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#1 2009-02-01 01:46:48

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Lockhart's Lament

A very well put argument against the way maths is taught in schools:

http://www.maa.org/devlin/LockhartsLament.pdf

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#2 2009-02-02 02:18:23

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: Lockhart's Lament

I'd like to add: this really is very good.

Last edited by Daniel123 (2009-02-02 02:18:33)

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#3 2009-02-02 08:46:11

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,664

Re: Lockhart's Lament

A man after my own heart!

I like the article (but don't agree with everything). I hope it results in "shifting the pendulum" a little.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#4 2009-02-02 12:47:53

bossk171
Member
Registered: 2007-07-16
Posts: 305

Re: Lockhart's Lament

In my English 101 class I had to write an expository essay about anything I wanted (first draft due today) I sat down to start writing about fundamental flaws in mathematics education today. I quickly realized that I'm not a good enough to express everything I wanted to express about the subject and I opted to write about the disturbing role product placement plays in today's media.

After putting my finishing touches on my first draft last night, I checked this forum to see if I'd missed anything interesting and imagine how shocked I was to read exactly the essay I wanted to write. Absolutely phenomenal I printed it out and read it and was impressed by every word of it.

Just curious MathsIsFun, what parts didn't you agree with?


There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

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#5 2009-02-02 18:31:02

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,664

Re: Lockhart's Lament

I agree with the positive aspects ... playing with the concepts, thought-provoking questions, generally having fun, etc ... Yay ! This is the best way to learn. smile

I am sure it would be an absolute delight to have Paul Lockhart as a teacher.

But let's not "throw the baby out with the bath water" as the saying goes. An agreed-upon set of core skills are important ... for employers, Universities and society in general. Let us improve on that.

I would LOVE to read your essay bossk171 (if you ever finish it) ... or better still, what could we do to improve things?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#6 2009-02-03 02:35:37

bossk171
Member
Registered: 2007-07-16
Posts: 305

Re: Lockhart's Lament

My essay isn't very good, I'm not a very good writer (which is why I frequent Math-Is-Fun forums and not Boring-essays-that-I-have-to-write-because-my-English-teacher-told-me-so-and-I-just-want-to-get-through-English-101-so-can-eventually-graduate-and-get-a-good-job forums).

If it were about math I'd definitely post it here for some feedback, but it's just about product placement so I don't think it'll interest anyone.

I see what you're saying about throwing out the baby with the bathwater,  my biggest concern is with the de-emphasis on terminology. It might be boring to learn the vocab, but necessary for communicating your findings and interacting with others. I just started an accelerated math club of sorts at my local elementary school with nine 6th graders. I'd like to do exactly what this paper describes only we will be saying "tetrahedron" instead of "triangle thingies" Using correct terminology allows you work together to find solutions and that is essential to any exploratory math course. We won't, however, be taking vocab quizzes or anything ultra-lame like that.


There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

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#7 2009-02-03 08:48:43

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,664

Re: Lockhart's Lament

Yes, terminology makes it easier to discuss things and is important.

I try not to let it get in the way, though. I think it can be built up gradually as you learn. For example you can say "top" and "bottom" of a fraction, and then later on introduce "numerator" and "denominator" as you learn more (so you can say "common denominator" instead of "common bottom" I suppose smile )


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#8 2009-02-03 12:52:58

bossk171
Member
Registered: 2007-07-16
Posts: 305

Re: Lockhart's Lament

I agree 100% with that, MathsIsFun. I told the kids that I will always make my best effort to use the right terminology, but that they should be more concerned with conceptualization than terminology.


There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

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#9 2009-04-02 10:52:24

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,664

Re: Lockhart's Lament


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#10 2009-04-03 11:38:50

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Lockhart's Lament

The original pdf posted by Daniel123 is
very interesting.  I read the whole thing
word for word, and I don't read a lot, though
I am starting to read more.  My favorite
parts of his lament were the actual mathematical
examples he uses like the right triangle twirled
180 in the circle!!!  I think schools are
starting to do some of what he is proposing,
but they are having it as a separate course,
aside from the math course.  My son takes
some course that is mostly creative thinking and problem solving.   Unfortunately, the only
reason he's in the class is because he is
one of the advanced students, and gets
special time off to do that I think.  Kind of
not fair really for others who miss out.


igloo myrtilles fourmis

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#11 2009-04-03 22:32:46

integer
Member
Registered: 2008-02-21
Posts: 79

Re: Lockhart's Lament

Suppose:
Your are a teacher.
You have two students. 
Each student brings you a paper with some "art work" on it.
Paper 1 shows a railroad track, and looks as if it were a picture.
It is not a tracing.  You know it is the result of the students own work.
You know that because you saw the students doing it.
Paper 2 shows a free hand drawn rectangle with diagonals connecting
the corners.

