COMET • Vol. 5, No. 34 – 21 December 2004


(1) National Board Certification for California Mathematics Teachers

Source: Kay Garcia, NBPTS, California Department of Education


In November 2004, nineteen California mathematics teachers learned of their national certification by the National Board for Professional Teaching Standards (NBPTS). The NBPTS offers two certificates for mathematics teachers. The Early Adolescence/ Mathematics (EA/MATH) certificate is appropriate for teachers who teach students ages 11-15, and the Adolescence and Young Adulthood/Mathematics (AYA/MATH) certificate is appropriate for teachers who teach students ages 14-18.  Both certificates are appropriate for teachers who know the full range of the school mathematics curriculum: algebra and functions; geometry; calculus; discrete mathematics; and statistics and data analysis.

California currently has 224 math teachers who have earned National Board certification, including 131 AYA/MATH and 93 EA/MATH.  You will find the names of the 3,088 NBCTs in California on the National Board Web site:

If you would like additional information, please contact Kay Garcia, NBCT, at the State Department of Education. Kay may be reached at or by calling (916) 323-5832.

(2) A 2005 Overview of National Board Certification

Source: Kay Garcia, NBPTS, California Department of Education


What is National Board Certification?

The National Board for Professional Teaching Standards offers advanced certification in twenty-seven certificate areas based on student age range and subject matter taught. In response to specific prompts, teachers must create a portfolio of their teaching practice. The portfolio includes written analyses of student work and classroom videos as well as documentation of the teacher’s involvement in a professional community and community outreach.  The four-part portfolio is assembled over the course of several months of a school year.  Candidates must also attend a one-day Assessment Center where they are asked to respond to six, 30-minute prompts on content knowledge for their certificate area. California currently has 3,088 National Board Certified Teachers (NBCTs). Many of them report that this is the most rewarding professional development experience of their careers.

How Long Will It Take?

The process is designed to be completed during one school year, but candidates are allowed to “bank” passing scores and resubmit portions of the portfolio and retake assessment center exercises for two additional years. This means that candidates have a total of three years to successfully complete the process. Approximately 40% of first-time candidates achieve National Board certification.

How Much Does It Cost?

The assessment fee is $2,300 (but see CSP below). Retakes are $350 per entry.

California Incentive Awards

California has a one-time incentive award of $20,000 available to NBCTs who teach in schools with a statewide API ranking of 5 or below. This incentive is subject to funding in the annual Budget Act. The 2004 Budget Act provides $7.5 million for this purpose.

Candidate Subsidy Program (CSP)

Federally funded fee subsidies are available through the California Department of Education.  Applications are available from February through October at

The National Board also offers scholarships. For information about the National Board Scholarship Program, call 1-888-908-FEES or visit

In addition, many school districts offer teachers local fee subsidies, local incentives, increased salary, release time, and logistical support.

More Information

The National Board For Professional Teaching Standards maintains a web site with detailed information about the process as well as online candidate resources.  Please visit

You may apply online or request a free application from the National Board that includes a useful guide about the process by calling 1-800-22TEACH.

The California Department of Education maintains a web site with specific information for California teachers seeking national certification.  This includes information about a fee subsidy, the incentive award, candidate support, district support and university-based support, including the potential linking of a master’s degree with the process of national certification.  Please visit

National Board Resource Center – Stanford University

If you would like to receive periodic information via email from the National Board Resource Center (NBRC) at Stanford during your candidacy, please visit and sign up for the NBRC LISTSERV.


(1)  The Total Cost of the Gifts in “The Twelve Days of Christmas” (2004)

Source: PNC Bank – 29 November 2004


In 1984, after all the receipts were added up, the cost of “The Twelve Days of Christmas” would have set you back $12,623–the goods alone accounting for 62 percent of your total bill.  Today, the numbers tell a different story.  The total cost has climbed to $17,297, a 1.6 percent annualized increase over 20 years, but services now account for 74 percent of the index, indicating a steady rise in the cost of skilled labor while the price of two turtle doves and three French hens may be a little easier on your wallet.

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

The Christmas Price Index has consistently reflected changes in the economy and continues to do so in the 20th anniversary version.  The 2.4 percent year-over-year increase in the index closely mirrors that of the government’s Consumer Price Index–a widely used measure of U.S. inflation.  Not only is the high cost of fuel reflected in the cost to deliver a pear tree, but this year’s index also underscores the trend to outsource labor.  Skilled labor mentioned in the song, such as wages for the dancing ladies have increased 5.5 percent annualized over 20 years versus the maids-a-milking, which have only seen a 2.2 percent annualized pay raise.  In the broader economy, the outsourcing of less skilled labor is helping to keep those wages low.

“The Christmas Price Index reflects the changing economic mix in the U.S. away from manufacturing to a more service based economy,” said Jeff Kleintop, chief investment strategist for PNC Advisors.  “The abundance of cheaper labor in countries such as India and China has resulted in pressure on U.S. manufacturers to outsource unskilled labor. As a result the cost of skilled dancers has steadily increased while the unskilled milk maids haven’t managed an increase in pay for their services in many years.”

