**ARTICLES & ANNOUNCEMENTS (NATIONAL FOCUS)**

**(1) "Benoît Mandelbrot, Novel
Mathematician, Dies at 85" by Jascha Hoffman**

Source: The New York Times - 16 October 2010

URL: http://www.nytimes.com/2010/10/17/us/17mandelbrot.html

Benoît B. Mandelbrot, a maverick mathematician who developed
the field of fractal geometry and applied it to physics, biology,
finance and many other fields, died on Thursday [October 14] in
Cambridge, Mass. He was 85...

Dr. Mandelbrot coined the term "fractal" to refer to a new
class of mathematical shapes whose uneven contours could mimic the
irregularities found in nature.

"Applied mathematics had been concentrating for a century on
phenomena which were smooth, but many things were not like that: the
more you blew them up with a microscope the more complexity you found,"
said David Mumford, a professor of mathematics at Brown University. [See
article below about Mumford's latest honor.] "He was one of the primary
people who realized these were legitimate objects of study."

In a seminal book, The Fractal Geometry of Nature, published in
1982, Dr. Mandelbrot defended mathematical objects that he said others
had dismissed as "monstrous" and "pathological." Using fractal geometry,
he argued, the complex outlines of clouds and coastlines, once
considered unmeasurable, could now "be approached in rigorous and
vigorous quantitative fashion."

For most of his career, Dr. Mandelbrot had a reputation as an
outsider to the mathematical establishment. From his perch as a
researcher for I.B.M. in New York, where he worked for decades before
accepting a position at Yale University, he noticed patterns that other
researchers may have overlooked in their own data, then often swooped in
to collaborate.

"He knew everybody, with interests going off in every possible
direction," Professor Mumford said. "Every time he gave a talk, it was
about something different"...

In the 1950s, Dr. Mandelbrot proposed a simple but radical way
to quantify the crookedness of such an object by assigning it a "fractal
dimension," an insight that has proved useful well beyond the field of
cartography.

Over nearly seven decades, working with dozens of scientists,
Dr. Mandelbrot contributed to the fields of geology, medicine, cosmology
and engineering. He used the geometry of fractals to explain how
galaxies cluster, how wheat prices change over time and how mammalian
brains fold as they grow, among other phenomena.

His influence has also been felt within the field of geometry,
where he was one of the first to use computer graphics to study
mathematical objects like the Mandelbrot set, which was named in his
honor.

"I decided to go into fields where mathematicians would never
go because the problems were badly stated," Dr. Mandelbrot said. "I have
played a strange role that none of my students dare to take"...

Instead of rigorously proving his insights in each field, he
said he preferred to "stimulate the field by making bold and crazy
conjectures" - and then move on before his claims had been verified.
This habit earned him some skepticism in mathematical circles.

"He doesn't spend months or years proving what he has
observed," said Heinz-Otto Peitgen, a professor of mathematics and
biomedical sciences at the University of Bremen. And for that, he said,
Dr. Mandelbrot "has received quite a bit of criticism."

"But if we talk about impact inside mathematics, and
applications in the sciences," Professor Peitgen said, "he is one of the
most important figures of the last 50 years"...

[For more details, visit the NYT Web site above.]

.......................

Related articles:

**(a) "Benoît Mandelbrot Obituary" by
Nigel Lesmoir-Gordon**

**
Source: Guardian - 17 October 2010**

http://www.guardian.co.uk/science/2010/oct/17/benoit-mandelbrot-obituary

...Mandelbrot, born into a Lithuanian-Jewish family living in
Warsaw, showed an early love for geometry and excelled at chess: he
later admitted that he did not think the game through logically, but
geometrically. Maps were another inspiration. His father was crazy about
them, and the house was full of them...

At the start of his groundbreaking work, The Fractal Geometry
of Nature, [Mandelbrot] asks: "Why is geometry often described as cold
and dry? One reason lies in its inability to describe the shape of a
cloud, a mountain, a coastline or a tree." The fractal geometry that he
developed helps us to describe nature as we actually see it, and so
expand our way of thinking.

The world we live in is not naturally smooth-edged and
regularly shaped like the familiar cones, circles, spheres and straight
lines of Euclid's geometry: it is rough-edged, wrinkled, crinkled and
irregular. "Fractals" was the name he applied to irregular mathematical
shapes similar to those in nature, with structures that are self-similar
over many scales, the same pattern being repeated over and over.
Fractal geometry offers a systematic way of approaching phenomena that
look more elaborate the more they are magnified, and the images it
generates are themselves a source of great fascination...

