Math class needs a makeover
-
0:00 - 0:03Can I ask you to please recall a time
-
0:03 - 0:05when you really loved something --
-
0:05 - 0:07a movie, an album, a song or a book --
-
0:07 - 0:10and you recommended it wholeheartedly
-
0:10 - 0:12to someone you also really liked,
-
0:12 - 0:14and you anticipated that reaction, you waited for it,
-
0:14 - 0:17and it came back, and the person hated it?
-
0:17 - 0:19So, by way of introduction,
-
0:19 - 0:21that is the exact same state
-
0:21 - 0:24in which I spent every working day of the last six years. (Laughter)
-
0:24 - 0:26I teach high school math.
-
0:26 - 0:29I sell a product to a market
-
0:29 - 0:32that doesn't want it, but is forced by law to buy it.
-
0:32 - 0:35I mean, it's just a losing proposition.
-
0:35 - 0:38So there's a useful stereotype about students that I see,
-
0:38 - 0:40a useful stereotype about you all.
-
0:40 - 0:42I could give you guys
-
0:42 - 0:44an algebra-two final exam,
-
0:44 - 0:46and I would expect no higher
-
0:46 - 0:48than a 25 percent pass rate.
-
0:48 - 0:51And both of these facts say less about you or my students
-
0:51 - 0:53than they do about what we call math education
-
0:53 - 0:55in the U.S. today.
-
0:55 - 0:58To start with, I'd like to break math down into two categories.
-
0:58 - 1:01One is computation; this is the stuff you've forgotten.
-
1:01 - 1:03For example, factoring quadratics with
-
1:03 - 1:05leading coefficients greater than one.
-
1:05 - 1:07This stuff is also really easy to relearn,
-
1:07 - 1:09provided you have a really strong grounding
-
1:09 - 1:11in reasoning. Math reasoning --
-
1:11 - 1:13we'll call it the application
-
1:13 - 1:15of math processes to the world around us --
-
1:15 - 1:17this is hard to teach.
-
1:17 - 1:19This is what we would love students to retain,
-
1:19 - 1:21even if they don't go into mathematical fields.
-
1:21 - 1:23This is also something that, the way we teach it in the U.S.
-
1:23 - 1:25all but ensures they won't retain it.
-
1:26 - 1:27So, I'd like to talk about why that is,
-
1:27 - 1:30why that's such a calamity for society, what we can do about it
-
1:30 - 1:32and, to close with, why this is an amazing time
-
1:32 - 1:34to be a math teacher.
-
1:34 - 1:36So first, five symptoms
-
1:36 - 1:38that you're doing math reasoning wrong
-
1:38 - 1:40in your classroom.
-
1:40 - 1:43One is a lack of initiative; your students don't self-start.
-
1:43 - 1:45You finish your lecture block
-
1:45 - 1:47and immediately you have five hands going up
-
1:47 - 1:49asking you to re-explain the entire thing at their desks.
-
1:49 - 1:51Students lack perseverance.
-
1:51 - 1:53They lack retention; you find yourself
-
1:53 - 1:55re-explaining concepts three months later, wholesale.
-
1:55 - 1:57There's an aversion to word problems,
-
1:57 - 1:59which describes 99 percent of my students.
-
1:59 - 2:01And then the other one percent
-
2:01 - 2:03is eagerly looking for the formula
-
2:03 - 2:05to apply in that situation.
-
2:05 - 2:07This is really destructive.
-
2:07 - 2:10David Milch, creator of "Deadwood" and other amazing TV shows,
-
2:10 - 2:13has a really good description for this.
-
2:13 - 2:15He swore off creating
-
2:15 - 2:17contemporary drama,
-
2:17 - 2:19shows set in the present day,
-
2:19 - 2:21because he saw that when people fill their mind
-
2:21 - 2:24with four hours a day of, for example, "Two and a Half Men," no disrespect,
-
2:24 - 2:26it shapes the neural pathways, he said,
-
2:26 - 2:29in such a way that they expect simple problems.
-
2:29 - 2:32He called it, "an impatience with irresolution."
-
2:32 - 2:35You're impatient with things that don't resolve quickly.
-
2:35 - 2:38You expect sitcom-sized problems that wrap up in 22 minutes,
-
2:38 - 2:41three commercial breaks and a laugh track.
-
2:41 - 2:43And I'll put it to all of you,
-
2:44 - 2:47what you already know, that no problem worth solving is that simple.
-
2:47 - 2:49I am very concerned about this
-
2:49 - 2:52because I'm going to retire in a world that my students will run.
