COMET • Vol. 1, No. 18 – 28 July 2000


(1) “‘Research Based’ Mathematics Education Policy: The Case of California 1995-1998” by Bill Jacob and Joan Akers.

Source: International Journal for Mathematics Teaching and Learning.

Available for downloading by going to and navigating to the IJMTL page.

Abstract (by the authors): In December 1998, the California State Board of Education adopted a new Mathematics Framework. The state had adopted Mathematics Standards the previous year, and the legislature appropriated one billion dollars for new standards-based instructional materials. The forward of the new Framework claims it provides “research-based information about how children learn.” The research described in the Framework supports an extreme (and expensive) shift in state policies on instructional materials, classroom instruction, professional development and assessment.

In this article the authors examine the history and content of the Framework’s research base. Since the State Board adopted the Framework with such enthusiasm, it is important for the research community to understand why. In part this was due to a public perception of a need for more ‘basics.’ But, a major reason is that prominent mathematicians authored key Framework sections and then endorsed the instructional strategies outlined by the psychologists who assembled the research. The Framework was supposed to present a balanced program including basic skills, conceptual understanding and problem solving. This paper takes a close look at the mathematician and psychologist authors’ views of each. The analysis reveals that although many of their ideas about mathematics teaching and learning are incompatible, overall their positions were combined in a way to mutually reinforce each other.

(2) “Davis Angry about TV Ad” by Aurelio Rojas

Source: Contra Costa Times – 28 July 2000

Supporters of a school voucher initiative began airing a television ad Thursday that uses film footage of Gov. Gray Davis criticizing the academic performance of California students. The governor says it falsely implies that he endorses the measure. The governor – who in fact opposes Proposition 38 [backed by venture capitalist Tim Draper] – issued a statement saying backers of Nov. 7 ballot measure “should be ashamed of themselves for their outright deception”…

If approved, the measure would offer parents a $4,000 publicly financed annual voucher, for each child in school, that could be used for private schooling. Opponents contend taxpayers cannot afford the price tag, but supporters say it would save money because California spends much more than $4,000 on each student….

“We’ve made substantial progress– double-digit improvement in the primary schools– which is a source of pride and I think will motivate everyone to do even better … My point is schools are finally moving in the right direction, test scores are going up. Our goal now is to stay the course, not put the car in reverse,” [Davis said.]


(1) “Music on the Mind” by Sharon Begley

Source: Newsweek — 24 July 2000

If you were to peek inside Sandra Trehub’s lab, you might easily mistake it for one of those obnoxious superbaby classes… But the University of Toronto psychologist isn’t trying to teach infants the finer points of Vivaldi. She is, instead, trying to shed light on whether the human brain comes preloaded with music software the way a laptop comes preloaded with Windows. In one test, Trehub varies the pitch, tempo and melodic contour of music, and finds that babies can detect changes in all three…

Music has charms to soothe a savage breast, but scientists are finding that it works those charms through the brain. At a recent conference of the New York Academy of Sciences, Trehub and dozens of other scientists interspersed their PET scans and MRIs with snatches of Celine Dion and Stravinsky as they reported on the biological foundations of music. Besides the musical babies, several other lines of evidence suggest that the human brain is wired for music, and that some forms of intelligence are enhanced by music. Perhaps the most striking hint that the brain holds a special place in its gray matter for music is that people can typically remember scores of tunes, and recognize hundreds more. But, we can recall only snatches of a few prose passages…

The most controversial finding about the musical mind is that learning music can help children do better at math. When a researcher at the recent conference in New York brought up these studies, he got an auditoriumful of laughs. Yet the link, reported in 1997 by Gordon Shaw of the University of California, Irvine, and Frances Rauscher at the University of Wisconsin, has held up. Last year Shaw compared three groups of second graders: 26 got piano instruction plus practice with a math video game, 29 received extra English lessons plus the math game and 28 got no special lessons. After four months the piano kids scored 15 percent to 41 percent higher on a test of ratios and fractions than the other kids. This year, Shaw reported that music can help bridge a socioeconomic gap. He compared second graders in inner-city Los Angeles to fourth and fifth graders in more affluent Orange County, Calif. After a year of piano, the second graders who received twice-a-week piano training in school scored as well as the fourth graders, who did not; half of the second graders scored as well as fifth graders.

But might music work its magic simply by making school more enjoyable, or because music lessons bring kids more one-on-one time with teachers? If that were so, then music should bring about improvements in many subjects. But it doesn’t. Although kids who receive music training often improve somewhat across the board due to the “good mood” and attention effects, finds psychologist Martin Gardiner of Brown University, “they just shoot ahead in math. This can’t be explained by social effects or attention alone. There is something specific about music and math.” That something might be that music involves proportions, ratios, sequences-all of which underlie mathematical reasoning.

