COMET • Vol. 6, No. 10 – 31 March 2005


(1) Be a Part of the NCTM Annual Meeting in Anaheim, 6-9 April 2005

Are you planning to attend the NCTM conference in Anaheim next week? If so, the Local Arrangements Committee is still seeking volunteers to assist in a variety of capacities and would appreciate your help! If you are interested in volunteering, please contact Janet Trentacosta as soon as possible with your available times/days: Also let Janet know which of the following committees interest you:

= Hospitality: Staffs the Hospitality Desk during the Annual Meeting hours; offers attendees information on, and directions to, local services, sites, and events.

= Meeting Rooms: Checks meeting rooms at every room changeover; places “Session Full” signs outside of meeting rooms; changes signs for following-day presentations.

= NCTM Bookstore: Assists staff in unpacking, sorting, and displaying NCTM materials; supports staff in assisting Bookstore customers during exhibit hours; helps box the remaining materials at the end of the meeting.

= Signs: Arranges signs to be placed outside each session room and changes signs as needed.

= Speaker Support: Staffs the speaker check-in support desk and speaker support room.

= Special Needs: Assists individuals with special needs; assists with special needs equipment.

= State/Local Affiliates Booth: Staffs the California Mathematics Council (CMC) booth; offers attendees information on the state and local mathematics affiliates; provides information on CMC publications.

= Student Hosts: Finds and helps train students to work as helpers at the Annual Meeting.

= Technology: Hosts and assists in the Cyber Cafe and/or computer workshop labs.

As a volunteer at the NCTM Annual Meeting, you will be provided with a complimentary t-shirt. Please email your size to Janet: M  L  XL  XXL

* For more information on the NCTM conference in Anaheim, visit the following Web site:  A useful online conference planner is available at  Search for sessions by key words or speaker names, add the sessions to your planner, and print out your personal conference schedule!

(2) [California Education] Fact Book 2005

Source:  California Department of Education
URL (Fact Book):

A Message from the State Superintendent of Public Instruction, Jack O’Connell:

[A] new resource, Fact Book 2005, includes a wealth of data and background about programs in California public schools and at the California Department of Education. The document answers many of the questions that educators, students, parents, elected officials, policymakers, media representatives, and others have about our school system. Our schools deserve our attention and our support, particularly during these difficult fiscal times. I appreciate your interest in learning more about California’s public education system, and I hope you find Fact Book 2005 useful. It can be downloaded at

(3) California Ed-Data Partnership Website Now Features The New Base API Scores

Source: “New From EdSource” (29 March 2005) –  or (650) 857-9604.

Clear, user-friendly reports on the new Base API scores are now available at the Ed-Data website.  In addition, new accountability reports provide performance data for school districts and the state as a whole.  Just go to, select the school or district of interest, and choose Accountability from the Select Report pull-down menu. On the tab labeled API Base, you will see the 2003-04 data just released by the California Department of Education, as well as Base APIs from previous years.  The reports include information about schools and districts and about their significant subgroups of students, including various ethnicities and students who are socioeconomically disadvantaged, disabled, or English learners. Other helpful features that you can find by clicking on the tabs are (a) API Growth reports for school districts and the state and (b) Adequate Yearly Progress (AYP) reports that are required by the federal No Child Left Behind Act (NCLB).

The California Ed-Data Partnership is unique to our state and includes the California Department of Education, the Alameda County Office of Education, FCMAT, and EdSource. Watch the website for a new release coming soon that will provide a robust new way to compare districts. It will use multiple criteria including student performance and demographics, teacher characteristics, and financial data.

(4) MSRI Conference: The Mathematical Knowledge for Teaching (K-8): Why, What and How?

Source: Mathematical Sciences Research Institute (MSRI); Marianne Smith, MSRI Communications Consultant

This workshop, which will be held on the Asilomar Conference Grounds in Pacific Grove on May 25-28, is the second conference in the MSRI series, “Critical Issues in Mathematics Education.” The deadline for registration is May 15 (or April 10, if you are applying for a travel grant). The conference itself is free of charge.

The conference takes as a premise that improving students’ mathematics learning depends on improving mathematics teaching, for which teachers’ knowledge of mathematics is a key factor. It will bring together different groups for whom issues of teachers’ mathematical knowledge are of critical concern, and explore current perspectives, evidence, and programs. Three questions structure its highly interactive design:

1.  Why should K-8 teachers know mathematics?

2.  What is the nature of the knowledge of mathematics needed for effective teaching?

3.  What can mathematics departments and schools of education do to help teachers develop such knowledge?

The conference will foster productive partnerships among research mathematicians, mathematics educators, educational researchers, teachers of school mathematics, and policymakers that will support them in their efforts.

