Don't Let Math Pull the Wool Over Your Eyes

Previous Topic Next Topic
 
classic Classic list List threaded Threaded
8 messages Options
Reply | Threaded
Open this post in threaded view
|

Don't Let Math Pull the Wool Over Your Eyes

Jerry Becker
Don't Let Math Pull the Wool Over Your Eyes
***************************************
From the Wall Street Journal, Saturday, January 5, 2013. See http://professional.wsj.com/article_email/SB20001424127887323374504578219873933502726-lMyQjAyMTAzMDAwNTEwNDUyWj.html?mod=wsj_valettop_email
**************************************
THE NUMBERS GUY
 
Don't Let Math Pull the Wool Over Your Eyes

By Carl Bialik

This column will make the case that many people, including holders of graduate degrees, professional researchers and even editors of scientific journals, can be too easily impressed by math. A mathematical model (Tpp = T0 - ŸT0d2f - ŸTpdf) is developed to describe sequential effects.

Did that second sentence make the first more persuasive? It did for most participants in a recent intriguing experiment whose result suggests people often interact with math in a way that isn't very logical. Other research has shown that even those who should be especially clear-sighted about numbers-scientific researchers, for example, and those who review their work for publication-are often uncomfortable with, and credulous about, mathematical material. As a result, some research that finds its way into respected journals-and ends up being reported in the popular press-is flawed.

In the latest study, Kimmo Eriksson, a mathematician and researcher of social psychology at Sweden's Mälardalen University, chose two abstracts from papers published in research journals, one in evolutionary anthropology and one in sociology. He gave them to 200 people to rate for quality-with one twist. At random, one of the two abstracts received an additional sentence, the one above with the math equation, which he pulled from an unrelated paper in psychology. The study's 200 participants all had master's or doctoral degrees. Those with degrees in math, science or technology rated the abstract with the tacked-on sentence as slightly lower-quality than the other. But participants with degrees in humanities, social science or other fields preferred the one with the bogus math, with some rating it much more highly on a scale of 0 to 100.

"Math makes a research paper look solid, but the real science lies not in math but in trying one's utmost to understand the real workings of the world," Prof. Eriksson said.

Several of the authors of the three papers whose material Prof. Eriksson harvested said they generally agreed with that conclusion. "Disciplines with less math emphasis could benefit from more exposure to mathematical logic so that when it is used it is accepted for its rigor rather than because it awes the reader," said Geoff Kushnick, co-author of the evolutionary anthropology paper, published in 2002.

Prof. Eriksson's finding, published in November in the journal Judgment and Decision Making under the title "The Nonsense Math Effect," is preliminary but unfortunately not surprising, other researchers said. It documents a familiar effect, said Daniel Kahneman, professor emeritus of psychology and public affairs at Princeton University. "People who know math understand what other mortals understand, but other mortals do not understand them. This asymmetry gives them a presumption of superior ability."

Prof. Kahneman and other scholars have documented how numbers can warp rather than enhance logical thinking. For example, German researchers asked 52 lawyers to propose sentences for hypothetical repeat shoplifters after having rolled dice to determine the hypothetical sentencing demand by prosecutors. Lawyers who rolled dice that showed a higher requested sentence tended to hand out longer sentences themselves, even with identical facts in the case and the knowledge that the demanded sentence was entirely random. Tying decisions to a proposed number, even when it is random or misguided, is known by psychologists as anchoring and helps explain why a "50% off" sale can seem so compelling even when the original price was vastly inflated.

Prof. Eriksson's study shows how people can stumble when exposed to math outside their field of expertise. Articles in scientific journals, however, typically are reviewed by experts who read the whole paper, not just abstracts. Yet even here, there is evidence that professional researchers often botch statistics in their work, but are allowed to publish problematic data. Writing in Nature last month, cell biologist David L. Vaux decried the continuing publication, including in Nature, of papers with problems such as miscalculated margins of error. "The fact that these scientifically sloppy papers continue to be published means that the authors, reviewers and editors cannot comprehend the statistics, that they have not read the paper carefully, or both," said Prof. Vaux, of the University of Melbourne in Australia.

Martin T. Wells, a biostatistician at Cornell University, has another explanation, chalking up occasional sloppiness in statistics to the pressure to publish early and often. "It's a bit frustrating," he said. "As a biostatistician you want to do things right, and some researchers just want to get off on the cheap analyzing data."

Alan Sokal, the physicist who in 1996 hoaxed a journal of cultural studies with an article he wrote as a jest that the journal published, called Prof. Eriksson's study "very interesting." He would like it replicated with a more credentialed group, such as university professors, who are more likely to review articles for publication.

