Mathematics educators now vie with a multitude of digital entertainment options to capture adolescents’ interest. To compete more aggressively for students’ attention, mathematics software should adopt the very strategies that have made these other media so successful.
Wulsin offers four recommendations:
- Presenting examples in high-resolution video. “Video lets students watch the sweat beading on the athlete’s temples, see the whoosh of wind in the skydiver’s hair, hear the rev of the daredevil’s motorcycle. A photograph or cartoon cannot beat video in its fidelity and power to captivate.”
- Connecting to students’ interests. “Monitoring a breeding bunny population would show the process of exponential growth. Baseball batting averages could introduce percentages.”
- Showing appealing faces. “These videos could occasionally feature famous sports or entertainment figures. What if Michael Phelps calculated the volume of an Olympic swimming pool or BeyoncÃ© computed the time delay needed for speakers at an outdoor concert? Why not let Danica Patrick figure the monthly payment on an auto loan?”
- Holding students’ attention. “Make students laugh through physical comedy or corny one-liners. Introduce them to interesting people with magnetic personalities.”
This is a decidedly mixed bag of tricks. The first two of those recommendations are superficially useful but wrong on substance. The other two recommendations suggest students are like small animals – either raccoons, easily engrossed by pretty shiny things, or puppies who can be counted on to swallow a vitamin if it’s packed inside a lump of peanut butter. Both students and educators of students ought to be offended.
And then he misses one of the biggest reasons why MTV is more appealing to students than math:
Without narrative, all of Wulsin’s efforts are doomed. If Wulsin’s mathematical task lacks a compelling, clear premise in its first act, obstacles, conflict, and tension for your classroom heroes to resolve in its second act, and a cathartic resolution in its third act that leads naturally and necessarily to more mathematics in its sequel, he’s screwed. I don’t care if he recruits LeBron James to tell knock-knock jokes in hi-def about the area of a basketball court, his students won’t care.
2011 Apr 19: Updated to add a direct link to the article. (Thanks, Coquejj.)
2011 Apr 19: Wells Wulsin responds in the comments.
MichaelApril 18, 2011 - 8:25 pm -
The other thing that is missing in the suggestion is the drama. I am sure if kids watch Snookie doing calculus and she said it was cool and you were not cool if you did not do calculus, then more kids would be interested in calculus.
Perhaps Kim Kardashian can tweet about passing Algebra in High School. Oh, wait someone would have to pay her for that. Nevermind.
It is all about social programming. Period.
To suggest that such methods should be used for educational purposes, well . . . I am not expert enough to predict that outcome. Maybe history can tell us something.
Perhaps if our Federal Government, social media, and entertainment industry advertised more about getting as much education as you can, pass high school, and do your best in school, then that alone, could be the best use of technological resources. But that is my opinion.
DavidApril 18, 2011 - 8:28 pm -
Wow, yeah. Disapointing he missed that!
Lance BledsoeApril 19, 2011 - 3:02 am -
I’m intrigued by your assertions about the best real-world math problems having a narrative arc (I read your EdWeek piece, BTW), not least because I find my students’ interest level skyrockets any time I introduce any sort of “story about math” into my teaching. Even when its just tangential to the actual lesson (e.g., “Once, when Gauss was a kid, his teacher made his class add up all the numbers from 1 to 100…”), any sort of story almost always grabs their attention. I suspect we humans are just wired that way.
At the risk of sounding like the crotchety old teacher stereotype, however, I’m going to suggest a bigger reason that MTV is more appealing to students than math: MTV is entertainment.
And when I say entertainment, I mean it’s something that is absorbed passively, with almost no effort required of the viewer. While math can be interesting, engaging, and sometimes even fun, math is never going to be “entertaining” in this way because math is not a passive activity. It requires some degree of effort (some might say work) in order to fully engage with it. Some of my students’ lives are so saturated with entertainment that they’re actually offended if anyone suggests there might be some other form of activity that they could engage in.
This is the biggest challenge I find myself dealing with in my teaching, and I think your “math as narrative” approach addresses it well. The narrative element seems to be an effective hook to capture the students’ interest, then draw them into the actual work (and ultimately enjoyment) of math.
CoquejjApril 19, 2011 - 3:37 am -
First of all, you can find the article (for free) on his site:
About the content, I think he even misses the most important thing about superficial attention: many students lose their interest when you’re getting into Math, no matter what you have been making before.
