachers could incorporate this material seamlessly with the material present while being able to make sure that all aspects of the lesson are taught.

  44. i took university physics, and that was not how my questions were at all…
    you couldn't just "plug it into the formula"
    we had to make our own formula using calculus and linear algebra

  45. I have watched this video many times and each time it inspires me.  Dan Meyer suggests that problems with too much guidance stifles thinking.  By stripping away all the excess information, we can allow our students to think critically and solve real-life problems.  What a great idea!

  46. A kinetic energy formula? Really? You give THAT as your example?
    Physicists routinely use formulas in problems and they typically
    go way beyond the "reasoning" your are talking about in math classes;
    and, I know because I have taught BOTH physics and math classes.
    In science formulas represent physical laws and MUST be used to
    solve problems in that context–so it is counterproductive to suggest
    they not.

  47. Excellent presentation. I'd like to add one more point, making interesting math games for computers, tablets & mobiles by a group of educators, children psychologists, sociologists, & software developers. Something like Angry Birds but for math.

  48. I think this is a very interesting view on using textbooks in mathematics. My students I have taught in the past have each had individual issues with the textbook, may that be not understanding the wording of textbooks or may that be they know how to decode the textbook. When I was in high school I knew how to decode the textbook and I did well through cheating through the textbook. Overall great concept.

  49. I love using Dan Meyers videos in class. But if your classroom management isn't on point, things can go awry.

  50. Seems like visual learning is the way to go. We need to restructure the traditional learning system to be more visual based and incorporate active learning and make learning fun. 😊

  51. See now coming in December 2017 a new system that teaches how to use your school text books and popular video games, such as Math, for a more exciting and engaging form of higher learning, scholars around the world have been trying to solve, just sign up a vimeo.com under WORLDWIDEGAMINGUNIVERSITY.COM, for only 5 dollars for subscriptions. the revolution has begun!

  52. People be careful of this guy Dan Mayers, he is a scam artists, a scammed my niece made her leave her husband to moved to Oakland to have an affair with him. His wife found out went by my nieces house started cutting my nieces tire. Be aware of him people.

  53. Dan Meyer has done a truly inspring job in this Ted talk. Meyer does an excellent job outlining a varitey of issues surrounding a typical math classroom. At its core, Meyer is suggesting that educators need to stop their traditional practices, and introduce a problem based approch to teaching. Furthermore, he suggests educators should refrain from providing students with too much assistance, but instead, allow them to think critically and develop a more authentic learning experience; one which is more true to their own life. The key emphasis is placed on the fact that to be successful in mathematics, we need to promote patient problem solving skills, which is not found in tradition textbook style of teaching (it is very cookie cutter). Having spent over a decade in math classes myself, it is regretable that the majority of Math classes continue to use a traditional textbook based learning process. It is clear that making vast changes to the math curriculum is not an easy feat, as the problem continue to persist 8 years later. Nonetheless, I myself plan to take a page from Dan Meyer's Talk, and work towards implementing his suggestions into my own classoom someday.

  54. This wouldn’t change anything. Just shift some things around. The stupid kids might now understand math a little more, but the smart kids would be sitting there yawning as they are perfectly capable of painting a picture in their own heads without you drawing anything. This really sounds like you want to teach math to kids with ADD.

    You can’t fix primary education because the problem is mainly in the home. In my country, for example, if a kid was behind in math or native language at a young age, the parents would be notified and parents would feel ashamed. So the parents would do everything to teach their kid so he can catch up and not get held back a year and be called stupid by peers. In US, good luck finding a parent who would teach his 4 year old how to read. And if the kid does bad at school, it’s always the teachers fault…

    The other problem with US is that you have kids of different IQ in the same classroom. Generally speaking, you’ve got Hispanics and blacks who are significantly behind in every subject trying to learn alongside whites and Asians and Indians who are years ahead in IQ

  55. Math is not supposed to be “fun”. It can be fun to many without pictures or slides or word problems. There are some students who actually go to school to learn and you will take that fun from them by forcing an entire class to slowly chew up a 5 second problem for 20 minutes

Leave a Reply

Your email address will not be published. Required fields are marked *