COMET • Vol. 4, No. 34 – 21 December 2003


(1) California Subject Examinations for Teachers (CSET)


Information about the California Subject Examinations for Teachers (CSET) is available at the above Web site.  Mathematics subtest descriptions, along with sample questions and responses, can be found at A computer-administered practice test for “CSET: Multiple Subjects” is available for download at

A number of county offices and universities throughout the state are offering CSET preparation assistance to current and prospective teachers. Linda Apple coordinates the CSET preparation program for Orange County. Classes and materials provide an overview of the content domains for subject matter understanding described in the state curriculum frameworks. Study guides can be purchased separately from the courses and are available by contacting Linda at (telephone: 714-966-4156). Multiple Subject study guides cost $15 each for the seven tested areas. The three math subtest guides for Single Subject cost $30 each, as do the six science guides.

(2) Evaluation of the Accreditation Framework Policies and Procedures

Source: California Commission on Teacher Credentialing (CCTC) E-News – 19 December 2003)

This month, the California Commission on Teacher Credentialing received a summary of the evaluation of California’s Accreditation System that was conducted by American Institutes for Research (AIR).  The PDF version of the full report can be downloaded at For additional information, please contact Cheryl Hickey: or 916-327-8663.

From the Executive Summary of the Report:

States ensure the quality of their K-12 teachers and other educators through two mechanisms: licensure of individuals and accreditation of the training programs that prepare these individuals. Accreditation is an assurance of excellence in the preparation of professional educators and an indirect check on quality. Accreditation can be done either by some branch of the state or federal government or by a professional organization. In California, the California Commission on Teacher Credentialing (CCTC) does both accreditation and certification, and candidates for credentials must be recommended by the CCTC – accredited educator preparation programs for their licenses to be granted by the Commission’s credentialing arm. These two processes have distinct objectives but serve a common set of purposes and function as an integrated system…

(3) EdSource Online


EdSource is a not-for-profit 501(c)(3) organization established in California in 1977. Independent and impartial, EdSource strives to advance the common good by developing and widely distributing trustworthy, useful information that clarifies complex K-16 education issues and promotes thoughtful decisions about California’s public school system.

Recent reports:

= “School Finance Highlights 2003-04” (November 2003)

The lion’s share of money for California’s public schools comes from the state budget. In 2003-04, it will provide less general purpose money to schools than in previous years, while sharply cutting some special programs. This two-page publication highlights the funding that K-12 education will receive overall for 2003-04, including local, state and federal sources.:

California has a new governor. And a new Education Secretary. What will that mean for public education in California? Find out what influence state officials have over public education in the School Management section:

= “How California Ranks: The State’s Expenditures for K-12 Education”

California’s national ranking on expenditures per public school student fell from 27th to an estimated 35th in 2001-02. California tops the list for teacher salaries, but comes in third highest in the size of classes. For more comparisons of California’s education expenditures with those of other states, download this report:


(1) Education’s Unsung Heroes Awards

Source: ING (a Financial Services Company)


ING initiated the Education’s Unsung Heroes Awards in 1995, as a reflection of its commitment to the educational community. The awards are given to K-12 educators pioneering new methods and techniques that improve student learning.

Educators submit applications describing projects they have initiated or would like to create. Their applications are judged on their innovative teaching methods, creative educational projects, and ability to make a positive influence on the children they teach.

Each year, 100 finalists are selected to receive $2,000 awards. Award checks are made payable jointly to the recipient and to his or her school. At least one award will be granted in each of the 50 United States, provided one or more qualified applications are received from each state. Of the 100 finalists, three are selected for additional financial awards – First Place gets an additional $25,000; 2nd Place gets an additional $10,000; and 3rd Place receives an additional $5,000.

The program is managed for ING by Scholarship America  (formerly Citizens’ Scholarship Foundation of America), a national nonprofit, educational support and student aid service organization.

