2 ms·

So which is the correct way to choose parameters for a problem? 1. Deliberately choose numbers that have no notable relationships with eachother that could mis

So which is the correct way to choose parameters for a problem? 1. Deliberately choose numbers that have no notable relationships with eachother that could mislead students. 2. Randomize parameters in an effort to introduce only as many trick questions as would occur randomly in nature (so, given small-valued problems like this one, maybe one question in a hundred will have tricky parameters by chance). 3. Deliberately choose parameters that are somewhat or even maximally tricky to ensure student's undertanding is robust in the face of misdirection. 4. A deliberate mix of 1 and 3, with easier questions to start and trickier questions always included but never too often and never too early. You seem to be advocating for #1, or possibly #2 (though I get the impression that if #2 were employed and trick parameters arose by chance on a quiz you would complain, bringing us back to #1). #4 seems like the best strategy to me, with an extra helping of tricks for my kids, please. It's not like you learn less when you get tricked. Quite the opposite!

tshaddox 3y ago
It's not nearly as complicated as all that. Just don't deliberately try to trigger a misleading pattern match. Almost any conceivable way you would naturally come up with a math exercise like this would not end up fooling people into giving an immediate incorrect answer. You have to go out of your way (or get very unlucky if you're choosing random parameters) to construct an exercise that will fool a large portion of people.
- rcoveson 3y ago
  > You have to go out of your way (or get very unlucky if you're choosing random parameters) to construct an exercise that will fool a large portion of people. That's not remotely true. You're generally picking small integers, here, and frequently dealing with problems that have very few parameters. "Species of birds in the genus Madeupicus all have the same proportions. Adult birds of one species in the genus have a wingspan of one meter and weigh one kilogram. How much do birds of a species in the genus with a two meter wingspan weigh?" This is a very similar problem to the one in the original example. It has the same trick, which is that the integers on either side of the equation are the same in the first example, but they will not be the same in the second equation due to dimensional scaling. Students do hundreds of math problems per week. Randomly-selected small integers will collide frequently. And that's all ignoring the benefits of surprising people, which you still tacitly deny. What are you optimizing your questions for, "fairness"? "Predictability"? That sounds like a great way to ensure as many people as possible who didn't actually understand the subject matter will pass your tests.

tshaddox 3y ago

It's not nearly as complicated as all that. Just don't deliberately try to trigger a misleading pattern match. Almost any conceivable way you would naturally come up with a math exercise like this would not end up fooling people into giving an immediate incorrect answer. You have to go out of your way (or get very unlucky if you're choosing random parameters) to construct an exercise that will fool a large portion of people.

rcoveson 3y ago
> You have to go out of your way (or get very unlucky if you're choosing random parameters) to construct an exercise that will fool a large portion of people. That's not remotely true. You're generally picking small integers, here, and frequently dealing with problems that have very few parameters. "Species of birds in the genus Madeupicus all have the same proportions. Adult birds of one species in the genus have a wingspan of one meter and weigh one kilogram. How much do birds of a species in the genus with a two meter wingspan weigh?" This is a very similar problem to the one in the original example. It has the same trick, which is that the integers on either side of the equation are the same in the first example, but they will not be the same in the second equation due to dimensional scaling. Students do hundreds of math problems per week. Randomly-selected small integers will collide frequently. And that's all ignoring the benefits of surprising people, which you still tacitly deny. What are you optimizing your questions for, "fairness"? "Predictability"? That sounds like a great way to ensure as many people as possible who didn't actually understand the subject matter will pass your tests.