COMET • Vol. 6, No. 04 – 9 February 2005


(1) Field Review Draft Mathematics Framework: Letter from the California Mathematics Council


The following was posted this morning on the Web site of the California Mathematics Council (CMC):

The board and members of CMC have been very active in the rewriting of parts of the Mathematics Framework. The current draft has been approved by the Curriculum Commission and is awaiting final approval in March by the State Department of Education. While we still have issues with some of the content, we were heartened by the process used for this re-write which was much more open than in the past.

The State Board is expected to discuss the document during its March session and determine the next steps eventually leading to new textbook adoptions. To view the latest version, go to and click on the 2004 Draft of the Mathematics Framework [].

The following is a letter that the California Mathematics Council sent to the Curriculum Commission regarding the January 28 draft. We encourage you to give your input to the draft as well.

Text of letter from CMC to the Curriculum Commission via

Dr. Tom Adams, Director,

Curriculum Frameworks and Instruction Resources Division, CDE

January 23, 2005

Dear Dr. Adams and members of the Curriculum Commission:

The California Mathematics Council (CMC), appreciates the extent to which our professional organization, along with many other stakeholders, has been able to provide input for the updated Mathematics Framework for California Public Schools. The responsiveness of mathematics subcommittee chaired by Dr. Norma Baker and the CDE staff to our membership has been outstanding. We note many changes in the draft versions of Chapters 10 and Appendix E that were available for the January 10 teleconference that we believe improve the quality and usability of the document. In this letter, we respectfully request that the full Commission consider additional changes to the framework which would benefit students and teachers in California classrooms.

1.  The criteria for selection of instructional materials should not limit the reference to CA standards only. Flexibility will improve opportunities for diverse learners. Suggested wording, beginning on line 8417: It should be clear in the materials that the mathematics students are expected to know and do are the California Mathematics Content Standards developed under Education Code Section 60605. The principles of instruction must reflect current and confirmed research. The materials must not conflict with the California Mathematics Standards or the Mathematics Framework.

Rationale: Boards of Education, schools, and teachers are faced with the challenge of preparing students for full participation in the work and civic life of the 21st Century. They are accountable to student outcomes as outlined in state and federal legislation. Within those strict measures, flexibility is required. As one of the most diverse states in the nation, with low rankings in many measures of student success, we owe our children the best the nation has to offer. Some instructional materials with researched success with diverse students were created for a larger market than California. Our students should not be denied access to effective materials. In addition, the National Council of Teachers of Mathematics (NCTM) Curriculum Standards for Mathematics offer broad organizing principles of the type that many teachers asked for during public comment. A copy of the entire set of NCTM algebra standards, K-12, is attached so that Commissioners and others can see that they present no conflict with the California Mathematics Content Standards.

2.  Every effort should be made to avoid the tracking that could result when students are placed in an intervention program without a clear and final exit plan. The core programs should be of such high quality that most students learn the materials well the first time. The first level of intervention should occur during the initial instruction in the basal program. At all times while a student is participating in intervention, access should be provided to the core grade-level mathematics.

3.  CMC maintains a neutral position on the design of Algebra Readiness materials. The focus on 7th Grade and Algebra I Standards in the most recent draft is an important step toward assuring students who need extra help are not left further behind. The intent to re-teach under-prepared students the foundational skills so that they understand and retain the knowledge and can apply it in more advanced settings is appropriate. We recommend flexibility at the district and site level to implement Algebra Readiness in a variety of configurations. On the other hand, we continue to be concerned about the mismatch between the Algebra Readiness standards and those in the CAHSEE. The workforce needs graduates who can apply mathematics in many settings, as presented at Superintendent O’Connell’s High School Summit last October. Without adequate experience using statistics, measurement, and geometry during their middle and high school years, students will not be prepared for future jobs. This leads us to support the current design of the CAHSEE.

4.  Technology tools should be used where appropriate to help students visualize abstract mathematical concepts such as functions and graphical representation of data, and perform complicated calculations with real-world data. The mathematics education community values fluency with the basic facts as well as the ability to use mental calculations, estimation, and technology, as appropriate, and know the value and restrictions of each. While early access to technology for basic skill practice may be problematic for some students, other uses such as pattern generation and analysis and the visual presentation of applications problems, are helpful to many. The labor force of California needs to be technologically literate. We need to harness the enthusiasm students already have for electronic devices and make sure that schools maximize opportunities for the mathematical applications theses devices provide.