The top three award winners are selected each year by ING’s Educators Advisory Board, which consists of seven distinguished educators from across the United States.

The Top 3 Winners of the 2003 EducationÍs Unsung Heroes Awards have been announced. You can also find out about all 100 $2,000 winners and their projects at the above Web site.

If you or someone you know leads or has an idea for an outstanding educational project, apply for the 2004 Education’s Unsung Heroes Awards today. To receive your application, download a pdf version of the application, call 1-866-464-8727, option 1, or ask your local ING representative.

The deadline for application is April 30, 2004. Winners will be announced in Fall 2004.

(2) “Charlotte, N.C., Students Lead in National 4th-Grade Math Test” by Kimetris N. Baltrip

Source: The New York Times – 18 December 2003


Fourth and eighth graders in the Charlotte, N.C., metropolitan region led the nation this year in the first test to compare mathematics achievement in 10 of the largest urban school districts, according to results released yesterday. New York City students came in second.

But even in the Charlotte-Mecklenburg district, just 41 percent of fourth graders and 32 percent of eighth graders scored at or above the proficiency goal in math. The national averages for fourth- and eighth-grade students who performed at that level were 31 percent and 27 percent, respectively.

In New York, 21 percent of fourth graders and 20 percent of eighth graders were at or above proficiency in math.

The results are from the 2003 Trial Urban District Assessment, part of the National Assessment of Educational Progress that is called the “nation’s report card.” A representative sample of 72,266 fourth and eighth graders from 1,159 schools was tested in January, February and March in Atlanta, Boston, Charlotte-Mecklenburg, Chicago, Cleveland, Houston, Los Angeles, New York, San Diego and Washington.

Reading scores among fourth and eighth graders were included in the results, which showed that Charlotte students in both grades outperformed their peers and surpassed the national average in proficiency by small margins. For fourth graders, New York and San Diego tied for second in the percentage of students proficient in reading. Among eighth graders, New York and Boston tied for second.

The New York schools chancellor, Joel I. Klein, said, “These results confirm that New York has the best system of public education of any major city in the United States.”

Education Secretary Rod Paige commended the districts, but said, “Average scores for all but one of the cities are below the national average in mathematics and reading, reflecting the tough road ahead.”

Last year, New York and Houston fourth graders led in reading and writing. This year, New York, Houston, Atlanta, Chicago and Los Angeles saw improvements in those scores, but none of those cities exceeded the national average.

Eighth graders in Charlotte were the only students to match the national average in reading this year.

Darvin M. Winick, chairman of the National Assessment Governing Board, which sets policy for the tests, said: “If you look at the schools and you look at comparison groups, these urban districts do just about as well as anybody else. I would say that the general perception that urban students perform less well than other students is not supported by these data.”

(3) “Results from the 2003 National Assessment of Educational Progress Trial Urban District Assessments for Reading and Mathematics” (Transcripts of StatChat)


Peggy G.  Carr (Associate Commissioner, Assessment Division at the National Center for Education Statistics) fielded questions about the NAEP Urban District Assessments for Reading and Mathematics. The transcripts are available at the above Web site. Archives of previous chats can be found at StatChatplus ( provides an opportunity to participate in online moderated discussions on issues important to the education community.

(4) Statement by U.S. Secretary of Education Rod Paige on Release of the Nation’s Report Card–2003 Trial Urban District Assessment (17 December 2003)


I’m very happy to see more local school districts courageously volunteering to take the National Assessment of Educational Progress, also known as the Nation’s Report Card. Stepping up to the assessment plate indicates how serious they are about improving academic performance for all students. Participating in the Nation’s Report Card for urban districts shows that these participants understand the importance of testing and how it can be used as a solid analytical tool for improvement.

