**ARTICLES & ANNOUNCEMENTS (CALIFORNIA FOCUS) **

**(1) California Mathematics
Council Seeks Videos of Exemplary Teaching**

**Source: **John Leamy, Mathematics Professor,
Columbia College

The California Mathematics Council (CMC) Awards Committee
invites you to submit a short video clip of excellent mathematics
teaching that we can post on the CMC website (http://www.cmc-math.org/) as an aid
to teachers seeking examples of outstanding teaching, as well as to
those who are preparing videos as part of the application process for
the Presidential Award for Excellence in Mathematics and Science
Teaching (PAEMST). (Please see http://www.cmc-math.org/PAEMST
for more information about this award; applications should be
available at http://www.paemst.org/controllers/app.cfc?method=view
around November 1.)

If anyone is aware of or has a collection of videos of classroom
teachers modeling excellent instructional techniques, please contact
Sandie Gilliam at Colorado College (sandie.gilliam@comcast.net)
or John Leamy at Columbia College (__leamyj@yosemite.edu__). We are
able to edit videos to highlight specific parts, so video length is
not an issue. Because of our proposed use, the videos would have to be
authorized for public dissemination.

_______________________________

**(2) State Schools Chief
Jack O'Connell Releases Revised Dropout and Graduation Rates Using
Individual Student-Level Data**

**Source: **California Department of Education

URL: http://www.cde.ca.gov/nr/ne/yr08/yr08rel131.asp

Last Thursday, State Superintendent of Public Instruction Jack
O'Connell released revised dropout and graduation rates for the 2006-07
school year that for the first time were compiled using Statewide
Student Identifiers (SSID).

"The revised graduation rate is up slightly to 67.7 percent and
the dropout rate is down nearly three points to 21.5 percent for
2006-07," said O'Connell. "Of course, I do not want to see any student
drop out of school--graduating from high school is critically important
for all students' future success. However, I am pleased that districts
are finding even more of our students still in our public school
system. The updated data indicate that our use of Statewide Student
Identifiers is working as intended. School districts now are highly
motivated to communicate with each other to track down students lost in
the system to determine their status."

Each K-12 student in a California public school is entered into
the SSID system and assigned an individual, yet non-personally
identifiable, number that is maintained throughout the student's
academic career. SSIDs allow for more accurate tracking of how many
students are or are not completing their education.

The dropout rates declined among two subgroups of concern in the
state's efforts to close the achievement gap. Among African American
students, the revised dropout rate is 36.2 percent, down 5.4 percent
from the 41.6 percent reported in July. Among Latino students, the
dropout rate is now 27.4 percent, down 2.9 percent from the July
report.

Students counted as dropouts include students who are known
dropouts and students considered "lost transfers," or students who
indicated they were transferring to another school but then were not
reported as enrolled anywhere else. The revised rates show 3,000 fewer
students reported as known dropouts and 14,000 fewer students reported
as lost transfers.

The revised rates also include an update on the number of
students who are neither graduates nor dropouts, now at 10.8 percent.
The latter group consists of students who completed or withdrew from
school, such as students who transferred to a private school, left the
state, took the General Educational Development Test (GED) to earn a
California High School Equivalency Certificate, or became a
"completer," such as a special education student who received a
certificate of completion or other credential in lieu of a diploma.
Each student, whether they graduated, withdrew from, or completed
school is assigned one of 28 "withdrawal codes."

The 2006-07 dropout rate cannot be compared to the prior year's
dropout rate of 13 percent because the numbers are based on different
information. Before SSIDs, dropout rates were derived using only
aggregate data of enrollment and dropouts collected annually through
the California Basic Educational Data System. Now, individual
student-level data allow districts and the state to collect and report
what becomes of students who leave school...