5.  The language of this framework should be consistent throughout. For example, it is disturbing that the word “balance” does not appear in Chapter 10, considering the emphasis on a balanced program in Chapter 1. Similarly, Appendix E includes frequent repetition of the phrase “concepts and skills” while remaining silent about the value of problem solving for students who are not at grade level. Appendix E should clearly state that problem solving is an important part of all students’ experience, including students in intervention programs.

The California Mathematics Council and its many associates remain committed to working with policymakers and leadership groups to assure the best programs for our students. We thank you for your consideration of our recommendations.



Sara Munshin

President, California Mathematics Council

Enc:  Principles and Standards for School Mathematics, pp. 394-395 (NCTM Algebra Standards)


(2) “Schools Bracing for Bush’s Budget Cuts” by Maureen Magee and Eleanor Yang

Source: San Diego Union-Tribune – 9 February 2005


California’s schools are bracing for a funding hit, outlined this week in President Bush’s proposed budget, that would eliminate 48 education programs and shift more money toward the national effort to raise student achievement and improve test scores.

The far-reaching cuts would terminate vocational education training, college readiness programs and early education initiatives, among others. The programs targeted have been deemed either ineffective or redundant.

The president’s spending plan includes about $1.5 billion next year to extend student achievement requirements and testing in the No Child Left Behind Act to high schools. Bush has also recommended increased funding of special education programs for disabled students and federal Title I grants to school districts with a heavy enrollment of disadvantaged children.

Bush’s $56 billion education budget is down $500 million, or 0.9 percent, from the current spending plan.

Gerry Shelton, director of fiscal and administrative services for the California Department of Education, said it is too soon to predict how California will fare under Bush’s budget.

The state receives about $7.5 billion a year in federal dollars for programs that run from kindergarten through 12th grade. That’s in addition to the approximate $53.6 billion in state and local money for California public schools.

“It’s kind of a wait and see,” Shelton said. “But we are especially concerned about Bush’s budget, when put hand in hand with the proposals in the state budget.”

Higher education officials were mixed in their responses to the proposed budget, applauding increases to student grant programs and criticizing cuts to programs designed to support low-income students who want to attend college.

The proposal would raise the maximum Pell grant by $500 to $4,550, over the next five years. Yet that increase would come at the expense of the elimination of the long-standing Perkins Loan program. The Perkins Loan program provides low-interest loans for middle-and lower-income families.

The intent is to use Perkins money to pay for the increases for the Pell grants and resolve a $4.3 billion shortfall in the program.

“If this were to work, and that’s a big caveat, it would help a lot more low-income students afford college,” said Kenneth Redd, director of research and policy analysis at the National Association of Student Financial Aid Administrators.

The president’s recommendations come as California school districts are reeling from some of Gov. Schwarzenegger’s education-funding choices.

“It’s disappointing, overall. We are getting hit by the governor and the president now,” said Scott Patterson, the chief financial officer for the San Diego Unified School District.

Under Bush’s budget, school districts would see a cut in federal money that helps pay for the day-to-day operations of schools, Patterson said.

Patterson and others expressed concern over the loss of some program funding. But they were hopeful that in the end, benefits would cancel out the losses to others.

Several programs proposed for elimination are designed to help prepare lower-income students for college Æ Gear Up, Upward Bound and Talent Search.

The threat to eliminate those programs prompted strong outcries from legislators, lobbyists and educators… More than 1 million students participate in the three programs, and receive help in core academic subjects.

Hector Garza, the president of the National Council for Community and Education Partnerships, called the proposed cuts to Gear Up “irresponsible and nonsensical.”

“If we can’t get our kids ready for college, the Pell Grants aren’t going to mean anything,” said Larry Perondi, area superintendent for Sweetwater Union High School District. “If education is a priority, (this budget proposal) is not showing it.”

Advocates of vocational education criticized the president for dismissing the importance of programs designed to prepare mostly high school students for the work force. The proposed budget would cut $1.2 billion from vocational education.

Legislators said yesterday they are prepared to fight many of the proposed cuts.