I think that’s another example of confusing education with entertainment.
curmudgeonApril 19, 2011 - 5:27 am -
While I hate to push the button marked “Praise Dan” too often, I do think that you have given us a shorthand for much of this … pseudocontext … and the suggestions fail because of it.
“What if Michael Phelps calculated the volume of an Olympic swimming pool” – really?
When would Michael ever care? On the other hand, he might be interested in split times and speeds and the differential changes made by a new type of suit with a 5% slicker surface.
“BeyoncÃ© computed the time delay needed for speakers at an outdoor concert?” Don’t make me laugh.
BeyoncÃ©’s job is to sing. When the hall was built, someone cared. Once. Then the problem was solved and everyone moved on. The audio engineer needed to know. The designer needed to know where to put the reflecting panels. But not Beyonce.
And the silliest one of all: “Why not let Danica Patrick figure the monthly payment on an auto loan?”
In a sport like NASCAR, which is run using computers, analyzed to death with computers, which has something like 200 different sensors on the cars taking measurements every 1/300th of a second generating GBs of data which is endlessly broken down before, during and after the race … and all we get is a suggestion that DP figure the monthly payment of an auto loan? (An application that nobody bothers to do anymore, by the way, they merely run freely available amortization tools.)
The other suggestions are interesting but not very illustrating. Breeding bunnies is not exponential in practice and fairly complicated unless you have a fur farm nearby. Baseball batting averages are great for introducing percentages. Once.
Hi-res video is valuable except when it’s not. The video has to show a problem. If it shows the sweat, blood and tears without a problem, then there is no point. Better to use a still picture that does than a video that doesn’t.
Making students laugh with corny one-liners that come out of nowhere only leads you nowhere. The jokes can be bad and yet still effective if they have context … the joke that always comes up during discussion of integral of 1/x: what’s the integral of dCABIN/CABIN? log(cabin), of course. and when you add “C”, you get houseboat.
paulApril 19, 2011 - 5:36 am -
I think there is a flaw in connecting with students (current) interests. The person who likes bunnies only pays attention when we talk about bunnies and the baseball kid only pays attention when we can relate the topic to baseball. How much math did they miss because we did not frame it in terms of their interest at the moment. We should find their interests and tie it when we can, better yet have them figure out how they could use the math in the topic of their choice. And won’t their interests change as they grow?
John T. SpencerApril 19, 2011 - 6:29 am -
Good narratives mean engaging conflict, deeper themes and relatable characters.
MTV doesn’t offer that.
My students are of the MTV generation, I suppose and yet they are tired of MTV. They are tired of teen moms crying without ever finding a deeper meaning.
My students are looking for authenticity, for identity, for the meaning behind the meaning. My students thirst for social engagement, for broadening a worldview.
On my best days, I can show how math hits the deeper narrative in a way that MTV cannot, because ultimately MTV is limited to the medium whereas my classroom is a community; a very human community that understands the humanity of math.
Matt EApril 19, 2011 - 6:38 am -
Lance Bledsoe: That’s it on the nose. Math is not a passive activity.
Dan: I was hoping against hope as I read Wulsin’s recommendations that you would call BS on them, and I wasn’t disappointed!
Matt EApril 19, 2011 - 6:47 am -
H. Wells Wulsin, is a graduate student in physics at Stanford University in Palo Alto, California. He taught high school physics and chemistry for three years in Washington, D.C.
That makes me feel a little better, actually…
Shawn CornallyApril 19, 2011 - 8:41 am -
As a working teacher, when I read those four bullets I can’t help but get a little acid reflux. It smacks of all the classic things we try to do when we treat students as if they’re a different species.
They’re people. They think interesting things are interesting, and they think boring things are boring. I don’t care how “beautiful” pure math has become to you after you’ve suffered through years of poor educational practices. Many students won’t choose that much suffering; a lot of smart people are thinking, “Hey, I can earn an MBA and not have to be so bored, and probably make way more money.”
Narrative is the key, but you can’t just use your knee-jerk definition of the word. You have to really remember falling for a book, story, or article. You have to remember what it was like to have to know what happens next. In our case, what happens next needs to involve imaginary numbers or whatever.
