COMET • Vol. 8, No. 08 – 11 March 2007


California State Board of Education Appoints Additional Content Review Panel (CRP) Members for the 2007 Mathematics Primary Adoption 

CRP Contact: Mary Sprague – – 916-319-0510

Last Thursday (March 8), the State Board of Education appointed the individuals listed below to serve on a Content Review Panel for the 2007 Mathematics Primary Adoption. (CRP applications are still being accepted. Contact Mary Sprague for more information.)

    • Babette Benken (CSU, Long Beach)


    • Jerome Dancis (University of Maryland)


    • Scott Farrand (CSU, Sacramento)


    • Ricardo Fierro (CSU, San Marcos)


    • Brad Huff (


    • George Jennings (CSU, Dominguez Hills)


    • Philip Ogbuehi (Los Angeles Unified School District)


    • Angelo Segalla (CSU, Long Beach)


    • Jean Simutis (CSU, East Bay)


    • Christopher Yakes (CSU, Chico)



(1) “The Infinite Mind” Presents “Numbers and the Mind”


“The Infinite Mind” is a radio program broadcast weekly on National Public Radio (NPR). The show was created by Bill Lichtenstein, President of Lichtenstein Creative Media, Inc. Its Executive Producer is Lichtenstein’s wife, June Peoples. Abstracts of many of the shows broadcast since 1998 (along with audio from recent broadcasts) are available at

[Excerpt from a (New York) Daily News article available at] “The model for this show was ‘Cosmos,'” says Lichtenstein, referring to the 1980s public television series about the universe. “We try to make neuroscience entertaining…”

[Excerpt from a Boston Globe article available at]  Both Lichtenstein and Peoples say that one of the things that distinguishes ”The Infinite Mind” is its broad approach. ”Each week,  ‘The Infinite Mind’ takes on an issue that in some way relates to the human mind,” Lichtenstein says. ”It can be medical; it can be social. It can be metaphysical. We spend an hour examining it from as many perspectives as we can, so that at the end of the hour you understand that subject in a way you didn’t before. It can range from a medical issue, like multiple sclerosis, to something like left-handedness or dopamine or writer’s block.”


This past week, the show’s topic was “Numbers and the Mind.” 
 The audiocast (RealAudio) of the show is currently available free of charge at the above Web site.  The following information about this show is available at


Why are some people math whizzes while others are scared to do simple arithmetic without a calculator? This week we explore differences in math ability; new and old debates on math education (remember “The New Math?”); the link between autism and skills in rapid-fire calculation; and Hollywood’s fascination with brilliant, troubled mathematicians. Plus a trip to AT&T’s research labs and some of the best minds working in mathematics today. Guests include Brian Butterworth, Professor of Cognitive Neuropsychology in the Institute of Cognitive Neuroscience at University College in London; Keith Devlin, executive director of The Center for the Study of Language and Information at Stanford University; Jeremy Kilpatrick, professor of mathematics education at the University of Georgia; Gary Mesibov, professor of psychology at The University of North Carolina; Jerry Newport; and AT&T mathematics researchers David Applegate and Jeff Lagarius.

In an introductory essay, host Dr. Fred Goodwin recalls his attempt to devise a theorem that would trisect an angle, one of geometry’s long-standing problems. The attempt failed to yield a workable theorem, but it did teach him the joy and discipline of sustained scientific effort. As a research scientist investigating the human mind, Dr. Goodwin relied on the same sense of passionate investigation that he’d unleashed in high school geometry. “For that,” he concludes, “I’ll always thank my high school math teacher… and that stubborn theorem”…

