Should 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?

Agreed. 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 Dintersmith

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.

Hi Ted, I don’t think anybody here has expressed anything close to an objection to this. I’d love if my efforts in class helped students tackle problems out of 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 less likely 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?

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.

“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

*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.

I 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!

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:

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.

I’m going to restate my claim, though. Even if this task did have 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 between the actual applications of math to the world and the presentation of those applications to students.

Jane Taylor:

When 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.

Restating my claim: there are 100 different directions that question can go in terms of the work students do in class and 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:

I 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.

Is it possible to rank these in order of concreteness?

hexagons, health insurance, hydraulic engineering, hydrogen gas, and heptominoes

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.

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.