The brain seems to be a sponge for music and, like a sponge in water, is changed by it. The brain’s left and right hemispheres are connected by a big trunk line called the corpus callosum. When they compared the corpus callosum in 30 nonmusicians with the corpus callosum in 30 professional string and piano players, researchers led by Dr. Gottfried Schlaug of Beth Israel Deaconess Medical Center in Boston found striking differences. The front part of this thick cable of neurons is larger in musicians, especially if they began their training before the age of 7. The front of the corpus callosum connects the two sides of the prefrontal cortex, the site of planning and foresight. It also connects the two sides of the premotor cortex, where actions are mapped out before they’re executed. “These connections are critical for coordinating fast, bi-manual movements” such as those a pianist’s hands execute in an allegro movement, says Schlaug. The neural highway connecting the right and left brain may explain something else, too. The right brain is linked to emotion, the left to cognition. The greatest musicians, of course, are not only masters of technique but also adept at infusing their playing with emotion. Perhaps this is why.

Whatever music does to the brain, scientists figured you would have to actually do music to get the effects. Well, maybe not. Researchers led by Dr. Alvaro Pascual-Leone of Beth Israel taught nonmusicians a simple five-finger piano exercise. The volunteers practiced in the lab two hours a day for five days. Not surprisingly, the amount of territory the brain devotes to moving the fingers expanded. But then the scientists had another group think only about practicing that is, the volunteers mentally rehearsed the five-finger sequence, also for two hours at a time. “This changed the cortical map just the way practicing physically did,” says Pascual-Leone. “They make fewer mistakes when they played, just as few mistakes as people actually practicing for five days. Mental and physical practice improves performance more than physical practice alone, something we can now explain physiologically.”

Pianists Artur Rubinstein and Vladimir Horowitz were legendary for hating to practice. Rubinstein simply disliked sitting in front of the piano for hours on end; Horowitz feared that the feel and feedback of pianos other than his beloved Steinway would hurt his concert performance. But both men engaged in extensive mental rehearsals. “Mental imagery may activate the same regions of the brain as actual practice, and produce the same changes in synapses,” says Josef Rauschecker of Georgetown University. Advice to parents trying to get children to practice: keep this to yourself.

(2) “Educators Adopt New Guidelines for Math” by Scott S. Greenberger

Source: The Boston Globe – 26 July 2000

Hailed by state officials as a compromise, a new math teaching guide cruised to final approval yesterday with some teachers still insisting it sacrifices real understanding on the altar of algorithms.

“Back to basics is moving backward. Number-crunching alone is no longer enough,” said Lee Stiff, president of the National Council of Teachers of Mathematics, who traveled from Washington to testify against the guide.

In approving a new math “curriculum framework” by a 7-1 vote, the state Board of Education ended a bitter, yearlong debate over how math should be taught and how closely classroom instruction should mirror the MCAS.

“This is a document that can be used to help our young people succeed in mathematics, which they’re not doing today,” said state Education Commissioner David P. Driscoll, a former math teacher who took over creation of the guide after it became mired in controversy.

Curriculum guides, which are required under the state’s 1993 education reform law and must be updated periodically, lay out what students should know in each grade. The controversy over the math guide began in the spring of 1999, when the Department of Education rejected a draft produced by a panel of mathematicians.

The panel said its guide would promote a deeper understanding of mathematical principles, instead of just forcing students to memorize functions and formulas. But state officials, along with some teachers and parents, said it was vague and weak on basic skills such as addition and subtraction. The frameworks are supposed to serve as a guide for MCAS test-makers, but the state said the panel’s version included too much that couldn’t be tested.

The department produced a revised guide in February. But members of the panel and others attacked it as a throwback to old-fashioned “drill and kill” math and little more than a list of items to be tested.

Instead of the framework driving the Massachusetts Comprehensive Assessment System exam, they said, the test was driving the curriculum.

Yesterday, Driscoll sat stone-faced as critics came forward before the vote to denounce the guide as “deeply flawed” and “rife with errors and inconsistencies.” Eight of the 10 speakers opposed the guide, and their comments elicited loud applause from a crowd that filled the boardroom at the department’s Malden headquarters.

James Kaput, a mathematician at the University of Massachusetts-Dartmouth, said the guide “trivializes math” by breaking it into “easily and cheaply assessed bits.”

But Wilfried Schmid, a Harvard mathematician who helped the department put together the final version of the guide, said that much of the criticism came from a “vocal minority” of math teachers trying to promote new theories at the expense of traditional teaching methods that work. Schmid said the guide wasn’t the proper forum to settle the teaching debate that divides the math community.

