In case this whole series seemed to you like a bit of a straw man (it did to Kate Nowak and Michael Pershan) here’s the New York Times Editorial Board:

A growing number of schools are helping students embrace STEM courses by linking them to potential employers and careers, taking math and science out of textbooks and into their lives.The high school in Brooklyn known as P-Tech, which President Obama recently visited, is a collaboration of the New York City public school system and the City University of New York with IBM. It prepares students for jobs like manufacturing technician and software specialist.[..]

Though many of these efforts remain untested,

they center around a practical and achievable goal: getting students excited about science and mathematics, the first step to improving their performance and helping them discover a career.

Pick any application of math to the job world and I promise you I can come up with 50 math problems about that application that students will *hate*. Get a little coffee in me and I’ll crank out 49 more. It’s that *one* problem, the one out of 100 that students might enjoy, that’s *really* tricky to create, and often times its “real world”-ness is its least important aspect.

Chris Hunter reminds me (via email) that the British Columbia Institute of Technology has made a similar bet on “real-world” math. Here’s an example:

Once again, we’re asking students to substitute given information for given variables and evaluate them in a given formula. Does anyone want to make the case that our unengaged students will find the nod to structural engineering persuasive?

The “real world” isn’t a guarantee of student engagement. **Place your bet, instead, on cultivating a student’s capacity to puzzle and unpuzzle herself**. Whether she ends up a poet or a software engineer (and who knows, really) she’ll be well-served by that capacity as an adult and engaged in its pursuit as a child.

**Featured Comments**

Chris Hartmann points out that these application of math to jobs often miss the math that’s most relevant to those jobs:

And, in the job world a lot of the mathematics isn’t done by human minds or hands anymore, with good reason. Faster, more accurate means are available using technology. What often remains is puzzling out the results.

The telling thing is that the Times’s example of a real world problem that real world people can’t solve, that of calculating the cost of a carpet for a room, is pretty much a guaranteed loser for any math class that I have ever taught at any level.

On the other hand, yesterday I had a room full of third round algebra students engrossed in building rectangles with algebra tiles. That’s about as non real world as it gets.

The moment of inertia for rotating a I-beam about its long axis has no practical relevance in structural engineering. This is a fake-world problem, of no interest either mathematically or to engineers.

There are real-world applications for moment of inertia problems, but this is not one of them.

This seems to be a perennial favorite. In 2011 the Times asked if we needed a new way to teach math, with this quote:

“A math curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. ”

I’m certain I could find an example of such an article from every few years …

## 21 Comments

## Chris Hartmann

December 10, 2013 - 4:59 pmWell said, Dan! And, in the job world a lot of the mathematics isn’t done by human minds or hands anymore, with good reason. Faster, more accurate means are available using technology. What often remains is puzzling out the results. Looking for opportunities to improve performance, cut costs, attract users. Thanks.

## Mr K

December 10, 2013 - 5:18 pmThe telling thing is that the Times’s example of a real world problem that real world people can’t solve, that of calculating the cost of a carpet for a room, is pretty much a guaranteed loser for any math class that I have ever taught at any level.

On the other hand, yesterday I had a room full of third round algebra students engrossed in building rectangles with algebra tiles. That’s about as non real world as it gets.

## gasstationwithoutpumps

December 10, 2013 - 5:19 pmThe moment of inertia for rotating a I-beam about its long axis has no practical relevance in structural engineering. This is a fake-world problem, of no interest either mathematically or to engineers.

There are real-world applications for moment of inertia problems, but this is not one of them.

## Howard Phillips

December 10, 2013 - 5:42 pmWell, it might just help if the person who set the question had actually seen an I-beam.

A lot more could be achieved by setting the task “Rip this question to bits. Ask why anybody would want to know the moment of inertia of an object whose destiny is to be fixed down. etc etc”.

## Joe Schwartz

December 10, 2013 - 6:30 pmOne more example of the folks at the New York Times leading cheers for the corporate reform movement. For another great example, see “Jersey Jazzman” take down Thomas Friedman…

http://jerseyjazzman.blogspot.com/2013/12/the-mustache-of-understanding-tries-to.html

## Priscilla Bremser

December 10, 2013 - 7:33 pmThank you for this, and for the whole series. I’d been avoiding a close reading of the NYT editorial, but I had to in order to add it to my running list of articles about math with irksome opening lines. Citing your post made it easier: http://tinyurl.com/md6u8y4

## Simon Terrell

December 10, 2013 - 7:37 pmI worked in the telecom industry and sort of came to my job obliquely. I did not have a math major so felt I was supposed to be out of my league. I quickly came to find that many of the engineers I worked with rarely relied on the high level math that they had studied but their problem solving skills and creativity.