-
2:52 - 2:54I'm doing bad things
-
2:54 - 2:56to my own future and well-being
-
2:56 - 2:58when I teach this way.
-
2:58 - 3:01I'm here to tell you that the way our textbooks -- particularly
-
3:01 - 3:04mass-adopted textbooks -- teach math reasoning
-
3:04 - 3:06and patient problem solving,
-
3:06 - 3:09it's functionally equivalent to turning on "Two and a Half Men" and calling it a day.
-
3:09 - 3:11(Laughter)
-
3:11 - 3:14In all seriousness. Here's an example from a physics textbook.
-
3:14 - 3:16It applies equally to math.
-
3:16 - 3:18Notice, first of all here,
-
3:18 - 3:20that you have exactly three pieces of information there,
-
3:20 - 3:22each of which will figure into a formula
-
3:22 - 3:24somewhere, eventually,
-
3:24 - 3:26which the student will then compute.
-
3:26 - 3:28I believe in real life.
-
3:28 - 3:30And ask yourself, what problem have you solved, ever,
-
3:30 - 3:32that was worth solving
-
3:32 - 3:34where you knew all of the given information in advance;
-
3:34 - 3:37where you didn't have a surplus of information and you had to filter it out,
-
3:37 - 3:39or you didn't have sufficient information
-
3:39 - 3:41and had to go find some.
-
3:41 - 3:44I'm sure we all agree that no problem worth solving is like that.
-
3:44 - 3:47And the textbook, I think, knows how it's hamstringing students
-
3:47 - 3:50because, watch this, this is the practice problem set.
-
3:50 - 3:52When it comes time to do the actual problem set,
-
3:52 - 3:54we have problems like this right here
-
3:54 - 3:57where we're just swapping out numbers and tweaking the context a little bit.
-
3:57 - 4:00And if the student still doesn't recognize the stamp this was molded from,
-
4:00 - 4:02it helpfully explains to you
-
4:02 - 4:05what sample problem you can return to to find the formula.
-
4:05 - 4:07You could literally, I mean this,
-
4:07 - 4:10pass this particular unit without knowing any physics,
-
4:10 - 4:13just knowing how to decode a textbook. That's a shame.
-
4:13 - 4:16So I can diagnose the problem a little more specifically in math.
-
4:16 - 4:18Here's a really cool problem. I like this.
-
4:18 - 4:20It's about defining steepness and slope
-
4:20 - 4:22using a ski lift.
-
4:22 - 4:24But what you have here is actually four separate layers,
-
4:24 - 4:27and I'm curious which of you can see the four separate layers
-
4:27 - 4:30and, particularly, how when they're compressed together
-
4:30 - 4:32and presented to the student all at once,
-
4:32 - 4:35how that creates this impatient problem solving.
-
4:35 - 4:37I'll define them here: You have the visual.
-
4:37 - 4:39You also have the mathematical structure,
-
4:39 - 4:41talking about grids, measurements, labels,
-
4:41 - 4:43points, axes, that sort of thing.
-
4:43 - 4:46You have substeps, which all lead to what we really want to talk about:
-
4:46 - 4:48which section is the steepest.
-
4:48 - 4:50So I hope you can see.
-
4:50 - 4:52I really hope you can see how what we're doing here
-
4:52 - 4:54is taking a compelling question, a compelling answer,
-
4:54 - 4:56but we're paving a smooth, straight path
-
4:56 - 4:58from one to the other
-
4:58 - 5:00and congratulating our students for how well
-
5:00 - 5:02they can step over the small cracks in the way.
-
5:02 - 5:04That's all we're doing here.
-
5:04 - 5:06So I want to put to you that if we can separate these in a different way
-
5:06 - 5:08and build them up with students,
-
5:08 - 5:11we can have everything we're looking for in terms of patient problem solving.
-
5:11 - 5:13So right here I start with the visual,
-
5:13 - 5:15and I immediately ask the question:
-
5:15 - 5:17Which section is the steepest?
-
5:17 - 5:19And this starts conversation
-
5:19 - 5:22because the visual is created in such a way where you can defend two answers.
-
5:22 - 5:24So you get people arguing against each other,
-
5:24 - 5:26friend versus friend,
-
5:26 - 5:28in pairs, journaling, whatever.
-
5:28 - 5:30And then eventually we realize
-
5:30 - 5:32it's getting annoying to talk about
-
5:32 - 5:34the skier in the lower left-hand side of the screen
-
5:34 - 5:36or the skier just above the mid line.
-
5:36 - 5:38And we realize how great would it be
-
5:38 - 5:40if we just had some A, B, C and D labels
-
5:40 - 5:42to talk about them more easily.
