A Sports Illustrated editor emailed me last week:
I’d like to write a column re: how sports could be an effective tool to teach probability/fractions/ even behavioral economics to kids. Wonder if you have thoughts here….
My response, which will hopefully serve to illustrate my last post:
I tend to side with Daniel Willingham, a cognitive psychologist who wrote in his book Why Students Don’t Like School, “Trying to make the material relevant to students’ interests doesn’t work.” That’s because, with math, there are contexts like sports or shopping but then there’s the work students do in those contexts. The boredom of the work often overwhelms the interest of the context.
To give you an example, I could have my students take the NBA’s efficiency formula and calculate it for their five favorite players. But calculating — putting numbers into a formula and then working out the arithmetic — is boring work. Important but boring. The interesting work is in coming up with the formula, in asking ourselves, “If you had to take all the available stats out there, what would your formula use? Points? Steals? Turnovers? Playing time? Shoe size? How will you assemble those in a formula?” Realizing you need to subtract turnovers from points instead of adding them is the interesting work. Actually doing the subtraction isn’t all that interesting.
So using sports as a context for math could surely increase student interest in math but only if the work they’re doing in that context is interesting also.
After my AP stats exam, I had my students come up with their own project to program into their TI-83 calculators. The only one I remember is the student who did what you suggest — some kind of sports formula for ranking. I remember it because he was so into it, and his classmates got into it, too, but I hardly knew what they were talking about.
He had good enough explanations for everything he put into the formula, and he ranked some well known players by his formula and everyone agreed with it. But it was building the formula that hooked him, and then he had his calculator crank out the numbers.
Mike LawlerSeptember 19, 2014 - 8:42 am -
I was lucky to do some work behind the scenes with the promotion promising a $1 billion prize if someone filled out a perfect bracket during the NCAA men’s basketball tournament.
Lots of fun (and some fairly advanced) math and I think a great example for kids to see a neat “real world” math problem..
jim cibulkaSeptember 19, 2014 - 8:56 am -
The most important thing sports can do is to be an analogy for how we give structure and mentally organize knowledge, in my humble opinion.
Coaches do not just throw kids out on the field; they give them structure for where and how to play. This is just like how physics experts organize problems according to models instead of superficial features (from how people learn). Sports skills are like factual procedural knowledge . .. the arrangement of the players, such as a 4-4-2 alignment in soccer is more akin to conceptual knowledge.
To involve sports more, perhaps we should look into why teams run a 4-4-2 in soccer, or play man / zone defense and relate this to why we would use models in science and math.
BrandonSeptember 19, 2014 - 9:18 am -
This is exactly why it takes up until graduate school in order for many students get to see what math is all about – creating instead of following.
To give one example: In my text analysis class we’re trying to figure out how to compare two documents (say a sentence on a web page).
One could say “I really like Lebron James because he has a high shooting percentage, defends well, and gets his teammates involved.”
Another could say “Lebron James is overrated, he doesn’t rebound well, his shooting percentage is not that high, and anyone who defends him is dumb.”
We learn to “vectorize” the sentences and see the commonalities and differences in the words used in order to create a model that tries to determine overall feelings. It’s called sentiment analysis, a part of machine learning (artificial intelligence).
But vector work in and of itself is dreadful. No one wants to calculate cross products or dot products. But the ideas behind them – how do we determine what words are relevant? And the results! It’s amazing how accurate a simple model like this is…. What lives behind the algorithms is wonderfully perplexing.
What I really struggle to understand is, why can’t we start with these types of analysis to introduce tools around vector manipulation rather than the two years of classes on matrices that I was forced to take that were completely devoid of context and mainly involved definition and proof memorization? We try to follow the footsteps of these medieval mathematicians who were doing mathematics for its own sake, but there are way more interesting applications, cutting edge stuff, that most of my high schoolers last year could have done.
Dave NielsenSeptember 19, 2014 - 9:20 am -
It’s all just glitter. Problems about sports? Showing work in a drawing app an on iPad? Teaching class outside for a day?
It’s one big category of ways to get a short-term bump in student attention. It’s not outright terrible; a teacher can make it through a school year by swapping in a new bag of glitter each time the old one stops being shiny, and do alright.
Eliminating psuedocontext, bringing in the 3 act structure — it’s about building natural curiosity in students, right?
I have less than average interest in sports…but when Dan says “The interesting work is coming up with the formula…” my brain just WANTS to solve that problem.
That’s why I read math teacher blogs even though I’m not a math teacher. I read Dan’s in particular because I feel like he’s trying to solve a problem, and that’s where I want to be. It’s compelling. Somehow that internal drive got planted in my brain, and I don’t know how (yet). All I know is I’m thirsty for solving the problem of how to get students thirsty about solving problems.