This is an honest example that shows Dan’s point, I think.

## Dan Meyer

December 10, 2013 - 7:40 pmReal helpful commentary, team. I’ve added a bunch of it to the main post.

## Garret Schneider

December 11, 2013 - 3:52 amIt sounds like an updated trade school,, which is what a lot of students need. I work in a low income area, and 75% of the students who go to college drop out before the first semester.

They don’t need college. They need a job that a program like that offers them. The school/article may miss the point of applied math, but if the students can see a direct result of what they learn get them a job or solve an issue, they’re going to care.

## Galen

December 11, 2013 - 4:49 amI just started reading your blog and have kind of skipped around so I apologize if you address this elsewhere, but what do you say to the claim that it is an equitable practice to create authentic problem solving opportunities (maybe those are supposed to be “real world” problems)? Most of the research I had read through this summer agreed that “authentic problems” and “applied math” is a critical factor in the engagement of students of color (to be very general). Thanks!

## Jane Taylor

December 11, 2013 - 7:51 amWhen I saw the two boards, I wanted to go get a board and try standing on it. How much weight could we put on the board in each position before it broke? That would be an engaging problem.

## Brendan Murphy (@dendari)

December 11, 2013 - 8:02 amHow can anyone possibly think this thing with an I-Beam would be engaging. They give you a formula and basically say here are new numbers, go back to the formula and plug them in, I’ll let you know if your ability to be a calculator is up to snuff.

## Zack

December 11, 2013 - 8:11 amI think there’s a conflation of issues going on here. The goal of any class should be to have every activity be as engaging as possible, but that will vary person-to-person so having different styles of instruction is what great teachers do.

That’s entirely a separate issue from the real-worldyness of an activity. It seems to be that the objective there is to bridge the wholly abstract ‘planet-math’ with things that are in student’s experience. So that they can ground what they have learned/are about to learn in some connections. But that only applies if the context is something that students have some existing knowledge of personally and can use to help the mathematics make sense.

The discrepancy is that there’s lots of awfully mundane boring stuff in the ‘real-world’, but anyone who thinks bringing that garbage into a classroom would boost engagement has clearly spent 0seconds teaching a classroom.

## Dan Meyer

December 11, 2013 - 9:16 amGalen:Curriculum should function as both a window out to other cultures and a mirror back to our own. No argument there. But there is such variation in what we call “real world” problems, I’m suspicious whenever I see it in a prescription. (eg. “Math just needs to be

real world.”)This blog series might seem to contradict my enthusiasm elsewhere re “real world” math. My treatment of the real world in these problems, though, is based in a particular theory rather than in the mistaken belief that all tasks are created equal so long as they include the “real world.”

gasstationswithoutpumps:I’m going to restate my claim, though. Even if this task

didhave practical interest for structural engineers, its presentation here will move the needle on student engagement only a fraction of a degree. There’s a long perilous road betweenthe actual applications of math to the worldandthe presentation of those applications to students.Jane Taylor:Restating my claim: there are 100 different directions that question can go in terms of

the work students do in classand only a handful of those will actual leave kids feeling mathematically powerful and capable.Here’s one direction:

“The maximum load a board can hold before it snaps is given by the formula: [formula involving cross-sectional area and mass]. Dan weighs 90kg and the dimensions of the board are 2 inches by 4 inches by 70 inches. Will the board hold his weight?”

I have no confidence this task will result in the sense of accomplishment and connection the editors of the NYT seem to think it will.

There are, perhaps, other ways to present this kind of task, though. Which is my point. The “real world”-ness or “job world”-ness of the task is one of its least effectual variables.

Zack:Is it possible to rank these in order of concreteness?

I have loads of confidence in your thesis that we need to bridge the abstract and the concrete. (Or as Hayakawa put it a long time ago, ascending and descending “the ladder of abstraction.”)

I can’t confidently say that hexagons are abstract and health insurance is concrete to a middle school student, though.

## josh g.

December 11, 2013 - 9:38 am“On the other hand, yesterday I had a room full of third round algebra students engrossed in building rectangles with algebra tiles. That’s about as non real world as it gets.”

*That* sounds more real to me than this I-beam problem.

You’re holding something. You have a physical, concrete-thinking activity to do with it. How is that not real to the kids? They’re holding it in their hands.

