COMET • Vol. 5, No. 15 – 19 May 2004


(1) NCLB Introductory Authorizations Source: California Commission on Teacher Credentialing (CCTC)


At the March 2004 [CCTC} meeting, staff presented proposed additions to Title 5, California Code of Regulations, which would establish authorizations that would be compliant with the Highly Qualified Teacher requirement of the No Child Left Behind Act. The Commission directed staff to return at the May meeting with a new name for the authorizations and a proposal that would provide flexibility.

Several options were presented to the Commissioners at the May meeting, with the CCTC staff recommending that “the Commission adopt Option 1 and … approve the two additions to Title 5 of the California Code of Regulations for purpose of beginning the rulemaking file for submission to the Office of Administrative Law and scheduling a public hearing [mostly likely during the August Commission meeting].” Option 1 was subsequently approved by the Commissioners. Details of this option may be found in the PDF file above. Excerpts appear below:

Proposed New Name

Staff is proposing the title of No Child Left Behind Introductory Authorizations and No Child Left Behind Specific Authorizations to identify the specific purpose of these authorizations. These authorizations will be listed on the credential as NCLB Introductory (Subject) and NCLB (Subject), such as NCLB Introductory Art and NCLB Geography…

Title 5 80089.3. No Child Left Behind (NCLB) Introductory Authorizations

(a) The holder of a valid teaching credential specified in Education Code Section 44256(a) and (b) may have one or more of the subjects listed in subsection (b) added as an NCLB introductory authorization. Equivalent quarter hours may be used to meet the semester hour requirement. The candidate shall verify completion of either (1) or (2) below:

(1) a collegiate major from a regionally accredited college or university in a subject or in a subject directly related to each subject from subsection (b) to be listed, or

(2) 32 semester hours of non-remedial collegiate coursework in a subject listed in subsection (b). Included within the 32 semester hours is a minimum of three semester or four quarter hours in each of the specific content areas listed for the subject in subsection (b) except for Science which requires a minimum of six semester or eight quarter hours in each of the specific content areas listed. A grade of “C” or above in any course used to meet the provisions of this subsection shall be required. Non-remedial coursework for the purposes of this section shall be defined as coursework that is applicable toward a bachelor’s or a higher degree at a regionally accredited college or university.

(b) The following subjects may be added as NCLB introductory degree authorizations to a valid teaching credential specified in Education Code Section 44256(a) and (b):

…(4) Mathematics with the content areas of algebra, advanced algebra, geometry, probability or statistics, and development of the real number system or introduction to mathematics; …

(6) Science with the content areas of biological sciences, chemistry, geosciences, and physics

(c) A subject specified in subsection (b) as an NCLB introductory degree authorization authorizes the holder to teach only the subject matter content typically included for that subject in curriculum guidelines and textbooks for study in grades 9 and below to students in preschool, kindergarten, grades 1-12, or in classes organized primarily for adults.


Related report:

“Highlights of the Commission–May 5-6, 2004” by Edith Thiessen

Source: Credential Counselors & Analysts of California


(2) Governor’s Budget 2004-2005 — May Revision

Source: California Department of Finance


Governor Schwarzenegger’s May Revision to his proposed 2004-2005 state budget is available as a PDF file at the above Web site. Pages 15-29 address K-12 education expenditures, and pages 30-36 address higher education expenditures.


(1) “Discovering Where Light Bulb Flashes” by Marianne Meadahl

Source:  Simon Fraser University News – 1 April 2004


The world’s top mathematicians do some of their best work in the shower, while cooking, or even while asleep.

That’s how several internationally reputed math geniuses describe what happens when the proverbial light bulb goes on, otherwise known as the ah’ha experience, that pivotal moment when they think “eureka,” as the solution to a problem suddenly becomes clear. SFU education doctoral student Peter Liljedahl surveyed 25 mathematicians to determine how those moments are achieved.

Most said how the idea came about–and how it made them feel–held greater significance than the idea itself. “It was Monday morning in the shower, in conversation, while falling to sleep – these are how they remember their greatest ah’ha moments,” says Liljedahl. “Through their use of metaphors and visual imagery in describing these moments, it also became very clear that what mathematicians do is a highly creative process.”

Liljedahl wanted to study what prompted these moments to see if they could be manufactured in a controlled setting, like a classroom. He expected to find something more firmly rooted in their ideas. Instead, the mathematicians often conveyed the essence of these moments without telling him anything about such details.

“Usually the ideas were not that significant,” he says. “But the mathematicians painted these incredible pictures around them that were very personal and had deep pedagogical implications.

“They also showed an incredible respect and acceptance of the fact that a huge part of the mathematical process relies on chance, which has critical implications for problem solving.”

Among survey participants were five Fields medallists, including Italian mathematician Enrico Bombieri, a leading authority on number theory and professor of mathematics at Princeton University. The medal is comparable to a Nobel prize.

Liljedahl, who collaborated with SFU mathematics professor Peter Borwein, based his work on a survey created in the 1940s by Jacque Hadamard, who studied the psychology of mathematical invention.

Liljedahl didn’t expect to draw such personal responses. Many mirrored the words of Dusa McDuff, a mathematics professor at the University of New York at Stony Brook and a major participant in calculus reform.

“In my principle discoveries I have always been thinking hard trying to understand some particular problem. Often, it is just a hard slog. I go round arguments time and again seeking for a hole in my reasoning, or for some way to formulate the problem. Gradually some insights build and I get to know how things function. But the main steps come in flashes of insight.

“This can occur while I am officially working. But it can also occur while I am doing something else, having a shower, doing the cooking. I remember the first time I felt creative in math as a student, trying to find an example to illustrate some type of behavior. I’d worked on it all evening with no luck.

