2008 Archive‎ > ‎

Vol. 9, No. 27 - 12 November 2008

In This Issue...


Curriculum Commission--November Agenda; Application Deadline is Friday

Source: Curriculum Development and Supplemental Materials Commission (Curriculum Commission)
URL: http://www.cde.ca.gov/be/cc/cd/

The agenda for the November 20-21 meeting of the Curriculum Commission is available for download from http://www.cde.ca.gov/be/cc/cd/ccpubmtgmins2008.asp

The agenda includes the following item (November 20):

5. Mathematics Subject Matter Committee (10:45 to 11:30 a.m.)

A. Plan and Timeline for the Revision of the Mathematics Framework (Information/Action)

B. Application Form for the Mathematics Curriculum Framework and Evaluation Criteria Committee (Information/Action)

C. California Standards Test (CST) for Eighth Grade Mathematics (Information/Action)

D. Other Matters/Public Comment

Members of the Curriculum Commission serve on Subject Matter Committees. Assignments for 2008 include the following:

Hope Bjerke, Chair
Glee Johnson, Vice Chair
Lucy Medina
Bama Medley
Richard Wagoner

(Note: Hope Bjerke is a Math Coach/Trainer for the 
Tehama County Office of Education and will be presenting a session at the CMC-N conference on December 5. Bama Medley is a Middle School Science/Math Specialist, Santa Maria-Bonita School District. Richard Wagoner is a mathematics teacher at San Pedro High School, LAUSD)

Bama Medley, Chair
Richard Wagoner, Vice Chair
Hope Bjerke
Linda Childress
Glee Johnson

Reminder: Applications for service on the Curriculum Commission are due this Friday. For more information, see http://www.cmpso.org/comet/2008/2008_10_04.html#ca5



(1) Proof by Computer

Source: American Mathematical Society - 6 November 2008
URL: http://www.ams.org/ams/press/hales-nots-dec08.html

New computer tools have the potential to revolutionize the practice of mathematics by providing far more-reliable proofs of mathematical results than have ever been possible in the history of humankind. These computer tools, based on the notion of "formal proof," have in recent years been used to provide nearly infallible proofs of many important results in mathematics. A ground-breaking collection of four articles by leading experts, published last Thursday in the Notices of the American Mathematical Society (http://www.ams.org/notices), explores new developments in the use of formal proof in mathematics.

When mathematicians prove theorems in the traditional way, they present the argument in narrative form. They assume previous results, they gloss over details they think other experts will understand, they take shortcuts to make the presentation less tedious, they appeal to intuition, etc. The correctness of the arguments is determined by the scrutiny of other mathematicians, in informal discussions, in lectures, or in journals. It is sobering to realize that the means by which mathematical results are verified is essentially a social process and is thus fallible. When it comes to central, well-known results, the proofs are especially well checked and errors are eventually found.

Nevertheless the history of mathematics has many stories about false results that went undetected for a long time. In addition, in some recent cases, important theorems have required such long and complicated proofs that very few people have the time, energy, and necessary background to check through them. And some proofs contain extensive computer code to, for example, check a lot of cases that would be infeasible to check by hand. How can mathematicians be sure that such proofs are reliable?

To get around these problems, computer scientists and mathematicians began to develop the field of formal proof. A formal proof is one in which every logical inference has been checked all the way back to the fundamental axioms of mathematics. Mathematicians do not usually write formal proofs because such proofs are so long and cumbersome that it would be impossible to have them checked by human mathematicians. But now one can get "computer proof assistants" to do the checking. In recent years, computer proof assistants have become powerful enough to handle difficult proofs.

Only in simple cases can one feed a statement to a computer proof assistant and expect it to hand over a proof. Rather, the mathematician has to know how to prove the statement; the proof then is greatly expanded into the special syntax of formal proof, with every step spelled out, and it is this formal proof that the computer checks. It is also possible to let computers loose to explore mathematics on their own, and in some cases they have come up with interesting conjectures that went unnoticed by mathematicians. We may be close to seeing how computers, rather than humans, would do mathematics.

The four Notices articles explore the current state of the art of formal proof and provide practical guidance for using computer proof assistants. If the use of these assistants becomes widespread, they could change deeply mathematics as it is currently practiced. One long-term dream is to have formal proofs of all of the central theorems in mathematics. Thomas Hales, one of the authors writing in the Notices, says that such a collection of proofs would be akin to "the sequencing of the mathematical genome."

