COMET • Vol. 1, No. 11 – 20 April 2000


I will be in New Orleans from April 22-29 attending the AERA conference and hope to see some of you at the SIG-Research in Mathematics Education meeting.

The California Curriculum Correlating Council (4Cs) archives COMET at


(1) California Mathematics Institutes:

Information about these institutes was mailed to all schools and principals in the state and is also available at

(2) “Math Mastery is After-school Magic”

by Suzanne Pardington
Source: Contra Costa Times — 13 March 2000
[The UC Berkeley] after-school tutoring program, “Break the Cycle,” matches some of the state’s most successful students with its least achieving ones, in hopes that the undergraduates will pass on their good study habits and a love of learning.

Break the Cycle founder and Executive Director Ronnie Stevenson says he hopes the program will become a model for after-school programs nationwide. “I’m trying to spark a national crusade,” he says. His efforts may be boosted by federal and state lawmakers, who are pressuring school districts to improve test scores at the nation’s most troubled schools. Some educators are turning to after-school programs as a way to reinforce and enhance what students learn in class. President Clinton has proposed spending $1 billion over the next five years on grants to start after-school programs.

What sets Break the Cycle apart, Stevenson says, is the one-on-one tutoring from college students, constant assessment of whether kids are learning, and positive reinforcement with prizes and praise… The Cal [UC Berkeley] interns each coach three children at a time through math problems, based on skills they will have to know on a statewide achievement test at the end of the school year. Every day they are pulled out of their two-hour tutoring sessions to take a quiz. Twice a week, they take a “mastery” test on a certain skill, say multiplying fractions or long division.

If they pass, they get prizes, ranging from pencils to medals and trophies. The ultimate prize is a 2 1/2-foot purple trophy with the student’s name engraved, awarded to those who excel on the state tests…

Third-grade teacher Vera Nobles says other students in the school see the children with awards and want to be in the program. But only 90 students in second through fourth grade are chosen on the recommendation of teachers and administrators. Many fall in the middle of the pack academically — the ones who get the least attention in regular classes….

“It helps with the high-level thinking skills and putting all the parts together,” she says. “It boosts their self-esteem. They are very proud of those awards.”

Stevenson says he’s giving children the early help he wishes he’d had himself. Twelve years after he graduated from Berkeley High School with a 2.1 GPA, Stevenson was admitted to UC Berkeley under an affirmative action second-chance program. With the help of tutors, he learned the study habits he lacked as a child. After two years, he was an honor student.

“That’s how you excel at Cal — it’s all about the number of hours you put in,” he says. “I thought, ‘Why do I have to be 31 years old before I find this out?'”

Stevenson started Break the Cycle in 1985 in junior high and high schools in Berkeley. In 1990 the focus shifted to elementary schools, where he felt the program could have greater impact. “If we support young people early, it will pay off,” he says.

Berkeley Pledge took Break the Cycle under its wing about four years ago, after the University of California ended affirmative action in admissions. Berkeley Pledge was founded as a “K-12 pipeline” to help students in poor areas — many of whom are minorities — do better in school.

It operates similar outreach programs throughout the Bay Area, including math and reading tutoring, teacher workshops, and mentorships at several West Contra Costa and Berkeley schools. Washington and Malcolm X in Berkeley are the only schools hosting Break the Cycle, Stevenson says. At Washington, West Contra Costa Unified School District provides $65,000 of the cost of the program, and the university contributes $88,000, he says.

Stevenson doesn’t plan to expand to other schools. Instead, he is developing a series of videos and handbooks for other organizations to use as a guide to start their own programs. The next essential step, he says, is an outside evaluation to prove he’s not just tooting his own horn.

“I’m not saying this is the answer for all the schools,” he says. “But if we’re talking about making a successful effort in teaching in traditionally underachieving schools, this is a way: putting undergraduate students in the classroom. It energizes the children and impacts their attitude toward learning — how much they think about school after school”…


The National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics was released in Chicago last week at NCTM’s largest conference in history (nearly 21,000 registrants). Information about the conference and this new publication can be found at Following are several news reports on the “Standards 2000” document.


(1) “Teachers Group Recommends Math Lessons in Preschool Education”

by Richard Lee Colvin
Source: Los Angeles Times — 13 April 2000 (now archived)
The professional organization of math teachers recommended Wednesday that lessons begin in preschool and that all students, not only those bound for college, take four years of math in high school.

The new standards released by the National Council of Teachers of Mathematics break down goals for students by grade levels and categories, including geometry, algebra, measurement, data analysis and problem solving. Other recommendations include allowing the use of calculators at all age levels and requiring students to be familiar with algebra and geometry by the eighth grade.

