COMET • Vol. 7, No. 33 – 4 December 2006


(1) Presidential Awards for Excellence in Mathematics and Science Teaching: Application and Nomination Forms for 2007 are Now Available


The Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST) is the nation’s highest commendation for K-12 math and science teachers. The award recognizes a combination of sustained and exemplary work, both inside and outside the classroom. Each award includes a grant of $10,000 from the National Science Foundation (NSF) directly to the recipient (no longer to the school). Awardees use the money at their discretion to promote math and science education. Awardees also receive an expense-paid trip to Washington, DC, during which each receives a certificate signed by the President. Awardees also attend seminars and engage in professional discussions with their peers and with national legislators and education policy-makers. Awardees also receive a selection of gifts from private-sector contributors to the program. In mathematics, California selects up to 3 finalists. They each receive an additional $1000 from the California Mathematics Council (CMC).

Forms are now available for secondary teachers for the 2007 award (elementary teachers will have an opportunity to be nominated for the 2008 award). Anyone (e.g., principals, teachers, students, and other members of the public) may nominate a teacher for this award. Self-nominations will not be accepted. The nomination and application forms may be downloaded from the PAEMST web site: and

In California, teachers must submit their completed application packets by May 1, 2007 to:

Sandie Gilliam

California PAEMST Mathematics Coordinator

2100 Nelson Rd

Scotts Valley, CA  95066

831-335-1677 (home & fax)

(2) First Saturday Administration of the Mathematics Portion of the High School Exit Exam Will be on December 9

Source: California Department of Education

Last Friday, State Superintendent of Public Instruction Jack O’Connell announced that students will be taking the California High School Exit Exam (CAHSEE) on Saturday, December 1, the first time the test has ever been offered on a weekend…

O’Connell sponsored legislation in 2006 to fund the additional Saturday administration of the exit exam. The English-language arts portion of the test was offered Saturday, December 2 at approximately 140 school districts around the state. This coming Saturday, December 9, the mathematics portion of the exam will be offered.

Students who are in eleventh or twelfth grade, or adult students enrolled in a California public school, are eligible to take the test during this weekend administration.


(1) “Potential of Global Tests Seen as Unrealized” by Debra Viadero

SourceEducation Week – 29 November 2006

In 1958, a group of international scholars met in Hamburg, Germany, and hatched an idea for a huge study to measure student learning around the globe.

They saw the world as one big educational laboratory, with each country acting as its own naturally occurring experiment. If tests could gauge the effects of those experiments, the researchers reasoned, the results might yield a bonanza on how best to teach children.

Nearly 50 years later, the project they had in mind is called the Trends in International Mathematics and Science Study, or TIMSS–one of the biggest and most influential assessment programs in the world. Yet it still hasn’t delivered on its early promise, say experts who attended a conference [in Hamburg last] month aimed at rekindling the original vision of the program’s founders.

“It sort of became a cognitive Olympics instead,” said Judith Torney-Porta, a professor of human development from the University of Maryland College Park, referring to the country-by-country rankings for which the TIMSS reports are best known. The program, she said, “seemed to miss out on becoming a major contributor of international studies in identifying effective practices and adapting them.”

Ms. Torney-Purta, who in the 1960s took part in the development of what is now TIMSS, was among the group of international researchers who gathered for the Nov. 9-11 conference at the Brookings Institution. They shared the results of secondary analyses of data from TIMSS and other international studies, and encouraged more researchers to tap into the mounting troves of international achievement data.

“What we’ve got to do more of now are two things,” said Seamus Hegarty, the chairman of the International Association for the Evaluation of Educational Achievement, or IEA, which oversees TIMSS and other international studies. “We’ve got to ensure better, more systematic secondary analyses, and we’ve got to relate our findings to policy interests.”

At the Amsterdam-based IEA and other international-study centers, the data have indeed piled up since the late 1950s.

Just 12 countries took part in the earliest version of TIMSS, the First International Mathematics Study, or FIMS, which was published in 1967 using math data collected from 1961 to 1965. Since then, the IEA has administered at least four more cross-national studies in mathematics, science, or both, and the number of participating countries has grown with each test administration. TIMSS 2007, already under way, is expected to involve more than 60 countries.