Wells WulsinApril 19, 2011 - 9:02 am -
Thanks very much for responding to my MT article; one of the unfortunate things about MT is they don’t seem to have an online comments feature (someone correct me if I’m wrong).
Since this is my first post on your blog, I should say by way of introduction that I really enjoyed your TEDx talk (which I just happened to watch a week ago), and I think you have a lot of great ideas about teaching math. You also have a great sense of humor, which counts for a lot in education (one reason I loved my favorite math teacher in middle school was his deadpan humor). My brother, a middle school math teacher in DC, is also a fan of your blog, and alerted me to this posting.
Let me respond to a few specific points in your post.
* You don’t specify what is “wrong on susbstance” about my first two suggestions (using hi-res video and connecting to students’ interests). It may be obvious to other readers but was not to me.
* You then say that offense should be taken at the suggestion that students are attracted by pretty shiny things or are more likely to swallow sugar-coated medicine. Are you arguing that either of those assertions is false? It seems to me pretty clear that this behavior is characteristic not only of children but also of adults. We like to look at pretty things…we like to eat yummy treats. That’s human nature.
Now, I think your point is that educators should not devote their efforts to dressing up pedagogy in a superficial way (creating a pseudocontext) to make it more palatable to student tastes. And I would share that concern. But it seems to me that famous figures, interesting people (especially adolescents), and humor can all be used as hooks that capture students’ attention without distracting from the underlying content. This would not need to turn math into entertainment of the MTV variety (as a few commenters thought I was suggesting). The goal would be instead to connect math to things that matter to students already. Schema theory suggests that we learn new things more easily when we can relate them to familiar ideas. And more importantly, if these hooks can get students to spend more time engaged in math, that is a good thing.
I recognize that I am probably not going to persuade you (or most of your readers) on this point. But these kinds of strategies have never been tried before in a math software package, and if they do work, then the developers stand to make a lot of money, and it could help a lot of students. I can’t be sure how effective these strategies would be until they’re tried, but I have a lot of reasons (which I tried to explain in the article) to think that they have the potential to make a big difference. That’s why I’d like to see a publisher or software company invest a few million dollars to produce a really high-quality software product.
* I agree with you completely that narrative is very important, and you’re right that I didn’t mention it in the article. I think telling stories is very useful for engaging students, and I don’t think there’s anything that I recommended that would be incompatible with a strong narrative line, or with narrative-based problems.
If you’re doing a unit on calculating volumes, the lesson you describe in your TED talk about finding the fill-time of a water cooler is one great problem. But to learn to calculate volumes, you need to practice dozens and dozens of problems. And for practical reasons, not all of them can be as extensive or involved as the water cooler example. So if some practice problems are inspired by watching Michael Phelps calculate the volume of a swimming pool, that won’t interfere with longer narrative-driven problems. There are lots of ways to learn, and the more teaching strategies we use, the more likely students are to retain their understanding.
As a final note, I wrote this article because I am a big believer in the power of interactive educational software, but the packages I have looked at so far strike me as extremely boring and unattractive to students. If we can make math software more engaging, I think it could become a powerful tool to make math more accessible for millions of students.
BenApril 19, 2011 - 10:12 am -
All of the points have elements of superficiality…..but unfortunately that plays an important role in today’s classroom. That’s not to say that we have to fall into the trap of producing high quality edu-tainment ala Bill Nye, but your call for narrative differentiates what you’ve done in the past with your videos, and what’s being suggested by Mr. Wulsin.
I honestly couldn’t care if Michael Phelps is asking me to figure out the volume of the swimming pool, unless he can show me that he actually cares about knowing the volume. Not only that, but he would also have to “sell” the students that swimmers, and the general populace in general should care about the volume of a swimming pool.
What’s more important is that teachers serve as narrators/storytellers in their classroom. Building relationships with students means that it’s easier to pull off video without the need for “pretty faces”, although I doubt that would be a strong motivator unless you were able to produce differentiated video with various celebrities and entertainers asking the same question (I don’t care about Michael Phelps, but the Mythbusters would get me interested). It’s about knowing your audience, who you’re “selling” your story to, and only the teacher knows that audience well enough.
I would hold my most recent video story problem up to your standard, and let you tear it to shreds if it makes me a better narrator within my own students’ learning:
lukeApril 19, 2011 - 10:25 am -
Dear Mr. Meyer,
Could you please make a hierarchy of effective strategies for engaging students? At the top: real world, problem-based, etc. At the bottom: pseudocontext and shiny things.