“Education cuts are sending the wrong message to our kids,” said Rep. Susan Davis.

Related reports:

“Higher Education Community Issues Statement on President Bush’s FY 06 Budget” 

Source: American Council on Education – 7 February 2005


“President’s FY 2006 Budget Request for the U.S. Department of Education”


(3) “Gov. Battles Rising Criticism on Multiple Fronts” by Robert Salladay

Source: Los Angeles Times – 8 February 2005


Gov. Arnold Schwarzenegger is working to reverse declining public opinion over his handling of California schools, while facing mounting complaints about his planned government overhaul.

On Monday, Schwarzenegger visited his third school in 10 days. The event signaled that the otherwise highly popular governor is worried about a recent poll showing that 51% of voters disapprove of his school proposals. People surveyed also said education–not government reform, Schwarzenegger’s mantra this year–had become their biggest concern…

Schwarzenegger predicted that people would howl at his 2005 agenda, and he is being proved correct. His state budget proposal and five-part government reform agenda have energized a cadre of opponents, most of them characterized by Schwarzenegger as special interests…

Broadly, the governor’s agenda this year would change how legislative districts are drawn, allow state workers to enroll in 401(k) retirement plans, broaden his power to restructure government, institute a spending limit on state finance, and grant merit pay for teachers…

The California Teachers Assn. has been running pointed radio ads in several languages on 56 stations criticizing the governor’s education budget plan. Teachers say the governor went back on his promise to provide schools the full amount they are owed under Proposition 98, a constitutional provision that gives schools a fixed percentage of state revenue…


(4) “Governor Defends School Funding” by Ann E. Marimow

Source: Contra Costa Times – 9 February 2005


…On talk radio Tuesday, Schwarzenegger said, “even though you hear sometimes that I made cuts, which is totally ludicrous and wrong, we added $2.9 billion to education”…

It’s ironic for Schwarzenegger to be on the defensive about education. The governor’s first foray into politics in 2002 was a ballot initiative, Proposition 49, to provide state funding for after-school programs.

But the crux of the debate has as much to do with a perceived double-cross on the part of the governor as it does with the details of his new spending plan.

One year ago, the powerful education lobby and Schwarzenegger celebrated a budget compromise. Schools agreed to forgo $2 billion last year in exchange for protection from deeper cuts and a boost in funding if revenues increased.

The governor is today offering schools $2.9 billion more than they got a year ago. But that’s $2.3 billion less than they’re owed under the deal struck last year.

Moreover, the governor is proposing to make local schools pay millions in annual teacher-retirement payments that the state typically makes. And he’s proposing to change Proposition 98, the school-funding guarantee that many consider sacred.

Today, a broader coalition of education officials turns up the heat with a new advertising campaign to highlight the “governor’s broken promise to schools.”

Democratic consultants say the governor has picked a fight on the wrong issue with the wrong people. Richie Ross, a political consultant who helped pass Proposition 98, said Schwarzenegger is out-of-touch with what voters want on education.

“People like teachers more than they like politicians, even the politicians they like,” Ross said. “This is not a fight he wants to have.”

Ross said his polls echo the PPIC findings that voters consider education the most important issue facing the state in years.

Adding to the governor’s challenges, the nonpartisan Legislative Analyst’s Office, which advises lawmakers, Tuesday reported that Schwarzenegger’s proposed changes to Proposition 98 would put school spending on “cruise control.”

The LAO report says Schwarzenegger’s proposal would “add to the problems of autopilot spending” that Schwarzenegger says he wants to end.

As a recall candidate, Schwarzenegger skipped traditional campaign stops at the editorial boards of the state’s major newspapers. But over the past month, he has been making the rounds to promote his broader effort to revamp state government and clear up confusion about his plans for schools.

Assembly Republicans, with Education Secretary Richard Riordan, are this week helping spread the word that the governor’s new budget blueprint spends more — not less — than last year.

“We think that message is not getting out there as clearly,” said Assemblyman Guy Houston of Livermore. “It’s our job to help him to relay and communicate that message to the people.”

The governor has also returned to one of his favorite venues, chatting with friendly hosts on talk radio. When asked Tuesday if he is frustrated by the misrepresentations, Schwarzenegger said, “That’s not my style. I don’t get frustrated, I just fire back.