The question.
How do you grade the papers?  Which student should receive a promotion.


Suppose:
You have 2 employees.
You are charged with getting getting life saving food and water to a village
devastated by a natural diaster.
Your instructions to the employees.  Each is to load a truck with food & water
and get it to those who need it.

Hours later:
Employee 1 has truck 1 about 1/4 filled, nicely stacked, neatly arranged, and
looking very good.
Employee 2 has truck 2 filled, but it is stuffed, packed and obvious a few ruined
containers.

Which employee is going to mean the most to you?
Which one would you recommend for a promotion.

It is obvious that employee 1 enjoys his work and loves what he does.
Employee 2 just gets the job done.

Who would you want on your team.?

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#12 2009-04-04 02:12:27

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Lockhart's Lament

If it is a life saving disaster, then the faster #2 may be better even if
there is 1% loss of goods in careless handling.

I didn't know teachers gave promotions, but I think the traintracks should
get the higher grade since the number of pencil strokes is far greater.  If
the rectangle with diagonals was filled out more for beauty, that would be
nice.


igloo myrtilles fourmis

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#13 2009-04-04 05:02:52

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Lockhart's Lament

Back on the topic of Daniel123's pdf.
Einstein once said that:
...imagination embraces the entire world, and all there ever will be to know and understand.
So imagination should be encouraged if Einstein is right, at least more than
it is now in our schools.  Some compromise would be nice, but I think the
two courses idea, where one is rigid, and the other is freeform is a good way to do it because then you get benefits of both methods.


igloo myrtilles fourmis

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#14 2009-04-05 08:47:39

random_fruit
Member
Registered: 2008-12-25
Posts: 39

Re: Lockhart's Lament

I'd like to see the idea expressed by Paul Lockhart taken into English schools.  Every week I work with electricians who cannot recall Ohm's law (V = IR) and who cannot transpose it (I = V/R) and then who cannot use it to predict the current (I) given the voltage (V = 230) and a resistance (R = 0.35).  When I tell them to divide 230 by 0.35 they cannot operate the calculator in front of me to get the arithmetic result (go on, try for yourself... did you get 657?)  This matters for electrical safety! 

And so very often those who left school at 16 in England can't do this simple piece of maths, and think its nasty and evil and what they became an electrician to avoid.  If Paul Lockhard's approach will overcome this depressing mess, I'd think it wonderful, and I feel his point of view should be given a chance to make a difference.

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#15 2009-04-05 09:37:08

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,664

Re: Lockhart's Lament

Quite amazing, random_fruit! Surely electricians must be smarter than that?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#16 2009-04-15 02:05:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Lockhart's Lament

Hi random_fruit;

   Take heart, it is much worse over here, where a high school senior math teacher just told me that none of his students were capable of making change from a cash register. None were able to compute a 15% tip even though they are being taught AP Calculus. Something called "Teaching to the test". Part of the new philosophy that it is cool to be stupid and uncool to be a nerd.

bobbym


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#17 2014-10-06 16:07:02

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Lockhart's Lament

I think the book is A !athematician's lament

I read it yesterday!


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#18 2014-10-06 20:44:41

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Lockhart's Lament

How does it end?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#19 2014-10-07 00:42:21

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Lockhart's Lament

End?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#20 2014-10-07 00:46:58

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Lockhart's Lament

o0l4I7O.gif


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#21 2014-10-07 02:21:36

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Lockhart's Lament

I do not see the joke.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#22 2014-10-07 02:25:10

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Lockhart's Lament

Did you read the first post?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#23 2014-10-07 02:27:19

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Lockhart's Lament

Daniel123 wrote:

A very well put argument against the way maths is taught in schools:

http://www.maa.org/devlin/LockhartsLament.pdf

That is true.

I read the full thing and I loved it.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#24 2014-10-07 02:36:33

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Lockhart's Lament

Did you read the one on EM?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#25 2014-10-07 02:56:51

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Lockhart's Lament

Where?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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