The four articles are the following:

1. "Formal Proof" by Thomas Hales, University of Pittsburgh (http://www.ams.org/notices/200811/tx081101370p.pdf)
2. "Formal Proof---Theory and Practice" by John Harrison, Intel Corporation (http://www.ams.org/notices/200811/tx081101382p.pdf)
3. "Formal Proof---The Four Colour Theorem" by Georges Gonthier, Microsoft Research, Cambridge, England (http://www.ams.org/notices/200811/tx081101382p.pdf)
4. "Formal Proof---Getting Started" by Freek Wiedijk, Radboud University, Nijmegen, Netherlands (http://www.ams.org/notices/200811/tx081101395p.pdf)

The articles appear in the December 2008 issue of the Notices and are freely available at http://www.ams.org/notices


(2) Leading Public Universities Commit to Boosting Quality and Quantity of Science and Math Teachers

Source: National Association of State Universities and Land-Grant Colleges (NASULGC)
URL: http://www.teacher-imperative.org/archives/84

Take a look at the state of science and mathematics education in U.S. public schools, and you'll find an equation that simply doesn't compute. With too few highly qualified teachers and too many underachieving students, efforts to create a pipeline of well-prepared workers for the competitive 21st Century global economy are not measuring up.

To address this challenge, 79 colleges and universities in 32 states have thus far committed to the Science and Mathematics Teacher Imperative (SMTI), an ambitious effort by member institutions of NASULGC (National Association of State Universities and Land-Grant Colleges--the nation's oldest higher education association), to do the following:

- Substantially increase the number and diversity of high quality mathematics and science teachers in middle and high schools;
- Identify immediate and longer term needs for science and mathematics teachers in states where NASULGC member institutions are located; and
- Build partnerships among universities, school systems, state governments and other entities to address statewide needs for teachers on a sustained basis.

NASULGC-member institutions, the leading public and land-grant universities in each state, educate the largest cohort of undergraduate science, technology, engineering and mathematics (STEM) students on research-intensive campuses with influential colleges of education. By committing to this effort, NASULGC-member institutions are responding to the call for 10,000 new science and mathematics teachers in the National Academies report, Rising Above the Gathering Storm. The teacher imperative is supported thus far with grants from the Carnegie Corporation of New York, the National Science Foundation (NSF), and in-kind contributions of faculty from several universities.

"Higher education institutions have the potential to bring about tremendous improvements in U.S. mathematics and science achievement by educating a larger number of highly qualified teachers," said Richard Herman, chancellor of University of Illinois at Urbana-Champaign, who has been instrumental in guiding development of the initiative. "Yet for too long institutions like mine have stood aside on this important issue. We cannot continue on the sidelines. One of the best paths for meeting the need for more science and mathematics teachers is to commit ourselves to this important initiative and inspire more of the nation's top mathematics, science and engineering students to become our top teachers."

"Through their many existing initiatives and colleges of education, NASULGC-member institutions are well-positioned to make an impact on this issue. With tremendous enthusiasm, they are recognizing that collectively, they can make very significant progress in meeting national needs for far more highly qualified and diverse mathematics and science teachers for our schools," said Howard Gobstein, SMTI co-director and NASULGC vice president, research and science policy. "As their national association, we are honored to see so many outstanding academic leaders making this commitment on behalf of their universities. We look forward to welcoming many more institutions to become a part of this growing national effort, and will collaborate with appropriate national partners in other key education, government and private sectors."

During the official launch of SMTI at NASULGC's 121st Annual Meeting in Chicago (Sunday, Nov. 9 at 3:30 CST), a discussion panel encouraged leading public colleges and universities in every state to make the bold commitment to SMTI goals. NASULGC-member colleges and universities partnering in this effort are committing to:

= Work with state education partners to assess the need for science and mathematics teachers in their states;
= Set a numeric target or report a target already set as part of an existing effort (tied to the need in their state or region) for increasing science and mathematics teachers prepared by their campus over time;
= Supply to NASULGC periodic summary data and the status of their efforts with state education partners; and
= Designate appropriate faculty and staff to participate in SMTI meetings and Web-based communication to share among institutions their experiences and approaches from their varied participation in local and nationally funded initiatives.

For more information about the SMTI, please visit www.teacher-imperative.org


(3) President-Elect Obama Urged to Promptly Name White House Science Advisor

Source: FYI, the American Institute of Physics Bulletin of Science Policy News - 7 November 2008
URL: http://www.aip.org/fyi/2008/105.html

In October, almost 180 organizations, including the American Institute of Physics, the American Physical Society, the American Astronomical Society, and the American Association for the Advancement of Science (AAAS), signed letters to Senator Barack Obama and Senator John McCain, urging them to quickly appoint a White House Science Advisor by Inauguration Day. The letters also asked that this position be called the Assistant to the President for Science and Technology and that it be made a cabinet-level position.

A similar recommendation was made in a report issued last summer by the Woodrow Wilson International Center for Scholars (see http://www.aip.org/fyi/2008/088.html)

The first of three overarching recommendations in this report, "OSTP 2.0," stated: "The President should appoint a nationally respected leader to be Assistant for Science and Technology. This individual should serve at the cabinet level. The appointment should be made early in the new Administration, along with the appointments of heads of cabinet-level agencies."