SSIDs will eventually be tracked through the California
Longitudinal Pupil Achievement Data System, or CALPADS, which will
maintain longitudinal, individual student-level data including student
demographics, program participation, grade level, enrollment, course
enrollment and completion, discipline, state assessment, teacher
assignment, and other data required to meet state and federal reporting
requirements. CALPADS is scheduled to be fully implemented with all
districts in the 2009-10 school year. Until student-identifier data are
collected over four years, CDE will still be reporting an estimated
four-year graduation rate and a derived four-year dropout rate...

Senate Bill 1453, authored by former state Senator Dede Alpert,
was signed into law in September 2002 to require the assignment of
SSIDs. Local educational agencies have completed assigning all
California kindergarten through grade twelve public school students a
SSID. To download state-, county-, district-, and school-level dropout
data, please visit CDE's DataQuest at http://dq.cde.ca.gov/dataquest/
Downloadable data files will be uploaded in about two weeks and will
be available at http://www.cde.ca.gov/ds/sd/cb/studentdatafiles.asp

__________________________________________________

**ARTICLES & ANNOUNCEMENTS (NATIONAL FOCUS) **

**(1) Top 14 Science
Questions Facing America: Responses from John McCain and Barack Obama**

**Source**: Science Debate 2008

**URL**: http://www.sciencedebate2008.com/

U.S. Presidential Candidates John McCain and Barack Obama have
both submitted responses to questions posed by Science Debate 2008 on
the following topics: innovation, climate change, energy, education,
national security, pandemics and biosecurity, genetics, stem cells,
ocean health, water, space, scientific integrity, research, and health.

The candidates' responses appear side by side on the Web site
above.

_______________

__Note 1__: All candidates for Congress on the ballot in
November 2008 are being invited to let voters know where they stand on
health and research by filling out a brief questionnaire. Visit http://www.yourcandidatesyourhealth.org/
to search for candidate responses. http://www.yourcandidatesyourhealth.org/presidential.php
contains the responses of presidential candidates McCain and Obama.

__Note 2__: For a summary of John McCain's and Barack Obama's
education platforms, see *Education Week's* "McCain, Obama Spar
on Education" at http://www.edweek.org/ew/articles/2008/09/17/04prez_ep.h28.html

___________________________

**(2) "As Easy as 1, 2, 3:
Number Sense Correlates with Test Scores"**

**Source: **The** **Johns Hopkins
University** **

**URL**: http://www.jhu.edu/news/home08/sep08/number_sense.html

Knowing how precisely a high school freshman can estimate the
number of objects in a group gives you a good idea how well he has done
in math as far back as kindergarten, researchers at The Johns Hopkins
University found.

Good "number sense" at age 14 correlates with higher scores on
standardized math tests throughout a child's life, and weaker "number
sense" at 14 predicts lower scores on standardized tests, says Justin
Halberda, assistant professor of psychological and brain sciences in
the university's Krieger School of Arts and Sciences.

"We discovered that a child's ability to quickly estimate how
many things are in a group significantly correlates with that child's
performance in school math for every single year, reaching all the way
back to when he or she was in kindergarten," Halberda said.

Halberda teamed up on the research with colleagues Michele
Mazzocco, professor of psychiatry and behavioral sciences at Johns
Hopkins and Lisa Feigenson, Johns Hopkins assistant professor of
psychological and brain sciences.

Though people often think of mathematics as a pinnacle
intellectual achievement of humankind, research reveals that some
intuition about numbers, counting, and mathematical ability is basic to
almost all animals. For example, creatures that gather or hunt for
food keep track of the approximate number of food items they procure in
order to return to the places where they get the most sustenance.
Humans share this very basic "number sense," allowing them, at a
glance, to estimate the number of people in a subway car or bus,
Halberda says.

The Johns Hopkins team wondered whether this basic, seemingly
innate number sense had any bearing on the formal mathematics that
people learn in school. So the researchers asked 64 14-year-olds to
look at flashing groups of yellow and blue dots on a computer screen
and estimate which dots were more numerous. Though most of the children
easily arrived at the correct answer when there were (for example) only
10 blue dots and 25 yellow ones, some had difficulty when the number
of dots in each set was closer together. Those results helped the
researchers ascertain the accuracy of each child's individual "number
sense."

