Year: 2010

Total 151 Posts

[PS] iPhone / iPad Apps

This is winding down.

I’m mostly content with the two-part definition I set up two weeks ago. I’m also satisfied that pseudocontext is much less of a problem than real context that’s either a) poorly represented or b) poorly examined. Any final comments, questions, or challenges, get them on the record ASAP.

This winter I’m taking “The Design of Technologies for Casual Learning” with Shelley Goldman so I ran a quick survey of math apps for the iPhone and iPad. Scratch off all the drill and test-prep software and you have a lot of apps that are trying to make use of some kind of context. Do they represent pseudocontext or not?


Could you swap out “peacocks” for, well, anything without changing the implications of the problem? It fails definition #2, “operations that have nothing to do with the given context.” See another example.

The iLiveMath family includes iLiveMath Oceans, iLiveMath Animals of Africa, iLiveMath Animals of Asia, iLiveMath Speed, iLiveMath Trains, iLiveMath Entomology, iLiveMath Ford Cars, iLiveMath Farm Fresh. Each one is stuffed to overflowing with pseudocontext. Also, at $4.99 each, you’d wish they’d spellcheck this stuff even a little. (These are the promotional stills, incidentally.) Produced by a company called iHomeEducator, this stuff is obviously pitched at homeschoolers, which, as a homeschool graduate, kills me.

Princess Math

Fails definition #2 again. What does 2 x 2 have to do with a tiara?

Ninja Math

Ditto the others. You don’t really “use math to defeat” the boss. You’re doing math and the game rewards you by defeating the boss. I will break out the parade if someone can point me to the iPad game where you really use math to defeat the boss. That sounds awesome.

Dress Up Math

The operation, at last, matches the context. It fails definition #1, though, because there’s no way that pink blouse costs $4.00. Even I know that.

Mellyme, a five-star review of iLiveMath Animals of Asia:

This app is a very good concept and it works well in practice. It’s multimedia approach to word problem drills is genius. Kids can learn about various animals while doing math. The videos provided are great as well. Give at least one of this company’s apps a try. I have bought two from them-my daughter loved them both.

Okay, so here we go. Students can find pseudocontext interesting. Students can find real context boring. Reasons for the latter include poor representation and poor examination. Reasons for the former include social and academic pressures, enthusiastic teachers, and idiosyncratic student tendencies from which it’s really unwise to generalize to “all students” or even “my students.”

The problem with pseudocontext isn’t the risk of boring the majority of your classroom. It’s the message that this is how the world works and this is how we apply math to it. Pseudocontext teaches students — even the students who tolerate or even like pseudocontext — a lesson that is very hard to unlearn.

[WCYDWT] Pure Performance

Can I get forty comments on this video? The rest of this post (which I’ll update after we cross that threshold) depends entirely on the modal answer to the question, “what question perplexes you about this video?” Ask your own question before you look at the others.


My advance prediction for the responses was a million-way tie for third place with these two responses taking the top two spots:

  1. How fast was the car moving?
  2. How many frames were on the wall?

I couldn’t guess which would win and, in terms of our mathematical objective, it doesn’t matter. Both questions are tightly interwoven. (Many commenters, in fact, asked both questions.) It mattered to the production company, though. One is its premise. The other is its conclusion.

The results, through Yaacov’s comment:

Sarah Cannon: “How fast is the car driving?” +25 related
mirjam: “how many pictures?” +16 related
Brent Logan: “How did the car jump? There wasn’t even a ramp.” +7 related
Other questions. +7

The behind-the-scenes video is less helpful than you’d imagine so I spammed basically every production company that had anything to do with the ad, asking them for information. Everyone was extremely helpful (why is this such a revelation?) and eventually my query was routed to Peter McAuley, the visual effects supervisor, who dropped a pile of knowledge on me, which I’ve uploaded here and which he cross-posted in the fourth comment here.

Important questions your students may have to reckon with.

  1. How does this effect even work? More to the point, how does film work. The camera on the outside of the car is taking photos very quickly — at a rate of 24 frames per seconds. When they’re played back, our brains interpolate the rest of the motion and it looks smooth.
  2. Did the production company decide on the size of the frames and then figure out the speed or did they know the speed they wanted and then determine the frames? The production company figured the faster the speed, the more exciting the effect. At a certain speed, though, even the best digital sensor produced a “rolling shutter” effect (excellent animated explanation here) so they went with film, which looked good up to 40 kph. Which, bingo. That figure is crucial to every question.
  3. How long is the actual ad? This is the extended cut of a TV spot that ran for thirty seconds.

Start with discussion, brainstorming, estimation.

What’s your guess? How many frames do you think you saw fly by? How wide do you think each picture had to be? Give a number you know is too high / too low.

Gradually apply the mathematical framework.

Ideally, either on their own or throughout the class discussion, your students will realize they need a) the length of the ad [30 seconds], b) the speed of the car [40 kph], and c) the shutter speed of the camera [24 frames per second].

From there, the dimensional analysis is up to you and your students.

Show the answer.

Download the goods.

Zipped archive [135.2 MB] containing:

  • the extended commercial,
  • the behind-the-scenes video,
  • a PDF of the Peter McAuley’s e-mail.