Standards 2000 is the first revision of a 1989 document that brought both change and controversy to the nation’s classrooms. That early plan recommended making math more meaningful by changing the focus from drills, rules and rote learning to “real-world” problem solving. Critics berated it for fostering “fuzzy math” that they said undermined high academic standards.

The organization’s leaders said in interviews that their intent in the 1989 document was widely misinterpreted. The new prescription, they say, represents a concerted attempt to clarify their position.

“We’ve always been for students being able to compute with paper and pencil and being able to recite their basic facts, but we want them to be able to do more than that,” said Lee V. Stiff, the organization’s incoming president and a math education professor at North Carolina State University.

In 1989, the math council was the first of the professional education groups to issue standards in reaction to a woeful description of mediocrity contained in the “Nation at Risk” report on the public schools issued in 1983 by the Reagan administration.

Other groups followed with standards in English, science and history. All, to one degree or another, became mired in controversy, with conservative critics contending that they had more to do with political correctness than academic rigor.

The math standards had a profound impact on textbooks, teacher training and teaching methods used around the world, an impact that leaders of the math organization said far exceeded their expectations.

They also sparked a long-running debate over mathematics that has raged in classrooms, legislatures and even courtrooms, where parents have sued to restore traditional teaching methods to their schools.

Critics have charged that the early standards emphasized trendy teaching methods at the expense of correct answers and that math-like activities using objects such as M&Ms had squeezed aside numbers.

Although acknowledging the criticism, Joan Ferrini-Mundy, a former council president who headed a 26-member team that wrote Standards 2000, said the council has not altered its basic views of what adds up to good math education.

In particular, she said, the council remains committed to letting teachers and students develop alternatives to traditional arithmetic procedures. The council also approves of using calculators to help understand numbers.

But she said the writing team listened to critics and tried to provide greater guidance to teachers where warranted. Nonetheless, Ferrini-Mundy conceded that the new standards will not placate critics.

Richard Askey, a math professor at the University of Wisconsin at Madison and a vocal critic of the standards, disputed the statement that the 1989 recommendations had been misunderstood.

He said the council was very clear about how to teach many procedures and was simply wrong.

A new element of Standards 2000 is the inclusion of preschool recommendations. Children are able from a very early age to understand concepts such as less and more and to use blocks or their fingers to count, said Alfinio Flores, a professor of math education at Arizona State University.

According to the standards, teachers can help even the youngest children explore numbers and patterns and solve problems using calculators. California, while not prohibiting calculator use, discourages it before the sixth grade.

Standards 2000 also says that all high school students need four years of math, regardless of whether they want to attend college. According to a report this year from the Council of Chief State School Officers, about 39% of high school graduates now take that much math.

Alan Schoenfeld, a UC Berkeley mathematician who headed the high school writing team, said the point is that all students need to be able to think mathematically, not just for success in college but on the job and in life as well.

“Before, it was symbolic math for the elite and dump the others aside,” he said. “Now it’s a core understanding for everybody–and those who want and need more–give it to them.”

Council leaders said the vision contained in Standards 2000 will not be achievable unless teachers at all levels are given a chance to learn more mathematics themselves. Elementary and middle school teachers in particular, according to the council, often have not mastered the math that they are expected to teach their students.

(2) “Math Revisions Add Emphasis on Basic Skills”

by David J. Hoff
Source: Education Week — 12 April 2000

After setting off dramatic changes in math instruction 11 years ago, the National Council of Teachers of Mathematics this week is planning to unveil its latest version of standards for learning, teaching, and testing the subject.

The standards the group was to release April 12 at its convention in Chicago will place an expanded emphasis on basic skills and list specific tasks that students should accomplish at designated points in their K-12 educations, according to the president of the 100,000-member organization.

Such changes are intended to assuage critics of the 1989 document and its companions published in the 1990s, as well as to refocus teachers on the essence of what teaching mathematics entails, said [Dr.] Glenda T. Lappan, the NCTM president and a professor of mathematics at Michigan State University in East Lansing.

The original standards, Ms. Lappan said recently, put too much emphasis on new ideas, such as teaching conceptual understanding over basic skills and integrating electronic calculators into instruction.

“That became, in some places and for some teachers, the goal. They missed the main goal: that children become highly skilled in using mathematics,” Ms. Lappan said. “We’ve tried to be very clear [in the revised standards] that mathematics is the goal.”

