2 ms·

I mean, there’s a lot going wrong with this “lesson.” The exercise is pretty clearly designed to trick people, which is very counterproductive if the goal is to

I mean, there’s a lot going wrong with this “lesson.” The exercise is pretty clearly designed to trick people, which is very counterproductive if the goal is to teach people about multiplication or fractions or whatever. It’s really not that damning that a teacher would be fooled into skipping the actual work, since that deceit is clearly the entire point of choosing those numbers. It’s a bit like if a proofreading exercise in an English class deliberately did that trick where you put two “the”s next to each other but across a line break. That will often fool a skilled English writer, but that says nothing about the writer’s skill.

rcoveson 4y ago
While the teacher in the story obviously bungled it, I disagree with your interpretation of the lesson. The point is not to "teach people about multiplication or fractions or whatever". The point is to teach them to recognize dimensional parameters in a natural scenario. This can be counter-intuitive; we have a bias towards linear relationships. Somebody twice as tall is twice as heavy, thinks the child. Tricks ("surprises" is a less negative descriptor) are important because they wake your brain up. Most people don't like learning arbitrary things for their own sake, but they don't like being fooled either. Describe the base rate fallacy to a room of college students and it might stick for the rest of the semester, but give them this problem[0] and tell them how many licensed doctors it tricked (after you let them answer incorrectly, of course) and they might remember it for a while longer. 0. http://pi.math.cornell.edu/~mec/2008-2009/TianyiZheng/Bayes.html http://pi.math.cornell.edu/~mec/2008-2009/TianyiZheng/Bayes....
- tshaddox 4y ago
  If the point of the lesson truly was to identify that the exercise was chosen deliberately to be deceptive, then sure. But I doubt it. Your example is very different, because there’s no obvious answer that one might spit out instantly by doing naive pattern matching.
  - rcoveson 4y ago
    The fact that there is an obvious but incorrect answer that you might spit out if you were just pattern matching is the whole point. It tricks you into being wrong, which "tricks" you into wanting to know why, where before you might not have cared about the answer or the underlying reasoning at all. You think the question just accidentally picked tricky numbers? Or you think the reason that it picked them was just malice towards children?
    - tshaddox 4y ago
      > You think the question just accidentally picked tricky numbers? Or you think the reason that it picked them was just malice towards children? I think it's probably just abysmal pedagogy. This should be pretty clear given that almost the entire class and even the teacher fell for the trick, which shows that it's a terrible way to teach something and even a terrible way to test if they know how to do the thing you're wanting them to learn. The teacher and many of the children probably did in fact know how how to do the calculation and solve the problem, and would have done so if the numbers weren't very deliberately chosen to invoke a hasty pattern-matching reaction.
      - rcoveson 4y ago
        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!

rcoveson 4y ago

While the teacher in the story obviously bungled it, I disagree with your interpretation of the lesson. The point is not to "teach people about multiplication or fractions or whatever". The point is to teach them to recognize dimensional parameters in a natural scenario. This can be counter-intuitive; we have a bias towards linear relationships. Somebody twice as tall is twice as heavy, thinks the child. Tricks ("surprises" is a less negative descriptor) are important because they wake your brain up. Most people don't like learning arbitrary things for their own sake, but they don't like being fooled either. Describe the base rate fallacy to a room of college students and it might stick for the rest of the semester, but give them this problem[0] and tell them how many licensed doctors it tricked (after you let them answer incorrectly, of course) and they might remember it for a while longer. 0. http://pi.math.cornell.edu/~mec/2008-2009/TianyiZheng/Bayes.html http://pi.math.cornell.edu/~mec/2008-2009/TianyiZheng/Bayes....

tshaddox 4y ago
If the point of the lesson truly was to identify that the exercise was chosen deliberately to be deceptive, then sure. But I doubt it. Your example is very different, because there’s no obvious answer that one might spit out instantly by doing naive pattern matching.
- rcoveson 4y ago
  The fact that there is an obvious but incorrect answer that you might spit out if you were just pattern matching is the whole point. It tricks you into being wrong, which "tricks" you into wanting to know why, where before you might not have cared about the answer or the underlying reasoning at all. You think the question just accidentally picked tricky numbers? Or you think the reason that it picked them was just malice towards children?
  - tshaddox 4y ago
    > You think the question just accidentally picked tricky numbers? Or you think the reason that it picked them was just malice towards children? I think it's probably just abysmal pedagogy. This should be pretty clear given that almost the entire class and even the teacher fell for the trick, which shows that it's a terrible way to teach something and even a terrible way to test if they know how to do the thing you're wanting them to learn. The teacher and many of the children probably did in fact know how how to do the calculation and solve the problem, and would have done so if the numbers weren't very deliberately chosen to invoke a hasty pattern-matching reaction.
    - rcoveson 4y ago
      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!