Advanced Mathematical Concepts: Precalculus with Applications. Glencoe. 2006.

Pseudocontext

Amanda Dean:

It asks students to ignore reality in order to solve it. The wind would probably be moving the balloon as the balloonist tried to take these measurements, and it’s unlikely that the two angles could be measured from exactly the same vantage point. The problem also assumes that Groveburg is a flat city, or at least that the elevation of the soccer fields is the same as that of the football field.

And, while not pseudocontext, we have another situation where the author asks the student to solve for inconsequential measurements and ignore the consequential one:

The questions aren’t what you want to know. You want to know how high up the balloon is! It’s not like you can’t figure it out from the info given either. It can be done with the Law of Sines, which is the focus of the lesson.

And then we’re back to the pseudocontext:

If you do calculate the balloon’s height, you find that the balloon is about 1.24 miles above Groveburg, which is also unlikely since an average hot air balloon ride only goes up to 2000 feet.

Transcription:

A hot air balloon is flying above Groveburg. To the left side of the balloon, the balloonist measures the angle of depression to the Groveburg soccer fields to be 20° 15′. To the right side of the balloon, the balloonist measures the angle of depression to the high school football field to be 62° 30′. The distance between the two athletic complexes is 4 miles.

1. Find the distance from the balloon to the soccer fields.
2. What is the distance from the balloon to the football field?

Assignment:

1. Scan an example of pseudocontext.
2. Email it to dan@mrmeyer.com
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.

Jason Dyer passed me Richard Feynman’s essay, Judging Books by Their Covers, via email.

Which of the two parts of our working definition of pseudocontext does it exemplify? Justify your answer.

[BTW: I’d say this exemplifies both definitions nicely. I’ve highlighted the passages.]

Anyhow, I’m looking at all these books, all these books, and none of them has said anything about using arithmetic in science. If there are any examples on the use of arithmetic at all (most of the time it’s this abstract new modern nonsense), they are about things like buying stamps.

Finally I come to a book that says, “Mathematics is used in science in many ways. We will give you an example from astronomy, which is the science of stars.” I turn the page, and it says, “Red stars have a temperature of four thousand degrees, yellow stars have a temperature of five thousand degrees . . .” — so far, so good. It continues: “Green stars have a temperature of seven thousand degrees, blue stars have a temperature of ten thousand degrees, and violet stars have a temperature of . . . (some big number).” There are no green or violet stars [def’n #1 – dm], but the figures for the others are roughly correct. It’s vaguely right — but already, trouble! That’s the way everything was: Everything was written by somebody who didn’t know what the hell he was talking about, so it was a little bit wrong, always! And how we are going to teach well by using books written by people who don’t quite understand what they’re talking about, I cannot understand. I don’t know why, but the books are lousy; UNIVERSALLY LOUSY!

Anyway, I’m happy with this book, because it’s the first example of applying arithmetic to science. I’m a bit unhappy when I read about the stars’ temperatures, but I’m not very unhappy because it’s more or less right — it’s just an example of error. Then comes the list of problems. It says, “John and his father go out to look at the stars. John sees two blue stars and a red star. His father sees a green star, a violet star, and two yellow stars. What is the total temperature of the stars seen by John and his father?” — and I would explode in horror.

My wife would talk about the volcano downstairs. That’s only an example: it was perpetually like that. Perpetual absurdity! There’s no purpose whatsoever in adding the temperature of two stars. Nobody ever does that [def’n #2 – dm] except, maybe, to then take the average temperature of the stars, but not to find out the total temperature of all the stars! It was awful! All it was was a game to get you to add, and they didn’t understand what they were talking about. It was like reading sentences with a few typographical errors, and then suddenly a whole sentence is written backwards. The mathematics was like that. Just hopeless!