The final document is significantly different from the proposed revisions that the NCTM circulated for discussion in October 1998, Ms. Lappan said. It includes, for example, a detailed chart explaining what skills students should acquire in each of four grade-level bands and in each discipline of mathematics.

But the messages of the 1989 standards and the 1998 proposed revisions remain the same: Mathematics teachers need to reach all children by offering a variety of instructional strategies that encourage students to learn the concepts that lie under the algorithms they are learning….

Renewed emphasis on the basics will reflect what the writers of the original standards actually wanted but failed to communicate as they tried to incorporate new ideas into math classrooms, NCTM supporters say.

“The conceivers had in mind all along that basic skills are very important,” said Jerry P. Becker, a professor of mathematics curriculum at Southern Illinois University Carbondale and a former NCTM board member. “If they pay some more attention to that, it would be very good.”

The Gold Standard

In 1989, the NCTM released its Curriculum and Evaluation Standards for School Mathematics, a unique document at the time that defined what students should know and be able to do in the subject throughout their precollegiate schooling. Two years later, the group unveiled its standards for teaching the subject. It completed a trilogy in 1995, with standards for assessing student progress toward meeting the standards.

The Reston, Va.-based group began the process of revising the standards in 1996, soliciting comments for two years before releasing a draft for comment…

The math standards helped inspire a flurry of activity to write companion pieces for just about every subject taught in U.S. schools, from English and science to physical education and the arts. Standards for some other subjects were clouded in controversy from the start, especially in English and history, but the NCTM standards were widely accepted before some parents, educators, and policymakers started challenging them in the mid-1990s.

Dramatic changes in the content and methods of math instruction in the nation’s classrooms have resulted from the NCTM standards, according to Ms. Lappan and others.

“They are not far from the fingertips of almost anybody we deal with in the math community,” said Christopher T. Cross, the president of the Council for Basic Education, a Washington-based organization active in the national-standards movement. “Despite the criticisms, they have established themselves as being very credible. Of all the standards [in various subjects], they by far are the most known, the most accepted, and the most influential.”

“The NCTM standards have certainly reshaped how people talk about mathematics,” said Larry Cuban, an education professor at Stanford University. “There has been tremendous action in terms of districts and states adopting them. When you talk about implementation, you get much more variation. That is not unlike what has happened with every single curriculum reform in the past century.”

Mr. Cuban agrees with Ms. Lappan and others that teachers have been “highly selective” in what portions of the standards they rely on. “A very tiny percentage have” adopted them as a whole, he said.

That has led to problems in several areas, Ms. Lappan acknowledged.

For example, while the 1989 standards say “calculators can be used as an effective instructional tool for teaching computational skills,” they don’t recommend that calculators replace memorizing the multiplication tables, as may have happened in some teachers’ classrooms.

Even some NCTM supporters say the organization has failed to communicate the messages underlying the standards. Many of the criticisms of the standards are “well-founded,” but exaggerated, said Guillermo Mendieta, the director of mathematics education initiatives for the Achievement Council, a Los Angeles nonprofit group trying to increase the number of minority students entering and succeeding in college.

Many of the problems are created because teachers don’t have the understanding of the subject, said Mr. Mendieta, who had threatened a hunger strike if the Los Angeles Unified School District eliminated a curriculum modeled after the standards. Late last month, the district decided to keep the curriculum for next year at least. “We’re fighting policy battles, when it’s implementation that counts,” Mr. Mendieta said.

Impact of State Tests

While the math teachers’ council is likely to find continued opposition from back-to-basics advocates, it also is facing threats from the increasing importance of statewide testing systems, Mr. Cuban said. The standards “are at odds with what the teachers and administrators perceive will be rewarded,” he said. “The NCTM standards are oriented to performance-based assessments and real-world problems.”

(3) “Teachers’ Organization Calls for Higher Math Standards”

by Rosalind Rossi
Source: Chicago Sun-Times – April 13, 2000

Four years of high school math–more than required by Illinois–and “fluency” in computation were among the national standards recommended Wednesday by the National Council of Teachers of Mathematics.

The Standards 2000 Project marked the first major revision of a set of 1989 math standards that spawned a wave of similar standards nationwide and, critics say, helped trigger “math wars.”

The highly influential council recommended four years of high school math…The council’s 1989 standards called for three years, officials said.

“What ‘Principles and Standards for School Mathematics’ has done is set higher standards for our students and higher standards for ourselves,” incoming council President Lee V. Stiff said Wednesday during the group’s national convention at Chicago’s Hyatt Regency.

Critics have charged that the council’s 1989 standards prompted schools to downplay basic computation and to introduce calculators to kindergarten students. Some back-to-basics advocates derided the new wave of teaching as “fuzzy math.”