While the ideas behind fractals, iteration and self-similarity
are ancient, it took the coining of the term "fractal geometry" in 1975
and the publication of The Fractal Geometry of Nature in French in the
same year to give the quest an identity. As Mandelbrot put it, "to have a
name is to be" -- and the field exploded...

______________________

**(2) Mathematician David
Mumford to Receive National Medal of Science**

Source (Para. 1): The White House

Source: Brown University

URL (WH): http://www.whitehouse.gov/the-press-office/2010/10/15/president-obama-honors-nations-top-scientists-and-innovators

URL (BU): http://news.brown.edu/pressreleases/2010/10/mumford

On Friday, October 15, President Obama named ten eminent
researchers as recipients of the National Medal of Science, and three
individuals and one team as recipients of the National Medal of
Technology and Innovation, the highest honors bestowed by the United
States government on scientists, engineers, and inventors. The National
Medal of Science was established by Congress in August 1959 and is to be
conferred directly by the President. The recipients will receive their
awards from President Obama at a White House ceremony later this year.

One of the recipients, David Mumford, is a professor emeritus
of applied mathematics at Brown University. "As collaborator and
catalyst, David Mumford was an early contributor to fields of inquiry
that have blossomed at Brown--brain science, computer vision,
neurobiology, cognitive science, the biology and psychology of
perception--and to his own areas of pure and applied mathematics," said
Brown President Ruth J. Simmons. "He continues to inspire collaborators
in many fields, former students now in productive careers, and his
professional colleagues in the United States and abroad."

Mumford’s contributions to mathematics fundamentally changed
algebraic geometry and brought him a variety of honors including the
Fields Medal, the highest award in mathematics (1974), and a MacArthur
Foundation fellowship (1987-92). He is perhaps best known for inventing
geometric invariant theory, a key tool in moduli theory, the study of
how the geometric structures in algebraic geometry vary. His subsequent
studies on the moduli space of curves have been an important tool in
string theory.

"For the first half of my career--about 20 years--I worked in
pure math, although I always had lots of interests outside of that,”
Mumford said. A conversation with a collaborator in Italy led to his
decision to turn toward applied mathematics, which he did while at
Harvard. His interest in applied math and his dedication to a
collaborative approach helped develop "a really terrific group jointly
at Harvard, MIT, and Brown." He joined the Brown faculty in 1996 as a
University professor in the Division of Applied Mathematics.

Mumford’s work in computer vision and pattern theory introduced
new mathematical tools and models from analysis and differential
geometry. His work in neurobiology in collaboration with Tai Sing Lee
led to new insights about the nature of computation in the human brain,
and he helped start Brown’s vigorous interdisciplinary Brain Science
Program. He is now turning his attention once again to pure mathematics
and to the history of mathematics.

He also maintains collaborations and communication with
professional colleagues, whose work he values and understands. While
honored and grateful for his most recent honor, Mumford keeps those
colleagues in his thoughts. "I did some nice things, but so did a lot of
other people," he said. I’m pleased that this medal will bring
attention to the important role of science and mathematics in our
society."

______________________

**(3) New Meta-analysis Finds
Negligible Gender Differences in Mathematics Performance **

Source: University of Wisconsin, Madison - 11 October 2010

URL: http://gse.berkeley.edu/admin/publications/news/1010linn.html

The mathematical skills of boys and girls, as well as of men
and women, are substantially equal, according to a new examination of
existing studies published in the current issue of Psychological
Bulletin.

One portion of the new study looked systematically at 242
articles that assessed the mathematics skills of 1,286,350 people, says
chief author Janet Hyde, a professor of psychology and women's studies
at the University of Wisconsin-Madison.

These studies, all published between 1990 and 2007, looked at
people from grade school to college and beyond. A second portion of the
new study examined the results of several large, long-term scientific
studies, including the National Assessment of Educational Progress.

In both cases, Hyde says, the difference between the two sexes
was so close as to be meaningless.

Sara Lindberg, now a postdoctoral fellow in women's health at
the UW-Madison School of Medicine and Public Health, was the primary
author of the meta-analysis.

The idea that both genders have equal math abilities is widely
accepted among social scientists, Hyde adds, but word has been slow to
reach teachers and parents, who can play a negative role by guiding
girls away from math-heavy sciences and engineering. "One reason I am
still spending time on this is because parents and teachers continue to
hold stereotypes that boys are better in math, and that can have a
tremendous impact on individual girls who are told to stay away from
engineering or the physical sciences because 'Girls can't do the math.'"

Scientists now know that stereotypes affect performance, Hyde
adds. "There is lots of evidence that what we call 'stereotype threat'
can hold women back in math. If, before a test, you imply that the women
should expect to do a little worse than the men, that hurts
performance. It's a self-fulfilling prophecy.

