COMET • Vol. 3, No. 01 – 8 January 2002


(1) Mathematics Subject Matter Requirements (California)

Source: California Commission on Teacher Credentialing – 21 December 2001


Part I: Preliminary Mathematics Subject Matter Requirements

[Part I describes subject matter requirements for Single Subject (Mathematics) Credential candidates within the following six domains: algebra, geometry, number theory, probability and statistics, calculus, and the history of mathematics.]

= Part II: Subject Matter Skills and Abilities Applicable to the Content Domains of Mathematics

Candidates for Single Subject Teaching Credentials in mathematics use inductive and deductive reasoning to develop, analyze, draw conclusions, and validate conjectures and arguments. As they reason, they use counterexamples, construct proofs using contradictions, and create multiple representations of the same concept. They know the interconnections among mathematical ideas, and use techniques and concepts from different domains and sub-domains to model the same problem. They explain mathematical interconnections with other disciplines. They are able to communicate their mathematical thinking clearly and coherently to others, orally, graphically, and in writing, through the use of precise language and symbols.

Candidates solve routine and complex problems by drawing from a variety of strategies while demonstrating an attitude of persistence and reflection in their approaches. They analyze problems through pattern recognition and the use of analogies. They formulate and prove conjectures, and test conclusions for reasonableness and accuracy. They use counterexamples to disprove conjectures.

Candidates select and use different representational systems (e.g., coordinates, graphs). They understand the usefulness of transformations and symmetry to help analyze and simplify problems. They make mathematical models to analyze mathematical structures in real contexts. They use spatial reasoning to model and solve problems that cross disciplines.

(2) Request for Proposals (RFP) for the Development and Administration of Subject Matter Examinations for Prospective Teachers

Source: California Commission on Teacher Credentialing – 21 December 2001


The California Commission on Teacher Credentialing issues teaching credentials. One of the requirements for a teaching credential is competence in the subject(s) in which the credential authorizes instruction. California law provides two optional ways of meeting the subject matter competence requirement. Credential candidates can either (a) complete a Commission-approved subject matter program at a college or university or (b) pass one or more examinations adopted by the Commission for this purpose. The Commission strives to make these two options as equivalent as possible.

The purpose of this RFP is to secure a contractor to develop and administer new subject matter examinations for prospective teachers who choose to meet the subject matter competence requirement by taking exams. Exams are needed for all credential areas. This includes a new examination for prospective elementary teachers. This examination will include the following subject areas: reading, language, and literature; history and social science; science; mathematics; physical education; visual and performing arts; and human development. Content specifications for this exam have been developed and adopted by the Commission. They are available at

In addition, new examinations in…thirteen subject areas are needed for prospective secondary teachers…

The contract term will be from approximately March 2002 through October 2006, and will include test administrations through June 2006. The new elementary subject matter examination, and the new exams in English, mathematics, science, and social science, are to be ready for initial administration approximately half way through the 2002-03 testing year. Exams in physical education, art, music, and languages other than English, and the new PET exam, are to be ready for initial administration approximately half way through the 2003-04 testing year. The remaining exams are to be ready for initial administration approximately half way through the 2004-05 testing year. (Proposal Deadline: February 19, 2002)

(3) California Science Framework Draft Review

Source: Art Susman, WestEd – – 22 December 2001

The draft California Science Framework was [posted] on the Web on December 19 for public comment []. The State Board of Education (SBE) will review and hear that public comment at its meeting in Sacramento on January 9th. [The Framework will be presented to the SBE as an action item at its 6-7 February 2002 meeting]… This Framework is the document that will support the implementation of the science standards, drive science programs, and ultimately define how California’s students will learn science… The document will direct state policies for the next six years.

Any person interested in personally addressing the SBE during its January 9, 2002, meeting should contact the SBE Office at (916) 653-7016.  Each person…will have two minutes to provide oral input during the public hearing section of the agenda…

(4) State Education Chief’s Term Wanes” by Suzanne Pardington

Source: Contra Costa Times – 7 January 2002


…Term limits will push [Superintendent of Public Instruction Delaine] Eastin from office after two terms later this year. Her successor, up for election in March, will inherit a job with little direct authority over education policy and a history of clashes with the governor and state Board of Education so disruptive that some educators and lawmakers want to replace the elected office with an appointed one.

Indeed, the state’s educational power-sharing structure has long been criticized as a multiheaded beast. There is no clear line of command and no single place to lay blame when things go wrong.

The governor holds the purse strings. State legislators draft and vote on education bills, more than 500 a year. The 11-member Board of Education, appointed by the governor, adopts K-8 textbooks and state schools policy. There is even a secretary of education to advise the governor on school issues.

