A Mathematician’s Lament,by Paul Lockhart

[Mike Sadofsky]

Here is a link to a lengthy article in which a professor of mathematics dissects the way in which the topic is taught in schools.�
His philosophy appears to be in sympathy and compatible with the philosophy underlying the Sudbury Valley School
(although he demonstrates no awareness of it).

http://www.mathteacherctk.com/blog/wp-content/uploads/2008/03/lockhartslament.pdf

I ran across this article some time ago, and, just this morning tripped over another link to it and reread it.� It
might be of interest to folks on this list.

Mike

The art is not in the �truth� but in the explanation, the argument. It is the argument itself which
gives the truth its context, and determines what is really being said and meant. Mathematics is
the art of explanation. If you deny students the opportunity to engage in this activity� to pose
their own problems, make their own conjectures and discoveries, to be wrong, to be creatively
frustrated, to have an inspiration, and to cobble together their own explanations and proofs� you
deny� them mathematics itself. So� no, I�m not complaining� about the presence of facts and
formulas in� our mathematics classes, I�m complaining� about the lack� of mathematics in� our
mathematics classes.

(emphasis added)

[Alan Klein]

In 1969 (or so) there was a wonderful little book with the unfortunate title of "The Student as Nigger" which was mostly about how grad students were exploited by their schools.

There is a wonderful essay in it, however, that mirrors what you have sent us, Mike. The author writes a pretend report on a research project in which the researchers are trying to teach walking as we teach reading. They strapped kids down on their backs so that if they had learned any walking on their own they would forget how. Then they "taught" the subjects the act of walking broken into its constituent parts ("the subpatellar thrust", for example), complete with diagrams and lot so practice of the parts (but not of waling itself).

The report is positioned as a request for more funds to continue the research. They note that no one has learned to walk yet, but they are showing promising signs of progress!

~Alan Klein

On Mon, Oct 3, 2011 at 12:19 PM, Mike Sadofsky <mike.s...@gmail.com> wrote:

Here is a link to a lengthy article in which a professor of mathematics dissects the way in which the topic is taught in schools. 

His philosophy appears to be in sympathy and compatible with the philosophy underlying the Sudbury Valley School
(although he demonstrates no awareness of it).

http://www.mathteacherctk.com/blog/wp-content/uploads/2008/03/lockhartslament.pdf

I ran across this article some time ago, and, just this morning tripped over another link to it and reread it.  It

might be of interest to folks on this list.

Mike

The art is not in the “truth” but in the explanation, the argument. It is the argument itself which

gives the truth its context, and determines what is really being said and meant. Mathematics is

the art of explanation. If you deny students the opportunity to engage in this activity— to pose

their own problems, make their own conjectures and discoveries, to be wrong, to be creatively

frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you
deny  them mathematics itself. So  no, I’m not complaining  about the presence of facts and
formulas in  our mathematics classes, I’m complaining  about the lack  of mathematics in  our
mathematics classes.

(emphasis added)

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[Mike South]

On Mon, Oct 3, 2011 at 11:19 AM, Mike Sadofsky <mike.s...@gmail.com> wrote:

Here is a link to a lengthy article in which a professor of mathematics dissects the way in which the topic is taught in schools. 

His philosophy appears to be in sympathy and compatible with the philosophy underlying the Sudbury Valley School
(although he demonstrates no awareness of it).

http://www.mathteacherctk.com/blog/wp-content/uploads/2008/03/lockhartslament.pdf

I ran across this article some time ago, and, just this morning tripped over another link to it and reread it.  It

might be of interest to folks on this list.

I put some thoughts on it here when it was making the rounds back then:

http://leftoverpi.nfshost.com/blog/2008/05/lockharts_lament_part_1_lead_a.html

included there is a link to another piece that is similar, but which (upon rereading all these years later) really could use some editing.  It's hard to tell where it's going until you get to the last couple sentences, which was kind of the point, but it's poorly executed.  It's basically an unedited brain dump of what I was thinking at the time; only interesting if you want to see that two math types came up with something close to the same "lament" completely independently:

http://fulcrum.org/features/mountain.html

When you've waded through the first three paragraphs remember I warned you it was circuitous.

mike

Mike

The art is not in the “truth” but in the explanation, the argument. It is the argument itself which

gives the truth its context, and determines what is really being said and meant. Mathematics is

the art of explanation. If you deny students the opportunity to engage in this activity— to pose

their own problems, make their own conjectures and discoveries, to be wrong, to be creatively

frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you
deny  them mathematics itself. So  no, I’m not complaining  about the presence of facts and

formulas in  our mathematics classes, I’m complaining  about the lack  of mathematics in  our
mathematics classes.

(emphasis added)

[Jim Whiteford]

A belated thanks for this. Maths is so often the focus of school - and so often the extreme of the argument. Either it's the worst, most boring torture anyone remembers, or it's the most essential lifeline a school can give a kid for the future - and all ways to improve its teachability are Important. (Especially if the town you're in has an industrial heritage...) 

So I appreciated hearing from someone who is both enamoured of the subject, and infuriated by what schooling has done to it. I also began to get a glimpse into what maths may really be about, something that escaped me during all my compulsory tuition. 

And it highlights a broader phenomena. 

