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.
William CareyJanuary 8, 2017 - 10:44 am -
I suspect, but am not sure, that this might be a third motif in pseudocontextual questions: including a picture to make sure you know what the thing being discussed *actually is*.
We’ve written a question that uses the word “tornado” somewhere in the question. In case you do not know what one of those is, here is a picture of a tornado.
It’s like combining a mini-vocabulary lesson with a math problem. The difficulty is that if you don’t know what tornados are and do, if you don’t have some intuitive sense of tornados, you have no meaningful chance of being able reason quantitatively about them.
I’m eager to find out!
Amy RoedigerJanuary 8, 2017 - 6:37 pm -
This is the first one I guessed correctly, so I am feeling pretty proud of myself. I was trying to think of a way to save the problem – like many provide an actual aerial photo of tornado damage and asking how we could find the area without saying it’s a parallelogram with maybe the chance for scaling and stuff. So I googled that and found tornadoes leave a pretty typical pattern of damage and it seems to never be a parallelogram.
Dan MeyerJanuary 8, 2017 - 7:02 pm -
Randal BlackwoodJanuary 8, 2017 - 7:26 pm -
Actually in the context of this problem, they may actually have a winner here. Note the parallelogram represent an area the meteorologists have set as an area under tornado warning, meaning that a tornado is present in the area or imminent. Thus the area represents where tornadoes may appear, not the area that will be damaged by a tornado. Here is an example close to the textbook problem, illustrates a trapezoid not a parallelogram, but you get the gist: http://bnonews.com/news/index.php/news/id4419
CurmudgeonJanuary 8, 2017 - 8:05 pm -
Damn, I can’t help it …
It’s kinda parallelogram-ish, you know.
William CareyJanuary 9, 2017 - 3:02 am -
I was right! It was a vocabulary lesson for people who don’t know what tornados are.
The little map is even worse. It’s called a “real world example”, so we should be able to find a real Lake county that’s bounded by Knox, Adams, Lucas, and Fox counties, right? Right?
No. There are five Lake Counties in the US: IL, FL, OH, MI, IN. The only state with both a Lake County and a Knox County seems to be Ohio, but they’re nowhere near each other.
BenJanuary 9, 2017 - 9:39 am -
The “real -world link” is utterly pointless, completely unrelated even to the pseudocontext. It reinforces the impression that mathematicians are enamored with numbers for their own sake. Who are we, the Count?
Mr HendersonJanuary 13, 2017 - 2:11 am -
In Year 6 in the UK we’re just getting ready for our SATS tests and are blogging some real world questions that we’ve (the children) have come up with. Hopefully we don’t see this sort of real-world-that-never-really-happens-outside-of-a-textbook-so-isn’t-really-real example in the actual exam!
Suzanne von OyJanuary 28, 2017 - 7:43 pm -
I just LOVE that you called this pseudocontext delicious. :) So funny. Keep ’em coming.
This issue of contextual nightmares has bothered me since I was sitting in the student’s desk, learning Algebra 1, Geometry, and Algebra 2. It is so easy to see through the veil of pretend real-world-application that I have always felt disingenuous when I have given my own students problems that are supposedly great applications of the math we’re doing.
Thank you for your Saturday reminders that those of us who dry heave a little every time we see a pseudocontext problem are not alone.