Conference organizers: Deborah Ball, Chair (University of Michigan), Herb Clemens (Ohio State University), David Eisenbud (MSRI), Jim Lewis (University of Nebraska)

Committed speakers (as of March 11, 2005):

Scott Baldridge, Lousiana State University

Hyman Bass, University of Michigan

Sybilla Beckmann, University of Georgia

Ken Gross, University of Vermont

Ruth Heaton, University of Nebraska

James Hiebert, University of Delaware

Heather Hill, University of Michigan

Roger Howe, Yale University

Jim Lewis, University of Nebraska

Liping Ma, Carnegie Foundation for the Advancement of Teaching

Jim Milgram, Stanford University

David Monk, Pennsylvania State University

Ira Papick, University of Missouri

Randolph Phillipp, University of California at San Diego

Paul Sally, University of Chicago

Lee Shulman, Carnegie Foundation for the Advancement of Teaching

Akihiko Takahashi, DePaul University

Kristin Umland, University of New Mexico

Hung Hsi Wu, University of California at Berkeley

Funding: Funding is sometimes available to support workshop attendance. Students, recent PhDs, women, and minorities are particularly encouraged to apply. Please send an email explaining your interest in the workshop along with your registration form. If you are a student, please also solicit a letter from a faculty advisor. Otherwise, submit a current vita or bibliography. Funding awards are made typically 6 weeks before the workshop begins. Requests received after that point are considered only if additional funds become available.

Registration: Please register on-line at

(The funding section of the form follows the registration section.)

For more information:

Questions about this workshop may be emailed to


(1) Excellence in Science, Technology, Engineering, and Mathematics Education (ESTEME) Week – April 11-16


The U.S. Department of Education (ED) and the National Aeronautics and Space Administration (NASA) are partnering with other U.S. Government agencies and scientific societies to sponsor activities for 2005’s “Excellence in Science, Technology, Engineering, and Mathematics Education (ESTEME) Week.” This year’s ESTEME week will be April 11–16, 2005. The activities during ESTEME Week are an opportunity for the nation’s schools to focus on improving math and science education. You can participate by attending or helping to produce a public event, or by supporting a hands-on science experience in your home, school, and community. Visit the above Web site for more information.

(2) “Math Emerges as Big Hurdle for Teenagers” by Debra Viadero

Source: Education Week – 23 March 2005

Researchers from the United Negro College Fund went to West Virginia last year and asked 62 high school dropouts in the federal Job Corps program a simple, open-ended question. “What was it about school,” they wanted to know, “that caused you to quit?”

With surprising consistency, a majority of the participants, most of whom were African-American or Hispanic, gave the same answer: “Math.”

Though the results are not scientific, they point to a challenge that confronts policymakers and educators as they campaign to make American high schools more academically rigorous. Experts agree that if the goal is for all students to graduate from high school ready for college or other postsecondary study, schools have their work cut out for them, at least in mathematics.

The challenge may be particularly daunting, these experts add, when it comes to the kinds of students drawn to training programs like the Job Corps–students who are members of minority groups or those who fall at the lower end of the academic-achievement scale. Yet, they note, the emphasis at the federal level so far has primarily been on improving reading…

National statistics bear out observations that high school math is a struggle for many students–not just those who are low-achieving or disadvantaged in some way.

On the 2000 National Assessment of Educational Progress test in math, 17 percent of high school seniors scored at the “proficient” level–just under half the percentage scoring at that level on the NAEP reading test. Twenty-two percent of college freshmen…are identified as needing remedial math, according to the National Center for Education Statistics…

On 12th grade NAEP math tests given in 2000, black and white students were separated by a gap of 34 scale-score points–about the same as in 1990. (Among younger students, mathematics differences on NAEP tests narrowed slightly between black and white students over roughly the same period.)

“It doesn’t matter whether they’re male or female, African-American students do tend to experience mathematics in school in a qualitatively different way than other folks,” said Danny Bernard Martin, an associate professor of mathematics education at the University of Illinois-Chicago.

The “algebra for all” movement begun in the 1990s is a case in point, he said. Prompted by studies showing that algebra was a “gatekeeper” course that paved the way for students to take higher-level math and go on to college, many districts began requiring students to take a first-level algebra course by 8th or 9th grade.