"Parents and teachers give little implicit messages about how
good they expect kids to be at different subjects," Hyde adds, "and that
powerfully affects their self-concept of their ability. When you are
deciding about a major in physics, this can become a huge factor."

Hyde hopes the new results will slow the trend toward
single-sex schools, which are sometimes justified on the basis of
differential math skills. It may also affect standardized tests, which
gained clout with the passage of No Child Left Behind, and tend to
emphasize lower-level math skills such as multiplication, Hyde says.
"High-stakes testing really needs to include higher-level
problem-solving, which tends to be more important in jobs that require
math skills. But because many teachers teach to the test, they will not
teach higher reasoning unless the tests start to include it."

The new findings reinforce a recent study that ranked gender
dead last among nine factors, including parental education, family
income, and school effectiveness, in influencing the math performance of
10-year-olds.

Hyde acknowledges that women have made significant advances in
technical fields. Half of medical school students are female, as are 48
percent of undergraduate math majors. "If women can't do math, how are
they getting these majors?" she asks.

Because progress in physics and engineering is much slower, "we
have lots of work to do," Hyde says. "This persistent stereotyping
disadvantages girls. My message to parents is that they should have
confidence in their daughters' math performance. They need to realize
that women can do math just as well as men. These changes will encourage
women to pursue occupations that require lots of math."

_____________________

**(4) Common Core State
Standards for Mathematics--Implementation Support
from NCTM**

Source: National Council of Teachers of Mathematics (NCTM)

URL: http://www.nctm.org/news/highlights.aspx?id=26084&blogid=6806

The National Council of Teachers of Mathematics (NCTM) has
posted a PowerPoint file on its Web site "to inform teachers and to
support them in implementation of the Common Core State Standards
[(CCSS)]. Other presentations for grade bands are under development and
will be made available soon." Download the file from the Web page above.

Also on this Web page is a link to the joint statement in
support of the CCSS issued by NCTM, the Association of Mathematics
Teacher Educators (AMTE), the Association of State Supervisors of
Mathematics (ASSM), and the National Council of Supervisors of
Mathematics.

For more information about NCTM's initiatives related to the
CCSS, read NCTM President J. Michael Shaughnessy's report located at http://www.nctm.org/about/content.aspx?id=26483

__________________________

**(5) "Making Math Lessons as
Easy as 1, Pause, 2, Pause..." by Winnie Hu**

Source: The New York Times - 30 September 2010

URL: http://www.nytimes.com/2010/10/01/education/01math.html

By the time they get to kindergarten, children in this
well-to-do suburb [(Franklin Lakes, N.J.)] already know their numbers,
so their teachers worried that a new math program was too easy when it
covered just 1 and 2--for a whole week.

"Talk about the number 1 for 45 minutes?" said Chris Covello,
who teaches 16 students ages 5 and 6. "I was like, I don't know. But
then I found you really could. Before, we had a lot of ground to cover,
and now it's more open-ended and gets kids thinking."

The slower pace is a cornerstone of the district's new approach
to teaching math, which is based on the national math system of
Singapore and aims to emulate that country's success by promoting a
deeper understanding of numbers and math concepts. Students in Singapore
have repeatedly ranked at or near the top on international math exams
since the mid-1990s.

Franklin Lakes, about 30 miles northwest of Manhattan, is one
of dozens of districts, from Scarsdale, N.Y., to Lexington, Ky., that in
recent years have adopted Singapore math, as it is called, amid growing
concerns that too many American students lack the higher-order math
skills called for in a global economy.

For decades, efforts to improve math skills have driven schools
to embrace one math program after another, abandoning a program when it
does not work and moving on to something purportedly better. In the
1960s there was the "new math," whose focus on abstract theories spurred
a back-to-basics movement, emphasizing rote learning and drills. After
that came "reform math," whose focus on problem solving and conceptual
understanding has been derided by critics as the "new new math."

Singapore math may well be a fad, too, but supporters say it
seems to address one of the difficulties in teaching math: all children
learn differently. In contrast to the most common math programs in the
United States, Singapore math devotes more time to fewer topics, to
ensure that children master the material through detailed instruction,
questions, problem solving, and visual and hands-on aids like blocks,
cards and bar charts. Ideally, they do not move on until they have
thoroughly learned a topic.

Principals and teachers say that slowing down the learning
process gives students a solid math foundation upon which to build
increasingly complex skills, and makes it less likely that they will
forget and have to be retaught the same thing in later years.

And with Singapore math, the pace can accelerate by fourth and
fifth grades, putting children as much as a year ahead of students in
other math programs as they grasp complex problems more quickly...

[Visit http://www.nytimes.com/2010/10/01/education/01math.html
to read the rest of this informative article.]