PwolfApril 19, 2011 - 12:14 pm -
Having a video of someone famous doing a math problem is similar to what we already have (having the book or the teacher do it) in that they are all doing the work for the student. Not that examples aren’t needed and that direct teaching is all bad (I adopted Dan’s minimal-text PowerPoint style for my lecture notes, which I do in my class a good 70% of the time), but we have all of this computing power, why not use it to make the two most important components of the class, the student and the problem, the stars of the show when possible?
Speaking of sports (with all the Phelps, Patrick, James talk), I’ve been wanting to do a quantitative analysis of whether Blake Griffin’s over-the-hood-of-a-Kia jump is actually more impressive than Serge Ibaka’s from-behind-the-free-throw-line dunk.
louiseApril 19, 2011 - 12:46 pm -
I have 15 year olds. “Michael Phelps is planning on swimming in an olympic pool. Unfortunately he has been preceded by the high school swim team, one of whom has peed in the pool. The high school student expelled 200ml of urine. Michael wants to know, what is the ratio of pee to swimming pool water?” if you want to , you can ask what they think is the acceptable minimal level of pee in the pool. You can invent a pee-meter to see if it measures the level of pee. You can introduce the probability of drinking a molecule of dinosaur pee when you drink a glass of water, and thence onto water conservation.
DaveApril 19, 2011 - 12:52 pm -
My take on early psuedocontext discussions here is that psuedocontext is not ideal. It’s not 100% ineffectual, it’s just not ideal. I don’t think anyone would deny that a teacher can probably get some traction with the right shiny things: throw a class set of iPads in the mix, an IWB, a little bit of Beyonce and Michael Phelps, and you can probably hold students’ attention really well…
…until the novelty wears off, and then you’re searching for the next shiny thing. I’d be willing to hear an argument that a perpetual stream of shiny things could be a successful way to teach students, theoretically. There are enough shiny things in the world to accomplish that. You could do that, and probably get the test scores you need, if you stick with it.
But…really? At best, that’s a _good_ plan that is directly in opposition to the _great_ teaching that we’re trying to hone in on. What happens when those shiny things students are outside of the school? It seems like leaning towards real applications of math and learning for the sake of learning is a much safer bet for students’ futures than learning because Michael Phelps is on the IWB.
BenApril 19, 2011 - 5:54 pm -
It’s not about stringing together an endless stream of shiny things to catch students’ eyes. It’s about digging into their pre-existing knowledge, and hooking what they’re about to learn to what they already know.
Activating prior knowledge, no matter how it’s done, is a very sound, and effective, educational practice. If you can scaffold the learning about to come upon what the students already know, then you don’t always have to go with shiny, and thus where this entire thread has been derailed.
I believe Mr. Wuslin was making an argument that the pre-existing knowledge was that of media, and what makes it attractive, when he should have been more focused on that actual content.
Bowen KerinsApril 19, 2011 - 7:37 pm -
Two things came to mind for me in this discussion.
1) I immediately thought of this video: http://www.youtube.com/watch?v=eVtCO84MDj8
When students are passive observers, they barely learn anything, no matter how high-quality the lipstick may be. Video has the “power to captivate” but captivation and learning are very different things.
2) I reject the notion that we need these kinds of carrots to make mathematics meaningful to students. Students’ experience is their reality, and I want math to be part of that reality. Therefore, true mathematical thinking needs to be part of students’ experience. It becomes part of their world.
Our Algebra 2 curriculum starts with students asked to find rules that match input-output tables. They’re not told what to do and the tables get progressively more difficult. When asked what they thought of the lesson, several students said it was “more realistic”, even though it’s nothing but inputs and outputs (not even a pseudocontext). It’s the mathematics, the thinking, that was real to them. Thinking about a problem and how it might be solved becomes part of students’ reality, and I think that ropes in a lot more kids than the suggestions provided in the article.
Kids don’t work on math outside of class because they want to see more Michael Phelps. They work on math outside of class because -they love math-. So let’s work on that. I have seen some good ways to use multimedia toward the goal of improving mathematical thinking skills, but these suggestions don’t seem to lean in that direction.