“The answer came in a flash, unexpectedly, while I was showering the next morning. I saw a picture of the solution, right there, waiting to be described.”

Participants also suggested dialogue and learning math through direct contact with people were key factors in how they processed problems.

Liljedahl’s work could lead to new strategies for teaching math in the classroom. He has since restructured a math course on problem solving to monitor the occurrence of ah’ha moments. During a trial run, he gave a class of university students more time, more direct contact and encouraged them to keep journals documenting their feelings, and even their failed attempts, during the process. “It’s clear that to be able to produce such moments they need room to move and time to incubate and talk things through,” surmises Liljedahl.

Not only is the ah’ha experience accompanied by an emotional response, Lijedahl says that response can be substantial enough to alter the negative belief structures and poor attitudes of resistant mathematics students.

(2) “Adding Up” by Etienne S. Benson

Source:  Monitor on Psychology – May 2004


Why is it that some students find math easy, while others struggle with it throughout their school years? And what explains those rare students, one in 10,000 or fewer, who can master advanced mathematics at an early age and with little training?

These are age-old questions, and attempts to answer them in terms of pure and simple biology are just as unsatisfying as explanations in terms of the environment alone, say many researchers.

But a new study suggests that, whatever their ultimate cause, differences in brain activity between mathematically gifted and nongifted students do exist, even at a relatively young age. The study, published in Neuropsychology (Vol. 18, No. 2), was authored by cognitive psychologists Harnam Singh, PhD, a researcher at the U.S. Army Research Institute for the Behavioral and Social Sciences in Fort Benning, Ga., and Michael O’Boyle, PhD, a psychology professor at the University of Melbourne.

Singh and O’Boyle used functional magnetic resonance imaging to measure the brain activity of 36 adolescents of either high mathematical ability–as identified through a gifted and talented program at Iowa State University–or average ability. They focused on 13- and 14-year-old students, rather than older teenagers or adults, to reduce the effect of training as much as possible, says O’Boyle.

The researchers’ results indicate that mathematically gifted students are unusually adept at coordinating the activity of the two cerebral hemispheres, which may make it easier for them to learn complex mathematics. Such students found it easier to combine information from the left and right visual fields than nongifted students, and they also engaged the two halves of the brain more equally, including areas associated with attention and planning…


Related information:

(a) “Imaging Study Shows Brain Maturing”

Source: National Institute of Mental Health – 17 May 2004


The brain’s center of reasoning and problem solving is among the last to mature, a new study graphically reveals. The decade-long magnetic resonance imaging (MRI) study of normal brain development, from ages 4 to 21, by researchers at NIH’s National Institute of Mental Health (NIMH) and University of California Los Angeles (UCLA) shows that such “higher-order” brain centers, such as the prefrontal cortex, don’t fully develop until young adulthood…

(b) Brain Research

Source: Riptides – May 2004


The May 2004 issue of “Riptides” provides links to a number of sites providing current information on brain research. One example is provided below:

The National Academies Press offers one of the best and most extensive collections of the leading work on brain-based learning and teaching strategies. Books may be purchased or read free online. For example, the publishers offer a free, updated version of the book “How People Learn: Brain, Mind, Experience, and School: Expanded Edition” at Look for “The Great Brain Debate,” a discussion of the connections between brain research and education, by National Academies Press in 2005.

(3) Professional Development Opportunity–“Seeing Math” Telecommunications Project

Source:  Robert Tinker, The Concord Consortium

URL (Ready to Teach):

The Seeing Math project, funded in part by the U.S. Department of Education, develops multimedia case studies and digital tools for elementary and middle school mathematics teacher professional development.

Internet-based video case-based teacher professional development that combines face-to-face and online learning environments provides high-quality extensive, affordable and interactive professional development and access to networked communities of elementary and middle school math educators.

The Seeing Math project has recently expanded to address the problem of under-qualified secondary mathematics teachers. The Concord Consortium’s Seeing Math Telecommunications Project and the Public Broadcasting Service’s (PBS) Teacherline Project–both funded by the U.S. Department of Education–have joined to create a program called “Ready to Teach,” which addresses the problem of under-qualified secondary mathematics teachers.

Participating teachers will receive high-quality online professional development. Pilot testing of a subset of the Algebra I modules began during the fall of 2003. Additional modules are being tested now. Participants interested in being part of the research study will be compensated for taking and administering pre- and post-tests and completing an end-of-course survey.

We are currently (and urgently) seeking 40 teachers who would be willing to give their students a 20-minute test now, and then take the online Algebra professional development course next year. There is an honorarium of $500 each year.

We are looking for teachers to participate in the “Ready to Teach” course who are:

*  Secondary educators teaching Algebra I or II

*  Upper-level elementary or middle school teachers teaching Pre-algebra or Algebra I

*  Pre-service teachers who are preparing to teach secondary mathematics

*  Math curriculum and professional development specialists

*  Certified or uncertified Algebra teachers wishing to develop their content knowledge or teaching methods

Teachers should be willing to spend at least four to six hours per week on course assignments. The course is conducted online, so participating teachers must have access to both school and home computers. Participants can work on assignments at their convenience and complete them by the end of the week. Assignments include a mix of math problems, reading, reflection, observation, writing, and discussion. In any module, teachers may expect to:

*  Work on algebra problems (using a software interactive or on paper)

*  Observe student thinking using videos

*  Reflect on their own learning and obstacles to learning

*  Tie these elements to their own practice and textbook

*  Take part at least three times per week in online discussions

Graduate credit is available. Participants carry out additional work in their classrooms, and produce reports and lesson plans.

Individual teachers and school districts are welcome to participate.

If you are interested, visit and fill out the online form. If you have any questions, please contact Robert Tinker at