The three million students in these 10 large urban districts are demographically different from many of their peers elsewhere nationally: they are almost twice as likely to be economically disadvantaged and are more likely to be minorities. These children are often the ones who are left wandering in the academic shadows of their more privileged peers. But thanks to the leadership of President Bush, we as a nation have put our foot down–under the No Child Left Behind Act, we will no longer allow some children to get a quality education while others are simply brushed aside.

Testing is an important part of the historic No Child Left Behind Act, which requires that states conduct annual assessments in mathematics and reading in grades three through eight. Both No Child Left Behind and the Nation’s Report Card emphasize the importance of testing and that testing results be broken down by subgroups so we can find out where improvement is needed with all students.

Average scores for all but one of the cities are below the national average in mathematics and reading, reflecting the tough road ahead. Thanks to these assessments, we now have a better sense of where these districts are and where they need to go. This is something we can work on together. The cities involved realize this is a partnership and that is one reason they participated–they know that the federal government, states and local districts have to work in unison to improve education across America for all children. The department will always be a willing member of this partnership, one that will hold people accountable for improving education for America’s youths.

The achievement gap in these districts is something that I find truly worrisome. It is a problem nationally, but in a few of the districts tested, it is abysmal–double the national average at the fourth-grade reading level for blacks versus their white peers. As a nation, we must stand united against a culture that mocks academic success in certain communities. We must not allow the culture of mediocrity to take away some of our most promising, bright young minds simply because of their skin color, accent or accident of geography.

(5) “In Archimedes’ Puzzle, a New Eureka Moment” by Gina Kolata

Source: The New York Times – 14 December 2003


Twenty-two hundred years ago, the great Greek mathematician Archimedes wrote a treatise called the Stomachion. Unlike his other writings, it soon fell into obscurity. Little of it survived, and no one knew what to make of it.

But now a historian of mathematics at Stanford, sifting through ancient parchment overwritten by monks and nearly ruined by mold, appears to have solved the mystery of what the treatise was about. In the process, he has opened a surprising new window on the work of the genius best remembered (perhaps apocryphally) for his cry of “Eureka!” when he discovered a clever way to determine whether a king’s crown was pure gold.

The Stomachion, concludes the historian, Dr. Reviel Netz, was far ahead of its time: a treatise on combinatorics, a field that did not come into its own until the rise of computer science.

The goal of combinatorics is to determine how many ways a given problem can be solved. And finding the number of ways that the problem posed in the Stomachion (pronounced sto-MOCK-yon) can be solved is so difficult that when Dr. Netz asked a team of four combinatorics experts to do it, it took them six weeks.

While Dr. Netz acknowledges that his findings cannot be proved with absolute certainty, he has presented the work to other scholars, and they say they agree with his interpretation.

On a recent snowy Sunday morning at Princeton University, three dozen academics gathered to hear Dr. Netz speak, and then congratulated him, saying his arguments made sense. “I’m convinced,” said Dr. Stephen Menn, a McGill University historian of ancient mathematics, in an interview at the end of the two-hour session.

Among all of Archimedes’ works, the Stomachion has attracted the least attention, ignored or dismissed as unimportant or unintelligible. Only a tiny fragment of the introduction survived, and as far as anyone could tell, it seemed to be about an ancient children’s puzzle–also known as the Stomachion–that involved putting strips of paper together in different ways to make different shapes. It made no sense for a man of Archimedes’ stature to care about such a game. As a result, Dr. Netz said, “people said, `We don’t know what it is about.’ ”

In fact, he has concluded, the prevailing wisdom was based on a misinterpretation. Archimedes was not trying to piece together strips of paper into different shapes; he was trying to see how many ways the 14 irregular strips could be put together to make a square.

The answer–17,152–required a careful and systematic counting of all possibilities. “It was hard,” said Dr. Persi Diaconis, a Stanford statistician who worked on it along with a colleague, Dr. Susan Holmes, who is also his wife, and a second husband-and-wife team of combinatorial mathematicians, Dr. Ronald Graham and Dr. Fan Chung from the University of California, San Diego.

