Lockhart's Lament
I came across this essay through a circuitous manner that seems to be representative of most of the way I learn, which is relevant to the lament because it is about how we learn and how we "should" learn and how one is the way of the individual and the other the way of the institution.
I am exploring (which is a kind way of saying attempting to teach myself) something about computer programming because I'm fascinated with Big Data and all that it can do and be. And to get to Big Data, I need to understand the basics. So I found an online textbook from MIT (Introduction to Computing: Explorations in Language), downloaded it and started reading. Within the first two pages, I was back at Google hunting for Lockhart's Lament which the author quotes:
"It may be true that you have to be able to read in order to fill out forms at the DMV, but that’s not
why we teach children to read. We teach them to read for the higher purpose of allowing them access to
beautiful and meaningful ideas."
Paul Lockhart, Lockhart’s Lament http://www.maa.org/devlin/LockhartsLament.pdf
Because I teach reading, I thought what Lockhart had to say worth looking at closer (this is why it takes me so long to complete anything because I'm always taking side roads, but this is also why I hated school--the side roads were not to be taken, and they were sooooo interesting). Anyway, in the Lament, Lockhart compares how we teach math to how we do NOT teach music (although we do kind of teach art this way and maybe even music? I haven't ever taken music in college but I know there are music theory courses, etc.) but his point was that we do not make our elementary school children take a bunch of course on music theory without allowing them to play the music first. But we do make our elementary students take math without getting to play with the math first. At least I think that's the analogy. (A funny aside, the computer book references Godel, Escher Bach by Hofstadter (I'm probably massacring that name) who is the author of the Analogies book I was just writing about yesterday. And here Lockhart is using analogy to help us make sense of his argument--just as Hofstadter argues in his book--I think. What a circle knowledge is).
And reading Lockhart's Lament makes me think I also want to be a mathematician! I've always been fascinated by math because it's so hard for me to figure out what it is, but it's always seemed amazing because of its inscrutability. But, I just never "got" math. Maybe in the same way I don't "get" art.
Quote from the Lament:
G.H. Hardy’s excellent description:
A mathematician, like a painter or poet, is a maker
of patterns. If his patterns are more permanent than
theirs, it is because they are made with ideas
omg! Who wouldn't want to be a mathematician?!
Here is another quote from the Lament:
"Now let me be clear about what I’m objecting to. It’s not about formulas, or memorizing
interesting facts. That’sfine in context, and has its place just as learning a vocabulary does— it
helps you to create richer, more nuanced works of art. But it’s not the fact that trianglestake up
half their box that matters. What matters is the beautiful idea of chopping it with the line, and
how that might inspire other beautiful ideas and lead to creative breakthroughs in other
problems— something a mere statement of fact can never give you."
What Lockhart seems to be focusing on is the generative effect of focusing on discovery and curiosity and exploration rather than the actual outcome, which is often the home/unschool mantra. Let the student pursue their interests, their discoveries, their curiosity, which will then lead to more discoveries and more curiosity, etc. If this in fact was what happened with "all" students, it would be a great argument, and it is certainly an exciting argument for those of us who do learn in this manner, but what if a student has no curiosity, no interest? And, yes people do exist like that? Also, can we pursue without having the tools in place to understand what we are pursuing As I currently pursue my interest in Web development, I can't just jump in and start developing (although someone else could). I have to go to the beginning and figure it out because that's how I learn best. Can we match up teachers with students with curriculum who are heading in the same or similar directions? Or is it just happenstance?
Lockhart also emphasizes how important it is to let students be "wrong". I'm fascinated with this issue and how I could incorporate being wrong into my classroom (see earlier post on this--can't remember exactly which one!). Students need to see the benefit of being wrong but how?
Math is both an art and a tool. How to teach it as both? How to do that with reading? Reading is not just for "work" but also for pleasure but more importantly also for curiosity and understanding and making sense of your own life. Yet, we don't teach it that way. We teach it as if it is detached from us.