In addition, the assessment organization has conducted cross-national studies in two other subjects, civics education and literacy. Data on student achievement are also accumulating through the Program for International Student Assessment, or PISA, a multinational study run by the Paris-based Organization for Economic Cooperation and Development.

“It’s a gold mine, really,” Jan-Eric Gustafsson, an education professor at Sweden’s University of Gothenburg, said of the TIMSS data.

Limiting Factors

So far, researchers have plumbed results from the various studies to look at how a wide range of educational factors might affect achievement.

Those factors include students’ attitudes and beliefs; variations in the size of schools and classes; students’ family backgrounds; classroom technology use; and the extent to which teachers use such approaches as group work and inquiry-driven instruction.

For instance, Elena C. Papanastasiou, a researcher from Intercollege in Nicosia, Cyprus, mined the TIMSS data archives to explore how computers and electronic calculators affect learning…

Age Shifts Eyed

One way to overcome the cultural and pedagogical differences across countries that hamper analyses of effective practices, Mr. Gustafsson suggested, might be to focus on the changes that occur within countries from one administration of a test to the next.

“The problem for cross-sectional analyses is that if you have a characteristic you want to measure, it tends to be correlated with a thousand other things,” he said. By looking over time within one country, he said, scholars might minimize those “nuisance” factors.

Mr. Gustafsson tested his idea with data for 15 to 22 countries that participated in TIMSS tests in both 1995 and 2003. His aim was to see if changes in students’ ages and in average class sizes within a country, from one test to the next, correlated with changes in achievement.

Mr. Gustafsson found some surprisingly large age differences. In Latvia and Lithuania, for instance, 4th graders were eight to nine months older in the 2003 assessments than their counterparts in 1995 were.

The Iranian 4th graders tested, by contrast, were three months younger in 2003.

The analysis showed that age changes were linked to achievement differences, with older students in every country outperforming their younger peers in the same grade. The relationships were strong enough, Mr. Gustafsson said, that TIMSS researchers might want to take them into account in interpreting country-by-country achievement gains–either by narrowing the testing window so that test-takers are closer in age or making statistical adjustments.

Changes in average class sizes from one test to the next, meanwhile, seemed to be important for 4th graders’ achievement and less so for 8th graders.

Covering Everything

Most researchers, though, have focused on curricula in an effort to discern why students in some countries tend to outshine the rest of the world, including the United States, in international comparisons.

As the principal of a Finnish intermediate-level school that is arguably the highest-scoring school in the world, Maarit Rossi, another conference-goer, has fielded many such queries. Finland ranked first in math in the 2005 PISA, and the 8th graders in Ms. Rossi’s school, Kirkkoharjun School in Kirkkonummi, scored highest in that nation.

Now studying in the United States on a sabbatical, Ms. Rossi sees obvious contrasts in U.S. and Finnish textbooks. The U.S. texts, she said, are much thicker and more cluttered than the ones her students use. “It’s impossible when you have 1,100 pages of math that you get the message,” she said.

William H. Schmidt, an education professor at the University of Michigan in Ann Arbor, would agree. He has conducted comparisons of U.S. math curricula and those used by countries that consistently score high on TIMSS. As early as the late 1990s, he characterized U.S. math classes as “a mile wide and an inch deep” compared with those of the high-scoring, mostly Asian, nations.

“It’s basically, you cover everything, everywhere, because somehow, somebody will learn something somewhere,” Mr. Schmidt told conference-goers.

More recently, his analyses have also shown that the high-performing countries teach math in a sequence that mathematicians see as more coherent, and that may be even more influential in promoting students’ understanding.

Another researcher at the Brookings Institution conference, however, said Mr. Schmidt was looking in the wrong direction for explanations of U.S. students’ lackluster performance.

“Sociological theories suggest that educational systems are becoming more similar around the world,” said David P. Baker, a professor of sociology and education at Penn State. Because most countries now manage and organize schools in much the same way and teach similar content, he argued, other factors, such as students’ family background, may explain more of the test-score variations between nations than differences in schooling.