Prof. Eriksson said he "would love to conduct a follow-up study with other samples," adding his paper didn't itself contain any deliberately faulty statistics to test whether readers would notice. "I wasn't clever enough to think of putting in some nonsense math of my own," he said.
------------------------------------
A version of this article appeared Jan. 5, 2013, on page A2 in some U.S. editions of The Wall Street Journal, with the headline: Don't Let Math Pull the Wool Over Your Eyes.
*******************************************
--
Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
625 Wham Drive
Mail Code 4610
Carbondale, IL  62901-4610
Phone:  (618) 453-4241  [O]
            (618) 457-8903  [H]
Fax:      (618) 453-4244
E-mail:   [hidden email]
Reply | Threaded
Open this post in threaded view
|

Re: Don't Let Math Pull the Wool Over Your Eyes

GS Chandy
Jerry Becker posted an 15, 2013 1:10 AM:

> ***************************************
> From the Wall Street Journal, Saturday, January
> 5, 2013. See
> http://professional.wsj.com/article_email/SB2000142412
> 7887323374504578219873933502726-lMyQjAyMTAzMDAwNTEwNDU
> yWj.html?mod=wsj_valettop_email
> **************************************
> THE NUMBERS GUY
>
> Don't Let Math Pull the Wool Over Your Eyes
> By Carl Bialik
>
Fascinating!  Researcher Nimmo Eriksson did a study  
in which he tagged on a "sentence containing a math equation (or something of that nature) to a totally unrelated passage (an abstract of some paper)".  

It appears that most participants, even those with advanced degrees, found the passage including the unrelated math sentence to be more convincing than the passage without the unrelated math sentence!
>
> "Math makes a research paper look solid, but the
> real science lies not in math but in trying one's
> utmost to understand the real workings of the
> world," Prof. Eriksson said.
>
But he DID find that those with degrees in math and
science to be less likely to be taken in.

>
> Those with degrees
> in math, science or technology rated the abstract
> with the tacked-on sentence as slightly
> lower-quality than the other. But participants
> with degrees in humanities, social science or
> other fields preferred the one with the bogus
> math, with some rating it much more highly on a
> scale of 0 to 100.
>
I.e., STEM may have some value - at least to lower
the possibility of the subject getting fooled by
something pretending to be scientific?

(I seem to recall, a couple of years ago, that a passage of utter gibberish pretending to be from some advanced technical discipline was highly rated by many who saw it - many of those also had advanced degrees in sociology and such).

GSC
Reply | Threaded
Open this post in threaded view
|

Re: Don't Let Math Pull the Wool Over Your Eyes

Haim-5
In reply to this post by Jerry Becker
Jerry P. Becker Posted: Jan 14, 2013 2:40 PM

>Alan Sokal, the physicist who in 1996 hoaxed a journal
>of cultural studies with an article he wrote as a jest
>that the journal published, called Prof. Eriksson's
>study "very interesting." He would like it replicated
>with a more credentialed group, such as university
>professors, who are more likely to review articles for
>publication.

   The notorious journal was "Social Text", published by Duke University Press.  This is the same Duke University of the infamous Gang of 88
http://en.wikipedia.org/wiki/Duke_lacrosse_case
The now famous article,
"Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity", may have been a hoax but it was certainly no jest.  "Transgressing the Boundaries" was a serious effort by Sokal to discredit "Social Text" and, by extension, to discredit the intellectual fraud that is Postmodernism.

   Sokal followed up with several books, including "Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science", "Beyond the Hoax: Science, Philosophy and Culture", "Intellectual Impostures", and a number of journal articles in which he discusses his intent.  Along with the famous,

"Higher Superstition"
http://www.amazon.com/Higher-Superstition-Academic-Quarrels-Science/dp/0801857074/ref=sr_1_1?ie=UTF8&qid=1358250132&sr=8-1&keywords=higher+superstition

Sokal's work is a well established part of what Wikipedia calls

"The Science Wars",
- -----------------------------------
http://en.wikipedia.org/wiki/Science_wars
In Higher Superstition: The Academic Left and Its Quarrels With Science (1994), the scientists Paul R. Gross and Norman Levitt attacked the anti-intellectual postmodernists, presented the shortcomings of relativism, and proposed that postmodernist critics knew little about the scientific theories they criticized and practiced poor scholarship for political reasons.
- ---------------------------

   "Poor scholarship for political reasons."  Now, there is a lovely turn of phrase that rather nicely characterizes what is laughingly known as education research.

Haim
No representation without taxation.
Reply | Threaded
Open this post in threaded view
|

Re: Don't Let Math Pull the Wool Over Your Eyes

Michael Paul Goldenberg
In reply to this post by Jerry Becker
No politics inform your criticism of education research or practice, of course.
Reply | Threaded
Open this post in threaded view
|

Re: Don't Let Math Pull the Wool Over Your Eyes

Haim-5
In reply to this post by Jerry Becker
MPG Posted: Jan 15, 2013 3:43 PM

>No politics inform your criticism of education research
>or practice, of course.