Dr. Fred Goodwin interviews Dr. Brian Butterworth, Professor of Psychology at University College, London. His books include What Counts: How Every Brain is Hardwired for Math. Dr. Butterworth contends that the vast majority of human beings are born with an innate concept of numbers, but that about one in twenty people seem to lack basic math abilities. These basic abilities include an intuitive understanding of numbers and counting, and they are controlled by the brain’s parietal lobes. Physicist Albert Einstein had abnormally shaped, unusually large parietal lobes. The site of the brain that controls number processing is adjacent to a circuit that controls finger movement, says Dr. Butterworth, and he points out that our ability to calculate is intimately related to fingers. Most children learn to count on their fingers and we refer to numbers as “digits,” after the Latin word for finger. Evidence for the development of the human capacity for counting goes back over thirty thousand years, says Dr. Butterworth, to signs of tallying on bone and on the walls of upper Paleolithic caves…

If you were a student in the sixties or early seventies – or the parent of one – you might remember the “New Math.” But whatever happened to the “New Math?” Phillip Martin reports. The Russian launching of Sputnik in 1957 stirred American fears that the United States was being left behind in the technological revolution of the space race. In response, American educators devised a new school mathematics curriculum that soon became known as “New Math.” It was easy to satirize, says songwriter Tom Lehrer. “It just seemed like a desperate attempt to keep up with the Russians.” Dr. Jeremy Kilpatrick, professor of mathematics education at the University of Georgia, says the “New Math” curriculum focused less on procedural-oriented mathematics, like adding, subtracting and multiplying, and more on the language of sets, relations, and functions… 

Dr. Jeff Lagarius, [a] mathematics researcher at AT&T Labs, made headlines in mathematics journals last year when he untied a complicated problem in “knot theory.” When he’s working on a problem, he says, “I think about it all the time. My shoulder muscles are tense… it’s slightly uncomfortable.” The relief comes in solving the problem, or recognizing that it’s not soluble and moving on. A long-standing interest of his is an infamous problem in mathematics called “The 3x + 1 problem.” He wants to prove something that mathematicians almost know to be true. Here’s how it works: You pick ANY positive integer. If it’s even, you divide it by two. If it’s odd, you multiply the number by three and add one. You keep repeating that process over and over again and the belief is that you’ll always get to one. For example – say you start out with five. Five times three plus one is sixteen. That’s an even number, so you divide that by two. You get eight. Divide that by two and you get four. Divide four by two and you get two. Divide two by two and you get one. Computers have checked this recipe for a million, billion numbers and it always yields a one. Mathematicians conjecture that it always works but they haven’t been able to figure out exactly WHY…

Next, Dr. Fred Goodwin interviews Dr. Keith Devlin, executive director of The Center for the Study of Language and Information at Stanford University and a consulting professor in Stanford’s department of Mathematics. Movie makers have released a number of movies in recent years that focus on troubled mathematical geniuses, including Academy Award winners “A Beautiful Mind” and “Good Will Hunting” and art house hit “Pi.” And there are more on the way – Miramax has optioned the rights to the Tony and Pulitzer Prize winning play “Proof.” Dr. Devlin says that the math in “Pi” was a bit too elementary for the character, who is meant to be an expert mathematician. “A Beautiful Mind” offers several apt cinematic renditions of complex mathematical ideas, he says. While a fear of math, dubbed “math anxiety” by many, is widespread, he says that a typical math problem is actually a lot less complicated in its web of relations than the plot of a typical soap opera episode… Next, Devorah Klahr reports on the link between autism, a neurological developmental disorder, and super-quick mathematical calculation. Soon after seeing the movie “Rain Man,” which featured Dustin Hoffman in the role of an autistic man, Jerry Newport was diagnosed with Asperger’s syndrome, a mild form of autism. Like the character Hoffman played, Newport can multiply four digit numbers very rapidly. About one in twenty people with Asperger’s syndrome develop such splinter skills in one of several fields, including music, art, and high speed mathematical calculation. Dr. Gary Mesibov, professor of psychology at The University of North Carolina suggests that autistic people’s tendency to develop a very narrow focus may be behind these abilities. That same narrow focus, he says, can also be an obstacle. “Things like algebra and trigonometry cause them difficulty because those require sequential processing of information which they’re not as strong at. And also it requires holding several concepts in their head at the same time.” Jerry Newport has learned to improve many of his social skills, a big challenge for people with autism. He says his calculating abilities made him feel like “the town freak” when he was growing up but that today he feels good about himself and his work in educating others about autism…