“I think that the people understand here in California that the special interests don’t like to make those kind of changes and reforms.”

Schwarzenegger returns to the airwaves today for another round of interviews.


(1) “NUMB3RS Gets the Math Right” by Keith Devlin

Source: Devlin’s Angle – MAA Online – February 2005


If you’ve read the January 21 issue of Math Games by my fellow MAA Online columnist Ed Pegg Jr. [], you will have some general background on the new CBS prime-time television series NUMB3RS

Surely almost anything that can improve the image of mathematics in the population at large deserves the support of the mathematics community.

The widespread ignorance among the general public of what mathematics is all about is testified by the fact that one of the criticisms of the new series after the first episode was screened on January 23 was that it defied credulity. Many TV critics, it seems, could not believe that mathematics could be used to help solve criminal cases in the way depicted in the program. Yet that first episode, like all the other upcoming episodes in the first season, is based on a real-life case. Not just loosely based on it, but closely so…

The mathematical formula you see actor David Krumholtz (who plays the mathematician) write on the blackboard in his home [during episode 1] is in fact the equation used in the real case. The other equations you see (and will see) in the series, including the water sprinkler example near the start of episode 1, were written by the series’ principal mathematics advisor, Gary Lordon, the head of mathematics at Caltech, by mathematics graduate students at Caltech, and by other professional mathematicians, a great many of whom the series producers have contacted to ask for help. (They sent a representative to the Joint Mathematics Meetings in Atlanta last month, to extend their network of contacts in the profession.) So much for all those TV critics who thought the plot was too implausible!

The second episode, which was broadcast on January 28, is based on a real life series of bank robberies in Maryland last year. In that case, a mathematician in Arkansas provided the pattern analysis that resulted in the police lying in wait at the bank when the gang struck…

If the series does go down the tubes after a few episodes, it won’t be because the math is wrong. The producers have gone to great lengths to get the math right. (They also have a real-life FBI agent on the set to make sure the police stuff is correct as well.) Nor is Krumholz’s portrayal of the math genius off the mark. Okay, he’s cuter than most of us, but looks apart, his character seems to me like an amalgam of a half dozen mathematicians I have met. (In preparing for the role, Krumholz hung around Caltech for a while, seeing what real mathematicians are like.) Sure, the writers and the actors employ dramatic license in their portrayal of mathematicians and what is involved in doing mathematics… But at heart they get the mathematician and the math right.

Failure of the show is also unlikely to result from viewers being put off by the math. When CBS tested an early version of the pilot, the sample audience was not only intrigued by the math, they said they wanted more of it in the show! Similar highly positive responses to the dramatic portrayal of mathematicians and mathematics followed both of the stage plays Breaking the Code and Proof and each of the movies Good Will Hunting, Pi, and A Beautiful Mind.

…But if NUMB3RS does make it, it could do wonders for the general perception of mathematics among the general public, and perhaps stimulate more young people to go into the field…


(2) “Spellings to Listen, But Not Retreat, on NCLB” by Erik W. Robelen and Lynn Olson

SourceEducation Week – 9 February 2005


U.S. Secretary of Education Margaret Spellings said last week that there “is room to maneuver” through the administrative process in carrying out the No Child Left Behind Act. But, she cautioned, “I donÍt want people to think that No Child Left Behind is up for grabs. ItÍs not.”

Ms. Spellings, who took office Jan. 20, emphasized in a Feb. 4 interview with Education Week that there are some “bright-line pieces of this statute that are nonnegotiable.” One of those, she said, is annual testing in grades 3-8, which she called “integral to the implementation of everything.”

President BushÍs administration has given a lot of time and resources to help states put the tests in place, she said, “so don’t be coming down here and telling me you haven’t done it.”

Despite many calls to amend the law in Congress, Ms. Spellings also expressed no desire to go that route. ñI hope that the Department of Education will be the first place that people seek a solution,î she said.

But she maintained that refinements and modifications could be done through administrative actions “without running to the Congress and asking for a statutory change”…


(3) “First Lady Wants Students on Best Behavior” by Elise Castelli

Source: Los Angeles Times – 9 February 2005


When her husband announced the Helping America’s Youth initiative during last week’s State of the Union address, Laura Bush found herself with a new role–heading up a $150-million program.