   Oh, my!  But you have been gone a long time.  I am the guy who points out that when it comes to education issues, it is all politics all the time.

   Specifically, I have asserted that there are no technical issues, whether in math education or gifted education or remedial education or, really, in any education field or practice.  Everybody knows what to do and how to do it.  In fact, that is the basis of "Haim's Challenge".

   You may recall that the issue comes up from time to time, why is there no technical discussion on pedagogy, math pedagogy or any other.  Plainly, it is because there is nothing to discuss.  Well, if there are no technical problems, what is driving the failure in education?

   All together now:  It's the politics, stupid.

Haim
No representation without taxation.
Reply | Threaded
Open this post in threaded view
|

Re: Don't Let Math Pull the Wool Over Your Eyes

Michael Paul Goldenberg
In reply to this post by Jerry Becker
Oh, sure. Your other tired hobby horse besides "The Education Mafia" and your pretense that you would take action against one or more of its members.

Boring. And as every teacher of mathematics who stops to consider teaching as more than the pouring of sacred truths into empty heads, baloney.

But nothing new there, either, from your oeuvre. You do make true part of Wayne's mantra about nothing new under the sun.
Reply | Threaded
Open this post in threaded view
|

Re: Don't Let Math Pull the Wool Over Your Eyes

GS Chandy
In reply to this post by Jerry Becker
Haim posted Jan 16, 2013 3:43 AM:

>
> MPG Posted: Jan 15, 2013 3:43 PM
>
> >No politics inform your criticism of education
> research
> >or practice, of course.
>
> Oh, my!  But you have been gone a long time.  I am
> am the guy who points out that when it comes to
> education issues, it is all politics all the time.
>
> Specifically, I have asserted that there are no
> no technical issues, whether in math education or
> gifted education or remedial education or, really, in
> any education field or practice.  Everybody knows
> what to do and how to do it.  In fact, that is the
> basis of "Haim's Challenge".
>
> You may recall that the issue comes up from time
> ime to time, why is there no technical discussion on
> pedagogy, math pedagogy or any other.  Plainly, it is
> because there is nothing to discuss.  Well, if there
> are no technical problems, what is driving the
> failure in education?
>
>    All together now:  It's the politics, stupid.
>
> Haim
> No representation without taxation.
>
"What is driving the failure in education?"

Oh, my!  You REALLY, TRULY want to learn the answer to your question?  

May I suggest that some 'honest research' would surely get you all the answers you need to this important question.  To do needed honest research, check out:
http://mathforum.org/kb/thread.jspa?threadID=2419536 .  (The attachments to the post indicate some practical tools that could help you do it, i.e., 'honest research'.  I should note that these practical tools are not quite enough: you should also really, truly WANT to do it - this is crucial).

You may also obtain some insights by looking at:
http://mathforum.org/kb/message.jspa?messageID=8070310  which also contains some useful ideas about 'honest research'.

GSC
("Still Shoveling!")
Reply | Threaded
Open this post in threaded view
|

Re: Don't Let Math Pull the Wool Over Your Eyes

kirby urner-4
In reply to this post by Haim-5
On Tue, Jan 15, 2013 at 2:13 PM, Haim <[hidden email]> wrote:

<< SNIP >>

>    Specifically, I have asserted that there are no technical issues, whether in math education or gifted education or remedial education or, really, in any education field or practice.  Everybody knows what to do and how to do it.  In fact, that is the basis of "Haim's Challenge".
>

I've never really understood "Haim's Challenge" is there has been
plenty of debate about pedagogical as well as andragogical techniques.

This whole thing about distance education and using a combination of
screens, keyboard, and site visits, is pretty much new ground.  The
Internet is in its infancy.

Or when you teach in a classroom and every student has a workstation
and free license to browse the Internet as the teacher is talking:
that raises its own pedagogical issues.

Twenty years ago, I was envisioning that by now Hewlett-Packard would
have entire classrooms where the teacher could

(a) put any student's screen on the big screen in front
(b) share one screen with all student screens
(c) lock down student keyboards and mouse temporarily
(d) allow students to share with other students in teams

and so on.  This never materialized.  We're seen a lot more activity
around "clickers" than I expected.

There's no agreement on basic content either?  Should Euclid's
Algorithm for the GCD be included in K-12?

I say "of course, no question about it".

But it's not there, in most curricula.  But then most curricula suck
to the high evens.

No mention of "tetravolumes" in the whole of K-12?  That's not a
school, that's a day care center (for the teachers).

Kirby



>    You may recall that the issue comes up from time to time, why is there no technical discussion on pedagogy, math pedagogy or any other.  Plainly, it is because there is nothing to discuss.  Well, if there are no technical problems, what is driving the failure in education?
>
>    All together now:  It's the politics, stupid.
>
> Haim
> No representation without taxation.