It may be worthy of a totally different discussion around the merits of interactive educational software, which is what the MT article was written toward. I get how this software is pretty solid at teaching processes and skills, but how can interactive software teach mathematics for deep understanding?
Dan MeyerApril 19, 2011 - 7:44 pm -
Hi Wells, thanks for your response. Rather than bounce something back to you point-by-point, I’ll clarify my general impression that your argument is of the form “kids like [x] therefore math should be more like [x]” where x = high-definition video, their own interests, celebrities, and jokes. You spend a great deal of time convincing the reader that these are things students like and explaining their curricular applications but very little time justifying their value for learning itself.
It’s true, for instance, that kids (and we) are inclined towards shiny stuff. We’re also inclined towards nudity. And cruelty. Why do you recommend we exploit a child’s basic tendencies in one case but not another? Why is having Danica Patrick calculating the monthly payment on an auto loan good for learning while having her perform that same calculation in a bikini wrong? The distinction may seem obvious to you but this is your proposal’s next-of-kin. Your appeal to schema theory here is the beginning of some kind of conceptual framework but your equation of “Michael Phelps” to “familiar ideas” is a fairly loose interpretation of the theory.
It’s also true that none of your recommendations are incompatible with narrative. You ignore it but you don’t disqualify it. Money spent hiring Justin Bieber to engage students in rote tasks, though, is money that won’t be spent developing narratives to engage students in rich tasks. Column-inches may be effectively infinite online but R&D budgets are not. I admire your goal of increasing access to math but resources are zero-sum and your means are orthogonal to my own.
Jason DyerApril 19, 2011 - 8:41 pm -
I s’pose I ought to chip in something, given my involvement with videos for teaching algebra through the medium of motocross.
I think the best problems (not all turned out great on camera) came off my research that were based entirely off reading about the sport and technology of motocross, rather than trying to start with a math problem and devise situations where the motorcycles are props. For instance, Japanese motorbikes use liters, so a unit conversion question was quite natural. There also is the occasion to mix oil at certain proportions, so I got a problem from that. Just looking at different cc engines, I saw the effect of doubling volume not doubling the sides, so I did a question on that.
Trying to do a logarithm problem based on decibels of engines, well, um. I should’ve thought a little harder about what would be filmable.
Oh, and we attempt a motocross ramp question (like the article), which would’ve worked with better graphics but the budget wasn’t there.
Jason DyerApril 19, 2011 - 8:45 pm -
Oh, and don’t we have some more recent “what the youth are doing these days” touchstone than MTV? I remember when I was a teenager being warned about the supposed brain rot that accompanied the channel.
DougApril 19, 2011 - 9:15 pm -
@Jason Dyer – About your motorcross problem, you just alienated half your kids by creating a question mostly of interest to boys. Do you also create problems about converting makeup from France?
Wells WulsinApril 19, 2011 - 10:48 pm -
Thanks for your follow-up response. I tip my hat to bloggers like you who can churn out high-quality commentary day after day. I tried writing my own blog some time back, but it took so much time that I hardly ever posted. So I hope your advisor cuts you some slack: the discussion you generate here is a valuable service to the community.
On the issue of resources, the great thing about software is that as the number of users goes to infinity, the fixed costs go to zero. If it takes millions of dollars to produce good software, that’s fine, as long as you can get a large number of people to use it.
More importantly, I disagree that our methods are orthogonal to each other. We may not be parallel, but our dot product is certainly positive! The narrative approach to problem-solving that you recommend in your TED talk is great, but problems of that kind are very involved, take a lot of time, and require a lot of teacher guidance. Even if an excellent teacher had access to a deep reservoir of well-conceived problems of the water-cooler-filling variety, students would still need to spend some time doing shorter practice problems (after all, they will have to take the SAT some day).
And software is well-suited to practicing large numbers of problems. “Drilling” may have a negative connotation in teaching, but any good coach knows its value. I’ve only really looked at two Algebra software packages: I CAN Learn, and the Cognitive Tutor. The former I found to be poorly designed; the latter has been thoroughly researched and tested but strikes me as deathly boring from a students’ perspective. My goal in writing the article was not to argue that “kids like [x] therefore math should be more like [x]”. Rather, I wanted to point out that if software is going to be in our bag of tricks, we might as well make it as effective as possible. And that means it has to hold onto students’ interest.
