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A beautifully written and tragic essay. (Note: What follows is US-centric.) After nine years of teaching mathematics courses (one semester as an undergraduate

A beautifully written and tragic essay. (Note: What follows is US-centric.) After nine years of teaching mathematics courses (one semester as an undergraduate, 4.5 years as a graduate student, and 4 years as an assistant professor) and navigating university politics, I'm convinced that this is, at its heart, a cultural issue. There's a hatred of mathematics in mainstream American culture that runs very, very deep. And it will probably take generations to change that (if changing it is even possible at this point).

chrisdone 12y ago
America, Britain, France, Italy, etc. education systems built upon "getting results" seem to end up ruining the subject they're trying to teach.
- sp332 12y ago
  How do you get results then? Ignore the results?
  - wyager 12y ago
    Encourage freedom of thought instead of preparing students for some standardized test. It's crazy how much the AP/IB and SAT tests dictate the direction and content of high school curricula. It gets much better at the college level, because teachers don't have to prepare students for anything in particular.
  - j2kun 12y ago
    Invest in the infrastructure.
  - setr 12y ago
    By developing the argument. The correct answer isn't nearly as important as forming a strong argument, at least in the process of learning, as a well written argument will naturally lead you towards the correct answer. Its the reason why "showing your work" is taken so strongly. The flaw being that you're not showing your work so much as you're showing your ability to follow a defined series of actions. The grade school test doesn't ask you to think of a procedure to resolve some stated question. It asks if you already have it memorized, as the formula was handed to you in a prior lecture. Ideally, the test should ask the student to form an argument, thus showing mastery over the knowledge that precedes its creation. This would be judged, and of the students ability to consistently dot the i's and cross his t's, expected but given a minor role (as it is in "real life", mistakes are inevitable and its why we check our work twice, and then give it to others to check again.)
  - saraid216 12y ago
    "Get results" is code for "reduce people to statistics, then optimize for a convenient statistic". It's like dealing with a homeless problem by shipping them all to some other town.
GregBuchholz 12y ago
>There's a hatred of mathematics in mainstream American culture that runs very, very deep. And it will probably take generations to change that (if changing it is even possible at this point). Could you explain further? It seems like you believe that something should change, but it is not clear if you are saying that the "mathematics" or the mainstream American culture should change. Lockhart's gist is that of course "everyone" hates "mathematics", because they are being presented with a dried up empty shell that only superficially resembles real "mathematics". Are you disagreeing with Lockhart, and think that the culture should embrace the "mathematics" as-it-stands? Or are you saying that it is unlikely that reforms will be possible to change the system to present "mathematics" in the way Lockhart would approve of? Or are you saying that even Lockhart's "mathematics" is and will always be hated by mainstream American culture?
- jackmaney 12y ago
  > Could you explain further? It seems like you believe that something should change, but it is not clear if you are saying that the "mathematics" or the mainstream American culture should change. The culture needs to change. Full stop. I just have no idea how to do it. > Are you disagreeing with Lockhart Nope. > Or are you saying that it is unlikely that reforms will be possible to change the system to present "mathematics" in the way Lockhart would approve of? Not exactly what I was saying, no. Changing "the system", however, will be extremely difficult at best, though. > Or are you saying that even Lockhart's "mathematics" is and will always be hated by mainstream American culture? That remains to be seen.
  - GregBuchholz 12y ago
    Interesting. I would have thought that "the culture needs to change" is in direct opposition to Lockhart's thesis. My reading of his essay is that people are rightly justified in hating the "mathematics" that was forced upon them. I wonder if this difference in reading is some sort of confirmation bias, reading into an essay what we each want to hear? On a more meta-level, I wonder if that quality improves or detracts from an essay. Or maybe that quality isn't a part of the essay as much is it is attached to the subject or the reader? Something I'll have to ponder some more.
davidtanner 12y ago
I studied mathematics as an undergraduate and it does seem that the very mention of math tends to scare and alienate some people. If you don't mind, I'd be very curious to hear you elaborate further on this subject.
dxbydt 12y ago
>There's a hatred of mathematics in mainstream American culture that runs very, very deep Completely agreed. As an immigrant, I can say it is very much a US thing. Haven't seen this much math-hate, but more importantly, math-utilitarianism, as in the US. In Asian countries & in Europe ( UK, France especially), people don't constantly fixate on stupid questions like "what is it good for ? ", which is ultimately a proxy for "how do I make money with this thing ?". But when I taught math here in the US as a graduate student TA, the majority of questions focussed on this single metric - usefulness. So math texts here are forced to invent bogus problems like "You want to house pigs with 500 feet of fencing. What dimensions of your rectangular pen will house the most hogs ?". Then the American kid says, Ah! Now I see the point of all this! Let l be the length of my pen and b its breadth. You want me to maximize the area of my pen lb subject to 2l+2b=500 so I can house the most pigs! Ok so I see that b = 250-l, so lb is 250l - l^2, so I take its derivative & equate to zero & l=125, b=125, and that's the biggest pen that can house the most pigs. Very nice! In other countries, you simple wouldn't come up with all these sort of bogus utilitarian problems in animal husbandry. Students here learn exponentials & Taylor expansion as part of "how do I compute compound interest on my bank account", because that's supposedly the only legitimate use of e^x ! I honestly found teaching pre-calc, calc-1 & calc-2 a complete travesty, because the theorems & the entire courseware was essentially perverted - it was all in service of how to make use of the math for some bogus application, rather than learn it for its own good. The worst was when I had to teach how the horizontal range of parabolic trajectories varied - the textbook had examples of the US bombing Japan, & the students went to work computing the best possible angle for firing the missile, so that it would fly across in a parabolic trajectory and land the farthest thus maximizing its horizontal range & kill the most number of Japanese! There was no thought given to how violent & nasty this was. I actually have very radical ideas about how things should be taught - like you must learn Rolle's theorem before learning shit like pre-calc. Learn as much of undergrad real analysis before you get into application oriented shit like calc-1, calc-2 etc. Don't bring in garbage like LCR circuitry into pde's, even though yes, you can use a third order differential equation to compute current through an LCR circuit. Applications have their place, but such an overemphasis on application is simply not healthy. It actively distorts the culture & the body politic. Note that American students don'r ask "what use is rock and roll ? otr what use is hbo ? or what use is literature ?" all those things are given a free pass. But when it comes to math, suddenly use becomes the primary criterion. Read pages 6-7, & especially 12 of Lockhart's lament, where he chooses to parody this point of view via Simplicio.

