I encountered Lockhart's _Lament_ back when I was in college, and I had lots of resentment about it. I can't remember if I actually read it or someone else's article lauding Lockhart, but either way, the sense I got was that the author wanted to do away with problem sets in favor of appreciating concepts and teasing out moments of insight.
The problem is, insight doesn't happen on command. If you the student aren't getting that insight, then staring at your homework page quite possibly won't give it to you either. You can reread the textbook, or go to office hours, or something - there are things that might help - but they might not help immediately. You might end up not having it in time for the homework deadline, or even the exam.
Some people will get that insight quickly, and I'm fine with recognizing them. But I'm not fine with failing everyone else, or even giving them a lower GPA in this age of grade inflation, or making the dedicated students among them keep pounding their heads against the wall.
Yes, if there was a reliable way to teach concept-appreciation and moments of insight, that could be great. But I haven't seen that reliable way, and I don't think Lockhart has either.
A lot of your criticisms are valid, though I would say, having read it, that things are more nuanced. I'm just going off the cuff here, but imagine that there are three tiers of math aptitude: low, medium and high. Lockhart is mostly focused on the high aptitude (as you point out) but I think the medium aptitude would benefit from turning the dial a couple notches towards insight and away from problem sets. Which leaves the low aptitude individuals. Clearly it's going to be difficult to get them to experience any epiphanies, but then we shouldn't demand that they all take 3-4 years of math in order to graduate. Because then in addition to not giving them any insight, we give them an eternal hatred of math.
This might be Lockhart's biggest potential contribution. Not how to give insights to the gifted but how to remove loathing from the ungifted.
That's a good point, but not actually the one I was trying to make.
Even high-aptitude students aren't always going to get the epiphanies at once, or even within a few days. They're more likely to understand the concept on a basic level, but not necessarily grok it on the deep level.
I know that when I was taking calculus, it took me at least a month to grasp derivatives. By the end of the semester, I had them and could write proofs about them - but if you'd asked me for those proofs before I got to that point, there would've been a whole lot of thumping my head against the wall.
Yes, in the abstract, I like insight a lot more than problem sets. But when you're asking for something challenging due tomorrow, I'll take a problem set hands down, because I can be more clear what will get me to completing it. So if you're moving the dial towards insight, you're also going to need to reform the whole homework and assessment system. I do like that notion, but it's an even bigger project than the one Lockhart is talking about.
I encountered Lockhart's _Lament_ back when I was in college, and I had lots of resentment about it. I can't remember if I actually read it or someone else's article lauding Lockhart, but either way, the sense I got was that the author wanted to do away with problem sets in favor of appreciating concepts and teasing out moments of insight.
The problem is, insight doesn't happen on command. If you the student aren't getting that insight, then staring at your homework page quite possibly won't give it to you either. You can reread the textbook, or go to office hours, or something - there are things that might help - but they might not help immediately. You might end up not having it in time for the homework deadline, or even the exam.
Some people will get that insight quickly, and I'm fine with recognizing them. But I'm not fine with failing everyone else, or even giving them a lower GPA in this age of grade inflation, or making the dedicated students among them keep pounding their heads against the wall.
Yes, if there was a reliable way to teach concept-appreciation and moments of insight, that could be great. But I haven't seen that reliable way, and I don't think Lockhart has either.
A lot of your criticisms are valid, though I would say, having read it, that things are more nuanced. I'm just going off the cuff here, but imagine that there are three tiers of math aptitude: low, medium and high. Lockhart is mostly focused on the high aptitude (as you point out) but I think the medium aptitude would benefit from turning the dial a couple notches towards insight and away from problem sets. Which leaves the low aptitude individuals. Clearly it's going to be difficult to get them to experience any epiphanies, but then we shouldn't demand that they all take 3-4 years of math in order to graduate. Because then in addition to not giving them any insight, we give them an eternal hatred of math.
This might be Lockhart's biggest potential contribution. Not how to give insights to the gifted but how to remove loathing from the ungifted.
That's a good point, but not actually the one I was trying to make.
Even high-aptitude students aren't always going to get the epiphanies at once, or even within a few days. They're more likely to understand the concept on a basic level, but not necessarily grok it on the deep level.
I know that when I was taking calculus, it took me at least a month to grasp derivatives. By the end of the semester, I had them and could write proofs about them - but if you'd asked me for those proofs before I got to that point, there would've been a whole lot of thumping my head against the wall.
Yes, in the abstract, I like insight a lot more than problem sets. But when you're asking for something challenging due tomorrow, I'll take a problem set hands down, because I can be more clear what will get me to completing it. So if you're moving the dial towards insight, you're also going to need to reform the whole homework and assessment system. I do like that notion, but it's an even bigger project than the one Lockhart is talking about.