DonSeptember 19, 2014 - 9:34 am -
I think you could expand out the meaning of “teach” in this context. When it comes to pseudocontext and window dressing around number grinding I completely agree with you. But I think the reporter’s angle could have some value in how sports can be a motivating factor for gaining competency.
If you at all like baseball and weren’t aware of Sabermetrics then reading Moneyball is a hugely exciting experience. It tweaks that part of our brains that I think is critically important for math learning – the desire to figure something out, and get one up on everyone else. We’re wired to get excited by that new tool, whether it be a cool bat or a new iphone.
Yeah, doing the same old calculator work with some sports labels is pointless. But for someone interested in Baseball in a way they aren’t interested in engineering I can see learning a new way to visualize a player’s worth as a motivator. It’s not like lifting weights to gain muscle is all that thrilling, but knowing it’s how you hit the ball farther can motivate you through those boring and painful bits.
Howard PhillipsSeptember 19, 2014 - 10:04 am -
One problem with “contexts” is, especially with sports, that not every student has an interest. So there is always a group of “what’s this got to do with me?”. The 3 act approach has more chance, as the context is less relevant. I am reminded of the wonderfully vague “when is a cylinder a disk?”. It soon doesn’t matter where the problem arose, as similar contexts rush in for attention.
Jason DyerSeptember 19, 2014 - 1:44 pm -
If I can drop a book recommendation here:
Statistical Reasoning in Sports
(One of the co-authors works in my district.)
Try the sample chapters. Chapter 1 opens with “Did LeBron James choke in the 2008 playoffs?”
TomSeptember 19, 2014 - 8:00 pm -
But everyone loves puppies right? We’ll just add “puppies” after every number and it’ll be awesome!
I have a similar plan for history where all the historical figures will be given nicknames associated with popular cartoon characters.
Kenneth TiltonSeptember 19, 2014 - 8:49 pm -
Puppies? Did someone say, “Puppies”? OK, now I am engaged.
First, I am reminded of the tweet from some girl sth like “Never mind the relevance, I know it is, my problem is passing this damn class.”
Second (and related) I am reminded of a rule in football: do not run your plays away from the great player, run them at them. Run the other way and they run you down from behind anyway. Like the young lady above: someone tried the relevance ploy on her and she saw through it like especially thin cellophane.
The right way to teach math is first to love it for itself, and then convey that. Attack the indifference head on, with your own greatest strength: math has elegance, power, and beauty.
If yer gonna die, die trying. Do not deny mathematics three times before the dawn. The puppies need their sleep.
Ted DintersmithSeptember 20, 2014 - 4:26 am -
You should visit some of the schools using N.B.A. Math Hoops or check out their website — http://www.nbamathhoops.org. Last school year some 40,000 inner-city kids were excited to learn math because it was connected to something they care about.
I’d echo Brandon’s point that it isn’t until graduate school when anyone gets to the point of doing anything remotely interesting when it comes to math. At least the way we teach math currently. And what percentage of middle-schoolers go on to take math in graduate school. .1%?
The fact is that the vast majority of time spent on math in middle and high school years is completely wasted or worse. Math teachers, and Dan’s blog draws many, hate to hear that. But it’s the sad, unforgivable truth of our current math curriculum. Some great teachers can get their students engaged, but most can’t, and the reason is that we have them do boring symbolic arithmetic with no plausible explanation for why they need to get good at it. We can, and have to, do better.
Fred ThomasSeptember 20, 2014 - 4:55 am -
Putting math into a context IS important, if only to remind students that they can and should use abstract math outside the math classroom. It is also very important to use a wide variety of contexts, so that all students get to see at least a few applications in areas that interest them. We have often found that seeing a few applications which students find interesting makes them more willing to put up with either pure math or contexts that don’t interest them (e.g., sports for those with no interest in sports, or puppy nutrition for those with no interest in animals).
Still, Dan hits the nail on the head in emphasizing that interesting work is more important than an interesting context. Fortunately, the world of careers is moving in a direction that favors interesting math work. Outside of school, the most dull and boring stuff (plugging numbers into formulas, solving algebraic equations and more) is very often done by computers. Good paying jobs depend more on the ability to set up the problems, to understand the difference between linear and other best fit options, and other higher-level problem solving skills.
Maybe there still needs to be some uninteresting, algorithm-based work in math classes (long division?), but there also needs to be an ample portion of work that is both interesting and important beyond the math class.
DG ReidSeptember 20, 2014 - 5:04 am -
I am an engineer/teacher, and I can tell you that the reason math is interesting to me is that it helps me solve problems. The problems come first. Trying to find a worldly example for each aspect of math is putting the cart before the horse. If you want to be able to solve the problems, learn the math. Unfortunately, most people are not problem solvers. They are handle turners (they do the same thing repeatedly), and resent having to learn math they will never use. Even as an engineer, I learned a great deal of math I never used.
