Tuesday, April 19, 2011

Math Reform: Games, Practice and Psuedocontext

More interesting to students.
Probably not good at being a teacher.
Dan Meyer found Mathematics v. MTV by H. Wells Wulsin in this month's Stanford Sound Off. H. Wells, a former physics and chemistry teacher at a Washington DC private school, is making the case that math software (and by extension, teachers) must change because of competition with MTV for the eyeballs of our students. Which is kinda amusing, since none of my students watches MTV for more than a tiny percent of their information-absorbing time. Facebook, iPod, games, texting, Facebook, YouTube, cellphone, texting. The TV might be tuned to MTV in the background, but more likely it's on Spongebob.

Anyway, he does have a point when he says, "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."

An issue I have is when he says, in the next breath, "Research shows that mathematics software can boost student learning, but these programs remain unpopular."  That's because software isn't always the answer. Teachers are primarily involved with new learning. New learning is rarely successful in a computer-learning environment because it usually needs an human explanation. If students could do this alone, you'd see a lot more kids taking summer classes online and getting credits. Repeat learning can be successful online (or by computer training) because the kids already know what the goal is, already have been taught the concept but just need repetition and practice.

The upshot of all of this?  You probably have done as much of this guy's ideas as is workable.

Back to our expert ... Wulsin offers recommendations that sound good in theory:

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 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?"

Holding students' attention. "Make students laugh through physical comedy or corny one-liners. Introduce them to interesting people with magnetic personalities."

Sounds good. Misses the point.

To engage learning, what you need is a good question that arises out of context, asked in a way that makes sense, posed by someone who actually needs to know the answer.  While I hate to push the button marked “Praise Dan” too often, I do think that he has given us a shorthand for much of this … pseudocontext … and the suggestions fail because of it.

Show appealing Faces

“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. Build your question from that and you'll have the class hooked. Bring in data from your pool at home and calculate the chlorine percentage. How many tabs go into this pool? In my case, it was the number of bottles of medicine I needed to add to a fishpond.

“or Beyoncé computed the time delay needed for speakers at an outdoor concert?”

Don’t make me laugh. Beyoncé’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 when she placed the venue's sound system. 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?”

Because she cares even less than your students do and they know it.

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 Danica figure the monthly payment of an auto loan? Lame. (BTW, amortization schedules? Even bankers and loan officers run freely available spreadsheet tools.)

How about spring displacement, fore and aft g-loading, pressure, O2 vs Temperature, wing downforce? Suspension settings, pitch attitude, adjusting control parameters, understeer, optimize torque during power down? Why not do this? Probably because it's more information than your kids can handle, that's why.

Going too far into the real-world is not only confusing, it's counter-productive. You spend way too much time explaining something that winds up being taken on faith rather than being understood and the math you wanted them to get is lost in the descriptions of the curve of the wheel-wells. The jargon of the job overwhelms them. I love the concert hall question but you'd have to remove a lot before it became an algebra I question.

The other suggestions are interesting but not very particularly useful. Rabbit populations are not exponential (more sinusoidal) and not very relevant to the kids unless you have a fur farm nearby, in which case you'll start up the PETA alarmists instead of the graph-makers. Fibonacci was just doing a thought experiment anyway - in practice, the numbers are fairly complicated unless none of the rabbits ever dies and they all have 2 kits per litter.

If you want to model things, you need to pick the model carefully or the idea will disappear in the myriad details. If the relationship is supposed to be linear, stay away from the exponential data, and vice-versa. If you pick a real-world problem, you need to make sure that it will work out as you expect.

Appeal to Kids' Interests

Mindlessly connecting to kid's interests is a bad idea for a couple reasons.

One, the kids aren't interested in things that are mathematical right now. They are social beings and putting them in a social situation but wanting them to be mathematical is a frustrating and pointless exercise akin to moving Mt. Fuji with a spoon.

Two, which kid's interests? Baseball and softball overlap, but the goth kid is in his anti-jock mode and deliberately tunes you out for trying and nobody can understand the Valley Girl accent you're attempting.

Baseball batting averages are great for introducing percentages. Once. After that, only baseball freaks care and only if it's "their guy." The other 96% of the class is totally bored. If the entire software package is developed around baseball, I'd scream, too.

Third, How do you Know? If a kid is interested in something that you know little about, you risk looking foolish and stupid -- which doesn't achieve the goal you are trying for. Your "real-world" question is obviously contrived and tedious. This is why the "psuedocontext" questions in the book are so discordant. They aren't written by real people.

This may be hard to believe, but kids are okay with just learning something mathematical. Raw, pure math. Give them this just before they really are going to use it for a question THAT INTERESTS YOU and you'll have succeeded.  Forget their interests. "What use do YOU make of it" would be a better idea.

Finally, kids change. MTV is so last week. If you base your software on what was current just ten years ago, 95% of their world wouldn't exist. Are they interested in Spongebob or iCarly or Jimmy Neutron? Kid fads go out of style way too fast to try and keep up and there is nothing so dated as a teacher (or a computer tutor) trying to achieve "relevance."

Use Hi-Res Video

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.

Make Students laugh

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 … like the joke that always comes up during discussion of integral of 1/x:

What’s the integral of $ \int \frac{dCABIN}{CABIN}$ ?
ln(cabin), of course. ("natural log cabin")
and when you add “C”, you get houseboat. (Better when you say it aloud.)

In the end

In the end, for me, it comes down to:
Get Real: real math, real problems.


  1. It feels like reading an argument between entertainers about what really makes entertainment - neither seems too concerned with the math. "Narrative arc" indeed!

    The best way to engage a kid in math is to teach him the next thing he is capable of learning to do by himself. Kids like doing math and getting right answers and doing harder problems.

    When we jump ahead, or when we drag and stop moving ahead, we lose kids. When the jump is big enough, we lose them forever. Michael Phelps can't bring them back. Neither can an entertainer/math teacher.


  2. So, the rain has stopped, the flood waters have receded, and the ark has struck ground on Mt. Ararat. Noah starts unloading the animals, two by two, per divine instruction. First down the ramp, the giraffes. "Go ye forth and multiply!" commands Noah, and the giraffes go off to fulfill his request. Next come the elephants. "Go ye forth and multiply!" commands Noah again. The elephants obey. And so it goes, each pair of animals disembarking, receiving their instructions, and going off to replenish their numbers. Last down the ramp come a pair of snakes. "Go ye forth and multiply!" commands Noah. The snakes stop on the ramp and stare at Noah. "I said, 'Go ye forth and multiply', serpents!" repeated Noah. Still the snakes hesitated. "GO YE FORTH AND MULTIPLY!!!" bellows Noah.

    "We can't!" says one snake. "We're adders..."


    Weeks later, Noah is out walking around surveying the landscape, assessing the flood damage. He stops to rest on the stump of a fallen tree. Indeed, there are many dead trees uprooted by the flood. As Noah is sitting there, he looks down and sees the adder ... and Mrs. Adder, and a nest full of baby adders! "Well, congratulations!" he exclaims. "But ... how did you do it? You told me you could not multiply!"

    The snake looks at him and says, "We learned we could do it by logs."

    (Yeah, none of the students I have gone over logs with found that amusing either!)

  3. "Raw, pure math." I really do like that phrase.

    You're right about the attempt to cater to students' interests. They have few if any interests that are genuinely mathematical. The point is to set up new interests in them, interests that they did not have before.

    We shouldn't attempt to shoehorn mathematics into the students world. Rather we should attempt to expand their world.