The I-beam problem, on the other hand, is abstract, distant. You have an opaque formula, no idea why it works, you’re just told to put numbers into it and solve.

I know this is not the definition of “real-world” that’s being put to question here, but I think it’s a more important distinction.

The NYT article sounds like it’s full of both horrible and great all at once, and doesn’t really know the difference. (Disclaimer: I skimmed it.)

Making math more real to students by connecting it with building, making, designing, or by using concrete representations of otherwise “fake-world” math might actually have some traction. Making math more “”””real”””” by putting it in a traditional word problem (which is all that I-beam problem is) will not change anything – every single textbook made, ever, has already tried that, and it sucks.

## Kyle Atkin

December 11, 2013 - 12:10 pmShould we be considering the goal of the task? If the goal of this task is to get students engaged in mathematics then I think most of us can agree to the fake-worldness of the task. However, if the intent is to have students substitute some given numbers and solve an equation, could it be argued that this task is more “real-world” than just presenting the stand alone equation?

## nerdypoo

December 11, 2013 - 3:28 pmThis seems to be a perennial favorite. In 2011 the Times asked if we needed a new way to teach math, with this quote:

“A math curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. ”

http://learning.blogs.nytimes.com/2011/08/26/do-we-need-a-new-way-to-teach-math/

I’m certain I could find an example of such an article from every few years, which seems to forget their 2008 article “Study says scrap balls and slices.”

This article suggested that when students learn “real-world” math, they often have trouble seeing the underlying mathematical concepts and thus have trouble transferring it to new situations (something we have all surely seen in our math class; change the parameters of a problem the students have done a million times and suddenly they’re flummoxed). They posit that in fact learning concepts in the abstract helps students apply it to various situations as the understanding is conceptual rather than contextual.

http://www.nytimes.com/2008/04/25/science/25math.html

## Ted Dintersmith

December 11, 2013 - 4:52 pmI know that Dan and many of the commenters here are committed to improving K-12 math education, for which I am grateful. But I’m at a loss to understand the feeding frenzy whenever anyone suggests that math taught in our schools should have more emphasis on applicability to real world situations. Somehow, that statement gets spun up (in a way that Glenn Beck would admire) to saying that all of math should be entirely based on applications to real world problems, no matter how boring or poorly posed the problems are.

Today’s reality is that in the vast majority of grade 7-12 math classes, students are performing tedious calculations by hand that can be readily done computationally. Worse, the years spent simplifying hairball algebraic expressions, solving simultaneous equations, memorizing the definitions of geometric shapes, memorizing trig definitions, or doing integrals and derivatives by hand comes at a huge price. Kids don’t really understand what a variable, function, or equation really mean, they don’t retain much of what they learn, they never get to what could actually help them in life, and many are bored to tears doing something only marginally more challenging than long division by hand. And survey after survey shows that the vast majority of adults don’t use anything beyond decimals, fractions, and percentages.

So I’d encourage this group to curb their Pavlovian response to anyone who suggests that at least some of the time kids spend on math should enable them to attack problems they see in the real world. In a world where over half of recent college graduates are under- or unemployed, where innovation is systematically eliminating routine jobs from the economy, when student engagement declines steadily year by year, and when the vast majority of grade 7-12 tests can be completed by anyone with access to Google search, we surely can all agree that we need to make profound changes in the way we educate kids, and stop sniping at others who ought to be allies.

## Dan Meyer

December 12, 2013 - 7:31 amKyleAgreed. As long we’re clear on what the problem

does(practices instrumental understanding) we can debate if it’s a worthwhile use of time. Right now we’re unclear what the task does.Ted DintersmithHi Ted, I don’t think anybody here has expressed anything close to an objection to this. I’d love if my efforts

inclass helped students tackle problemsoutof class.These posts critique the idea that

any“real-world” task will get students to that place. It also advances the idea that pure math tasks can also equip students to develop their capacity to puzzle and unpuzzle themselves later in life. (The opposite of “tedious calculations” isn’t “real-world problems,” in other words)Hypothetically, if assigning students the structural engineering task in this post made them

lesslikely to want to be a structural engineer,why wouldn’t you want to know about that?Why shouldn’t we talk about the best way to pose a structural engineering task, rather than assuming all those tasks are created equal?## Jeff Layman

December 17, 2013 - 9:00 pmHow do you see cultivating a student’s ability to puzzle and unpuzzle herself panning out in other content areas? I’d love to figure out how to do it with Social Studies.