This highlights a fundamental flaw in our educational system. We try to teach everything you might need to know before you hit 22 versus making it possible to conveniently learn something when you need it.
JeffSeptember 20, 2014 - 6:33 am -
Maybe you’re right from a mathematical context, but through the eyes of an educator, I think you’re passing up on an opportunity. Isn’t it our jobs as teachers not to decide for them what’s “boring” and “interesting”, but yet give them the knowledge and opportunity to make that decision for themselves? Sure, math will never be as “sexy” as sports, which is what makes sports so recreational – we can just go play or watch a game and get lost in it. Not try to introduce math into a students’ recreational life because you think it’ll be too “boring”? I guess I need to read Willingham’s book to understand this more.
You’re famous for your “is my shot going to go in?” experiment. I feel like there’s something you could’ve done along those lines to bring math and formulas into sport. Is my favorite team going to win the championship this year? Then use math as the means to the end response.
You’re good Mr. Meyer, but in this instance I feel you have up too easy, and I think it’s unfair you get to decide what’s boring to students. I was once told that as teachers we have one school day for every student we are going to try to reach on a personal level, and you may have just missed one.
SharonSeptember 20, 2014 - 6:52 am -
the funny thing is that kids can be very good at sport, and still will not know to answer simple questions as – how fast are you? whats your running speed? what’s the difference between – 6 minutes for a mile and 10 miles per hour?
I was teaching an athletes class, and when I start asking these questions they were very engaged.
Shooting rate (teaching percentage etc) I did with the basketball team, and first I’ve sent them to the court to bring their personal data. SO my experience is that Math & Sport can work together for the right class.
Kenneth TiltonSeptember 20, 2014 - 7:41 am -
I looked at NBA Math Hoops, did not see much math. Maybe 5% of the time spent playing the game goes into math, right? All that to teach number facts? With the number facts not at all relevant to basketball? You just have to find a square on the board that matches one of the results of all the possible computations off the dice throw?
I find this to be insulting to students. It says “we are going to trick you into learning number facts”. But kids are terribly bright. They know what we are doing when we wrap content in a game, especially in such a meaningless way. And when they see us doing that, they hear “The grown-ups concede that math is pointless so let’s bury it in a game.” Where it affects like 10% of the play.
Where is the math in the draft? The decision to foul? Is the probability of the three vs the two ever computed, or do they just see that the spinner wedge is a little smaller?
By the way, I hate hearing neither that math instruction needs to be better nor that schools should be turned inside out. But silly games that do not all make math relevant will not be part of that.
DG ReidSeptember 20, 2014 - 7:55 am -
I think it is good to remember that not all learning must be done in the classroom. In the case of sports and many other areas, experiments can be designed that students can do at home to explore mathematical principles. What is the cost per square inch of different sized pizzas, for example, or what shape container holds the most volume for the same perimeter and depth?
john edelsonSeptember 20, 2014 - 10:02 am -
This is a great question. It’s also been much studied.
My understanding is that relevance to interests is not the panacea to motivation for math that at first it appears to me.
I read a book recently that devoted entire chapters to this question: “Mathematics Education for a New Era.” Devlin was not encouraging in his presentation of research as a way to infuse math study with some energy. Of course, he seems to believe the current math curriculum should just die from irrelevance and be replaced with a new technology-based conceptual one.
BTW, I totally agree with him.
katenerdypooSeptember 20, 2014 - 10:22 am -
i’m actually a little excited for a project we’re doing this year that involves statistics and sports. it’s an interdisciplinary unit with PE. in PE they are doing various athletic events (track and field) and are recording all their times and distances, etc. then in math class they are going to organize and analyze the data and ultimately create their own triathlon where they will have to decide on how the points will be awarded for the various disciplines by looking at their rankings and the various averages, etc. we have a very mixed level class so the sophistication of their system will vary but they have to show that they’ve taken into account the averages and distribution among the class.
John LeeSeptember 20, 2014 - 4:32 pm -
There is a curriculum for Fantasy Football in the classroom. It is largely based on students calculating the scores of their teams every week–which I’ve always tended to agree (is monotonous and boring). But I’m starting a league for a class full of kids, trying to think of ways to use fantasy football/mathematics in an engaging way.
I’m thinking they still calculate the totals, because it has to be done. But also, some sort of data analysis program where kids look at the relevant statistics and make decisions based on them.
ChrisSeptember 20, 2014 - 5:39 pm -
OK OK, not for the secondary classroom but cool anyway :-) “Projectile Dynamics in Sport – Principles and Applications”
Dan MeyerSeptember 21, 2014 - 4:08 pm -
Hi everybody. I wanted to clarify something in light of several questions and critiques I’ve received here and via email. They read like this:
That’s not what I’m saying. I’m saying there is as much variation within sports application problems as there are between application problems and non-application problems.