He noted, for instance, that countries that do well on the international assessments tend to be those, such as Finland or Singapore, with less socioeconomic inequality among students. Countries with wide gaps between society’s haves and have-nots, on the other hand, tend to have greater variations in their own students’ test scores.

“The notion that the world is an education laboratory is a good fantasy to push to get funding,” Mr. Baker concluded. As schools become more and more similar around the world, he added, the possibility that researchers can distill best practices in education from international achievement is becoming more remote…

(2) Preparing Secondary Mathematics Teachers–Recommendations form CUPM

URL (12/06 column):

[This paragraph was taken from] The Mathematical Association of America’s Committee on the Undergraduate Program in Mathematics (CUPM) is charged with making recommendations to guide mathematics departments in designing curricula for their undergraduate students. CUPM began issuing reports in 1953, updating them at roughly 10-year intervals. Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide 2004was based on four years of work, including extensive consultation with mathematicians and members of partner disciplines… CUPM Guide 2004 contains the recommendations unanimously approved by CUPM in January 2003 [and is available for free download at]

Over the past two years, the CUPM Chair, David Bressoud, has written a series of articles related to the recommendations in the CUPM Curriculum Guide.  Topics include the following: learning to think as a mathematician, attracting and retaining majors, the role of technology, preparing K-8 teachers, the challenge of college algebra, targeting the math-averse, and many more. Each is available online at

This month’s topic is “Preparing Secondary Teachers” (, reproduced below:

 In writing this recommendation, the CUPM was very aware that it was moving outside of its area of expertise and into the purview of other committees. In particular, in 2001 the Conference Board of the Mathematical Sciences, an umbrella organization of the mathematical societies including AMS and MAA, issued its recommendations on The Mathematical Education of Teachers ( The CUPM recommendation is not intended to serve as a set of guidelines for pre-service teacher education in mathematics, but rather as a distillation of four of the most important and commonsense recommendations that have emerged in recent years.

One of the most important resources that any teacher can bring to the classroom is depth of understanding of the subject at hand. This includes knowing where it came from and why it arose, knowing the conceptual difficulties that people encountered during its development and the difficulties that students are likely to have as they master and learn to apply it, knowing how it relates to other parts of mathematics and to problems in other disciplines, and knowing when, why, and how prospective teachers will need to draw on this knowledge in the future. This depth of understanding includes a rich reserve of examples that illustrate different aspects of the topic, together with good questions that probe and test student knowledge at all levels from basic recall through sophisticated analysis, synthesis, and evaluation. It includes knowing when and how technology can be useful in helping students through a difficult conceptual point. It means knowing where this topic lies in the great web of mathematical ideas and how it relates to the ideas around it, those that should come before, those that will come after, and those that students might never see.

Four years of undergraduate mathematics is not sufficient to create this depth of understanding. Not even the additional years of graduate work will complete it. This is a bed of mastery that takes a lifetime to create, but it must be begun, and begun well, by the time the future teacher graduates with the bachelor’s degree. This includes beginning to string together the connections. This is why it is so critically important that future teachers receive a mathematics education that emphasizes connections. They need to learn to look for them. Whether learning analysis, algebra, or geometry, prospective teachers need to understand how the mathematics they see as undergraduates is connected to the mathematics they will be teaching.

There are now many excellent resources to assist in putting together such a program. The Illustrative Resources ( lists many of them. An article that I consider particularly insightful is H. Wu’s “On the education of mathematics teachers” ( . For those who are interested in working with pre-service teachers, the PMET program (Preparing Mathematicians to Educate Teachers; runs workshops, publishes information, helps to create and maintain networks, and provides mini-grants to support work in this area.


(3) Google for Educators


[Promotional description of Google for Educators] Google recognizes the central role that teachers play in breaking down the barriers between people and information, and we support educators who work each day to empower their students and expand the frontiers of human knowledge. This website is one of the ways we’re working to bolster that support and explore how Google and educators can work together.

