This Week’s Installment
What mathematical skill is the textbook trying to teach with this image?
(If you’re reading via email or RSS, you’ll need to click through to vote. Also, you’ll need to check that link tomorrow for the answer.)
Team Me: 5
Team Commenters: 4
William Carey has offered two additional genres of pseudocontext that are worth your attention:
One motif in pseudocontextual questions seems to be treating as a variable things that, you know, don’t vary.
The car question follows a fascinating pattern that shows up in lots of physicsy work: it begs the question. Physicists like to measure things. Sometimes measuring something directly is tricky (or impossible), so we measure other things, and then calculate the thing we actually want.
Questions like that have as their givens the thing we can’t measure and ask us to calculate the thing that we can measure. It’s absolutely backwards.
Every Saturday, I post an image from a math textbook. It’s an image that implicitly or explicitly claims that “this is how we use math in the world!”
I post the image without its mathematical connection and offer three possibilities for that connection. One of them is the textbook’s. Two of them are decoys. You guess which connection is real.
After 24 hours, I update the post with the answer. If a plurality of the commenters picks the textbook’s connection, one point goes to Team Commenters. If a plurality picks one of my decoys, one point goes to Team Me. If you submit a mathematical question in the comments about the image that isn’t pseudocontext, collect a personal point.
(See the rationale for this exercise.)
The commenters bit down hard on the lure this time, folks. The correct answer — “calculating area of parallelograms” — was selected least.
Delicious pseudocontext, right? The judges all suffered massive strokes when they saw this problem so I couldn’t get their official ruling, but I don’t think it matters. This context fails the “Come on, really?” test for pseudocontext.
“This unpredictable force of nature is threatening a precisely-bounded parallelogram? Come on, really?”
How could we neutralize the pseudocontext? I would be thrilled to see a task that invited students to select and approximate important regions with various quadrilaterals, but let’s not lie about where our tools are useful.