Ask me to pick a random sports application lesson and use it in a random class and I honestly would not be able to predict if it would interest students or not.
My uncertainty isn’t just on account of all the students who don’t find sports interesting. (Though that’s important.) It’s because some of those tasks will involve boring work within an interesting context. In those situations, the boring work often beats the interesting context.
I’m familiar enough with Brandon and Ted’s work and I disagree so viscerally with both of their comments I feel I have to have misinterpreted them.
Their comments amount (in my interpretation) to telling students, “None of this will be interesting for sixteen years. But once you finish that undergrad math degree and decide to pursue graduate mathematics, it’s going to be great.” If that’s the value proposition for a math education, why would anybody bother?
DG ReidSeptember 21, 2014 - 4:52 pm -
The vast majority of people will not use math beyond the basic four functions. A much smaller percentage will use decimal arithmetic beyond two places and fractions. A tiny percentage of that will use algebra, and only a vanishingly small percentage will use math beyond algebra. Why is it that everyone should even take algebra?
Why can’t we just teach everyone math through fractions and let those who are interested go further instead of trying to find some way to make everyone interested in higher math? They aren’t, and experience has shown that they will not do well in a subject they don’t like.
I would do horribly in geology. It is not that I couldn’t understand the material – I just don’t care much about it. I am glad there are geologists and mathematicians. I just don’t want to be one. Once again, the problem is that there is no practical method of gaining higher education after one starts working unless you are in just the right circumstances in just the right place. If I need to learn non-linear partial differential equations, there should be a way for me to without having to change jobs and addresses to get near a university that has a nighttime extension program.
Stop trying to teach everyone what only 1% of the people will need, and focus on changing the system so people can learn what they need when their situation dictates they need it.
Dan MeyerSeptember 21, 2014 - 4:58 pm -
The fraction standards in the CCSS max out at fifth grade. If you had given me the option to opt out of subjects at age ten, I would have opted out of everything except PE and video games.
That seems like the abdication of an adult’s responsibility to me.
Clara MaxcySeptember 22, 2014 - 1:26 am -
DGReid says: focus on changing the system so people can learn what they need when their situation dictates they need it.
That is a good representation of the lessons I am trying to build. Learning something when you need it is the key to keeping students interested. Learning math is about so much more than using the math in a job, although for artists and engineers and medics and scientists and salespeople and managers and entrepreneurs…. Well, anyway, it is about opening up the student to possibilities. Students, particularly 7-11, even some 12 graders, don’t know how much is out there that they don’t know. If we can learn to facilitate “wondering” and curiosity and the “need to learn”, we have affected the way that child looks at life, whether they become a mathematician or not. Under your other assumptions, since I was not very good at sports, I shouldn’t have been required to play softball or volleyball or try archery or golf (all painfully required of me in my PE classes thru my senior year). However, I learned a respect for those things that has stayed with me. Perhaps we just want access to these things so that these kids we teach will have a chance at something they might not otherwise ever know existed! (And as an adult, I returned to those things: softball, volleyball…. I’m still not very good, but I know how to play, and how to teach others to play. And I would not have had those joys, without those terribly awkward years in PE! High school can be a taste of a university education (at least in the broadness of disciplines taught), as long as we realize our students are learning about the disciplines, not just the actions taken within the disciplines.
DG ReidSeptember 22, 2014 - 4:42 am -
Clara Maxcy said:
Students, particularly 7-11, even some 12 graders, don’t know how much is out there that they don’t know.
The advice I give to virtually everyone I meet who is thinking about the future is: Before you decide there is something you want to do or become, talk to someone who has done it.
My final semester of undergraduate studies in engineering, we had a series of engineers from industry come in and discuss what they actually did. OMG! Where were they during my first semester when I really needed this kind of insight? Even in high school, I believe it would be beneficial for actual doctors, engineers, etc. to come in and talk not to seniors, but to freshmen to give them some insight as to what will be required of them four years hence. It is all well and good to try to make individual classes interesting, but students should keep their eye on the goal.
Conversely, it would be almost equally good to have some minimum wage graduates come in and cite the consequences of not preparing for life after graduation.
BrandonSeptember 22, 2014 - 1:50 pm -
Clarification, I said: “This is exactly why it takes up until graduate school in order for many students get to see what math is all about — creating instead of following.”
I meant this has been my history in math classes. I spent way too much time plugging in players’ attributes to someone else’s formula.
When I tried to try to have classes where students produced those formulas (in a different context), every year I had to fight the same battles against parents, students, administrators and at time other professional teachers.
“If that’s the value proposition for a math education, why would anybody bother?”
That’s pretty much why I left.
Dan MeyerSeptember 22, 2014 - 2:40 pm -
@Brandon, roger that. Glad to hear you’re feeling good about your new thing and it’s nice to see you check in with your math teaching folk once in awhile.