An article in the latest issue of Mathematics Teacher advocates fighting fire with fire in the competition between math class and the media for students’ attention. We are exhorted to Present Examples in High-Resolution Video, to Connect to Students’ Interests, to Show Appealing Faces and to Hold Students’ Attention
As examples of Connecting to Students’ Interests, H. Wells Wulsin offers,
Monitoring a breeding bunny population would show the process of exponential growth. Baseball batting averages could introduce percentages. Such applications of mathematics to daily life would help students build important links between new ideas and the concepts they already understand.
The article continues. Under Showing Appealing Faces, Wulsin advocates,
What if Michael Phelps calculated the volume of an Olympic swimming pool or Beyoncé computed the time delay needed for speakers at an outdoor concert? Why not let Danica Patrick figure the monthly payment on an auto loan?
I have to confess that I find the whole piece a little depressing for two reasons.
(1) Dissemination of the 1989 standards
I can cite examples of rabbit population contexts for exponential growth going back to the original NSF-funded curricula of the early 1990’s. But I doubt the example below is the first time bunnies appeared in an algebra book.
Bunnies in Connected Mathematics, circa 1998
And baseball batting averages date back much, much farther back in Algebra I curriculum.
Batting averages in Algebra I, Modern Edition, circa 1970. Note the annotation at the bottom of the page.
Is this the progress we have made in disseminating the vision of the 1989 NCTM Curriculum and Evaluation Standards? Have we made so little progress that these examples still make for a viable opinion piece in Mathematics Teacher?
(2) Lipstick on a pig
The present guru of high-resolution video in math class is Dan Meyer. I worry that when people look at Meyer’s work, they see the glitzy exterior, not the instructional techniques the technology supports.
Dan is a handsome enough guy (Show Appealing Faces) and his escalators problem has high-enough production values (Present Examples in High-Resolution Video). But that’s not what his work is really about. It’s about storytelling-about putting students in a situation where they ask the mathematical question that we know will be productive. High-resolution video makes this easier to do, but it’s not the core of the idea.
The core of the idea is that we are engaged with the story. We see Dan about to go up the down escalator and it makes us wonder (1) whether he’ll do it without falling flat on his face and (2) if he does do it, how long will it take? The viewer is invested in the narrative.
So here’s a question that points out the distinction I think is important.
Why does Michael Phelps care what the volume of the swimming pool is?
There is no story here; no narrative. If I don’t believe Michael Phelps cares about the volume of the pool (and I do not believe that-just to be clear), then why should I care about the volume of the pool?
Making Michael Phelps (or Beyoncé, or Danica Patrick, or even Danica McKellar) the handsome spokesman for the same old word problem hardly advances an agenda of real and engaging mathematics for real students, nor one of turning students into believers that a mathematical perspective on their everyday world might be (1) useful or (2) intellectually stimulating. It’s just lipstick on a pig.
You may or may not be bored by my salt problem. But there’s a reason for computing the volumes. There’s a story-someone is going to fill that container by opening a brand-new box of salt. It’s unclear at the outset whether it will all fit in there-the new container is shorter but wider.
While we don’t need to compute the volume to find out whether the salt will fit, we can. And the more carefully we measure and compute, the better we should expect our prediction to be. And in a middle school classroom, this is likely to get some students’ competitive juices flowing.
Why do we want to know the volumes of these containers? Because we want to correctly predict how the story is going to end, and because we want to be more right than our classmates.
I would gladly put the Morton Salt girl up against Michael Phelps in a year-long curricular grudge match. Which will engage students with more mathematics over the course of 180 school days: filling Tupperware with salt or pep talks from Olympians?