Though the onetime teacher and librarian has gone to schools to promote such administration policies as No Child Left Behind, the first lady’s visits are now related to a program of her own that aims to reduce violence and gang activity among at-risk youth, especially minority boys.

On Tuesday, she appeared at George Washington Elementary School in Baltimore, where she spoke to 100 students, teachers, community activists and state officials about the relationships among classroom management, behavior, learning and success.

“Research shows that children who are overly aggressive as early as the first grade are at a greater risk for delinquency, dropping out of school, drug abuse and depression later in life,” Bush said. “Here in the Baltimore public school system, children with behavioral problems in poorly managed first-grade classrooms were up to 20 times more likely to be severely aggressive in middle school compared to similar children in well-managed first-grade classrooms.”

She cited one of the school’s approaches to teaching proper behavior–the “good behavior game”–as a model for keeping children in school.

Shortly before her noontime speech, Bush observed a first-grade class engaged in the game during a reading lesson. The children were divided into teams, and any child who acted out while the class completed an exercise would get the entire team a check mark for bad behavior…

“This team-based structure uses peer encouragement to help children follow rules and learn how to be good students,” Bush said. “The students quickly learn that their success is tied to their team.”

The game is part of a program created by Dr. Sheppard Kellam, a senior fellow at the American Institutes for Research, called “Whole Day First Grade.” Introduced 20 years ago in 24 Baltimore schools, the program focuses on improving educators’ teaching and classroom management skills, and communication with families.

“The risk factors that Mrs. Bush has referred to–early aggressive disruptive behavior–are highly correlated with academic achievement,” Kellam said Tuesday.

In her remarks, Bush noted that according to Kellam’s research, 86% of at-risk youth who participated in the Whole Day program graduated from high school, compared with 19% of those who did not.

Kellam said government at all levels needed to respond if programs like his were to move across the country…


(4) “Boys Only/Girls Only” by Melanie Ave

SourceSt. Petersburg Times – 2 February 2005


…At Woodward Avenue Elementary School in Volusia County, Florida, teachers are experimenting with same-sex classes, a growing but controversial trend in public education. Six classes of kindergarteners, second-graders and fourth-graders are part of a voluntary program aimed at reducing the academic differences between boys and girls.

Halfway through the program’s first year, administrators and teachers like what they see. “So far,” said principal JoAnne Rodkey, “it’s been a wonderful learning experience”…

[Most same-sex schools fell out of favor after the 1972 passage of Title IX, which barred sex discrimination in public schools.  In 2002, the federal No Child Left Behind Act allowed some flexibility in offering same-sex schools and classrooms.] The number of U.S. public schools offering same-sex classes grew from just four eight years ago to 154 this year, according to the National Association for Single Sex Public Education. Like Woodward, most are coeducational schools that offer some single-gender courses.

Advocacy groups such as the American Civil Liberties Union and the National Organization for Women oppose the change.  Kathy Rodgers, president of Legal Momentum, a women’s rights group in New York City, said same-sex education is discriminatory…

Supporters say same-sex classes are not inherently discriminatory and can be beneficial to students. Some studies show disadvantaged children blossom when taught separately.

Rosemary Salomone, a law professor at St. John’s University and a graduate of an all-girls Catholic high school, says same-sex schools should be available in the public arena just as they are in the private realm.

“For me, it’s largely an equity problem,” said Salomone, author of the book Same, Different, Equal. “Poor parents have not had the same choice that the wealthy have.”

Principal JoAnne Rodkey decided change was needed at Woodward after she reviewed the school’s test scores. Girls outpaced boys in reading and writing, and boys led the way in math. Though the state gave the school an A based on student performance, she knew it could do better.

Rodkey began researching same-sex education, sought teacher volunteers and went to the Volusia County School Board for approval. It gave the school a year to test the approach.

Plenty of parents agreed to enroll their children, who are at a wide range of ability levels. The two sexes are only apart for their academic classes. They eat and attend physical education classes together.

Denise Lane signed up her 5-year-old, Jacob, for Michaelos’ class. “I know boys and girls tend to learn differently,” said Lane, a child care worker. “Girls are more into coloring and detail. Boys are more into learning by building things and using their hands…”

Rodkey thinks all-boy classes are harder to teach. Two of the seven teachers who do not want to return to the same-sex classes next year teach boys. Michaelos is one of them.

