COMET • Vol. 1, No. 15 – 3 June 2000


(1) California Professional Development Institutes for Mathematics


A statewide listing of all institute dates and university contacts is available at . “The California Professional Development Institutes offer a wide array of options for teachers of mathematics who would like to improve their own content knowledge in mathematics and who are interested in improving the mathematics achievement of their students. [These] institutes will be offered to teams of teachers during the summer of 2000 with follow-up during the 2000-2001 school year” ( Institute participants receive a stipend of $1000-$2000 depending upon the length of the institute. For more information, contact Georgia Makris at or 510-987-9510.

(2) Update on the Mathematics Framework for California Public Schools

The errata list for the Mathematics Framework is available at . You can download the Framework at


(1) “A Difficult Formula: Math = Fun” by Daniel McGinn

Source: Newsweek — 5 June 2000

At most colleges there’s only one thing less popular than a calculus class: a 9 a.m. calculus class. But on a recent morning at Williams College, all 50-odd seats are filled as Edward Burger teaches differentiation. Not even Burger, a former stand-up comic, can turn 8×3+2x into fodder for Jay Leno. But he can try. As students work problems, their professor clambers between rows, offering encouragement. When the class seems particularly hung up–doesn’t anyone remember the quadratic formula?–he coaxes a woman into singing the formula, to the tune of “Jingle Bells” (hum along: “Negative B/plus or minus the/square root of B squared…”).

This is math? It is at Williams College. “We do whatever it takes to get the biggest audience possible,” says department chair Colin Adams. And it’s working. Next week the elite liberal-arts school in Massachusetts will graduate a record 42 students with bachelor’s degrees in mathematics. That’s 8 percent of the class–at a time when just 1 or 2 percent of students nationally choose math as a major (chart). Even at Williams math can’t compete with the hottest major, economics. But the subject has earned a respectable buzz, which may offer larger lessons for educators clinched in a national debate over math. The issues are complex but boil down to one thing: how to excite kids about math? At Williams the answer is fun, imaginative teaching.

In the ’70s and ’80s, Williams’s math department was like that of most schools: arrogant and uncompromising. “The sense was that math ought to be hard, and only the best and brightest students should be taking it,” says Olga Beaver, who joined the faculty in 1979. So tough introductory classes acted as filters, causing many students to find a different major. But in the late ’80s a new generation of faculty arrived and made intro classes less intimidating. They developed courses that would appeal to nonmajors, like math for finance and math for medicine. In classrooms, teachers began assigning more group projects to combat the image of math as a solitary pursuit.

The bigger changes came as the department focused on hiring great teachers, regardless of their research specialty. Two of Williams’s 12 math professors have been named the country’s best collegiate math teacher in recent years; Burger is a finalist this year. In 1995 Williams swiped a star statistics professor from Princeton; now 40 percent of Williams undergrads take stats. Make no mistake: the school is still teaching tough material. In differential geometry one morning, Frank Morgan fills whiteboards with incomprehensible stuff. (Sorry, professor: you lost NEWSWEEK at “hello.”) But to make it accessible he describes the history behind the theories, from Kepler to Newton to Einstein. Later Morgan takes a seat among the students and stares at the board with them. “Don’t be scared,” he says. “Just enjoy watching how complicated it is.”

Students have learned to find beauty in that complexity. Sitting around the library, five students recall Tom Garrity teaching an entire class while hopping on one foot, just to keep kids interested. But they also remember struggling through marathon take-home exams and burning through erasers long past midnight. Most intended to major in something else, but were wooed by personable professors who teased them with challenges. After graduation a few will become mathematicians, but most will take jobs in finance, computers or a host of other fields. But Shara Pilch, who graduates with a math degree next week, intends to use this equation on younger students. “When I do a math problem, I can feel my neurons grow,” she enthuses. Pilch will begin firing neurons as a high-school teacher in Webb, Miss., next fall.

(2) “New, New Math = Controversy”

SourceCBS News Online — 28 May 2000,1597,200272-412,00.shtml
[Broadcast Transcript] You don’t have to spend much time in Marie Tourini’s 6th grade classroom to understand why she is a convert to new math, reports CBS News Correspondent John Roberts.

“I see more student engagement. I see more students feeling comfortable and becoming involved in the discussion and the thinking process,” explains Tourini.

This is not the new math that became popular in the 1960s. This is new new math — memorization is no longer emphasized. Neither are the mechanics of addition, subtraction, multiplication and division. Instead, children are encouraged to use language and problem solving skills to find answers to problems. And the answers don’t have to be exact. That’s all made new math pretty controversial.