They then examined the teenagers' record of performance in
school math all the way back through kindergarten, and found that
students who exhibited more acute number sense had performed at a
higher level in mathematics than those who showed weaker number sense,
even controlling for general intelligence and other factors.

"What this seems to mean is that the very basic number sense
that we humans share with animals is related to the formal mathematics
that we learn in school," Halberda concludes. "The number sense we
share with the animals and the formal math we learn in school may
interact and inform each other throughout our lives."

Though the team found this strong correlation between number
sense and scholastic math achievement, Halberda cautions against
concluding that success or failure in mathematics is genetically
determined and, therefore, immutable.

"There are many factors that might affect a person's performance
in school mathematics," Halberda says, "What is exciting in our result
is that success in formal mathematics and simple math intuitions
appear to be related."

Future directions for research include investigating the
trainability of one's number sense and seeing how early help in number
sense could affect later formal math learning.

Funding for this research was provided by the National
Institutes of Health.

**Watch a Video of the Study Task:**

In this video clip (http://tinyurl.com/52y6ah),
entitled "Spots Before Their Eyes," you will see three students taking
the numerical acuity assessment. Each trial involves a very brief
flash of blue and yellow dots. For each flash, the students are
deciding whether there are more blue or more yellow dots. The full
assessment lasts ten minutes. From the students performance, the
researchers are able to determine the acuity of their "number sense"
and then correlate it with school math performance.

**Test Your Approximate Number Sense:** Follow
this link to an interactive test available on *The* *New York
Times* website: __http://tinyurl.com/5jxs9k__

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

__Related Articles:__

**(a) "How One's 'Number
Sense' Helps with Mathematics" by Rob Stein**

**Source**: *Washington Post* - 8 September
2008

**URL**: __http://www.washingtonpost.com/wp-dyn/content/story/2008/09/07/ST2008090701940.html
__

**(b) "Gut Instinct's
Surprising Role in Math" by Natalie Angier**

**Source**: *The New York Times* - 16
September 2008

**URL**: http://www.nytimes.com/2008/09/16/science/16angi.html?em

Excerpt:

Given the antiquity and ubiquity of the nonverbal number sense,
the researchers were impressed by how widely it varied in acuity. There
were kids with fine powers of discrimination, able to distinguish
ratios on the order of 9 blue dots for every 10 yellows, Dr. Feigenson
said. "Others performed at a level comparable to a 9-month-old," barely
able to tell if five yellows outgunned three blues. Comparing the
acuity scores with other test results that Dr. Mazzocco had collected
from the students over the past 10 years, the researchers found a
robust correlation between dot-spotting prowess at age 14 and strong
performance on a raft of standardized math tests from kindergarten
onward. "We can’t draw causal arrows one way or another," Dr. Feigenson
said, "but your evolutionarily endowed sense of approximation is
related to how good you are at formal math."

The researchers caution that they have no idea yet how the two
number systems interact. Brain imaging studies have traced the
approximate number sense to a specific neural structure called the
intraparietal sulcus, which also helps assess features like an object’s
magnitude and distance. Symbolic math, by contrast, operates along a
more widely distributed circuitry, activating many of the prefrontal
regions of the brain that we associate with being human. Somewhere,
local and global must be hooked up to a party line.

Other open questions include how malleable our inborn number
sense may be, whether it can be improved with training, and whether
those improvements would pay off in a greater appetite and aptitude for
math. If children start training with the flashing dot game at age 4,
will they be supernumerate by middle school?...