The supply and demand lessons of “Economics 101” are also apparent in this year’s Index.  Take, for example, the 29.4 percent decrease in the price of the five gold rings.  International demand has driven the commodity price of gold to all-time highs, but demand for plain gold rings in the U.S. has seen a significant drop, forcing retailers to lower prices in order to move merchandise.  So those considering a trip to the jeweler to find that special gift this year may want to consider adding a little sparkle or you could find yourself standing in the return line on December 26th.

The feathered friends in the song are flying at all altitudes and have proven to show the most fluctuation in price through the life of the index.  The partridge and swans are relatively steady from last year according to the Cincinnati Zoo & Botanical Garden.  However the price for French hens and geese saw significant increases, which may be due to fewer hatchlings during this breeding cycle creating an imbalance in the supply-demand chain.  Turtle doves, on the other hand, may have had a more fruitful breeding cycle creating an oversupply of birds and a 31.0 percent decline in price.  All told, the cost of the birds in the Christmas classic totaled $4,201, just 1.5 percent more than the $4,138 it would have cost a year ago.

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 the repetitions.  The price tag for the 364 items this holiday season is $66,334, up from $65,264 in 2003.  The 1.6 percent increase pales in comparison to last year’s 19 percent increase, which may be due to lower consumer confidence this season according to Kleintop…

(2) Free Newsletter from the International Organization of Women and Mathematics Education (IOWME)

Source: Joanne Rossi Becker (, former U.S. Coordinator, IOWME


URL (ICMI Newsletters):

The International Organization of Women and Mathematics Education (IOWME) is affiliated with the International Commission on Mathematics Instruction (ICMI), which sponsors the quadrennial International Congress on Mathematical Education (ICME).

Several times a year, IOWME distributes a newsletter electronically and free of charge to those interested in issues of gender and mathematics, especially from an international perspective. The next ICME conference will be held in Monterrey, Mexico on 6-13 July 2008. As the ICME conference draws near, the IOWME newsletter will provide conference information and opportunities for involvement.

If you would like to receive the IOWME newsletter, please send your name and email address to the U.S. Coordinator, Olof Bjorg Steinthorsdottir at the University of North Carolina. Her email address is

(3) NCTM Presidential Web Chat: “Beyond ‘Pockets of Wonderfulness” by Cathy Seeley

Source: National Council of Teachers of Mathematics

URL (President’s Message):

URL (Web chat transcripts):

A third-grade class is engaged in an innovative lesson on multiplication. An algebra teacher tries a new approach to teaching functions. A mathematician initiates contact with a high school to help the students with their work on statistics. What do these isolated events have in common? They all represent what I would call “pockets of wonderfulness”–separate events that may be grounded in NCTM’s Principles and Standards for School Mathematics or may take a step toward a more effective mathematics program. Pockets of wonderfulness can appear in essentially any type of school setting. Students get excited, learn something new, and become motivated to pursue their study of mathematics. So what’s the problem?

The problem is that when great events happen in isolation from the larger system within which they operate, we may not reap the maximum benefit. Educators generate tremendous power in by talking to one another and working together. Articulation and collaboration are important tools for making lasting systemic change…

Pockets of wonderfulness are, in a word, wonderful. Using great materials that engage and challenge students in rich mathematical tasks, or implementing an effective practice where students have to think and communicate mathematically, can have positive results for students. For teachers, learning about and trying out a student-centered classroom or giving an increased emphasis to understanding is part of healthy professional growth. Our challenge as educators is to capture wonderful ideas and multiply their payoff by working with colleagues to plan for and build on what each teacher does. When we do this, students’ learning becomes continuous and cumulative, resulting in achievement that grows by leaps and bounds from year to year.

What challenges have you found in reaching out to other teachers within or across levels? Have you felt frustrated trying to implement a wonderful idea that you may have learned at a workshop or from a journal? What successes have you had in implementing a program within a system? If you are the only math teacher in a school, does your situation make innovation harder or easier? [These questions were addressed in President Seeley’s President’s Chat, held on Monday, December 13. Visit the Web page above to read the archived discussion.]

(4) NCTM Presidential Web Chat: “Engagement as a Tool for Equity” by Cathy Seeley

Source: National Council of Teachers of Mathematics


Many excellent teachers have discovered that their students can be more successful when they are engaged in doing mathematics–writing about mathematics, modeling mathematical situations, discussing mathematics, exploring mathematical ideas–rather than watching their teacher do mathematics. This means teaching in ways that are different from the way in which most of us were taught–by being told what we needed to know. Today’s most successful mathematics classrooms look considerably different from even the best classrooms of my childhood, where lecture by the teacher was the mode…

There are many variations on classroom practices that actively engage students in their own mathematics learning. But implementing any approach based on student engagement can raise many questions for teachers. How does this approach foster computational proficiency that is likely to be on a high-stakes test? How do I adapt existing materials for a more engaging approach? How do I learn to pose questions to stimulate students’ thinking, especially if I don’t necessarily know all the answers? These are important questions that can form the basis for many types of professional development and support for teachers. In addition to professional development, teaching for student engagement calls for course materials that are conducive to engaging students in rich tasks. It also requires at least as much work as preparing a good teacher-centered lesson. But the labor is clearly worth the effort when student engagement leads to learning for more students than we have ever reached before.

