Wesley: This is a reasonable enough problem. In particular, the context is not flatly untrue, nor are the operations wholly irrelevant to the context.

To the extent that pseudocontext is a continuous measure (rather than a binary measure) I’ll agree this particular problem isn’t the worst one we’ve featured. But I’m compelled by the fact that a student who knows the actual context of hot air balloons is at more of a disadvantage than a student who is oblivious to hot air balloons, particularly with the height extension.

The student who knows that hot air balloons don’t float a mile in the air will doubt her mathematical analysis – even though it’s correct – simply because the authors didn’t trouble themselves to get the context right. That’s fantastic, frankly. That’s pseudocontext.

jon: Isn’t finding pseudocontext problems taking the easy way out of this. How about amassing a collection of good problems?

Been giving that a shot for the last four years or so.

jon: I will again argue, every textbook bound word problem I have encounted can be considered pseudocontext.

Here’s a sample homework assignment I grabbed randomly out of the IMP curriculum. There are any number of ways we could improve this problem, but where do you find the pseudocontext here?

I would really love to see the good ones that already exist.

Being an engineer, I would try to make an assumption — either that one telephone pole is sufficiently far away to be at a nearly zero-degree angle, or that both poles are roughly equidistant.

Then … aargh! I’m trying to use similar triangles to find the solution, but I’m not sure I have enough known variables.

(Now where the heck did I put that new laser rangefinder…)

If the question introduced enough other facts that it added value by helping the student learn to cut through the noise to get the pertinent facts that would be one thing. This does not.

Simply altering the problem to be one where the rider took off from one field and is traveling to the other would be all it would take to make the question seem to have some sort of purpose. The total distance between the two fields could be known and the question could be to determine what fraction of the trip has completed. The balloon could be over a landmark where the distance to one field is known but not the other – determine total distance.

Provide time already passed, ask whether the balloon will get them to the next field in time for the 3pm kickoff. Trivial algebra (assuming a constant speed :) but it make the context MEAN something. That’s not an issue of a possibly better-written question, it’s what provides any reason at all for the details.

There’s a lot of awful pseudocontext in the world. This is a reasonable enough problem. In particular, the context is not flatly untrue, nor are the operations wholly irrelevant to the context.

Yes, I could make up better problems on this situation. No, this one is not my nominee for the math hall of fame. But it’s not in a class with some of the filth we’ve seen here.

If we’re to stand against pseudocontext, it has to have a boundary. Moreover, the boundary should be distinct from “Is it the best problem you could write about this situation?” Flagging this problem as pseudocontext blurs that boundary.

The measurements could be made easily, though, since the balloons are never traveling very fast, usually less than 5mph. Secondly, the direction of travel is intimated to be perpendicular (left side” and “right side”) to the line between fields so a couple hundred feet of travel isn’t going to change those angles appreciably. (That might be an interesting exploration, though.)

The problem should ask for the height of the balloon and the horizontal distance to the field or a prospective landing spot so the balloonist can start a steady descent. This all assumes that the balloon does not have a GPS or an altimeter and that none of the passengers has a smartphone ….