-
5:42 - 5:45And then as we start to define what does steepness mean,
-
5:45 - 5:47we realize it would be nice to have some measurements
-
5:47 - 5:50to really narrow it down, specifically what that means.
-
5:50 - 5:52And then and only then,
-
5:52 - 5:54we throw down that mathematical structure.
-
5:54 - 5:56The math serves the conversation,
-
5:56 - 5:58the conversation doesn't serve the math.
-
5:58 - 6:01And at that point, I'll put it to you that nine out of 10 classes
-
6:01 - 6:03are good to go on the whole slope, steepness thing.
-
6:03 - 6:05But if you need to,
-
6:05 - 6:07your students can then develop those substeps together.
-
6:07 - 6:10Do you guys see how this, right here, compared to that --
-
6:10 - 6:13which one creates that patient problem solving, that math reasoning?
-
6:13 - 6:16It's been obvious in my practice, to me.
-
6:16 - 6:18And I'll yield the floor here for a second to Einstein,
-
6:18 - 6:20who, I believe, has paid his dues.
-
6:20 - 6:23He talked about the formulation of a problem being so incredibly important,
-
6:23 - 6:25and yet in my practice, in the U.S. here,
-
6:25 - 6:27we just give problems to students;
-
6:27 - 6:30we don't involve them in the formulation of the problem.
-
6:31 - 6:33So 90 percent of what I do
-
6:33 - 6:35with my five hours of prep time per week
-
6:35 - 6:38is to take fairly compelling elements
-
6:38 - 6:40of problems like this from my textbook
-
6:40 - 6:43and rebuild them in a way that supports math reasoning and patient problem solving.
-
6:43 - 6:45And here's how it works.
-
6:45 - 6:47I like this question. It's about a water tank.
-
6:47 - 6:49The question is: How long will it take you to fill it up?
-
6:49 - 6:51First things first, we eliminate all the substeps.
-
6:51 - 6:53Students have to develop those,
-
6:53 - 6:55they have to formulate those.
-
6:55 - 6:58And then notice that all the information written on there is stuff you'll need.
-
6:58 - 7:00None of it's a distractor, so we lose that.
-
7:00 - 7:02Students need to decide, "All right, well,
-
7:02 - 7:04does the height matter? Does the side of it matter?
-
7:04 - 7:07Does the color of the valve matter? What matters here?"
-
7:07 - 7:10Such an underrepresented question in math curriculum.
-
7:10 - 7:12So now we have a water tank.
-
7:12 - 7:14How long will it take you to fill it up? And that's it.
-
7:14 - 7:16And because this is the 21st century
-
7:16 - 7:19and we would love to talk about the real world on its own terms,
-
7:19 - 7:22not in terms of line art or clip art
-
7:22 - 7:24that you so often see in textbooks,
-
7:24 - 7:26we go out and we take a picture of it.
-
7:26 - 7:28So now we have the real deal.
-
7:28 - 7:30How long will it take it to fill it up?
-
7:30 - 7:32And then even better is we take a video,
-
7:32 - 7:35a video of someone filling it up.
-
7:35 - 7:37And it's filling up slowly, agonizingly slowly.
-
7:37 - 7:39It's tedious.
-
7:39 - 7:41Students are looking at their watches, rolling their eyes,
-
7:41 - 7:44and they're all wondering at some point or another,
-
7:44 - 7:47"Man, how long is it going to take to fill up?"
-
7:47 - 7:52(Laughter)
-
7:52 - 7:55That's how you know you've baited the hook, right?
-
7:56 - 7:59And that question, off this right here, is really fun for me
-
7:59 - 8:01because, like the intro,
-
8:01 - 8:04I teach kids -- because of my inexperience --
-
8:04 - 8:06I teach the kids that are the most remedial, all right?
-
8:06 - 8:09And I've got kids who will not join a conversation about math
-
8:09 - 8:11because someone else has the formula;
-
8:11 - 8:14someone else knows how to work the formula better than me,
-
8:14 - 8:16so I won't talk about it.
-
8:16 - 8:19But here, every student is on a level playing field of intuition.
-
8:19 - 8:22Everyone's filled something up with water before,
-
8:22 - 8:25so I get kids answering the question, "How long will it take?"
-
8:25 - 8:28I've got kids who are mathematically and conversationally intimidated
-
8:28 - 8:30joining the conversation.
-
8:30 - 8:33We put names on the board, attach them to guesses,
-
8:33 - 8:35and kids have bought in here.
-
8:35 - 8:37And then we follow the process I've described.
-
8:37 - 8:39And the best part here, or one of the better parts
-
8:39 - 8:41is that we don't get our answer from the answer key
-
8:41 - 8:43in the back of the teacher's edition.
