Month: October 2010

Total 19 Posts

[PS] Sandbags & Hot Air Balloons

[BTW: My opinion is that this isn’t pseudocontext for reasons I elaborate on in this comment.]

Calculus: Early Transcendental Functions. Larson Hostetler, Edwards. 2003. Houghton Mifflin.


Greg Hitt (a/k/a Sarcasymptote):

Et tu, Calculus?

Seriously, you are when I started to love math. Up until I met you, I trudged through year after year of pseudocontext, merely completing tasks only because they needed to be done and not out of some enjoyment or aching desire to do it. Then, you came along, and blew my freaking mind with your applicability. You were the math that worked.

And now look at you. Really, Calculus? Answer me this:

  1. What in the hell are you talking about? This is one of the most poorly worded questions I’ve ever seen. And is it common practice for someone to be so cavalier as to heave sandbags over the side from almost 200 feet in the air, all while carefully measuring both the height above the ground and the angle of elevation to the sun? I don’t know, because I don’t care about hot air balloons. I don’t know anyone who does.
  2. Why are we worried about the rate of the movement of the shadow? Is the rate that a shadow moves across the ground useful for any situation? Is there some arbitrary race between the shadow of a sandbag and a log floating down a river? Seriously, related rates should be much more applicable than this.
  3. This is textbook, er… textbook. We could pretend to think about how to model the height, but instead, let’s just skip the thinking and go right to a formula.


Moving Shadow. A sandbag is dropped from a balloon at a height of 60 meters when the angle of elevation to the sun is 30° (see figure). Find the rate at which the shadow of the sandbag is traveling along the ground when the sandbag is at a height of 35 meters. [Hint: The position of the sandbag is given by s(t) = 60 – 4.9t2.]


  1. Scan an example of pseudocontext.
  2. Email it to
  3. List the textbook title, edition, and publisher.
  4. Give me your interpretation of the term “pseudocontext.”
  5. Let me know if you’d like credit (name, blog or twitter) or if you’d prefer anonymity.

Toaster Regression

David Cox has WCYDWT by the throat. He used digital video, Adobe AfterEffects, and MovieMaker to export a clever visualization of toaster times versus toaster settings.

Toaster Question from David Cox on Vimeo.

Not that he asked, but I wouldn’t change a lot here. I’d rather see the data for settings one through four and use those to regress the eighth setting. By providing the seventh setting and asking for the eighth, he’s made it easier for students to jump right into the math which makes it less likely that my remedial students will invest a guess.

I would have also sped up the first four videos (even more) because I want my students’ impatient toe-tapping aligned to the question, “when will it end?” not before.

It’s really strong work, though, and you’re only going to see more of it from David because it just gets easier and easier to clear the annoying technical hurdles of video production. Soon he won’t even notice them and it’ll be as if there isn’t anything in between the curriculum he can imagine and the curriculum he can create.

It’s Everywhere

Santa Cruz Sentinel, today:

The City Council will consider a proposal today to establish a citywide pay-by-cell phone system that would allow motorists to start, finish and extend time for meters or fee-based parking spots. [..] Consumers would pay a fee of 35 cents per transaction, or 25 cents for frequent users if they are willing also to pay a monthly access fee of $1.75.

Is pseudocontext a failure of imagination or is it a symptom of laziness? Because this sort of thing just isn’t hard to find.

You Are At A Different Stadium

Ben Blum-Smith submits the quintessential teacher-review of Waiting for Superman:

Where did you think great teachers come from? That they spring fully formed from the head of Zeus? Just about everybody who’s an accomplished teacher used to be an ineffective teacher, and as the maker of a documentary about first year teachers, I’m totally confused that you don’t seem to understand this. If you want to talk about great teachers, but don’t have anything to say about the conditions under which teachers become great, you are at a different stadium than where the game is happening.