________________________________

**(3)** **New
Study Shows the Unintended Consequences of Moving More Pupils Into
Eighth Grade Algebra and Other Advanced Math Classes **

**Source: ** The Brookings Institution

**URL**: http://tinyurl.com/4xnjah**
**

**URL**: http://www.brookings.edu/reports/2008/0922_education_loveless.aspx

**URL** (Report): http://tinyurl.com/3mcvv6** **

A new report from the Brown Center on Education Policy at the
Brookings Institution finds that the nation's push to challenge more
students by placing them in advanced math classes in eighth grade has
had unintended and damaging consequences, as some 120,000
middle-schoolers are now struggling in advanced classes for which they
are woefully unprepared.

"The 'democratization of algebra' sounds like a worthy goal--it
certainly stems from good intentions," says Tom Loveless, the Brown
Center's director and author of the new study, which is being released
as an advance excerpt of the 2008 Brown Center Report on American
Education. But, he adds, "when a large number of students who don't
even know basic arithmetic are placed in classes with students several
grade levels ahead of them, the result is false democratization. That's
bad for the misplaced students, and it's bad for their well-prepared
classmates too."

Algebra in eighth grade was once reserved for mathematically
gifted students. But a campaign to extend algebra to many more eighth
graders, which began in the 1990s on the grounds that greater equity
and future opportunities require broader access to algebra, has had
considerable success: The proportion of eighth graders taking algebra
nearly doubled from 1990 to 2007, reaching 31 percent, and today more
U.S. eighth graders take algebra than any other math course. Until now,
however, no empirical evidence has existed to demonstrate whether the
push for universal eighth- grade algebra is a good idea, particularly
for students who have weak math skills.

The new Brown Center study tackles this question by examining
rarely used research data from the National Assessment of Educational
Progress (NAEP). Unlike most NAEP data, these restricted- use files
allow investigators who have obtained a license to drill down and
examine student-level information on a nationally representative sample
of 160,000 eighth graders.

The results are sobering. Between 2000 and 2005, as enrollment in
advanced math classes rose among eighth-graders and enrollment in
basic math declined, there was a significant jump in the percentage of
very low scoring students in advanced courses. Among students in the
bottom 10 percent nationally on the NAEP math test, enrollment in
advanced math classes rose from 8.0 percent in 2000 to 28.6 percent in
2005. The percentage of low achievers enrolled in basic courses fell
from 73.7 to 46.3 percent.

During the same period, students in the 10th percentile and below
more than doubled as a proportion of those in advanced classes, the
study finds, rising from 3 percent in 2000 to 7.8 percent in 2005. That
might at first glance seem to be a trivial percentage, but it adds up
to a significant number of students–about 120,000 nationwide.

Indeed, Loveless, himself a former public school teacher, notes
that having even two children performing significantly below grade
level in a class poses problems for classroom instructors, who may
water down instruction as a result. That can be bad news for the
well-prepared classmates of misplaced students. "Well prepared students
need a real algebra class, not a fake one teaching elementary school
mathematics," the report says.

The Brown Center study illustrates just how far "misplaced"
students lag behind their peers in advanced math classes. Despite being
enrolled in Algebra I, Geometry, and Algebra II, misplaced eighth
graders have NAEP scores well below average for *fourth*
graders...

The study also gives detailed information about the
characteristics of these misplaced students, their families, and their
schools. It finds that they are disproportionately black and Hispanic;
have parents whose own education is below the national average; come
from low-income households; attend large urban schools with
predominantly low socioeconomic status populations; and have math
teachers with less experience and mathematics training than the typical
teacher of advanced math students in eighth grade.

"No element of this story is educationally sound," the report
says. "No social benefit can be produced by placing students in classes
for which they are unprepared." It also notes that hundreds of
thousands of well-prepared students--"also predominantly black,
Hispanic, or poor"--are sitting in the same classrooms as misplaced
students and are "equally deserving of a good education."

The study makes a variety of reform recommendations that would
create a more realistic algebra policy, from early intervention and
teaching of basic skills to new research that tests the effectiveness
of different approaches to math remediation. As things stand, however,
the report concludes, the push for universal eighth grade algebra "is
creating more problems than it solves."