The state superintendent is left with administrative duties and a bully pulpit that, when used effectively, can sway the education agenda, but not set it…

As voters prepare to choose the next schools chief, the two top candidates, Assemblywoman Lynne Leach, R-Walnut Creek, and state Sen. Jack O’Connell, D-San Luis Obispo, are promising to lead the state to higher academic ground. The new superintendent’s success will depend largely on the ability to maneuver in this tricky political climate…

Educators say electing an adept schools chief is especially important as the state undertakes an ambitious experiment to improve student achievement through a system of rewards and punishments.

The kinks in the high-stakes testing and accountability program are notorious and numerous, including tests that aren’t aligned to what teachers are told to teach, lawsuits over the rules of the program and uncertainty about what to do if schools don’t improve…

Without the legal power to increase the state’s education budget or change education policy, the state superintendent must navigate a political battlefield from a supposedly nonpartisan position. Eastin, a Democrat known for her outspoken and combative style, has butted heads both with Davis, a fellow Democrat, and with Republican former Gov. Pete Wilson.

“It’s been extraordinarily difficult for her, and I think it’s always going to be difficult for any superintendent who has differences with the governor,” said Gerald Hayward, of Policy Analysis for California Education, a research group…

“He has so much power he can say do it my way or it’s not going to be done. That’s why the governor will always win,” said Hayward.

Given that fact, Hayward and a group of 25 educators and leaders of education organizations plan to recommend replacing the elected office with a governor’s appointee. It’s an idea that has come up repeatedly, but even supporters doubt voters, who must approve the constitutional change, would give up their right to elect a state official.

The group was charged with studying the state’s education governance system as a part of the development of the state’s first master plan for public education. They will propose the change to a legislative committee later this month. The full state Legislature is expected to consider the final plan in 2003.

An appointed superintendent should report directly to the governor, who should be solely responsible for the successes and failures of public schools, some educators say. If the governor, state board and superintendent have the same education agenda, they shouldn’t be mired in bickering and controversy that have slowed policy changes in the past, they say…

Despite the controversy surrounding the office, O’Connell and Leach believe that they can be effective educational leaders, regardless of who is governor.

The two other candidates are Katherine Smith, a school board president in Anaheim, and Joe Taylor of Los Angeles.

Leach, a Republican, said she’s not afraid to step on the superintendent’s bully pulpit to take on a governor with conflicting beliefs.

“I will bring my case to the parents and the taxpayers and the teachers of this state,” she said. “You have to keep pointing out that this is a problem, and these are the ways that we handle it.”

O’Connell said he has a good working relationship with Davis, but he’s ready to speak up when he disagrees, as he says he did when the governor proposed extending the middle school year last spring.

“It’s like talking to a spouse,” said O’Connell. “You have to be persuasive and understanding and see the other side.”




(1) “Bush Signs Education Bill” by the Associated Press (AP)

Source:  The New York Times (“News from AP”) – 8 January 2002


President Bush, acting Tuesday on his No. 1 domestic priority, signed into law a sweeping education bill that will require new reading and math tests, seek to close the education gap between rich and poor students and raise teacher standards.

“As of this hour, America’s schools will be on a new path of reform and a new path of results,” Bush said to an audience of hundreds at Hamilton High School, west of Cincinnati. “From this day forward, all students will have a better chance to learn, to excel and to live out their dreams”…Above him hung a sign bearing his campaign slogan on education, “No child left behind.” Eager to showcase the bipartisan achievement on a campaign promise, the bill signing opened a three-state victory tour…

“Most bills are signed at the White House. I decided to sign this bill in one of the most important places in America — a public school,” Bush said.

In a 12-hour, 1,600-mile swing, the president signed the bill in Ohio, home of GOP Rep. John Boehner; was giving an education speech in New Hampshire, the home state of GOP Sen. Judd Gregg; and touring a school in Massachusetts, home to Democratic Sen. Edward Kennedy. The fourth principal sponsor, Democratic Rep. George Miller of California, was traveling with Bush throughout the day. Bush visited California on Saturday…

The bill requires annual state tests in reading and mathematics for every child in grades three through eight, beginning in the 2005-06 school year. Schools will also have to test students in science in three grades…

Public schools where scores failed to improve two years in a row could receive more federal aid, but if scores still failed to improve, low-income students could receive tutoring or transportation to another public school…

Under the bill passed last month, a school in which scores failed to improve over six years could be restaffed.

Schools must raise the percentage of students proficient in reading and math and reach 100 percent within 12 years. Schools also must close gaps in scores between wealthy and poor students and white and minority students.

The bill requires states to ensure that within four years all teachers are qualified to teach in their subject areas.

Schools also must develop annual “report cards” that show their standardized test scores compared with both local and state schools.

“This is such a giant leap forward — it is actually a cultural shift, a different way of doing business,'” Education Secretary Rod Paige said in an interview.