“Boys require a lot more ingenuity and activity,” said Michaelos, 39, who has been teaching 10 years. “The noise level is different. I’m physically and mentally more tired after teaching the boys. It takes me hours to do lesson plans.”

She thinks girls benefit more from being separate than boys, who need girls as role models.

Key to the success of same-sex classes and schools is teacher training, says Dr. Leonard Sax, executive director of the National Association for Single Sex Public Education. Teachers, especially all-boy educators, must learn the research and learning styles of boys and alter their methods accordingly.

To be truly effective with boys, teachers need to funnel their extra energy, not quash it.

“Boys need a teacher who is always moving and never standing still,” Sax said. “The problem with most elementary schools is the boys come in there and (are told), we need you to sit down and be quiet. That doesn’t come naturally.”

Woodward’s teachers have adapted their classrooms. During reading time in James and Deborah Roberts’ combined fourth-grade boys class, the boys are free to lounge on the floor, sit at desks or crowd under tables.  They get a 15-minute recess in the morning to burn off energy.

“It’s better than other classes,” said Monolito Hamilton, 10. “When I had girls in my class, they got almost everything they wanted. They told on us.”

Deborah Roberts has gotten used to the higher noise level and no longer is offended when the boys won’t make eye contact.

“Boys need fast-paced instruction,” she said. “You don’t have to dwell on things with boys. They’re very direct.”

Teachers in the all-girl classes have had few difficulties. Most of the problems have been about friendship disputes.

Some shy girls have come out of their shells without boys around. A few seem more assertive when tackling math and science lessons, teachers said.

Without the distraction of young boys, the girls are focused on their lessons. Many have excelled, teachers said…

Teacher Myrna Bedenbaugh, 57, could not be happier with her 17 second-grade girls.

Bedenbaugh realized how different the year was going to be on the first day of school. She had planned a week’s worth of basic rules and review. But the girls blew through her plans in one day. That had never happened in her 33 years of teaching coed classes.

“Everybody asks me how do I like it,” Bedenbaugh said, as she did a little shimmy. “Am I in heaven? Am I in heaven?”

Next door to Bedenbaugh, Mary Catherine Michaels uses a Jeopardy-like game to review a story her boys had just read, “How I Spent My Summer Vacation.” Her classroom has two cages with hamsters, a tank with salamanders and a bowl of mealworms.

The boys love competing, so she uses lots of games to teach. After they review the rules for Jeopardy–no cheating and no spying–the boys divide into teams and huddle with their arms around each other like they were on a football field…

Though Michaels plans to go back to a coed class next year, she says the experiment has improved her teaching skills.

“It’s been a phenomenal experience,” she said. “It’s changed the way I view boys. They can stay focused on an activity, we just have to hook them in.”


(5) Call for Volunteers: Algebra Diagnostic Assessment

Source: Helena Miranda — (via the NCSM distribution list)


The role that standardized tests play in today’s educational process has increased dramatically.  For many teachers, however, today’s standardized tests provide little new insight into the performance of their students.  Through funding from the National Science Foundation, the Technology and Assessment Study Collaborative at Boston College is attempting to develop tests that will provide more diagnostic information about student learning.  The first set of tests focuses on algebra and are designed to identify whether a given student’s achievement in algebra is being hindered by one or more common algebraic misconception.  If successful, these new tests will not only provide test scores that indicate how well a student is achieving in the area of algebra, but will also provide information to students and their teachers about misconceptions that an individual student holds which may be interfering with their achievement in algebra.

Currently, we are seeking teachers who are interested in helping us pilot this new approach to testing.  In total, there are seven 20-item pilot tests.  While teachers may ask their class to complete as many of these pilot tests as desired, we are seeking teachers who are willing to ask their class to complete at least two 20 item pilot tests and to complete a short survey.  These pilot tests will provide students and teachers with immediate feedback on the students’ performance and will provide information about misconceptions that individual students may hold.

To see a sample test, please visit

If you are willing to have your class participate in this pilot project, you can register your class for participation starting on March 1, 2005.  To do so, please visit our Web site ( beginning March 1.

Should you have any additional questions, please contact Helena Miranda at (617) 552-3646 or via email at