As a start, we’re inviting you to share your best ideas for using technology to innovate in the classroom.

[On the Web site–], you’ll find a teacher’s guide to Google products, including basic information about each tool (e.g., Book Search, Maps, Docs & Spreadsheets, Calendar, Personalized Home Page, etc.), examples of how educators are using them, and lesson ideas. You’ll also find lesson plans and videos from our partners at Discovery Education focusing on two of our most popular teaching tools: Google Earth and Google SketchUp.

We think of this site as a platform of teaching resources–for everything from blogging and collaborative writing to geographical search tools and 3D modeling software–and we want you to fill it in with your great ideas.

You can explore a Google tool you’ve never tried before, then tell us what you think about it. Or road test our lesson ideas, then follow the links to submit your own. And if you’d like to share your expertise with fellow educators, we encourage you to send us your story–we’d love to feature it on this site.

We also invite you to subscribe to the Google Teachers’ Newsletter–your source of authoritative updates on Google tools and features, tips, and other information relevant to teachers.

(4) Rose Math Professor’s Formula Featured on CBS’s NUMB3ERS”

Source: The Tribune Star – 28 November 2006

A formula developed by Rose-Hulman Institute of Technology [Terre Haute, Indiana] mathematics professor David Finn was featured on a recent episode of “NUMB3RS,” a CBS television show in which mathematics is used to help the FBI solve a wide range of challenging crimes in Los Angeles.

During the Oct. 13 episode, Finn’s model that describes the shape of a sugar cookie during the baking process appears on a blackboard. Above the formula is the phrase “From David Finn, R.E.U. “
Finn’s model is based on viewing cookie dough during the heating process as a liquid so it can be modeled as essentially a drop of water on a table. The equation arises from minimizing energy of the configuration (gravitational potential energy plus surface energy). The trick is that the interaction between the cookie sheet and the cookie also adds an energy term, wetting energy, that also defines the cookie’s final shape..

In a perfect world, this term is independent of position on the cookie sheet, and defines the angle of contact between the cookie and the cookie sheet as a constant. Theoretically, this means that drop-sugar cookies should be perfectly round, and defined uniquely by the size of the drop (volume and diameter of the cookie) once one knows the necessary parameters of the cookie dough.

“However, as any baker knows, cookies are not necessarily perfectly round,” Finn states. “Cookies are only mostly round, meaning that the angle depends on position on the sheet. The question then is to understand how the geometry of the ‘wetted domain’ [the area where the cookie sits on the cookie sheet] affects the shape of the cookie.”

This investigation into the shape of a cookie is part of a summer Research Experiences for Undergraduates (REU) program at Rose-Hulman, funded by the National Science Foundation. The mathematical study of baking cookies caught the attention of Ed Pegg Jr., who writes a column on mathematics for the Mathematical Association of America and serves as a math consultant for “NUMB3RS,” which resulted in Finn’s work appearing on “NUMB3RS.”

In the episode, Charlie Eppes (played by David Krumholtz) is seen writing equations on a blackboard, explaining to his colleague Amita Ramajuan (played by Navi Rawat) that he “is using differential geometry to perfect the chocolate chip cookie.” 
That’s when portions of Finn’s investigations and mathematical calculations appear on the blackboard.

“It was a thrill, a once-in-a-lifetime experience, to see my name on television,” Finn said. “It is great to see mathematics and mathematicians being highlighted on a national televised show, and it is ‘real’ mathematics. This shows the applicability of mathematics in the modern world, and hopefully will lessen some of the general complaints about mathematics that one always hears: ‘I just was never good at math’ and ‘Math just never made sense to me.'”

The episode might be rebroadcast during the holiday season.
 Texas Instruments is using “NUMB3RS” to highlight its “We All Use Math Every Day” math education initiative, in partnership with CBS and the National Council of Teachers of Mathematics. The program was specifically designed to help students (and their parents) realize how relevant math is to everyday activity and to understand the importance the subject plays in their future success.
 By tying the math used within each episode of “NUMB3RS” to classroom activities, teachers can increase student interest, especially among grades 9-12, with real-world examples such as baking cookies.