“The framework should talk about what the children need to know and when, and put it into context,” Schmid said. “We want to leave it to classroom teachers to decide exactly where to come down between a reform-oriented approach and something more traditional.”…

(3) “Math Teachers Worry New Frameworks Could Make Math More Confusing” by Heidi B. Perlman

Source: The Boston Globe — 25 July 2000

Barbara Goodman is worried a plan to change the way math is taught will show her daughter how to solve mathematical problems, but won’t help her understand how she came up with the answers.

Just five years after math educators began teaching students why math works not just how to add, subtract and multiply a new set of proposed regulations is aiming to bring the basics back into the classroom. Goodman is one of a growing group of teachers and parents concerned the new so-called curriculum frameworks will mean more rote memorization, and less focus on comprehension.

“I want my daughter to be able to do math on her feet,” she said. “I want her to be able to solve a problem in her head, but also know her multiplication tables”…

“The reality is students should have a math curriculum that challenges them, engages them and holds them up to high expectations,” said James Peyser, chairman of the Board of Education. “Not only do you need teaching methods that require more problem-solving, you also need a rich body of content that doesn’t turn math into something less than it should be”…

The current curriculum, written in 1995, encourages teachers to give students the freedom to use different techniques to get to the right answer…

“I know there is more than one way to skin a cat,” [Peyser] said. “But we need to teach the standard methods.”

But math professionals now say the new draft goes too far in the other direction. Educators say state officials have removed all reference to understanding the reasons behind math problems, a change that could leave behind those who aren’t math-naturals.

But mathematicians who helped make the revisions insist that adding basic theory to the frameworks does not remove its focus on understanding.

“We want children to learn basic fluency and computation. That’s all,” said Wilfred Schmid, a Harvard University math professor and a math adviser to the Department of Education. “Of course I’m in favor of understanding. But you don’t develop that without basic fluency first.”

“That’s the way it is in other countries, and that’s how it should be done here,” Schmid said.

But some teachers and parents aren’t so sure. “This is like going back to the 1950s,” said Deborah Shein-Gerson, an elementary math coordinator in the Brookline public schools.

Westwood parent Jan Weizel agreed…”It’s like we went through a Renaissance and now we’re entering a regression,” she said. “That worries me.”

(4) “Harcourt General Looking for a Buyer” by Mark Walsh

Source: Education Week — 12 July 2000

Harcourt General Inc., one of the nation’s largest educational publishers, surprised observers recently with the news that it was putting itself up for sale.

Among the Newton, Mass.-based company’s properties are names known throughout precollegiate education, such as Holt, Rinehart and Winston textbooks, Steck- Vaughn workbooks, and the Stanford Achievement Test.

Despite the publisher’s profitability and consistent revenue growth, its stock price has been depressed. That began to change last month when Harcourt announced that it was exploring strategic alternatives “to enhance shareholder value.” The stock, which had been trading on the New York Stock Exchange as low as $32.625 in the last year, immediately jumped about 31 percent, to $54.8125, on June 19, the date of the announcement.

“Harcourt General’s value in the public market does not presently reflect the quality of its businesses, record results, and bright prospects,” Chairman Richard A. Smith said in a statement last month. “By initiating this process now, we believe we can significantly accelerate the recognition of those values for our shareholders”…

Harcourt has confirmed it is looking for a buyer for the whole company, with a target price range around $5 billion, rather than selling off bits and pieces of itself…

Harcourt General took shape in 1991 when Mr. Smith’s family company, General Cinema Corp., bought the educational publisher known then as Harcourt Brace Jovanovich Inc. The new company adopted the Harcourt name and spun off General Cinema’s line of movie theaters as a separate company.

Harcourt traces its educational offerings back to 1919, when Alfred Harcourt and Donald C. Brace, two former classmates at Columbia University, started their own publishing house in New York City. The company, known for many years as Harcourt, Brace and Co., entered the textbook market in the 1920s.

Meanwhile, its trade, or consumer, imprints published such noted writers as T.S. Eliot, Sinclair Lewis, and Flannery O’Connor. By 1960, the publishing house became publicly traded on the stock market and merged with the World Book Co., a Yonkers, N.Y., publisher of educational tests, including the Stanford Achievement Test.

Harcourt now ranks fourth among U.S. K-12 educational publishers, both in American and worldwide sales, according to a 1999 report by Simba Information Inc., a Stamford, Conn., research firm that tracks educational publishing. The top three publishers in both categories were Pearson, McGraw-Hill, and Houghton-Mifflin Co., according to Simba.

Harcourt’s educational testing unit, Harcourt Educational Measurement, ranked second in sales behind McGraw-Hill’s CTB/McGraw-Hill testing unit for 1998, the most recent year covered in the Simba report.

Gail Kalinoski, the managing editor of Educational Marketer, a Simba-published newsletter, said Harcourt is on track to move up a notch or two in sales by K-12 textbook publishers.

“They’ve been doing well,” she said. “It seems like they’ve grown the company nicely and made good acquisitions, but nothing has made a difference with the stock price.”