In Gothenburg's local paper recently, there was a small report on the latest advice from the schools inspectorate to the teaching profession. Teachers are now being encouraged to minimise the amount of time pupils have to work on their own - in a project, in a class, whatever; teachers should strive to be active authorities in the students' work, closely overseeing it, setting goals, defining guidelines and so forth. This view was apparently backed up by various recent studies on the "effectiveness" - meaning lack of it - of pupil autonomy within a field of study. 

This is of course no surprise given the current government and the depressing educational reforms it has passed. More tests, more central governance, more old-fashioned style teaching, more grading, less aesthetic subjects - the pendulum swings away from "progressive" education back to the 50s, under a Minister for Education with an army background. 

But the article made me realise that while reading it, one of the conclusions many might draw is the old classic in our contemporary culture, that school does so much to perpetuate: give kids too much freedom, and they get it wrong; or they under-perform; they clearly need guidance in order to succeed. 

Someone like myself, who struggled with the extreme irrelevance of maths in school, finds it almost unthinkable that the subject may be philosophical, subjective and creative - it doesn't fit in the paradigm I've grown accustomed to, and absorbed through osmosis, a kind of cultural conditioning. And similarly, instead of perceiving the fundamental flaws of a national curriculum and standardised testing, and the fact that both of these things make any individual study deeply compromised, one's focus becomes the fallibility of the child and its need for guidance.

It seems to me that so often the arguments about schooling and education do not question many of the fundamental premises and structures that the existing system of compulsory schooling are based upon. Instead, the rhetoric tends to stoke half-truths and foggy fears, that serve to reinforce the monolithic status quo.  

I know I'm not stating anything people on this list haven't already worked through; I just wanted to share it. Perhaps it might spark further discussion?       

Thanks for listening, 

Jim. 

On Oct 3, 2011, at 18:19 PM, Mike Sadofsky wrote:

Here is a link to a lengthy article in which a professor of mathematics dissects the way in which the topic is taught in schools. 

His philosophy appears to be in sympathy and compatible with the philosophy underlying the Sudbury Valley School
(although he demonstrates no awareness of it).

http://www.mathteacherctk.com/blog/wp-content/uploads/2008/03/lockhartslament.pdf

I ran across this article some time ago, and, just this morning tripped over another link to it and reread it.  It

might be of interest to folks on this list.

Mike

The art is not in the “truth” but in the explanation, the argument. It is the argument itself which

gives the truth its context, and determines what is really being said and meant. Mathematics is

the art of explanation. If you deny students the opportunity to engage in this activity— to pose

their own problems, make their own conjectures and discoveries, to be wrong, to be creatively

frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you
deny  them mathematics itself. So  no, I’m not complaining  about the presence of facts and

formulas in  our mathematics classes, I’m complaining  about the lack  of mathematics in  our
mathematics classes.

(emphasis added)

[Karen Hyams]

This was the only benefit to studying algebra for me - I could see that while the process of math did not fit me, it was a beautiful way of expressing the world. I think mathematics are an art form now, in spite of my poor grades in the subject.

Karen

On Thu, Oct 27, 2011 at 10:03 AM, Jim Whiteford <jw4...@gmail.com> wrote:

Someone like myself, who struggled with the extreme irrelevance of maths in school, finds it almost unthinkable that the subject may be philosophical, subjective and creative - it doesn't fit in the paradigm I've grown accustomed to, and absorbed through osmosis, a kind of cultural conditioning.

--
My recent work:
http://www.karenhyams.com/

[Ida]

I'm one of those people that were not good at maths and suffered all
the anxiety of not understanding most of the curricula (late 60's,
public school in Portugal), so I was very pleased to read this
passionate text «A Mathematician's Lament» which is so up to date. I
believe that any area of knowledge can be exciting to learn. I wish I
had the opportunity to have enjoyed my schooldays. Unfortunately I was
always eager to go back home, to my comfortable environment. School
was mandatory as still is, but could be more attractive and
motivating.

Thanks to the newsletters of Prof. Stephen Downes I came across an
interesting website full of creative works that mingle interests in
art, math and music from an american lady called Vi Hart. In case you
don't know I would like to share it - http://vihart.com/everything/

On Oct 3, 5:19 pm, Mike Sadofsky <mike.sadof...@gmail.com> wrote:
> Here is a link to a lengthy article in which a professor of mathematics dissects the way in which the topic is taught in schools.

> His philosophy appears to be in sympathy and compatible with the philosophy underlying the Sudbury Valley School

> (although he demonstrates no awareness of it).http://www.mathteacherctk.com/blog/wp-content/uploads/2008/03/lockhartslament.pdf
> I ran across this article some time ago, and, just this morning tripped over another link to it and reread it. It

> might be of interest to folks on this list.

> MikeThe art is not in the truth but in the explanation, the argument. It is the argument itself which

> gives the truth its context, and determines what is really being said and meant. Mathematics is

> the art of explanation. If you deny students the opportunity to engage in this activity to pose

> their own problems, make their own conjectures and discoveries, to be wrong, to be creatively

> frustrated, to have an inspiration, and to cobble together their own explanations and proofs you

> deny them mathematics itself. So no, I m not complaining about the presence of facts and
> formulas in our mathematics classes,I m complaining about the lack of mathematics in our
> mathematics classes.(emphasis added)