“I think that they own it more,” says Tourini. “They understand it more than just having to memorize x and y.

Proponents of the new system say it’s not the math that’s new, it’s the teaching method.

“We know more about learning today than we did 20, 30 years ago,” says Fran Curcio, who helped develop the new curriculum. “And we know more about teaching than we did 20, 30 years ago.”

Curcio believes it keeps kids more engaged.

“It’s the problem that presents a situation that allows children learners to think about ‘What do I need, what do I know, what do I need to find out?'” she says. “And then they employ the tools of computation to solve the problem.”

But other mathematicians just hate new math, and believe it will not prepare students for college.

“There is a feeling among…a substantial part of the college and math research communities that some of what went on was that the baby got thrown out with the bath water,” said Dr. Sylvain Cappell, a mathematician at NYU’s Courant School of Mathematics.

“Look, we can’t change the fact that mathematics is hard. It’s hard for mathematicians too,” Cappell said. “One should approach math with a sense of play and a sense of fun as well as with the knowledge that it takes rigorous work. But it can’t just be feely-touchy. There is hard work to be done”…

“We all want to accomplish the same thing,” says Curcio. “That is to improve the mathematics curriculum, improve the success rate, and help children to feel good about themselves in the study of mathematics so they’ll go on to study more”…

(3) “The Math Meltdown” 

The 23 May 2000 and 30 May 2000 issues of the Christian Science Monitor contain Parts 2 and 3 of a 3-part series of articles pertaining to mathematics education. The titles and first paragraphs of these articles are found below, along with their URLs.

Articles from the 23 May 2000 issue:

(a) “The Roller Coaster Effect: In Math Education, Who Decides What Works Best?”
by Gail Russell Chaddock

Ever since William Hewlett and David Packard launched Silicon Valley out of a Palo Alto garage in 1939, math has counted for a lot in this town. Knowing your way around an algorithm is the sure way into the hottest high-tech market.

That’s why parents – many of whom were top math professionals at Stanford University or local software companies – took note when plans surfaced to revamp math in the middle schools. They didn’t like this new approach, especially after test scores plummeted. They also didn’t like being told that they’d have no say in how math was taught…

(b) “How a New Math Program Rose to the Top” by Mark Clayton

…Andover’s math test scores soar above those of most other schools in the state. Despite that, the prestigious school stopped offering its traditional math curriculum to new students in 1994 and began an experimental program known as Core-Plus Mathematics, based on National Council of Teachers of Mathematics 1989 (NCTM) standards…

(c) “Flaws in the Evaluation Process” by Mark Clayton

The Department of Education’s expert panel, assembled to find the best math programs in the United States, had a key problem, critics say. It relied heavily on studies of student achievement that were authored or co-authored by the directors of the programs themselves – or by people with close institutional or other ties to the program…

(d) “US School, Japanese Methods” by Marjorie Coeyman

Something exciting is happening at School 2 in Paterson, N.J. Students are starting to understand math concepts.

In 1998, at the end of the first year of an experiment in math education, eighth-graders at this struggling school saw their scores on standardized math tests jump 20 percent. Not only that, but their pass rate was 77 percent – much closer to the statewide pass rate of 86 percent. Scores from 1999 were similar…

(e) “How Japanese Students Learn Math: Teachers Get Good Results With Group Work, Problem-solving Approaches” by Marjorie Coeyman

A group of ninth-grade students are devising a formula for calculating the area of a stretch of winding road, and throughout the 50-minute period they remain intent on their task. They produce several possible solutions and reason them through until the principle behind the challenge is clear. At class’s end, some students linger for more problem solving.

It’s a typical slice of everyday life at this Japanese public school, run by the Japanese government for families living in the United States. It’s also one of many practices that teachers in Paterson, N.J., are taking in, intent on boosting their school’s math performance…

(f) “Department of Ed’s Top 10 Math Programs”

Below are math-reform plans that a US Department of Education expert panel calls “exemplary” or “promising,” along with their Web addresses…

(g) “Calculators in Class: Freedom from Scratch Paper or ‘Crutch’?” by Mark Clayton

…This isn’t just any math class. It is Core-Plus Mathematics, one of only five math programs designated as “exemplary” by the US Department of Education. The course emphasizes real-life problems, group learning, and weaving together subjects from algebra to trigonometry. It also uses calculators. A lot…

Articles from the 30 May 2000 issue

(a) “Changing America’s Path to Reform” by Marjorie Coeyman

…Math is moving to the top of the American educational agenda. Like School 2 in Paterson, N.J., thousands of schools around the United States are testing new approaches, spurred by a sense of urgency that American children are not keeping pace in a crucial area. The common goal: to set all students on paths that will open doors in a high-tech age.