In a concluding commentary, John Hockenberry recalls how he fell in love with math. It wasn’t the arithmetic or the industrial processing problems like figuring out how many donuts a baker can make out of a given amount of flour. (Why shouldn’t the baker figure it out for himself and leave the third grade math class out of his industrial processing problems?) No. It was algebra. Hockenberry fell in love with “x” in math class. She was next to the letter “m.” “m” described a slope but the siren appeal of “x” was that “x” could be …. anything.

(2) “Pi Day” Web Site


“Pi Day” (March 14, or 3.14) is fast approaching, and the number of Web sites devoted to activities for and information about this day is growing by the year. One such site is An excerpt from this Web site follows:


Welcome to, where our goal is to become the first and best place on the Web for teachers who want to find or share ideas for Pi Day activities, learning, and entertainment. We believe that promoting an enthusiasm for learning, through celebration and creativity, will lead only to a richer classroom environment and a deeper appreciation of mathematics.

Besides being a center for teaching ideas and resources, we’ll try to be your first stop for funny, smart, tongue-in-cheek tributes to the number pi. Our original gangsta rap, “Lose Yourself (In The Digits),” a parody of the well-known Eminem hit, has been performed live in front of hundreds of students, and made its 2006 debut in classrooms around the world as a free, downloadable mp3 file. We will continue to create our own content, and try to direct you via links to the best Pi Day creations on the Web.

Finally, we believe that mathematics classes are far too often isolated from other subjects, whereas courses like English and History often overlap and interact. To this end, we will strive to produce interdisciplinary content, both in stories and activities, for use either inside a math classroom, or as a way to invite other teachers to share in a school-wide Pi Day celebration.

Make sure to check in with us each year as Pi Day approaches, or any time you’re teaching about pi, to see what fun and useful things we might have in store for you….


More Pi Day Resources:

Download an extensive collection of pi facts, activities, and resources (the collection has been divided into two sections to speed download time and is in Microsoft Word format):

(3) “In Medieval Architecture, Signs of Advanced Math” by John Noble Wilford

Source:  The New York Times – 27 February 2007

In the beauty and geometric complexity of tile mosaics on walls of medieval Islamic buildings, scientists have recognized patterns suggesting that the designers had made a conceptual breakthrough in mathematics beginning as early as the 13th century.

A new study shows that the Islamic pattern-making process, far more intricate than the laying of one’s bathroom floor, appears to have involved an advanced math of quasi crystals, which was not understood by modern scientists until three decades ago.

The findings, reported in the [February 23] issue of the journal Science, are a reminder of the sophistication of art, architecture and science long ago in the Islamic culture. They also challenge the assumption that the designers somehow created these elaborate patterns with only a ruler and a compass. Instead, experts say, they may have had other tools and concepts.

Two years ago, Peter J. Lu, a doctoral student in physics at Harvard University, was transfixed by the geometric pattern on a wall in Uzbekistan. It reminded him of what mathematicians call quasi-crystalline designs. These were demonstrated in the early 1970s by Roger Penrose, a mathematician and cosmologist at the University of Oxford.

Mr. Lu set about examining pictures of other tile mosaics from Afghanistan, Iran, Iraq and Turkey, working with Paul J. Steinhardt, a Princeton cosmologist who is an authority on quasi crystals and had been Mr. Lu’s undergraduate adviser. The research was a bit like trying to figure out the design principle of a jigsaw puzzle, Mr. Lu said in an interview.

In their journal report, Mr. Lu and Dr. Steinhardt concluded that by the 15th century, Islamic designers and artisans had developed techniques “to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before discovery in the West.”