Lockhart quotes extensively from Godel, Escher, Bach which I have a copy of and have attempted to read. But I don't understand it. I just get lost. I can't quite get my mind around the idea that somehow this very complicated book (to me) is useful for understanding math as an art . . . .Why is the Godel, Escher Bach book so difficult to read? What would make it easier for me to understand? These are the questions I wish my students were asking and that I could answer.
Another quote:
"They [students] are being trained to ape arguments, not to intend them. So not only do they have no idea what their teacher issaying, they have no idea what they themselves are saying."
One of the things I emphasize in my classes is "USE YOUR OWN WORDS". And by emphasize I mean the students get their work back and have to redo it if it looks to me like they are using words they aren't familiar with. All vocab has to be re-written so that it makes sense to them, etc. But I still have students coming up to me on the last day saying, can we just quote. Students have been trained to "ape" and not to intend. They don't even know what "intending" is. And, it's so very hard to teach at this late date.
Is there some way to teach vocab through analogy, so that they have to understand the word enough to write an analogy about the meaning? How many vocab words would this work for? Would I need a book? And with the internet, students just look it up. . . how do we get them to intend?
A note added later: in Reading The Information (Glick), he states, "some mathematical facts are true for no reason. They are accidental, leaking a cause or deeper meaning" (p. 343). Is that possible? If they are true for "no reason", what does that mean? That some of math is entirely random or that its just part of the universe? Does "no reason" mean that humans can't figure it out or there is nothing to figure out?
Some criticism. First my comments and then some taken from elsewhere:
My comments: Reading Lockhart and then some of the posts discussing his work, I am struck with how difficult it is to come to agreement about teaching in classrooms perhaps because there are so many people involved in a classroom. Is it possible to "teach" all students in a classroom? If not, is there any alternative? I continually want to pull my son out of school to homeschool him because he comes home with ridiculous work that is clearly not "teaching" him in a meaningful way. In discussions with his teachers, they disagree. But at the heart of that disagreement is how we view teaching in a meaningful way, perhaps. But also is the realities of a classroom. Every time I stand in front of my students (college level reading right now), I know that some students get what I say, others are lost, some want to get it but can't, some have no interest but still somehow end up getting bits and pieces, still others are lost one day and found another, etc. And each day we come together and attempt to develop lessons that build on those that come before, which means that getting lost early on makes it almost impossible to ever "catch up." So, all of these factors are interacting while simultaneously, we might be working with a curriculum given to us by someone else that we don't really believe in or that isn't a good fit for most of our students or that we don't really even understand or aren't particularly interested in. All of these factors are present in a classroom so clearly there are no easy solutions.
Do we know what it is that our goal is? And by "our" here I mean any set of teachers in any classroom? I don't mean a particular goal of "the students will be able to do A" . I mean a larger pedagogical and ideological goal. I've tried to bring this up at meetings with other faculty but they do not seem to find this topic worth pursuing. But, how can we teach every day if we do not have some goal in mind to direct our teaching towards? If our goal is to turn out "educated citizens" our practice should be and will be very different if our goal is to find some way to hold teachers accountable. Is it possible for both goals to exist simultaneously? I don't know.
Comments, criticism from the same website where the lament was originally posted can be found here: http://www.maa.org/devlin/devlin_05_08.html
Lockhart’s Lament is an all suffering strawman-filled whine about how math is taught as a computation only course with no inkling of what math is about. His approach may be fine for gifted students but he falls prey to the same things Stephanie has brought out in her comment: he places critical and higher order thinking skills above the basics and does not see that mastery of the basics is essential to get to the lofty tower he enjoys occupying. He is a teacher by the way, at St. Ann’s school in Brooklyn. He teaches gifted and non-gifted students. The gifted students seem to do OK with his course; the non-gifted are in the same boat as the casualty cases from Everyday Math and other atrocities (from Barry Garelick posting herehttp://dianeravitch.net/2013/01/13/a-math-teacher-on-common-core-standards/comment-page-1/)
I am exploring (which is a kind way of saying attempting to teach myself) something about computer programming because I'm fascinated with Big Data and all that it can do and be. And to get to Big Data, I need to understand the basics. So I found an online textbook from MIT (Introduction to Computing: Explorations in Language), downloaded it and started reading. Within the first two pages, I was back at Google hunting for Lockhart's Lament which the author quotes:
"It may be true that you have to be able to read in order to fill out forms at the DMV, but that’s not
why we teach children to read. We teach them to read for the higher purpose of allowing them access to
beautiful and meaningful ideas."