“It goes further than anything in the past in terms of demanding accountability from states, school districts, individual schools and individual teachers and principals,” Paige said. “No longer can they hide, no longer can their results be hidden”…


Related story:

President Signs Education Bill” by Dana Milbank

Source: Washington Post –

(2) H.R. 1 – Full Text of Enrolled Bill (“To close the achievement gap with accountability, flexibility, and choice, so that no child is left behind”)


Especially see Title II-Part B: Mathematics And Science Partnerships


(a) PURPOSE- The purpose of this part is to improve the academic achievement of students in the areas of mathematics and science by encouraging State educational agencies, institutions of higher education, local educational agencies, elementary schools, and secondary schools to participate in programs that–

(1) Improve and upgrade the status and stature of mathematics and science teaching by encouraging institutions of higher education to assume greater responsibility for improving mathematics and science teacher education through the establishment of a comprehensive, integrated system of recruiting, training, and advising mathematics and science teachers;

(2) Focus on the education of mathematics and science teachers as a career-long process that continuously stimulates teachers’ intellectual growth and upgrades teachers’ knowledge and skills;

(3) Bring mathematics and science teachers in elementary schools and secondary schools together with scientists, mathematicians, and engineers to increase the subject matter knowledge of mathematics and science teachers and improve such teachers’ teaching skills through the use of sophisticated laboratory equipment and work space, computing facilities, libraries, and other resources that institutions of higher education are better able to provide than the elementary schools and secondary schools;

(4) Develop more rigorous mathematics and science curricula that are aligned with challenging State and local academic content standards and with the standards expected for postsecondary study in engineering, mathematics, and science; and

(5) Improve and expand training of mathematics and science teachers, including training such teachers in the effective integration of technology into curricula and instruction…

(3) Congressional Appropriations-ENC; Professional Development

Source: Art Sussman ( – 20 December 2001

…The Congressional Appropriations do include funds to continue the Eisenhower Regional Consortia (such as the one at WestEd serving California, Arizona, Nevada, and Utah) as well as the Eisenhower National Clearinghouse ( Two other federal initiatives that provide services at the regional level also received continuing funding in the federal budget that just passed. These are the Regional Technology in Education Consortia (RTEC) and the Comprehensive Centers…

The Triangle Coalition, a DC-area non-profit that promotes science, technology, and mathematics education provided [a] summary statement…regarding the recent Congressional funding decision [].

…The eventual impact of the Congressional Appropriation decision on science education and science professional development will depend on how the state and districts choose to spend their share of the Title II Part A Teacher Quality funds [see]

(4) “Madam, I’m 2002 — A Numerically Beautiful Year” by Alfred S. Posamentier

Source: The New York Times – 2 January 2002


Now, in the year 2002, we are the last generation for more than the next thousand years to experience two palindromic years in a lifetime. Palindromes in mathematics are numbers that read the same in both directions, like 2002 and 1991. In the English language there are very well-known palindromic words, like “rotator” and “reviver,” and there are also sentences that are palindromic, like “Madam, I’m Adam.”

Palindromic numbers are not only pleasing in appearance, but also harbor some nice, curious qualities. For example, take any number, write it in reverse order and add the two numbers. The sum will likely be a palindromic number, and if not, then simply continuing this process by adding the sum to its reverse should eventually lead to a palindromic number. This surprising result is the kind of discovery that can pique interest in numbers even in students indifferent to math.

Teachers should be able to capitalize on the beauty in mathematics, and specifically the charm of some numbers to hook students on studying mathematics. But qualified math teachers who might actually inspire children are in short supply, and math teaching in today’s schools is often dry and boring. The problem is not new. Math instruction at the elementary school level, when students form their first impressions about the nature of math and their own abilities with numbers, has historically been mediocre. Without a strong beginning, a student’s chances for sustaining interest in this field are very small indeed. The problem is compounded by relatively weak teaching at the secondary level as well…

At a time when there is a national shortage of math teachers, made worse by a low supply of math-prepared students, we must look beyond the quick-fix solutions. We must develop better and more creative training programs for elementary math teachers. We need to give them more classroom time on this subject. And when students begin to pursue the study of math, we must make the teaching profession more attractive, financially as well as by giving teachers more control of how they teach.

The point is to make math intrinsically interesting to children. We should not have to sell mathematics by pointing to its usefulness in other subject areas, which, of course, is real. Love for math will not come about by trying to convince a child that it happens to be a handy tool for life; it grows when a good teacher can draw out a child’s curiosity about how numbers and mathematical principles work. The very high percentage of adults who are unashamed to say that they are bad with math is a good indication of how maligned the subject is and how very little we were taught in school about the enchantment of numbers.


Letters in response to this editorial appeared in the 6 January 2002 edition of The New York Times under the heading “Math’s Inner Beauty Is Enough” (