chrisdone 12y ago

America, Britain, France, Italy, etc. education systems built upon "getting results" seem to end up ruining the subject they're trying to teach.

sp332 12y ago
How do you get results then? Ignore the results?
- wyager 12y ago
  Encourage freedom of thought instead of preparing students for some standardized test. It's crazy how much the AP/IB and SAT tests dictate the direction and content of high school curricula. It gets much better at the college level, because teachers don't have to prepare students for anything in particular.
- j2kun 12y ago
  Invest in the infrastructure.
- setr 12y ago
  By developing the argument. The correct answer isn't nearly as important as forming a strong argument, at least in the process of learning, as a well written argument will naturally lead you towards the correct answer. Its the reason why "showing your work" is taken so strongly. The flaw being that you're not showing your work so much as you're showing your ability to follow a defined series of actions. The grade school test doesn't ask you to think of a procedure to resolve some stated question. It asks if you already have it memorized, as the formula was handed to you in a prior lecture. Ideally, the test should ask the student to form an argument, thus showing mastery over the knowledge that precedes its creation. This would be judged, and of the students ability to consistently dot the i's and cross his t's, expected but given a minor role (as it is in "real life", mistakes are inevitable and its why we check our work twice, and then give it to others to check again.)
- saraid216 12y ago
  "Get results" is code for "reduce people to statistics, then optimize for a convenient statistic". It's like dealing with a homeless problem by shipping them all to some other town.