The Yellow Pages Are My PLC

This is a total gamechanger:

If I call a business or a government agency and represent myself as a math teacher who is curious about their work, they will spend a not-insignificant amount of time answering any question I have.

I’m 100% so far on, like, six attempts. I don’t know why I never tried this before.


Running list of examples that have made it to this blog:

  1. [WCYDWT] Pure Performance. I wanted to know the speed of the car in the video so I e-mailed the agency representing the director who then put me in touch with the visual effects supervisor.
  2. [It Got Away] Vermont License Plates. I called the Vermont DMV and received a trove of information about license plate issuance, including the combinations of letters they don’t allow.
  3. [It Got Away] Ladder Spreaders. I called Werner Ladder Co. and spoke to an engineer who gave me the skinny on ladder construction.
  4. Partial Product. The corporate grocery store told me no way that’d let me take photos on their counter so I head over to the local grocery store on the corner where the grocer, after we worked through our language barrier, let me set up my problem.
  5. Guggenheim. I called the Guggenheim’s public relations department, told them I thought Hans Peter Feldman’s exhibit was an excellent application of math and I wanted my students to experience it. I asked them for the blueprints to that room and they sent them. They told me I couldn’t pass them around, though, a request I’ll honor even though it bums me out.

[WCYDWT] Car Talk

Sometimes this stuff is just sitting there for the taking, like a gold brick in the middle of the road, and all it takes is the right kind of eye to see it. David Petro e-mailed me a link to an episode of the long-running radio series, Car Talk, which does all the heavy lifting for us. I just shot a couple of supplementary photos.

Start with discussion, brainstorming, estimation.

Rich, Car Talk caller [show page, direct download]:

The fuel gauge [on my 18-wheeler] is completely useless. It’s completely unreliable. So I have gone with a very low-tech method. I have gotten a wooden dowel which I use as a dipstick. Now the tanks on my 18-wheeler are cylinder-shaped and they’re on their sides. Now when I stick the dipstick in and I mark the level when the tank is completely full, it happens to be 20 inches. I mark ten inches at the half. My question is how I do I accurately mark one quarter?

I mean, seriously? Christmas already?!

I’d crop this clip pretty tightly. Rich says, “It obviously isn’t five inches,” but we’d rather put that to our students, asking them, “Just gimme a guess: how many inches do you think?” Some students — the impatient ones, maybe even a few advanced students — will snap to “five inches.” Have them sketch out their solution. Ask them if they still like it. Ask for a number they know is too large, too small.

Important questions your students may have to reckon with.

  1. What information do we care about here? What information don’t we care about here?
  2. Why does the trucker care about the level of a quarter tank anyway?
  3. If you try out your guess, is there more than or less than or exactly a quarter of a tank left?
  4. What kind of shape does the gas form in the bottom of the tank?
  5. How is that shape formed from other shapes and how could we find its area?

These questions and their answers will vary significantly with the particular math course you’re teaching.


One of the show hosts: [show page, direct download]:

We finally came up with the answer, that in order for his dipstick to work he’s gotta be about 5.96 inches off the bottom. That’s a quarter of a tank. And it seemed like it should’ve been a lot more than that.

The Goods

Voila: a zipped archive. Thanks, David.

Extra Credit Assignment

Someone cook up a dynamic Geogebra applet for this scenario and pass me a link.

BTW: Woo! Check out Tim’s.

BTW: Updated to fix an error in my math. Thanks, RM.

[WCYDWT] Grocery Shrink Ray

Start with discussion, brainstorming, estimation.

You run a Dollar Tree franchise. Everything costs a dollar.

You sell shampoo for a dollar — a popular brand called “White Rain.”

Problem: times are tough and the people who sell you the shampoo need to raise their prices higher than a dollar. What are your options at this point?

Teacher: write down student suggestions on the board. When someone suggests “sell less shampoo for the same price” resist the urge to declare, “Ahhh … that one’s eeeeenteresting,” thereby cluing your students to the fact that they weren’t really brainstorming, they were playing another game of “guess what the teacher wants to talk about.”

Spend a few seconds talking about, for instance, the student’s suggestion to rename the store. To what? Somewhere Around A Dollar Tree? You’re getting students all across the spectrum to invest in the problem and it’s costing you — what? — a few minutes.

Lower a little more structure onto the problem.

It turns out that “sell less shampoo for the same price” is exactly how that went down.

Teacher: “So what’s an interesting question we could ask here?”

Teacher: “How much extra are you actually paying here? What should the smaller bottle actually cost?”

Teacher: take guesses.

Your location in the scope and sequence of proportions will determine how much direct instruction your students will need here. That’s on you.

Issue extensions.

I dug through the entire Consumerist collection. The most valuable entries included both price and quantity.

Some of the others are great for discussion, though. Notice Dial’s effort to conceal the decrease with a taller, thinner container:

Tropicana’s opaque containers offer them enormous flexibility in the quantity of orange juice they give you:

And, if your class feels like venturing into some 3D geometry, ask your students how Yoplait has managed to shrink the amount of yogurt by 33% in a new container that looks nearly the same as the old.

The answer to that question (along with all the lesson materials) is located in this zipped archive.

[h/t MPG for the idea]