But how to do that is controversial. US teachers have developed a thick skin against frequent reforms that encourage wild swings or suggest a lost golden age of learning. They’re not helped in their day-to-day efforts by a culture which prizes reading far above math in early grades, and where kids can define “nerd” well before they learn to multiply…

(b) “Puerto Rico Closes the Gap” by Marjorie Coeyman

For all the debate about overhauling math education in the US, there have been few actual gains in student achievement. That’s why news of a program in Puerto Rico has drawn attention from those interested in math reform.

In 1992, the island launched an initiative in its public schools, aiming to close a 70-point gap between public school students and their private-school counterparts on standardized tests. Educators expected modest improvement, but got a lot more…

(c) “‘I’d Never Go Back to Old Ways'” by Marjorie Coeyman

“The children are doing the discovery, and that’s more difficult for them and sometimes more difficult for us,” says Wanda Collazo, who has been teaching eighth- and ninth-grade math for six years using the Puerto Rican Statewide Systemic Initiative, the island’s math-reform method. “But I would never go back to the other way”…

(d) “Grade-school Math is Not So Elementary” by Gail Russell Chaddock

If you’re wondering why your kids aren’t picking up how to divide fractions, it could be that their teachers don’t quite get it, either.

That’s the message from “Knowing and Teaching Elementary Mathematics” (Lawrence Erlbaum), a book that is becoming a stealth hit for math junkies on both sides of the “math wars,” and a must read for anyone interested in solving the problems of public schools…

(e) “In France, An Assumption that Math is Important” by Gail Russell Chaddock

Euclid would feel right at home in a math class in Paris. The geometry problems on the blackboard would look familiar to the third-century B.C. Greek mathematician, as would the method of work: methodical, clear, and anchored in the language of proof…

(f) “Saxon Math: Practice, Practice” by Gail Russell Chaddock

You’d be hard pressed to find anyone neutral about Saxon Math. For many recent graduates of teacher education programs, it’s the incarnation of “drill and kill” – devoutly to be avoided.

But don’t tell that to parents storming school boards and state legislatures to get Saxon texts into schools. They’re still wondering why their eighth-graders can’t figure 10 percent of 100 without the aid of a calculator, and are convinced Saxon will get classrooms back to basics – or sanity…

(g) “We’re Off to See the Tutor” by Mark Clayton

Move over ballet, soccer practice, and little-league baseball. One of America’s fastest-growing after-school rituals is piling kids into the car to go get tutored in math.

Amid rising parent concern that students just aren’t “getting it” at school, for-profit “math remediation” companies with names like Kumon, Sylvan, Score, and others are stepping in to fill the math gap…

(h) “More Challenge, not Less, Turns Kids Onto Math” by Marjorie Coeyman

William Johntz was casting about for ways to engage inner-city remedial students in math. Finally, it hit him: Give them harder material.

The year was 1963. But the counterintuitive approach that the mathematician, psychologist, and math teacher set in motion during his lunch hours in Berkeley, Calif., is going strong four decades later…


School’s In Conference

8-10 August 2000
Sponsored by the California Department of Education
Theme: “Spotlight on Accountability: From Policy to Partnerships”

“The State Superintendent’s Symposium on critical issues related to accountability will feature models of effective practice along with information that will impact California school operations during the coming year and beyond.”


(1) Apple Universe
This Web site contains over 20,000 resources and 1000 lesson plans (“units of practice”) for teachers.

(2) ERIC Digests
ERIC Digests are:

* short reports (1,000 – 1,500 words) on topics of prime current interest in education.

* targeted specifically for teachers, administrators, policymakers, and other practitioners, but generally useful to the broad educational community.

* designed to provide an overview of information on a given topic, plus references to items providing more detailed information.

* produced by the 16 subject-specialized ERIC Clearinghouses, and reviewed by experts and content specialists in the field.

The full-text ERIC Digest database contains 2,184 Digests published through March, 2000. The database is updated quarterly

(3) ERIC Clearinghouse on Assessment and Evaluation
“Your clearinghouse for assessment, evaluation, and research information”

* We provide balanced information concerning educational assessment, evaluation and research methodology.

* We provide resources to encourage the responsible use of educational data.

* We promote the best resources within our scope.

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).