“But ‘algebra’ is not algebra in every location,” Mr. Martin said, noting that many pupils got watered-down versions of the subject. “For many students of color, they may have taken the math requested, and then tried to enter college and tried to enter the workforce and found out they were not prepared”…

Experts agree that, at a minimum, the United States will have to improve preparation for math teachers at all levels if all students are to be held accountable for reaching higher levels of achievement.

Research is less definitive on what makes for good math instruction at the high school level, particularly for lower-achieving students. Indeed, federal education officials say, the reason the Bush administration has emphasized reading instruction up until now is that research in that subject is further along than studies on math instruction.

The enduring “math wars” are evidence that math educators and mathematicians remain divided, even in their own communities, on the proper focus of math study and how it should be taught…

(3) Characteristics of High-Performing, High-Poverty Schools

Source:  ASCD ResearchBrief, 3(6) – 15 March 2005

Do high-performing, high-poverty [elementary] schools share common characteristics or practices that differ from those found in lower-performing schools?

The Bottom Line:  High-performing, high-poverty schools seem to exhibit a number of common traits that differ significantly from practices in lower-performing, high-poverty schools, including a schoolwide ethic of high expectations; caring, respectful relations between stakeholders; a strong academic and instructional focus; regular assessment of individual students; collaborative decision-making structures and a nonauthoritarian principal; strong faculty morale and work ethic; and coordinated staffing strategies.

For more details on this study, access the Web site above or download the original report at

(4) Pushing Algebra Down: Transcript of Online Chat with NCTM President Cathy Seeley

Source:  National Council of Teachers of Mathematics

An increasing number of schools are choosing to offer, or require, a course in algebra for students in grade eight. While the motivation for pushing algebra down is admirable, it may not be the best solution for our students.

*  How do we make the development of algebra a continuous part of the pre-K–12 curriculum?

* How do we teach algebra at the secondary level in a manner that engages, challenges, and prepares all students for the mathematics they need for their future?

*  How do we give more to students without necessarily starting them earlier?

View the transcript of this March 16 online chat at the above Web address.

(5) “Proof Positive” by Lani Harac

Source: Teacher Magazine – 1 March 2005

After figuring out why many kids hate math, longtime educators Bob and Ellen Kaplan created an after-school program in which children as young as 5 formulate equations of their own–and actually enjoy doing it.

The unadorned fourth-floor classroom in Harvard University’s Science Center was an appropriate foil for the theories being discussed within it. On a chilly November evening as gray as the room itself, a rounded older man with a bushy white mustache conducted a math lesson on the concept of infinity.

“What we’re trying to figure out is if there’s a one-to-one correspondence between points on a line and points on a plane,” he told the 17 students, dragging chalk along the blackboard to create a square with dotted lines.

The students had already learned that a line consists of an infinite number of points; pick any two numbers (0 and 1, for example), and there’s always another between them (say, 0.5). The same is true for a plane, except each point is represented by two numbers, commonly called x and y coordinates, that relate to two perpendicular edges of the plane.

The class was trying to determine whether a plane and a line contain the same number of points–it was either that or acknowledge that there are different sizes of infinity. They’d studied, in particular, the work of Georg Cantor, a 19th century German mathematician who’d come up with a rule to establish the correspondence, but they hadn’t been told how he did it. And now, after adding, dividing, and trying other functions with various numbers, they were stumped.

Still, there was time left. “We’ve spent almost an hour on this,” said the instructor, Bob Kaplan. “Of course, Cantor spent three years nonstop.”

It’s important to note that these students weren’t Harvard undergrads. They were 9- and 10-year-olds voluntarily participating in what Kaplan and his wife, Ellen, call the Math Circle, their version of a roughly century-old Eastern European practice…

For all the talk about “math wars” in this country, most public school classes focus more on rote memorization than on theory. But the Kaplans, after 40-plus years as educators, believe that learning the mathematical process is an end in itself. The approach that they and their Math Circle instructors employ during these after-school sessions, which serve kids ages 5 to 18, is simple: present an abstract concept as a puzzle, then let the students wrestle with it and come up with their own solutions. Not only is the process fun, the Kaplans believe, but it can be applied to other subjects as well…

Each Math Circle class focuses on one topic per semester. Students are given a complex problem to solve and have to come up with ways to tackle it; the instructor simply facilitates the process. The classes take place once a week–either after school for an hour on weekdays or, for kids 11 to 18, three hours each Sunday. Tuition is $225 for 10 weeks ($450 for the Sunday session), although scholarships are available for families who need it. While some kids have been compelled by their parents to attend, most choose to be there, and close to 80 percent go to public schools.