Furthermore, there’s no reason that software can’t include lots of narrative-driven problems of the kind that you advocate. They would just have to be more guided and less open-ended than the water cooler problem. The advantage of software is that it frees up the teacher’s time to devote to the kinds of open-ended problems that do not lend themselves well to a computer program.
I’m a believer in a big-tent approach to education: there are lots of ways to learn and lots of ways to teach. So I think it pays to keep as many tools at your disposal as possible. One of them should be good software. That doesn’t mean that folks should stop developing good open inquiry problems. It will take many minds and many approaches to improve how kids learn math, but that doesn’t mean we aren’t all working toward a common goal. I think that you and I are on the same side of the barricades; we’re just holding up different sections of the banner.
Finally, we’d all like to see Danica Patrick in a bikini, but there are good reasons to keep that photo out of any educational materials. Same goes for violence, cuss words, etc. So I don’t think my position is much of a slippery slope.
Jason DyerApril 20, 2011 - 7:06 am -
@Doug: Yeah, we had discussions on that. (I didn’t choose the topic, it was chosen by the company CEO who had friends in motocross so it was an easy one to start with.) In fact it was all meant to be a series where the next one appealed more to the other gender side. (I think we were talking marine biology, but I’m fuzzy on the memories here.) Like a lot of series it didn’t get past the first installment, though. The idea would be to have a large set of topics with enough variety that the gender mix wouldn’t matter (and we could, in fact, have something on makeup if we wanted).
However, don’t whip out the stereotyping too fast: in my testing you would be surprised how many girls got into the motocross anyway.
Maria DroujkovaApril 20, 2011 - 8:07 am -
Wells, Dan and everybody,
I would like to recommend the recent discussion with Keith Devlin about his new big math game project (and the recent math game book). You can find the recording here: http://mathfuture.wikispaces.com/KeithDevlin
We also have two video-related events coming up at Math Future series. One is tonight, with Robert Ahdoot of YayMath! who films his math videos live as a part of his teaching – the only one to do so, to the best of my knowledge http://mathfuture.wikispaces.com/YayMath
The second relevant event is the brainstorm of mathematics education video series for TED-ED, led by David Wees and me on May 12th and titled “Making math real” http://mathfuture.wikispaces.com/RealMathTED
David makes a strong point about starting with the authentic context where math really happen.
I don’t know the first thing about sports, but I doubt swimmers care about pool volumes – though other professionals might, such as engineers. Swimmers care about streamlining their bodies. For example, there is a cool calculation of what shaving your legs or using the fabric modeled after shark skin does for your speed. I don’t think humans (celebrities included) should be invited to lie about their use of mathematics. If they honestly use any, they can share and the story will be interesting.
Look at actor commercials for World of Warcraft, where famous actors sound very authentic as they talk about enjoying the game in-character, and show what they do in-game. This can and should be done for mathematics.
Matt McCreaApril 20, 2011 - 12:35 pm -
If nothing else here, I appreciate a good debate, and as it was your article that began everything, I suppose it’s hats off to you for something engaging during my Spring Break.
I have to preface the rest of the argument by saying that I’m in favor of using technology like that for student practice in the classroom. Personally, I’ll take the Khan Academy over commercial software any day of the week, but to each his own I suppose. That said, I’m also well aware that in-depth problem solving is the bedrock of a great mathematics class, so in addition to some solid time practicing on problems, you have to pair it with strong problem solving a la WCYDWT. As far as this goes Wells, I think there’s a disconnect in our understanding, since I doubt there’s anyone reading this blog that doesn’t realize that not every problem can be modeled with a WCYDWT format, although that’s not the worst thing in the world to shoot for.
I won’t go to Dan’s extreme on the idea of shiny things embedded in problems, but I will echo his next idea of the zero-sum game. Sit in on a budget discussion for a school, and listen in on how much having Bieber in an adaptive math program tips the scale onto the side of buying the software. Further, take the time to develop and test this software (nobody will use it without a white paper describing its efficacy), and by the time that’s over, the fads you’ve integrated into the product have come and gone (as how many middle schoolers know who Michael Phelps is, and then ask how many care). The resources you would use, amazingly finite as they will be to be marketable to schools in the first place, will be wasted as the pop culture references will be too fleeting to have the intended impact in the first place. Even here, I believe you hold students to too low of a standard by not believing that they would be invested in their learning when it’s under their own control. As Bowen notes, student engagement can also come from their being in command on that learning taking place.