"This is not a call to lower expectations for what students can
learn," Loveless emphasizes. "Instead we have to give more students the
preparation they need to succeed in algebra. That won't be achieved by
designating an arbitrary grade in which all students are swept into an
algebra course, then turning a blind eye to the troubling results."

For a full copy of the report, visit http://tinyurl.com/3mcvv6

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

__Related Article__:

**"Low Performers Found Unready to
Take Algebra"** by Sean Cavanagh

**Source: ***Education Week* - 22 September
2008

**URL**: http://www.edweek.org/ew/articles/2008/09/24/05dilute_ep.h28.html

This article goes into more detail regarding the study's results
and implications, and includes reactions from Jeremy Kilpatrick
(University of Georgia) and Bob Moses (the Algebra Project).

_______________________________________

**(4) Titanic Primes
Raced to Win $100,000 Research Award**

**Source**: GIMPS (Great Internet Mersenne Prime
Search)

**URL**: http://www.mersenne.org/m45and46.htm
and http://www.mersenne.org/prime.htm

Researchers have discovered the two largest known prime numbers,
a whopping 12,978,189 and 11,185,272 digits long, as part of a 12 year
old world-wide volunteer computing project, the Great Internet
Mersenne Prime Search ("GIMPS"). The primes can be written shorthand as
2^43,112,609 - 1 and 2^37,156,667 - 1.

A nearly decade-long competition for a $100,000 award from the
Electronic Frontier Foundation ended closely when the larger prime
surfaced on a UCLA computer managed by Edson Smith just two weeks
before the second prime was found by Hans-Michael Elvenich's computer
in Langenfeld near Cologne, Germany. Both are among the 100,000
computers in GIMPS PrimeNet, a "grass-roots supercomputer" as *Science*
magazine describes it, which has been running continuously since 1996
and performs 29 trillion calculations per second.

"We're proud be to participants in GIMPS and grateful to the
UCLA Mathematics Department for providing computational resources to
the project," said Edson Smith, Computing Manager. Hans-Michael
Elvenich, a German electrical engineer and prime number enthusiast,
adds, "After four years of searching for a prime on GIMPS, finally a
great success!"

"These exciting discoveries are literally at the Internet's
'electronic frontier,'" says PrimeNet inventor, Scott Kurowski, a
software technologist in San Diego, California. "Developing
technologies and methods to apply the incredibly vast power of
cooperative research computing is why the Electronic Frontier
Foundation set up their grand challenge awards. It's serious research,
but fun and educational, too."

GIMPS founder George Woltman in Orlando, Florida said, "In
addition to congratulating and gratefully acknowledging the vast
contributions of our hundreds of thousands of participants over the
years, we're committed to giving $25,000 to charity, $50,000 to UCLA
for its part in the discovery, and most of what's left to other GIMPS
prime discoverers." He adds, "Our research project will soon offer the
chance to achieve the next challenge, the $150,000 award for an
immensely more difficult 100-million-digit prime. All you need to
participate is our free software download, and a lot of patience!"

For more information, see www.mersenne.org

___________________

__Related Article__:

**"UCLA
Mathematicians Discover a 13-Million-Digit Prime Number" by Thomas H.
Maugh II**

**Source**: *Los Angeles Times* - 27
September 2008

**URL**: http://www.latimes.com/news/science/la-sci-prime27-2008sep27,0,2746766.story

...While the prize money is nothing special, the bragging rights
for discovering the 46th known Mersenne prime are huge...

"We're delighted," said UCLA's Edson Smith, leader of the
effort. "Now we're looking for the next one, despite the odds," which
are thought to be about one in 150,000 that any number tested will be a
Mersenne prime.

Prime numbers are those, like three, seven and 11, that are
divisible only by themselves and one. Mersenne primes, named after the
17th century French mathematician Marin Mersenne, who discovered them,
take the form 2^p - 1, where p is also a prime number...

The prize will be awarded when the new prime is published, probably
next year...