Independently, a computer scientist, Dr. William H. Cutler at Chicago Rawhide, a manufacturer of oil seals in Elgin, Ill., wrote a program that confirmed that the mathematicians’ answer was correct.

Perhaps as remarkable as the discovery that Archimedes knew combinatorics is the story of a manuscript that dates to 975, written in Greek on parchment. It is one of three sets of copies of Archimedes’ works that were available in the Middle Ages. (The others are lost, and neither contained the Stomachion.)

“For Archimedes, as for all others from antiquity, we don’t have the original works,” Dr. Netz said. “What we have are copies of copies of copies.”

Investigators evaluate copies by asking whether they agree on the text they have in common, and by looking for unique passages, which lend them particular interest. By those measures, the manuscript was invaluable. But it was nearly lost.

In the 13th century, Dr. Netz explained, Christian monks, needing vellum for a prayer book, ripped the manuscript apart, washed it, folded its pages in half and covered it with religious text. After centuries of use, the prayer book–known as a palimpsest, because it contains text that is written over–ended up in a monastery in Constantinople.

Johan Ludvig Heiberg, a Danish scholar, found it in 1906, in the library of the Church of the Holy Sepulcher in Istanbul. He noticed faint tracings of mathematics under the prayers. Using a magnifying glass, he transcribed what he could and photographed about two-thirds of the pages. Then the document disappeared, lost along with other precious manuscripts in the strife between the Greeks and the Turks.

It reappeared in the 1970’s, in the hands of a French family that had bought it in Istanbul in the early 20’s and held it for five decades before trying to sell it. They had trouble finding a buyer, however, in part because there was some question of whether they legally owned it. But also, the manuscript looked terrible. It had been ravaged by mold in the years the family kept it, and it was ragged and ugly.

In 1998, an anonymous billionaire bought it for $2 million and lent it to the Walters Art Museum in Baltimore, where it still resides.

“I should emphasize how incredibly uncommon the situation is,” Dr. Netz said.

With the manuscript in hand, a small group of scholars set out to reconstruct the original Greek text. It was not easy. “You look with the naked eye and you see nothing, absolutely nothing,” Dr. Netz said.

Ultraviolet light revealed faint traces of writing, but it included both the prayers and the mathematics. “The major problem is the combination of the fact that many characters are hidden with the fact that many are so faint that they are invisible,” Dr. Netz said. Then there are the gaps where the pages were ripped or eaten away by mold.

Computer imaging helped. Dr. Roger Easton of the Rochester Institute of Technology, Dr. Keith Knox of the Boeing Corporation and Dr. William Christens-Barry of Johns Hopkins University managed to write programs to pick out writing from the “noise” around it, and in many places the Greek letters fairly pop off the computer screen.

“The product of the software is incredible,” Dr. Netz said. But it too has limitations, especially near the tattered edges of the pages. To reconstruct the writings, Dr. Netz and Dr. Nigel Wilson, a classics professor at Oxford University, are using every tool available: ultraviolet light, the computer images, Mr. Heiberg’s photographs and their own intimate knowledge of ancient Greek texts. Still, in some areas, “the text is likely to remain a conjecture,” Dr. Netz said.

It was chance that led Dr. Netz to his first insight into the nature of the Stomachion. Last August, he says, just as he was about to start transcribing one of the manuscript pages, he got a gift in the mail, a blue cut-glass model of a Stomachion puzzle. It was made by a retired businessman from California who found Dr. Netz on the Internet as a renowned Archimedes scholar. Looking at the model, Dr. Netz realized that a diagram on the page he was transcribing was actually a rearrangement of the pieces of the Stomachion puzzle. Suddenly, he understood what Archimedes was getting at.

The diagram involved 14 pieces, and the word “multitude” seemed to be associated with it. Mr. Heiberg and those who followed him thought this meant that you could get many figures by rearranging the pieces.