What the Kaplans–with help from a half-dozen other instructors–are not running is a tutoring or test prep program. Theirs is a nonprofit organization working in space donated by both Harvard and Northeastern universities, and many students are repeat participants. This past fall, 125 children were enrolled in the Math Circle, but attendance has been as high as 200, and thousands have “graduated” in the past 10 years.

Yasmin Siraj is a sibling of a former student. “I like learning about strategies, how to add numbers and subtract numbers really fast,” the 8-year-old says of her Math Circle experience. “Every problem we’ve tried, we’ve figured out the answer.”

Yasmin engages in a multitude of extracurricular activities, including figure skating. But her father, Ra’ad, says the alternative math lesson is worth fitting into the family’s busy schedule. “The focus is not on getting all the arithmetic right before you can tackle the advanced concepts,” he says. “The traditional curriculums don’t seem to capture the fun of math.”

This notion of fun is what got the ball rolling in 1994, when Ellen was teaching at the private Commonwealth School in Boston. Bob, who’d taught there for 34 years, had a taken a post elsewhere the year before, and they both continued to encounter kids resistant to learning mathematics. “We were sitting on our couch saying, ‘Isn’t it baffling? Students hate math,'” Bob recalled.

“And they don’t even know what it is,” Ellen interjected. “It’s not fair”…

They decided 10 years ago to call some friends and invite them to a Saturday morning get-together to simply “talk about math,” Bob said. “And that was the first Math Circle. Twenty-nine people came.”

The math circle idea isn’t new. It originated in Eastern Europe more than a century ago as an extracurricular way for educators and professionals to share with younger people the adventure of mathematical problem solving. Although many circles have popped up in the United States as prep groups for math olympiads, some hew to the original intent, and the Boston group specifically eschews competition, grades, and homework. Classes are open to kids of any skill level, although there is a certain amount of self-selection: More than half of the Kaplans’ alumni have gone on to study mathematics in college…

In its statement of beliefs, the National Council of Teachers of Mathematics explicitly notes the positive role of mathematical reasoning; president Cathy Seeley says that math circles like the Kaplans’ are not only educationally sound but also “likely to help students in their mathematical thinking.”

The irony is that when they were kids, the Kaplans hated math. Bob described his first encounter with the subject as “badly taught in a Quaker school in upper New York state.” He always failed math classes, “and I was rather proud of that,” he remembered. “Here was this nonsense that other people thought was worth a lot, … and I was damned if I was going to put a lick of work into it.”

He did, however, put effort into learning Greek, Sanskrit, and any other topic that would further his philosophy studies, his first love. But later, as a high schooler, “I came to realize [that] to attack the problems I was interested in, I’d have to understand some mathematics and also to approach the problems through mathematics,” he recalled. “And then the sheer beauty of it just hooked me”…

“When you’re in charge of it, as opposed to being the passive victim,” Ellen added, “you can make some sense of things, and you go over it until you can explain it to somebody else. I fortunately realized, ‘Now that I can explain it to somebody else, I won’t explain it to somebody else! I’ll let them have the same experience.’ “…

From the start, the couple opted to run the program independently so they could retain control of class content and managerial decisions. They’ve since written two critically well-received books, which attempt to do in print what they’ve done in the classroom: Bob’s The Nothing That Is: A Natural History of Zero, published in 1999; and their co-authored The Art of the Infinite: The Pleasures of Mathematics, in 2003…

The couple feels there aren’t enough educators who see things the way they do. Seeley of the NCTM characterizes U.S. math education as “sit and git”: The teacher talks, the students listen and then practice repetitive exercises. So the Kaplans have begun propagating their approach. In December, they demonstrated for educators and mathematicians at a conference in California, and they’ve already established circles in Great Britain. Their plans for 2005 include training sessions in Massachusetts, Indiana, and New York City and publication of their book about the Math Circle, Out of the Labyrinth: Mathematics Set Free.

They’ve also recruited internally: Sam Lichtenstein, an 18-year-old who joined the Math Circle shortly after its inception is now an instructor. A high school senior, he still attends the three-hour Sunday session. “We all work together to solve the problem,” he says. “In school, sometimes competition can detract from the overall experience.”

Lichtenstein, who’s considering a math-related major in college, takes classes at Harvard in place of those offered at his public school–a decision he attributes to his years with the Kaplans. The first thing he worked on at Harvard? Cantor’s theories about infinity. “That’s the seminal Math Circle class,” he says. “That’s what got me hooked.”