GregBuchholz 12y ago

>There's a hatred of mathematics in mainstream American culture that runs very, very deep. And it will probably take generations to change that (if changing it is even possible at this point). Could you explain further? It seems like you believe that something should change, but it is not clear if you are saying that the "mathematics" or the mainstream American culture should change. Lockhart's gist is that of course "everyone" hates "mathematics", because they are being presented with a dried up empty shell that only superficially resembles real "mathematics". Are you disagreeing with Lockhart, and think that the culture should embrace the "mathematics" as-it-stands? Or are you saying that it is unlikely that reforms will be possible to change the system to present "mathematics" in the way Lockhart would approve of? Or are you saying that even Lockhart's "mathematics" is and will always be hated by mainstream American culture?

jackmaney 12y ago
> Could you explain further? It seems like you believe that something should change, but it is not clear if you are saying that the "mathematics" or the mainstream American culture should change. The culture needs to change. Full stop. I just have no idea how to do it. > Are you disagreeing with Lockhart Nope. > Or are you saying that it is unlikely that reforms will be possible to change the system to present "mathematics" in the way Lockhart would approve of? Not exactly what I was saying, no. Changing "the system", however, will be extremely difficult at best, though. > Or are you saying that even Lockhart's "mathematics" is and will always be hated by mainstream American culture? That remains to be seen.
- GregBuchholz 12y ago
  Interesting. I would have thought that "the culture needs to change" is in direct opposition to Lockhart's thesis. My reading of his essay is that people are rightly justified in hating the "mathematics" that was forced upon them. I wonder if this difference in reading is some sort of confirmation bias, reading into an essay what we each want to hear? On a more meta-level, I wonder if that quality improves or detracts from an essay. Or maybe that quality isn't a part of the essay as much is it is attached to the subject or the reader? Something I'll have to ponder some more.

davidtanner 12y ago

I studied mathematics as an undergraduate and it does seem that the very mention of math tends to scare and alienate some people. If you don't mind, I'd be very curious to hear you elaborate further on this subject.

dxbydt 12y ago

>There's a hatred of mathematics in mainstream American culture that runs very, very deep Completely agreed. As an immigrant, I can say it is very much a US thing. Haven't seen this much math-hate, but more importantly, math-utilitarianism, as in the US. In Asian countries & in Europe ( UK, France especially), people don't constantly fixate on stupid questions like "what is it good for ? ", which is ultimately a proxy for "how do I make money with this thing ?". But when I taught math here in the US as a graduate student TA, the majority of questions focussed on this single metric - usefulness. So math texts here are forced to invent bogus problems like "You want to house pigs with 500 feet of fencing. What dimensions of your rectangular pen will house the most hogs ?". Then the American kid says, Ah! Now I see the point of all this! Let l be the length of my pen and b its breadth. You want me to maximize the area of my pen lb subject to 2l+2b=500 so I can house the most pigs! Ok so I see that b = 250-l, so lb is 250l - l^2, so I take its derivative & equate to zero & l=125, b=125, and that's the biggest pen that can house the most pigs. Very nice! In other countries, you simple wouldn't come up with all these sort of bogus utilitarian problems in animal husbandry. Students here learn exponentials & Taylor expansion as part of "how do I compute compound interest on my bank account", because that's supposedly the only legitimate use of e^x ! I honestly found teaching pre-calc, calc-1 & calc-2 a complete travesty, because the theorems & the entire courseware was essentially perverted - it was all in service of how to make use of the math for some bogus application, rather than learn it for its own good. The worst was when I had to teach how the horizontal range of parabolic trajectories varied - the textbook had examples of the US bombing Japan, & the students went to work computing the best possible angle for firing the missile, so that it would fly across in a parabolic trajectory and land the farthest thus maximizing its horizontal range & kill the most number of Japanese! There was no thought given to how violent & nasty this was. I actually have very radical ideas about how things should be taught - like you must learn Rolle's theorem before learning shit like pre-calc. Learn as much of undergrad real analysis before you get into application oriented shit like calc-1, calc-2 etc. Don't bring in garbage like LCR circuitry into pde's, even though yes, you can use a third order differential equation to compute current through an LCR circuit. Applications have their place, but such an overemphasis on application is simply not healthy. It actively distorts the culture & the body politic. Note that American students don'r ask "what use is rock and roll ? otr what use is hbo ? or what use is literature ?" all those things are given a free pass. But when it comes to math, suddenly use becomes the primary criterion. Read pages 6-7, & especially 12 of Lockhart's lament, where he chooses to parody this point of view via Simplicio.