“This is part of the reason people didn’t see what it was about,” Dr. Netz said. But the old interpretation seemed trivial, hardly worth Archimedes’ time.

As he examined the manuscript pages, piecing together their text, he realized that what Archimedes was really asking seemed to be, “How many ways can you put the pieces together to make a square?” That question, Dr. Netz said, “has mathematical meaning.”

“People assumed there wasn’t any combinatorics in antiquity,” he went on. “So it didn’t trigger the observation when Archimedes says there are many arrangements and he will calculate them. But that’s what Archimedes did; his introductions are always to the point.”

But did Archimedes solve the problem? “I am sure he solved it or he would not have stated it,” Dr. Netz said. “I do not know if he solved it correctly.”

As for the name, derived from the Greek word for stomach, mathematicians are uncertain. But Dr. Diaconis has a hunch.

“It comes from `stomach turner,’ ” he said. “If you get involved with it, that’s what happens.”

(6) “The 12 Days of Christmas”

Source: PNC Advisors (Pittsburgh, PA)


While stiff import competition is driving deeper discounts on merchandise sold in the United States, skilled labor cost is on the rise, resulting in a 16 percent increase in this yearÍs PNC Advisors Christmas Price Index–the biggest jump the Index has seen in its 19-year history.

Each year since 1984, PNC Advisors has provided a tongue-in-cheek economic analysis, based on the cost of the goods and services purchased by the True Love in the holiday classic, “The Twelve Days of Christmas.”

Indeed, the cost of the five gold rings dropped by 5.6 percent, and the pear tree is down a full 28.6 percent from last year.  However, these discounts were offset by the dancers, pipers and drummers who have seen significant increases in the cost of their services over 2002.

“The Index reflects the broader trend of productivity growth in the U.S. economy that has driven prices lower on goods while allowing prices for services to rise modestly,” said Jeff Kleintop, chief investment strategist for PNC Advisors. “Whereas in the mid-1980s the cost of the goods in the song dominated the Index, the trend over time has been toward lower goods prices, such as the pear tree, and higher prices for skilled labor, such as the pipers,” he said.

“The abundance of cheap labor in countries such as China have contributed toward increased pressure on U.S. manufacturers to outsource their unskilled labor overseas, and evolve toward higher-skilled areas, to maintain profitability. Unfortunately, the unskilled Maids haven’t managed an increase in price for their services in many years,” he added.

Two exceptions to this trend, however, are the swans and the calling birds, which cost significantly more this year.  Unlike 2002, when swans took a significant dive in price, these graceful feathered friends have bounced back to their 2001 level of $500 a piece, up from $300 last year, according to the Philadelphia Zoo. The four calling birds are also flying high at $400, more than a 26 percent increase from last year.  “The bird prices tend to be stable, except when supply and demand get out of sync, causing the prices to move dramatically,” said Rebekah McCahan, investment strategist who provides the research for the Christmas Price Index.  “The low inventory of calling birds and swans this year, combined with a resurgence in demand, has boosted prices Æ a sign of consumer confidence returning,” she added.  All told, the swans, geese, calling birds, French hens, turtle doves, and partridges cost over $4,100, representing about 25 percent of the overall Index.

As in the past, most items are more expensive to buy over the Internet, primarily due to the cost of shipping, which has gone up this year.

As part of its annual tradition, PNC Advisors also tabulates the “true cost of Christmas,” which is the total cost of all of the items in the famous carol, including all of the repetitions.  The price tag for the 364 items this holiday season is $65,264, up from 2002Ís true cost of $54,951.  This increase of nearly 19 percent shatters the previous record increase of 8.4 percent that was achieved in 1987.

“We have seen a record increase in the 2003 Index, possibly indicating that the fears over deflation that we saw last year may begin to recede, as general price levels begin to pick up and the outlook returns to one suggesting the economic recovery may be sustainable,” said Kleintop.