This Week’s Installment
What mathematical skill is the textbook trying to teach with this image?
Pseudocontext Saturday #4
- Reasoning with proportions (63%, 523 Votes)
- Calculating exponential growth (19%, 154 Votes)
- Simplifying expressions (18%, 151 Votes)
Total Voters: 828
(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: 3
Team Commenters: 0
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 judges rule that this problem satisfies both criteria for pseudocontext:
Given a context, the assigned question isn’t a question most human beings would ask about it.
I invite any commenter to rationalize the constraint that exactly 15 photos must be purchased and we don’t know which of them will be small or large. More often (always?) people begin with the photos they want, or perhaps they work from a total budget. “I can only buy 15 photos and the number of large photos I purchase can vary from zero to fifteen,” said no one ever.
Given that question, the assigned method isn’t a method most human beings would use to find it.
If most human beings were going to find out the cost of five large photos and ten small photos, they’d multiply each kind of photo by its price. Variables aren’t a useful tool.
So the textbook has made the world serve the math when math should serve the world. If the world doesn’t need math’s service, then math should be gracious enough to step out of the way.
I guessed correctly. The first and third choices made too much sense. Always step up to the plate thinking curveball.
The problem here is that the customer has no use for a general equation, but the store owner might–she’s got to deal with people who call in with all kinds of crazy orders and questions. Still, it’s unlikely the store owner would write an equation for just small and large pictures. It’s much more likely that she’d come up with a pricing scenario for unusual picture sizes.