“Fuzzy math. We cared about that a whole lot,” said Standards 2000 Project Chairwoman Joan Ferrini-Mundy, adding the group sought feedback from critics this time.

For example, while arithmetic was de-emphasized in 1989, the revised standards encourage computational “fluency.”

The 2000 standards still advocate introducing calculators to kindergartners, but not for developing computation skill…

Critic Chester E. Finn Jr., president of the Thomas B. Fordham Foundation, said many of the changes sounded like improvements but predicted math wars will still rage. “There’s a fair amount of damage that’s already been done,” Finn said. “You can’t put the toothpaste back in the tube.”

(4) “Swarthmore Sells Home of ‘Ask Dr. Math’ to WebCT”

by Martha Woodall
Source: The Philadelphia Inquirer, April 6, 2000

One million educators, students and parents visit the Math Forum online math community every month. “Ask Dr. Math” has been sold.

Math Forum, the venerable mathematics education site established by Swarthmore College that includes the popular homework help area “Ask Dr. Math,” has been acquired by WebCT, an education company.

Math Forum was created at Swarthmore College in 1996 with the help of a $3 million grant from the National Science Foundation. Officials from WebCT and Math Forum announced the all-stock deal yesterday. WebCT, which is based in Vancouver, B.C., and Peabody, Mass., has developed a course-management system that 39,000 instructors use to put material for college classes on the Web. Terms of the stock deal were not disclosed, but Swarthmore College, which spun off a company called in July to operate the site, will remain an investor in the larger company.

Officials said the sale assures that the award-winning Math Forum will continue to operate even though its National Science Foundation funding ended in February. “This is a great opportunity for us,” Stephen Weimar, the president of, said yesterday.

The Math Forum is an online math community visited each month by 1 million educators, students and parents. Math teachers use the site to communicate with each other, share teaching strategies, keep abreast of trends in mathematics education, and gather classroom resources from the site’s nearly 800,000 Web pages.

Students also are attracted to the site by its wealth of information about mathematics. Many tackle the “problems of the week” that are posted for various grade levels. Kindergartners through high school seniors know to click on the “Ask Dr. Math” area for help with math problems and homework tips. More than 200 “math doctors” around the world volunteer to answer students’ questions. The site is at

Carol Vallone, president and chief executive officer of WebCT, and Greg Jarboe, its vice president of marketing, said Math Forum would be integrated into WebCT’s electronic learning hub.

Math Forum will retain its name, and remain in Swarthmore. Its 25 employees, about half of whom are math educators, will continue to manage the site. And access to the site will remain free.

Officials said joining WebCT would not only keep Math Forum alive, but enable it to grow. “I think everybody [at Math Forum] is very excited,” said David Paul, CEO of He said officials at Math Forum began exploring options two years ago that would keep the project afloat after its funding ran out.

Math Forum moved to private offices off campus in the fall. Several private investors put up money to keep the project going, but it had continued to search for new partners. “We have had discussions with a wide range of potential merger partners and funding partners,” Paul said. “It was the result of that that led us to choose WebCT.”

He said the math company’s officials were attracted by WebCT’s interest in using the Math Forum model to develop similar online communities around other disciplines, its experience working with academic institutions, and its own roots in academe. WebCT evolved from a series of Web-based course tools that an instructor at the University of British Columbia designed to teach his classes.

As the senior program director in the National Science Foundation’s Education and Human Resources division, Nora Sabelli worked closely with the Math Forum. She said the agency encouraged project managers to obtain outside funding to sustain the projects the National Science Foundation has nurtured.

Because the Math Forum was a very successful project, she said she was not surprised by yesterday’s announcement. Sabelli said: “A large number of our more successful projects are finding more ways of bringing in sustained funding.”

(5) North Carolina Exit Exam

If you are interested in writing items for the North Carolina Exit Exam, contact Dan Mix at or 800-767-8420 ext. 7198 (Riverside Publishing).

Writers are needed for 7th and 8th grade mathematics, Algebra I, secondary-level social studies and secondary science. The expected turn-around time for items is 5-6 days; $20 per accepted item is paid to writers.

COMET is an online newsletter that seeks to provide timely information in a digest format about state (California) and national news, articles, events, opportunities, and web resources related to mathematics education. Information from a variety of print and online sources is compiled and distributed via COMET approximately once a week. The target audience includes California PreK-12 teachers of mathematics and school/district administrators, as well as university faculty throughout the nation who are interested in issues related to mathematics education (with a focus on California news).