We create a pseudocontext when at least one of two conditions are met.
First, given a context, the assigned question isn’t a question most human beings would ask about it.
Second, given that question, the assigned method isn’t a method most human beings would use to find it.
The dog bandana is the classic example. Given a dog, would most human beings wonder about the correct size of the bandana? Maybe. But none of them would apply a special right triangle to answer it.
Here’s the game. Every Saturday, I’ll post an image from a math textbook. It’ll be an image from one of the “Where You Will Use This Math!” sidebars.
I’ll post the image without its mathematical connection and offer five possibilities for that connection. One of them will be real. Four of them will be decoys. You’ll all guess which connection is real.
After 24 hours, I’ll update the post with the answer. If a plurality of the commenters picked the textbook’s connection, one point goes to Team Commenters. If a plurality picked one of my decoys, one point goes to Team Me. If you submit a word problem in the comments to complement your connection and it makes someone lol, collect a personal point.
- Fun. Teaching is a pretty serious occupation. It never fails to brighten my day when you all ping me with pseudocontext.
- Caution. My position is that we frequently overrate the real world as a vehicle for student motivation. I hope this series will serve to remind us weekly of the madness that lies at the extreme end of a position that says “students will only be interested in mathematics if it’s real world.” The end of that position leads to dog bandanas and other bizarre connections which serve to make math seem less real to students and more alien, a discipline practiced by weirdos and oddballs. Caution.
This Week’s Installment
Pseudocontext Saturday #1
- Calculating probabilities (49%, 185 Votes)
- Calculating the area of the sector of a circle (41%, 156 Votes)
- Finding the next term in a sequence of numbers (5%, 17 Votes)
- Multiplying binomials (3%, 10 Votes)
- Evaluating the quadratic formula (2%, 9 Votes)
Total Voters: 377
(If you’re reading via email or RSS, you may need to click through to vote.)
I’ll update this post with the answer in 24 hours.
BTW. Don’t hesitate to send me an example you’d like me to feature. My email address is firstname.lastname@example.org. Throw “Pseudocontext Saturdays” in the subject.
Polls are closed. The commenters got rolled on this one, with only 3% having guessed the actual application. So one point goes to Team Dan.
Most commenters guessed “calculating probabilities,” which likely wouldn’t have been a pseudocontext. Humans wonder lots of questions about probabilities when it comes to darts, many of which are most easily answered with mathematical tools.
But this is high-grade psuedocontext. Given a dartboard, few humans would wonder about the dimensions of a square that circumscribes it exactly. And even if they did wonder about it, none of them would name the radius r + 12. They wouldn’t even name it r. They wouldn’t use variables. They’d measure it.
The publisher included the dartboard as a means to interest students in special products. If you believe, as I do, that the publisher has done more harm than good here, positioning math as alien rather than real, what can be done? How do you handle special products?
Q #11: Pretend [certainly not a woman’s name] has no concept of darts, zero aim, and is liquored up at the bar anyway. What is the probability that he’ll hit a 20? Twice, with his eyes blindfolded?
Question: What percent of the dart board scoring area is red? white? blue?
Extension: Are the red, white, and blue percentages of area the same on an American flag?
Man, this “context” is an absolute embarrassment and wastes the time of students and teachers. This sort of thing is driven by textbook requirements for “full coverage” — some lessons have a useful “why” picture and description, therefore all of them must.
Scott Farrand reacts to the commenters’ loss:
Now I see how to make the dartboard fit into our task. First we each randomly assign each the five options that Dan gave us to 4 of the 20 sectors of the dartboard, so that 1/5 of the sectors correspond to each option. Now all we need is a blindfold, and … let’s see if we can improve our results from 3% correct to about 20% correct.