As far as integrating the narrative approach into an adaptive software program, I invite you to lead a classroom engaged in this type of problem solving. Going into a lesson like that, I’ll ask every math teacher in my department for help anticipating student questions and thoughts, and there hasn’t been a single time that we’ve accurately predicted everything that’ll come up. How can we expect a software program to be able to do that? Adaptive software works great for knowing what problems a student should work on, it’s horrible for knowing how to encourage a student work out an alternative solution or follow them down a tangential path. For a hypothetical situation describing this, imagine adaptive software in a first grade classroom working on a unit on geometric shapes. Student is asked to identify circles, easy enough. Student then asks “how many sides does a circle have?” Is the computer going to tackle this question?
I’m all for the big tent, but that doesn’t mean we shouldn’t be checking ideas at the door for relative merit before they’re welcomed in.
KarimApril 20, 2011 - 1:15 pm -
I’m 100% with Dan on this one. A good narrative is key, and the rest is just packaging. I love my Kindle, but would throw it away if the books weren’t any good.
According to a Raytheon study, 61% of middle schoolers would rather take out the trash than do their math homework. I don’t see what giving Danica Patrick an Expo marker would do, other than erode her own brand. Ultimately, the problem isn’t superficial but fundamental. To these kids, math is lame; it’s boring, meaningless and entirely irrelevant. We could shoot it in HD, but that would just highlight its acne all the more.
We have to change the content, and some of Dan’s WCYDWT prompts are some of the best I’ve seen. Why? Because they’re interesting. Period. Full stop. Because he asks a question, and I want to know the answer. You could give it to me on papyrus–write it in clay–and I’d say the same thing.
Ask interesting questions. It’s not romantic, and unlikely to attract much attention from Kleiner Perkins. But at the end of the day, humans are curious. It’s that simple.
@Wells, I agree with you that software can play an important role. Khan Academy. Virtual Nerd. These are great ways of practicing skills. But I have to disagree–and entirely–with the notion that “there’s no reason that software can’t include lots of narrative-driven problems of the kind that you advocate.” I started a website that writes math lessons around questions like, Is Wheel of Fortune Rigged? and Do people with small feet pay more for shoes?, and have often wondered how they would translate to an online-learning platform.
And you know what? I don’t think they would. You can create an algorithm to construct a ratio table (how many bankrupts per 33 spins) or calculate a unit cost ($/ounce for a pair of size-8 Nikes), but those are just the appetizers. The real lesson comes in the conversation–“Wheel of Fortune seems suspect, but we need more data” or “If Nike charged by weight, how would Foot Locker advertise this?”–which requires people. It requires a teacher. And at least right now, I’m not sure that can be replicated in HTML5.
Dan MeyerApril 20, 2011 - 2:09 pm -
Dunno if Wells is still around for this debate. (Certainly, we can all applaud him for going above and beyond the call of duty here.) If you’re around, Wells, I’m curious what this looks like. The details intrigue me. Let’s say you’re practicing ten volume problems – the usual – let’s say a few prisms, a few pyramids, a few spheres. What does the celebrity approach look like, exactly?
Is there a different celebrity for each problem? The same celebrity? Is the celebrity’s function to read the text of the problem as it would appear on screen under the typical scenario? Does the celebrity solve it also?
I wonder if Wells sees any diminishing returns to this format. Or would a student find the thirtieth celebrity introduction of a volume problem as engaging as the first?
Christine LenghausApril 20, 2011 - 4:15 pm -
I believe absolutely that there are many better ways that students can learn maths than the way we currently serve topics. However one comment keeps coming up in my mind – you can’t please all of the people all of the time, if you try to please everyone you will end up pleasing no-one. We need to find applications of maths (examples to hook them in and want to solve the problem (aka why), which are at their level of proximal development) that suits boys, girls, extroverts, introverts, outdoor/indoor type students, sporty etc. That’s where our experience of life needs to meet the world of the students.
BenApril 20, 2011 - 5:33 pm -
It’s like those “The More You Know” PSAs. They were clever, witty, and filled with A level talent when they first started. Now you’ve got nightly news staff and B level talent from cancelled shows doing cheesy versions of them. I can tell you which ones I would prefer, and like all great shiny things, eventually they get dull.