Paul Lockhart, Lockhart’s Lament http://www.maa.org/devlin/LockhartsLament.pdf
Because I teach reading, I thought what Lockhart had to say worth looking at closer (this is why it takes me so long to complete anything because I'm always taking side roads, but this is also why I hated school--the side roads were not to be taken, and they were sooooo interesting). Anyway, in the Lament, Lockhart compares how we teach math to how we do NOT teach music (although we do kind of teach art this way and maybe even music? I haven't ever taken music in college but I know there are music theory courses, etc.) but his point was that we do not make our elementary school children take a bunch of course on music theory without allowing them to play the music first. But we do make our elementary students take math without getting to play with the math first. At least I think that's the analogy. (A funny aside, the computer book references Godel, Escher Bach by Hofstadter (I'm probably massacring that name) who is the author of the Analogies book I was just writing about yesterday. And here Lockhart is using analogy to help us make sense of his argument--just as Hofstadter argues in his book--I think. What a circle knowledge is).
And reading Lockhart's Lament makes me think I also want to be a mathematician! I've always been fascinated by math because it's so hard for me to figure out what it is, but it's always seemed amazing because of its inscrutability. But, I just never "got" math. Maybe in the same way I don't "get" art.
Quote from the Lament:
G.H. Hardy’s excellent description:
A mathematician, like a painter or poet, is a maker
of patterns. If his patterns are more permanent than
theirs, it is because they are made with ideas
omg! Who wouldn't want to be a mathematician?!
Here is another quote from the Lament:
"Now let me be clear about what I’m objecting to. It’s not about formulas, or memorizing
interesting facts. That’sfine in context, and has its place just as learning a vocabulary does— it
helps you to create richer, more nuanced works of art. But it’s not the fact that trianglestake up
half their box that matters. What matters is the beautiful idea of chopping it with the line, and
how that might inspire other beautiful ideas and lead to creative breakthroughs in other
problems— something a mere statement of fact can never give you."
What Lockhart seems to be focusing on is the generative effect of focusing on discovery and curiosity and exploration rather than the actual outcome, which is often the home/unschool mantra. Let the student pursue their interests, their discoveries, their curiosity, which will then lead to more discoveries and more curiosity, etc. If this in fact was what happened with "all" students, it would be a great argument, and it is certainly an exciting argument for those of us who do learn in this manner, but what if a student has no curiosity, no interest? And, yes people do exist like that? Also, can we pursue without having the tools in place to understand what we are pursuing As I currently pursue my interest in Web development, I can't just jump in and start developing (although someone else could). I have to go to the beginning and figure it out because that's how I learn best. Can we match up teachers with students with curriculum who are heading in the same or similar directions? Or is it just happenstance?
Lockhart also emphasizes how important it is to let students be "wrong". I'm fascinated with this issue and how I could incorporate being wrong into my classroom (see earlier post on this--can't remember exactly which one!). Students need to see the benefit of being wrong but how?
Math is both an art and a tool. How to teach it as both? How to do that with reading? Reading is not just for "work" but also for pleasure but more importantly also for curiosity and understanding and making sense of your own life. Yet, we don't teach it that way. We teach it as if it is detached from us.
