The lecturer in our Numerical cognition course told us of a result that went along the following lines. A schoolteacher was trying to teach his students to do basic arithmetic, and seeing them get the calculations wrong time after time. Then one day he decided to follow them out into town, where he saw that some of his students handled arithmetic just fine when they were doing grocery shopping, or working part-time selling things. Inspired, he returned to class and reworded his assignments to be about shopping, and guess what happened? The students failed just as miserably as they had before. The cognitive context was just too dissimiliar to the environment where they’d picked up the practice.
I got the impression that this wasn’t just an isolated anecdote, but had also been replicated in more controlled studies. The reference he gave is to Jean Lave’s Cognition in Practice—I have a copy of the book from the university library, but haven’t had the time to read further yet. I’ll see if I can skim it through this evening to find the part he was talking about.
Back in high school I used to help my fellow students with chemistry problems. I noticed that many of them seemed to have a lot of trouble with what I thought were really easy problems. I noticed that many of the chemistry problems had obvious analogues in everyday tasks like baking cakes. I kept trying to reframe chemistry problems as baking problems, expecting that this would make everything easier. I thought my fellow students had some sort of aversion to chemistry but could handle baking easily enough.
This approach never got me anywhere even though I kept trying to make the problems more intuitive. In the end it hit me that the people having problems with the chemistry problems also couldn’t solve problems like “let’s say you want 50% more cupcakes, you have three more eggs and four more cups of wheat—can you do it?” The problem was never the chemistry, it was always that the basic math needed to solve the problems was genuinely hard for a lot of seemingly non-stupid people.
we vastly VASTLY underestimate how much of what seems like cognition in those around us is actually pattern recognition and completion learned by rote.
a super intelligent AI would surely feel the same way about us so called gifted folk.
This example helps clarify something for me. I don’t think it’s that the “cognitive context was...too dissimilar” for the students, I would guess that it’s that they don’t care in class. When they’re doing they’re job or shopping, they do care. But the obvious reply is: why do I hypothesize that cheating-examples make people care in a fictional context? Maybe someone can help say it clearly for me, but it just makes sense to me that math requires a higher threshold of “caring” than something like “cheating.” If I were reading a novel about a kid solving math problems in class, I’d probably wouldn’t care about the math problems, but if I were reading a novel and cheating was possible, it probably would cause a reaction. This is what I was trying to get at with testing “various types of emotionally-motivating things,” it just seems obvious that some things will evoke emotions in some contexts but not others, and some emotional responses will increase performance or some won’t, but I can’t put it better than that right now.
The lecturer in our Numerical cognition course told us of a result that went along the following lines. A schoolteacher was trying to teach his students to do basic arithmetic, and seeing them get the calculations wrong time after time. Then one day he decided to follow them out into town, where he saw that some of his students handled arithmetic just fine when they were doing grocery shopping, or working part-time selling things. Inspired, he returned to class and reworded his assignments to be about shopping, and guess what happened? The students failed just as miserably as they had before. The cognitive context was just too dissimiliar to the environment where they’d picked up the practice.
I got the impression that this wasn’t just an isolated anecdote, but had also been replicated in more controlled studies. The reference he gave is to Jean Lave’s Cognition in Practice—I have a copy of the book from the university library, but haven’t had the time to read further yet. I’ll see if I can skim it through this evening to find the part he was talking about.
Back in high school I used to help my fellow students with chemistry problems. I noticed that many of them seemed to have a lot of trouble with what I thought were really easy problems. I noticed that many of the chemistry problems had obvious analogues in everyday tasks like baking cakes. I kept trying to reframe chemistry problems as baking problems, expecting that this would make everything easier. I thought my fellow students had some sort of aversion to chemistry but could handle baking easily enough.
This approach never got me anywhere even though I kept trying to make the problems more intuitive. In the end it hit me that the people having problems with the chemistry problems also couldn’t solve problems like “let’s say you want 50% more cupcakes, you have three more eggs and four more cups of wheat—can you do it?” The problem was never the chemistry, it was always that the basic math needed to solve the problems was genuinely hard for a lot of seemingly non-stupid people.
we vastly VASTLY underestimate how much of what seems like cognition in those around us is actually pattern recognition and completion learned by rote.
a super intelligent AI would surely feel the same way about us so called gifted folk.
This example helps clarify something for me. I don’t think it’s that the “cognitive context was...too dissimilar” for the students, I would guess that it’s that they don’t care in class. When they’re doing they’re job or shopping, they do care. But the obvious reply is: why do I hypothesize that cheating-examples make people care in a fictional context? Maybe someone can help say it clearly for me, but it just makes sense to me that math requires a higher threshold of “caring” than something like “cheating.” If I were reading a novel about a kid solving math problems in class, I’d probably wouldn’t care about the math problems, but if I were reading a novel and cheating was possible, it probably would cause a reaction. This is what I was trying to get at with testing “various types of emotionally-motivating things,” it just seems obvious that some things will evoke emotions in some contexts but not others, and some emotional responses will increase performance or some won’t, but I can’t put it better than that right now.