Since last year, Harcourt has moved to position itself as a force in education over the Internet. For example, the company hired former Massachusetts Commissioner of Education Robert Antonucci in 1998 to develop Harcourt University, which offers online courses taught by a stable of university professors. Meanwhile, Harcourt’s main World Wide Web site,, has been retooled to offer everything from educational CD-ROMs to education tips for parents and students.

Other Deals

Meanwhile, McGraw-Hill’s $634.7 million purchase of Tribune Education on June 26 bolsters the New York City-based publisher’s educational lineup in several areas, analysts said.

Tribune’s educational properties included the Wright Group, NTC/Contemporary Publishing, and Everyday Learning/Creative Publications, all publishers of supplemental educational materials. Also included in the sale was Landoll Inc., a children’s trade publisher that holds the license to Winnie the Pooh.

“This is a good deal for McGraw-Hill,” Ms. Kalinoski of Educational Marketer said. “This puts them at the top for supplementals.”


(1) 2001 GIFT Grant Program Announced

Source: Charlene Chausis <>

Applications for the 2001 Growth Initiatives for Teachers (GIFT) Program — a $15,000 Grant for Secondary Science and Math Teachers — are now available (Deadline for submissions is January 12, 2001)

  • GIFT is a grant program for public and private school math and science teachers, grades 7 to 12, across the nation and in the District of Columbia and Puerto Rico.
  • The GIFT grant program was established by the GTE Foundation to promote the integration of math and science in the classroom, to encourage the innovative use of technology in education, and to provide recognition and new opportunities for outstanding teachers.
  • Each year, Verizon awards GIFT grants to 70 teams of one math and one science teacher from the same secondary school who have developed school enrichment projects that integrate math and science and use technology in an creative way. Each winning team shares a $15,000 GIFT grant — $8,000 to implement the school enrichment project and $7,000 ($3,500 each) for the participating teachers to pursue professional development activities…
  • Interested teachers who would like to receive an application by mail are encouraged to call 800-315-5010 or send e-mail to Applications are also available online at

(2) Call for Applications–Director, The Math Forum

[From the MER Forum] The following announcement seeking a new director of the Math Forum, an online math education community center, came from Gene Klotz, Professor of Mathematics at Swarthmore College and Senior Advisor and Founder, the Math Forum. He comments, “It’s a special opportunity to be able to step into a high level job directing a well-established Internet mathematics education company. I would like to see it go to someone who is steeped in the values and experience of the professional mathematics community, particularly the innovative edge




Directorship of the Forum should be a great job. We are an established quality institution, providing wonderful “traditional” web content but also on the cutting edge of new technological and educational developments. Not only that, we are staffed by extraordinarily competent people who are talented, caring, energetic, and interesting to work with. Our new association with the leader in Web-based learning, WebCT, will allow us to further enrich and develop our site while retaining the features that have so contributed to user satisfaction.

Even our locale is good. The Math Forum is in an idyllic college town 25 minutes’ drive from Philadelphia, a city rich in culture; 20 minutes’ drive from the Philadelphia International Airport; and about halfway between New York City and Washington, DC. We have splendid relations with Swarthmore College, which has its own beautiful arboretum, and hosts many cultural and academic events.


– Direct teams for growth and development of Math Forum projects (Ask Dr. Math, Teacher 2 Teacher, peer mentoring service, the Internet Math Library, six or more Problems of the Week (PoW) that offer on-line problem solving and student mentoring services and other new and on-going projects). (See

– Manage grant relationships, compliance activities, and lead new grant funding applications.

– Design system requirements, identify hardware/software and systems solutions.

– Set goals, prioritize, mentor, hire new staff, develop project budgets and allocate resources.

– Coordinate work between project management activities and WebCT systems development groups that provides the system infrastructure and programming for Forum projects and services.

– Integrate Forum activities into the WebCT hub and with other WebCT project teams in Boston and Vancouver.

– Represent the Forum/WebCT in appropriate mathematics/math education communities.

The Director will report to the Vice President, Communities, a sympathetic and knowledgeable person (Steve Weimar, former Director of the Math Forum).


– Knowledge of K-12 educational systems and pedagogy and on-line initiatives.

– Some experience in teaching mathematics.

– Administrative experience, project management, and personnel management in a collaborative environment with strong leadership, listening, communication skills and the proven ability to direct and motivate employees.

Please send all resumes to or fax to 978-538-0309

(M379CM. EOE).


United States Mint 50 State Quarters Program


This site contains teacher-created lesson plans for grades K-6 that utilize the state quarters. The lessons’ goals are based upon national curriculum standards for history, geography, and mathematics.

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 typically compiled and distributed via COMET every 1-2 weeks during the regular academic year. 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). Because COMET is based at California State University, Fresno, mathematics education opportunities in Central California are also included.