MichaelApril 21, 2011 - 6:37 am -
Right on! Narrative is an essential part of the math classroom!
GavinApril 21, 2011 - 4:10 pm -
@Dan: I think your comment above presumes too much of Wells’s idea, thinking it’s a pedagogy that has to apply all the time. Many people have made a similar, and incorrect, presumption of your ideas in the past.
gasstationwithoutpumpsApril 22, 2011 - 7:56 am -
The most successful math education software I’ve seen was the Math Blaster series for elementary math by the Davidsons. There was a little story and cartoon animation, but the main attraction for my son was that the puzzles were fun, not just drill.
I’m not convinced that “narrative arc” is needed for everything (I think Dan hits too hard on this point), but it certainly is much more important than hi-res video or celebrities.
I think that the attraction of WCYDWT is not so much the videos or the narrative as the puzzle. Pinning down what makes a puzzle fun is difficult, though, so narrative may be a good tool for more reliably creating student interest.
Wells WulsinApril 22, 2011 - 1:13 pm -
I am indeed still tuned in, but have been scrambling the past couple days to apply for jobs, finish a draft of a long-overdue thesis, and travel to my brother’s wedding (where I am now). But I’m glad this discussion continues!
In response to your question about how (or whether) to get LeBron or Danica into all the problems, I think I should clarify that I don’t envision attention-grabbing hooks in every problem of a software package. Hooks shouldn’t even be written into the majority of the problems. I just think their frequency should be greater than zero, which is roughly how often engaging devices are employed in the math software I’ve looked at.
But let me step back and try to factorize the issues of debate here. Some of the points I was trying to get across in the article are:
1) Math software could be a really powerful educational tool.
2) The math software packages currently available are skull-numbingly dull.
3) Math software would be more effective if it engaged students’ attention and interest.
4) To improve math software will require the efforts of seasoned math classroom teachers (not just software engineers and entrepreneurs).
If I can convince a reader of these four points, I consider my job essentially done. Now, I know that I also devoted a lot of attention in the article to the question of how to make software more engaging to kids. And most of the criticism from you and the other commenters has focused on those strategies. That is entirely legitimate–if I write it, others can critique it.
But if we can set aside the question of how to make software more engaging, I think most of us here can agree that software ought to be more engaging. As a way of quantifying this goal, let me propose a criterion for judging whether we have met this objective. Since I’m a modest guy, I’ll give it a modest name: the Wulsin Test.
An educational software package passes the Wulsin Test if a significant minority (let’s say 20%, to pick a round number) of students (taken from all levels–no fair creaming just the gifted kids) assigned to use the program in school voluntarily complete at least one unit (the equivalent of a textbook chapter) on their own, outside of school, without any academic incentive.
To my knowledge, no comprehensive educational math program has passed this test. They pretty much are all so boring that the only way students will spend time on them is if they are stuck in a classroom under the watchful gaze of a teacher. That shows that educational software is still in a very primitive stage. I believe that math software could pass the Wulsin Test with flying colors, and I expect it will be done relatively soon, probably within the decade.
I think the Wulsin Test is a worthy objective for math software developers and educators to strive for. But certainly it is not the only thing they should care about. If World of Warcraft were an educational program, it would pass easily. Software can be engaging without being effective. But being engaging does not preclude effectiveness. And so I think more educators should be trying to figure out how to make software better able to hold students’ interest.
Once some good educational programs become popular, then it will be much easier to answer the question of what particular strategies prove engaging–and effective. After all, software makes randomized trials pretty easy. With a large number of students using a software program, there will be a lot of data to evaluate what works and what doesn’t. Then the debate about methods can be grounded in evidence, rather than theoretical speculation–which is about all we can go on now. But the first step is to get kids to log on.
CourtneyMay 2, 2011 - 2:17 pm -
This debate is extremely interesting to me as both sides are arguing for genuine student engagement, however, via opposite sides of the pedagogical spectrum. I would agree that narrative is critical to most student’s level of engagement and that it has to be genuine. Although, I do see a space for celebrity hooks, I feel that a software package might be too much of a crutch for some and it would end up harming more than helping the cause. Genuine student questions in every subject should be what governs the curriculum. Adolescents (and children in general) are naturally curious, we simply do not structure our school days or curriculum around their interests or even developmental needs (in many cases).