Some of the most complex patterns, called “girih” in Persian, consist of sets of contiguous polygons fitted together with little distortion and no gaps. Running through each polygon (a decagon, pentagon, diamond, bowtie or hexagon) is a decorative line. Mr. Lu found that the interlocking tiles were arranged in predictable ways to create a pattern that never repeats–that is, quasi crystals.

“Again and again, girih tiles provide logical explanations for complicated designs,” Mr. Lu said in a news release from Harvard.

He and Dr. Steinhardt recognized that the artisans in the 13th century had begun creating mosaic patterns in this way. The geometric star-and-polygon girihs, as quasi crystals, can be rotated a certain number of degrees, say one-fifth of a circle, to positions from which other tiles are fitted. As such, this makes possible a pattern that is infinitely big and yet the pattern never repeats itself, unlike the tiles on the typical floor.

This was, the scientists wrote, “an important breakthrough in Islamic mathematics and design.”

Dr. Steinhardt said in an interview that it was not clear how well the Islamic designers understood all the elements they were applying to the construction of these patterns. “I can just say what’s on the walls,” he said.

Mr. Lu said that it would be “incredible if it were all coincidence.”

“At the very least,” he said, “it shows us a culture that we often don’t credit enough was far more advanced than we ever thought before”…


[See for links to more news coverage.]

(4) Governors Focus on STEM Education, Communicating Innovation

Source: National Governor’s Association – 25 February 2007
URL (Press release, includes photos):

On the second day of the National Governors Association (NGA) Winter Meeting (February 25), governors focused on the importance of science, technology, engineering and math (STEM) education in creating a competitive global economy.

STEM education is one of the central elements of NGA Chair Arizona Gov. Janet Napolitano’s Innovation America initiative (see below for the Executive Summary). Last Sunday’s plenary session at the J.W. Marriott Hotel provided governors an opportunity to hear from national experts on STEM and ask questions that have emerged as they begin to develop their own STEM agendas. Dr. James H. Simons, founder of Math for America and president of Renaissance Technologies Corp., opened the session with a keynote address focused on the importance of improving student achievement in math.

Following his address, governors heard from a panel of education experts, each of whom represented a different aspect of STEM education. Dr. William H. Schmidt, University Distinguished Professor at Michigan State University, spoke about the role of international studies in STEM reform. Mary Ann Rankin, dean of the College of Natural Sciences at the University of Texas at Austin, addressed the role of teacher preparation as part of a larger STEM capacity building reform. Dean Kamen, inventor (e.g., Segway), entrepreneur and advocate for science and technology, spoke about the role of innovation and education in the economy.

Noted communicator Frank Luntz closed the session with a presentation ( on effective ways to communicate the importance of innovation.

“The presentation by Dr. Simon and the panelists provided a variety of perspectives on the importance of developing a STEM policy agenda as a key component of making states more competitive,” said Gov. Napolitano. “Their personal experiences with science, technology, engineering and math education are excellent examples of how these skills contribute to economic success.”

“Governors are charged with determining how we can raise standards, strengthen the curriculum, improve teaching and motivate more students to pursue careers in science and technology,” said NGA Vice Chair Minnesota Gov. Tim Pawlenty. “I am confident my colleagues and I all learned valuable lessons in communicating these aims and crafting action plans to achieve them.”

At the session, NGA also announced the availability of grants to engage in K-12 STEM education redesign that supports a state economy’s innovative capacity. The State Centers for STEM Excellence grant program is made possible with the generous support of the Bill & Melinda Gates Foundation and the Intel Foundation. More information about the grant program is available on the NGA Web site.


Founded in 1908, the National Governors Association (NGA) is the collective voice of the nation’s governors and one of Washington, D.C.’s most respected public policy organizations. Its members are the governors of the 50 states, three territories and two commonwealths. NGA provides governors and their senior staff members with services that range from representing states on Capitol Hill and before the Administration on key federal issues to developing and implementing innovative solutions to public policy challenges through the NGA Center for Best Practices.