Lockhart quotes extensively from Godel, Escher, Bach which I have a copy of and have attempted to read. But I don't understand it. I just get lost. I can't quite get my mind around the idea that somehow this very complicated book (to me) is useful for understanding math as an art . . . .Why is the Godel, Escher Bach book so difficult to read? What would make it easier for me to understand? These are the questions I wish my students were asking and that I could answer.
Another quote:
"They [students] are being trained to ape arguments, not to intend them. So not only do they have no idea what their teacher issaying, they have no idea what they themselves are saying."
One of the things I emphasize in my classes is "USE YOUR OWN WORDS". And by emphasize I mean the students get their work back and have to redo it if it looks to me like they are using words they aren't familiar with. All vocab has to be re-written so that it makes sense to them, etc. But I still have students coming up to me on the last day saying, can we just quote. Students have been trained to "ape" and not to intend. They don't even know what "intending" is. And, it's so very hard to teach at this late date.
Is there some way to teach vocab through analogy, so that they have to understand the word enough to write an analogy about the meaning? How many vocab words would this work for? Would I need a book? And with the internet, students just look it up. . . how do we get them to intend?
A note added later: in Reading The Information (Glick), he states, "some mathematical facts are true for no reason. They are accidental, leaking a cause or deeper meaning" (p. 343). Is that possible? If they are true for "no reason", what does that mean? That some of math is entirely random or that its just part of the universe? Does "no reason" mean that humans can't figure it out or there is nothing to figure out?
Some criticism. First my comments and then some taken from elsewhere:
My comments: Reading Lockhart and then some of the posts discussing his work, I am struck with how difficult it is to come to agreement about teaching in classrooms perhaps because there are so many people involved in a classroom. Is it possible to "teach" all students in a classroom? If not, is there any alternative? I continually want to pull my son out of school to homeschool him because he comes home with ridiculous work that is clearly not "teaching" him in a meaningful way. In discussions with his teachers, they disagree. But at the heart of that disagreement is how we view teaching in a meaningful way, perhaps. But also is the realities of a classroom. Every time I stand in front of my students (college level reading right now), I know that some students get what I say, others are lost, some want to get it but can't, some have no interest but still somehow end up getting bits and pieces, still others are lost one day and found another, etc. And each day we come together and attempt to develop lessons that build on those that come before, which means that getting lost early on makes it almost impossible to ever "catch up." So, all of these factors are interacting while simultaneously, we might be working with a curriculum given to us by someone else that we don't really believe in or that isn't a good fit for most of our students or that we don't really even understand or aren't particularly interested in. All of these factors are present in a classroom so clearly there are no easy solutions.
Do we know what it is that our goal is? And by "our" here I mean any set of teachers in any classroom? I don't mean a particular goal of "the students will be able to do A" . I mean a larger pedagogical and ideological goal. I've tried to bring this up at meetings with other faculty but they do not seem to find this topic worth pursuing. But, how can we teach every day if we do not have some goal in mind to direct our teaching towards? If our goal is to turn out "educated citizens" our practice should be and will be very different if our goal is to find some way to hold teachers accountable. Is it possible for both goals to exist simultaneously? I don't know.
Comments, criticism from the same website where the lament was originally posted can be found here: http://www.maa.org/devlin/devlin_05_08.html
Lockhart’s Lament is an all suffering strawman-filled whine about how math is taught as a computation only course with no inkling of what math is about. His approach may be fine for gifted students but he falls prey to the same things Stephanie has brought out in her comment: he places critical and higher order thinking skills above the basics and does not see that mastery of the basics is essential to get to the lofty tower he enjoys occupying. He is a teacher by the way, at St. Ann’s school in Brooklyn. He teaches gifted and non-gifted students. The gifted students seem to do OK with his course; the non-gifted are in the same boat as the casualty cases from Everyday Math and other atrocities (from Barry Garelick posting herehttp://dianeravitch.net/2013/01/13/a-math-teacher-on-common-core-standards/comment-page-1/)
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