The letter to President-Elect Obama was sent under the leadership of the American Association for the Advancement of Science and the Association of American Universities. The full text of this letter follows:

"Dear Senator Obama:

"The next President of the United States will face a wide range of domestic and international challenges, from financial and regulatory reform to healthcare and rising energy costs, from global climate change to ensuring U.S. economic competitiveness and national security. These challenges share one thing in common: long-term solutions that will be impossible without groundbreaking scientific and technological advances. It is therefore critical that the next President seek out and rely upon sound scientific and technological advice early and often in the new Administration.

"Your responses to the Science Debate 2008 questions reflect your acknowledgment of the important role that science will play in a new Administration. With this in mind, it is essential to quickly appoint a science advisor who is a nationally respected leader with the appropriate scientific, management and policy skills necessary for this critically important role.

"For these reasons, the undersigned organizations representing the business, education and scientific communities urge you, if you are elected President, to appoint your White House Science Advisor by January 20, so this individual can participate immediately in coordinating relevant policy and personnel decisions relating to science and technology.

"We further urge that the next President give the science advisor the title of Assistant to the President for Science and Technology and assign the position a cabinet rank, the same status currently given to the Director of the Office of Management and Budget, the Administrator of the Environmental Protection Agency, and the U.S. Trade Representative.

"The next President must lead our country in addressing the national issues of concern to us all. To do so effectively, science and technology must be part of the solution. Putting a science advisor in place early, and providing this individual with adequate stature and authority within the White House, will help the new President effectively address the challenges we face."

For a complete list of the signatories to this letter, see http://www.aaas.org/news/releases/2008/1031letters.shtml


(4) Unraveling 'Math Dyslexia'

Source: University of Western Ontario
URL: http://communications.uwo.ca/com/western_news/stories/unravelling_'math_dyslexia'_20080924442792/

Research at The University of Western Ontario could change the way we view math difficulties and how we assist children who face those problems.

Daniel Ansari is an assistant professor and Canada Research Chair in Developmental Cognitive Neuroscience in the Department of Psychology at Western. He is using brain imaging to understand how children develop math skills, and what kind of brain development is associated with those skills.

An article by Ansari entitled "The Brain Goes to School: Strengthening the Education-Neuroscience Connection," will be published in Education Canada, a magazine of the Canadian Education Association. The article is currently online at http://www.cea-ace.ca/media/en/BrainGoesToSchool_Fall08web.pdf

In the article Ansari says technological advances such as fMRI have provided unprecedented insights into the working of the human brain.

"Research shows that many children have both dyslexia and dyscalculia," he says. "We are now exploring further the question of exactly what brain differences exist between those who have just math problems and those who have both math and reading difficulties."

Many children who experience mathematical difficulties have developmental dyscalculia--a syndrome that is similar to dyslexia, a learning disability that affects a child's ability to read. Children with dyscalculia often have difficulty understanding numerical quantity.

For example, they find it difficult to connect abstract symbols, such as a number, to the numerical magnitude it represents. They can't see the connection, for instance, between five fingers and the number ‘5.' This is similar to children with dyslexia who have difficulty connecting sounds with letters.

In a recent study, Ansari and graduate student Ian Holloway showed children who are better at connecting numerical symbols and magnitudes are also those who have higher math scores. A report of this research is forthcoming in the Journal of Experimental Child Psychology.

Ansari says parents and teachers are often not aware that developmental dyscalculia is just as common as developmental dyslexia and is frequently related to dyslexia. There is a great need to increase public awareness of developmental dyscalculia.

Using functional Magnetic Resonance Imaging (fMRI) to study the brains of children with math difficulties, Ansari says it becomes clear that children with developmental dyscalculia show atypical activation patterns in a part of the brain called the parietal cortex.

This research holds tremendous promise for people who, in the past, had simply accepted that they are 'not good at math.' Understanding the causes and brain correlates of dyscalculia may help to design remediation tools to improve the lives of children and adults with the syndrome.

"We have some cultural biases in North America around math skills," says Ansari. "We think that people who are good at math must be exceptionally intelligent, and even more dismaying and damaging, we have an attitude that being bad at math is socially acceptable. People who would never dream of telling others they are unable to read, will proclaim publicly they flunked math."

Ansari says math skills are hugely important to life success and children who suffer math difficulties may avoid careers that, with help, might be a great fit for them.

Ansari recently reviewed existing research in this field for the April edition of the journal Nature Reviews Neuroscience, and he hopes that news of this important research will also reach parents, teachers and individuals.

"A teacher who understands brain structure and function will be better equipped to interpret children's behaviors, their strengths and weaknesses, from a scientific point of view, and this will in turn influence how they teach," says Ansari.

COMET is sponsored in part by a grant from the California Mathematics Project.

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    Carol Fry Bohlin, Ph.D.
    Professor, Mathematics Education
    California State University, Fresno
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