-
8:43 - 8:46We, instead, just watch the end of the movie.
-
8:46 - 8:48(Laughter)
-
8:48 - 8:50And that's terrifying,
-
8:50 - 8:52because the theoretical models that always work out
-
8:52 - 8:54in the answer key in the back of a teacher's edition,
-
8:54 - 8:56that's great, but
-
8:56 - 8:58it's scary to talk about sources of error
-
8:58 - 9:00when the theoretical does not match up with the practical.
-
9:00 - 9:02But those conversations have been so valuable,
-
9:02 - 9:04among the most valuable.
-
9:04 - 9:06So I'm here to report some really fun games
-
9:06 - 9:08with students who come pre-installed
-
9:08 - 9:10with these viruses day one of the class.
-
9:10 - 9:13These are the kids who now, one semester in,
-
9:13 - 9:15I can put something on the board,
-
9:15 - 9:17totally new, totally foreign,
-
9:17 - 9:19and they'll have a conversation about it for three or four minutes more
-
9:19 - 9:21than they would have at the start of the year,
-
9:21 - 9:23which is just so fun.
-
9:23 - 9:26We're no longer averse to word problems,
-
9:26 - 9:29because we've redefined what a word problem is.
-
9:29 - 9:31We're no longer intimidated by math,
-
9:31 - 9:33because we're slowly redefining what math is.
-
9:33 - 9:35This has been a lot of fun.
-
9:35 - 9:38I encourage math teachers I talk to to use multimedia,
-
9:38 - 9:40because it brings the real world into your classroom
-
9:40 - 9:42in high resolution and full color;
-
9:42 - 9:45to encourage student intuition for that level playing field;
-
9:45 - 9:47to ask the shortest question you possibly can
-
9:47 - 9:50and let those more specific questions come out in conversation;
-
9:50 - 9:52to let students build the problem,
-
9:52 - 9:54because Einstein said so;
-
9:54 - 9:57and to finally, in total, just be less helpful,
-
9:57 - 9:59because the textbook is helping you in all the wrong ways:
-
9:59 - 10:02It's buying you out of your obligation,
-
10:02 - 10:05for patient problem solving and math reasoning, to be less helpful.
-
10:05 - 10:08And why this is an amazing time to be a math teacher right now
-
10:08 - 10:10is because we have the tools to create
-
10:10 - 10:12this high-quality curriculum in our front pocket.
-
10:12 - 10:14It's ubiquitous and fairly cheap,
-
10:14 - 10:16and the tools to distribute it
-
10:16 - 10:18freely under open licenses
-
10:18 - 10:21has also never been cheaper or more ubiquitous.
-
10:21 - 10:23I put a video series on my blog not so long ago
-
10:23 - 10:26and it got 6,000 views in two weeks.
-
10:26 - 10:29I get emails still from teachers in countries I've never visited
-
10:29 - 10:32saying, "Wow, yeah. We had a good conversation about that.
-
10:32 - 10:35Oh, and by the way, here's how I made your stuff better,"
-
10:35 - 10:37which, wow.
-
10:37 - 10:39I put this problem on my blog recently:
-
10:39 - 10:41In a grocery store, which line do you get into,
-
10:41 - 10:43the one that has one cart and 19 items
-
10:43 - 10:46or the line with four carts and three, five, two and one items.
-
10:46 - 10:49And the linear modeling involved in that was some good stuff for my classroom,
-
10:49 - 10:52but it eventually got me on "Good Morning America" a few weeks later,
-
10:52 - 10:54which is just bizarre, right?
-
10:54 - 10:56And from all of this, I can only conclude
-
10:56 - 10:58that people, not just students,
-
10:58 - 11:00are really hungry for this.
-
11:00 - 11:02Math makes sense of the world.
-
11:02 - 11:04Math is the vocabulary
-
11:04 - 11:06for your own intuition.
-
11:06 - 11:09So I just really encourage you, whatever your stake is in education --
-
11:09 - 11:12whether you're a student, parent, teacher, policy maker, whatever --
-
11:12 - 11:15insist on better math curriculum.
-
11:15 - 11:18We need more patient problem solvers. Thank you. (Applause)
- Title:
- Math class needs a makeover
- Speaker:
- Dan Meyer
- Description:
-
Today's math curriculum is teaching students to expect -- and excel at -- paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. At TEDxNYED, Dan Meyer shows classroom-tested math exercises that prompt students to stop and think.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TEDTalks
- Duration:
- 11:18
TED edited English subtitles for Math class needs a makeover | ||
TED added a translation |