
A Mathematician’s Lament (2002) [pdf] - Tomte
https://www.maa.org/external_archive/devlin/LockhartsLament.pdf
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joe_the_user
Oddly enough, I went to high school with Paul Lockhart and I too became
fascinated with math despite rather than because of our terrible high school
math program.

I think what originally got interested in math was the infamous "new math"
program [1] that existed in the 60s.

And the thing with New Math is that was abolished through a backlash of parent
and teachers because ... the parents and teachers couldn't understand the new
concepts.

And this is the thing. Math is both an abstract enterprise and an enterprise
of bookkeepers adding numbers on ledgers, parents adding up grocery bills and
so-forth. While New Math might have had some flaws in execution, any effort to
produce curriculum suited to students learning abstract mathematics is going
to run-up against the "readin', writin' and arithmetic" crowd in a similar
fashion to New Math.

[1]
[https://en.wikipedia.org/wiki/New_Math](https://en.wikipedia.org/wiki/New_Math)

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thearn4
This is a good point, and a relevant one when discussion Common Core with
people. At the surface level, I don't see anything in the new mathematics
curriculum that I would consider negative, but the biggest complaint I hear is
that parents can't understand it, and some teachers barely do either. But that
hints at a deeper problem.

~~~
joe_the_user
I think the reaction against New Math was a part of the general reaction
against all of what many viewed as the "weirdness" of the 60s, an anti-
intellectual attitude that was often used by powers-that-be that also felt
threatened by these upheavals.

My, I'd be happy if we had military dictatorship which imposed a new order
including the metric system, radians instead of degrees and algebra from 1st
grade onward. But I don't think that program would have a sufficient
constituency.

~~~
camelite
Wrong. It was a reaction against the utterly predictable failure of a
contentless approach to instruction which started and ended with the rhetoric
necessary to convince pseudo-intellectuals that supporting it demonstrated
political discernment and moral virtue.

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rfvwdfr
Can you please elaborate on what you mean by "contentless"? I just checked out
the wiki page on New Math and it seemed to have covered (with the exception of
inequalities) a few topics that usually get covered in the first couple of
chapters of an intro to abstract algebra book.

~~~
camelite
I was actually coming back to delete the original comment as it wasn't very
well thought through. I mean, sure, of course there was "content". There were
chapter headers as so on and so forth. It would be better to criticise the
absense of thought put into having a theory of instruction beyond "Experts do
this, therefore if we teach this, we'll create experts"

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vishvananda
I came across this recently. I had always wondered why I managed to find math
so fascinating when most of my peers hated it. I think I was just lucky enough
to see through the poor state of education into some of the magic underneath.
For a (partial) solution to the math education problem, Paul Lockhart has also
written a book called "Measurement"[1] which is a very entertaining read.

[1] [https://www.amazon.com/Measurement-Paul-
Lockhart/dp/06742843...](https://www.amazon.com/Measurement-Paul-
Lockhart/dp/0674284380)

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pagnol
It seems to me that the musician's nightmare is actually a lived reality for a
lot of people, it definitely was like this for me. As a child I took pleasure
in inventing melodies on our family's piano so that one observant family
member signed me up for piano lessons. I quickly came to hate my lessons so
thoroughly that I didn't touch a piano until I was in my mid-twenties, when I
rediscovered the joy of making music...

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TheOtherHobbes
It's basically the difference between authoritarian education and exploratory
play-led education.

Extremes of either seem to be destructive, but hitting the sweet spot where
the balance is just right is incredibly hard, and also incredibly demanding of
time and resources.

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ianai
Yes, current society and academia have it all wrong. Math is both celebrated
and scorned. It's somehow the most applicable thing in the world and yet
largely unemployable. People can't imagine a mathematician can do anything,
but know you need it to do most everything.

~~~
gajjanag
This is an astute observation.

The world leaders during WW2 recognized this - basically, when critical work
needed to be done, they knew whom they needed and roped in a large number of
the leading "dreamers/thinkers" of the time to work on the Manhattan Project.

The thing that saddens me is that it is often conflict and animosity that
awaken this recognition - other examples include the Cold War, artillery
calculations in WW1, etc.

~~~
ramblerman
To be fair most of the scientists on the Manhattan project were physicists.

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gajjanag
This issue is recognized by many professional mathematicians.

An example of a good effort to combat these tendencies is a course by Prof.
Bhargava at Princeton, where he introduces good mathematics through card
tricks and games:
[https://www.princeton.edu/main/news/archive/S36/37/98S70/ind...](https://www.princeton.edu/main/news/archive/S36/37/98S70/index.xml?section=featured)

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dang
[https://hn.algolia.com/?query=A%20Mathematician%E2%80%99s%20...](https://hn.algolia.com/?query=A%20Mathematician%E2%80%99s%20Lament%20%5Bpdf%5D&sort=byDate&dateRange=all&type=story&storyText=false&prefix&page=0)

... although I don't think we'd heard from a high-school classmate of the
author before.

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Chris2048
> all without the advice or participation of a single working musician or
> composer.

Some of the nest mathematicians are the worst teachers. They focus too much on
small details, as if they are carrying out their own usual role; and don't
intuitively explain the basics concepts that are now too ingrained for them to
easily recall the original difficulties they had with learning them.

Music and mathematics are not similar. I also imagine music is more subjective
/ less standardized. You might be better off with the majority of your time
spend with a music teacher than Elton John, for example.

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mortenvind
Are there any books with the same kinds of tasks that the author proposed to
his students? Would really like to improve my proofing skills.