(5) Innovation America: Building a Science, Technology, Engineering and Math Agenda

Source: National Governor’s Association (NGA)

Executive Summary

In the new global economy, states need a workforce with the knowledge and skills to compete. A new workforce of problem solvers, innovators, and inventors who are self-reliant and able to think logically is one of the critical foundations that drive innovative capacity in a state. A key to developing these skills is strengthening science, technology, engineering, and math (STEM) competencies in every K–12 student.

Results from the 2003 Third International Mathematics and Science Study, which measures how well students acquired the mathematics and science knowledge they have encountered in school, show that U.S. eighth and 12th graders do not do well by international standards. Further, our own National Assessment of Education Progress confirms persistent math and science achievement gaps between students relative to their race/ethnicity, gender, and socioeconomic status.

Three key issues have been identified as obstacles to having world-class STEM education system:

On a variety of STEM indicators it is clear that too many of our high school graduates are not prepared for postsecondary education and work. A recent study by ACT, Inc. has demonstrated that regardless of a student’s postsecondary pathway, high school graduates need to be educated to a comparable level of readiness in reading and math proficiencies. Nearly three out of 10 first-year college students are placed immediately into remedial courses. In the workforce, employers report common applicant deficiencies in math, computer, and problem solving skills. A wide variety of studies and indicators have demonstrated that our education system continues to fail to prepare many students for the knowledge based economy.

The second obstacle is the misalignment of STEM coursework. Currently, there is a lack of alignment between K–12 postsecondary skills and work expectations; between elementary, middle, and high school requirements within the K–12 system; and between state standards and assessments and those of our international competitors. This misalignment has resulted in a system in which students participate in incoherent and irrelevant course work that does not prepare them for higher education or the workforce.

Finally, the STEM teaching workforce is under-qualified in large part because of teacher shortages caused by attrition, migration, and retirement. This shortage has led to what has been called a “revolving door” of STEM educators. Many of those who are teaching STEM classes are unprepared and/or teaching out of their subject area; thus, students in STEM classes experience a lower number of highly qualified teachers during the course of their studies. Simply increasing the number of STEM teachers through financial incentives and other recruitment strategies will not solve the problem. States must also support high quality preparation and professional development for teachers that lead to improvements in large numbers of classrooms.

Governors are playing a lead role in restoring the value of the American high school diploma. Specific to STEM, states are increasing high school graduation requirements in math and science, strengthening math and science course rigor through expansion of Advanced Placement programs and alignment of ACT assessments and coursework, and building aligned K–16 data systems that can track student progress from K–12 into the postsecondary system.

A state with an effective STEM policy agenda uses its power to set academic content standards; require state assessments, high school graduation requirements, and content-rich teacher preparation and certification standards; and develop new models to support an effective K–12 STEM classroom.

Governors should lead efforts in their states to:

1. Align state K–12 STEM standards and assessments with postsecondary and workforce expectations for what high school graduates know and can do.

– States should focus on aligning standards and assessments with international benchmarks through state level participation in international assessments.

– States should align K–12 STEM expectations with all postsecondary pathways.

– States should align STEM expectations between elementary, middle, and high school levels to create a coherent K–12 system.

2. Examine and increase the state’s internal capacity to improve teaching and learning.

– States should use a process of international benchmarking to evaluate current capacity.

– States should support the continued development of K–16 data systems to track the STEM preparation of students.

– States should develop a communication strategy to engage the public in the urgency of improving STEM.

– States should develop or charge their P-16 councils to lead the alignment of STEM expectations throughout the education system and the workplace.

– States should support promising new models of recruiting, preparing, certifying, compensating, and evaluating teachers in STEM content areas.

– States should support extra learning opportunities to support STEM teaching and learning in the schools.

3. Identify best practices in STEM education and bring them to scale.

– States should create and expand the availability of specialized STEM schools.

– States should develop standards and assessments in technology and engineering as well as math and science.

–  States should support the development of high quality STEM curricula for voluntary use by districts.

– States should develop standards for rigorous and relevant CTE programs that prepare students for STEM related occupations.