I can offer several questions for your consideration (and for the November President’s Chat). Are you listening to the little voice inside you that asks you whether you are doing all you can to engage all your students in their own learning? Do you have some examples to share of student-engagement strategies that help all students, including those who have not been previously successful? What models have been most effective for you? What lessons have you learned that might help other teachers engage their students? What programs and services can NCTM offer that would help you and your colleagues improve your ways of teaching?

[The transcript from this November 16 Presidential Chat is available at the above Web site.]

(5) “Teenager Wins Siemens’ Top Prize” by Tracey Wong Briggs

Source: USA Today – 7 December 2004


A San Diego-area teen who used scavenged parts to invent a gyroscopic generator to turn ocean waves into electricity won the top $100,000 individual scholarship [on December 6] in the Siemens Competition in Math, Science and Technology.

Working in his garage for more than a year, Aaron Goldin, a senior at San Dieguito High in Encinitas, used parts from a reel-to-reel tape recorder, an answering machine and a computer printer to create his environmentally friendly Gyro-Gen. Goldin, 17, spun off the idea from an ocean-wave-powered vehicle, a concept pondered by engineers at the Scripps Institution of Oceanography, where he volunteered. In trying to use a gyroscope’s motion resistance to work against a wave, he realized it might be possible to use it to generate power.

“I had no idea I’d end up here,” Goldin said Monday. “You just don’t expect to be the one. That was an amazing surprise. I almost cried when I found out.”

Yueqi “Lucie” Guo and Xianlin Li, both 17, of Durham, N.C., won top honors in the team category for their research on the genetics of breast cancer. Both are seniors at the North Carolina School of Science and Mathematics. They will split a $100,000 scholarship.

The national honors were announced at a meeting of the American Association for the Advancement of Science in Washington, D.C. The sixth annual high school science research competition awarded $624,000 in scholarships at the national and six regional events.

(6) “Math Educators Find Common Denominators” by Valerie Strauss

Source: Washington Post – 21 December 2004


Confused by the latest “good news-bad news” headlines about how U.S. students compare in math with their peers in foreign lands? Wondering whether the math program at your child’s school is teaching addition better than another program might?…

This month’s release of international comparisons of math performance highlighted the confusion. One study showed that U.S. eighth-graders made significant gains compared with their counterparts worldwide, climbing several places — to 15th out of 45 countries — since the international math rankings came out nine years ago.

Yet another recent study suggested the opposite of progress — that 15-year-olds in the United States lag behind their peers in most other leading industrialized nations in the ability to solve real-life math problems.

Some mathematicians and educators even disagree on whether international comparisons are valid. R. James Milgram, a Stanford University mathematician, said yes; Jeremy Kilpatrick, a University of Georgia professor, said different cultures and educational systems skew the results.

There may be some room for hope of a truce in the math wars, according to Milgram and Kilpatrick, both of whom attended a “peace summit” designed to see whether common ground could be found.

Richard J. Schaar, a mathematician and senior vice president of Texas Instruments Inc., wooed the two scholars, plus three other figures in math education, to Washington early this month. Also attending was Harvard University Professor Wilfried Schmid, who, like Milgram, criticizes “reform” math programs for failing to teaching children the fundamentals.

Kilpatrick and two other leading math educators at the gathering, the University of Michigan’s Deborah Loewenberg Ball and Joan Ferrini-Mundy of Michigan State University, hold the view that the reforms are helping students better understand math because they do not rely on memorizing correct answers.

To the surprise of all, there was more agreement than they had imagined, several participants said, suggesting that they may be moving toward a “centrist position.” Among the topics they said they agreed on:

* Heavy reliance on calculators in the early elementary grades is a bad idea.

* Elementary school children must have automatic recall of number facts, meaning that, yes, they have to memorize multiplication tables.

* Children must master basic algorithms. The meeting participants spent time defining the word “algorithm,” which means a set of rules for solving a problem in a finite number of steps.

Schmid called it “significant that we do have agreement in this group… To me, it is an indication that we are moving toward peace in the math wars.”

Participants said parents can take these areas of agreement and look for them in their children’s math programs. The group plans to continue meeting and to issue a report with math education goals, Schaar said…

In an effort to help bring clarity to the math wars, the Mathematical Sciences Education Board of the National Academy of Sciences reviewed 147 studies done on the effectiveness of 19 math programs used in schools today. The conclusion, released this summer: Not one study had been carried out well enough to prove a program’s effectiveness.

“Don’t believe a thing said to you associated with the phrase ‘research shows,’ ” said W. Stephen Wilson, a Johns Hopkins University mathematics professor.

There are programs successful in some schools, but there isn’t a single best one, according to experts, who emphasize it often comes down to teachers: how well they understand math and how much they have been taught about the program their school is using.

“All the program can do in the best case is be correct, efficient and accessible. Then it is up to the teacher,” Schmid said.