COMET • Vol. 9, No. 21 – 29 September 2008

ARTICLES & ANNOUNCEMENTS (CALIFORNIA FOCUS)

(1) California Mathematics Council Seeks Videos of Exemplary Teaching

Source: John Leamy, Mathematics Professor, Columbia College

The California Mathematics Council (CMC) Awards Committee invites you to submit a short video clip of excellent mathematics teaching that we can post on the CMC website (http://www.cmc-math.org/) as an aid to teachers seeking examples of outstanding teaching, as well as to those who are preparing videos as part of the application process for the Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST). (Please see http://www.cmc-math.org/PAEMST for more information about this award; applications should be available at http://www.paemst.org/controllers/app.cfc?method=view around November 1.)

If anyone is aware of or has a collection of videos of classroom teachers modeling excellent instructional techniques, please contact Sandie Gilliam at Colorado College (sandie.gilliam@comcast.net) or John Leamy at Columbia College (leamyj@yosemite.edu).  We are able to edit videos to highlight specific parts, so video length is not an issue.  Because of our proposed use, the videos would have to be authorized for public dissemination.

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(2) State Schools Chief Jack O’Connell Releases Revised Dropout and Graduation Rates Using Individual Student-Level Data

Source: California Department of Education
URL: http://www.cde.ca.gov/nr/ne/yr08/yr08rel131.asp

Last Thursday, State Superintendent of Public Instruction Jack O’Connell released revised dropout and graduation rates for the 2006-07 school year that for the first time were compiled using Statewide Student Identifiers (SSID).

“The revised graduation rate is up slightly to 67.7 percent and the dropout rate is down nearly three points to 21.5 percent for 2006-07,” said O’Connell. “Of course, I do not want to see any student drop out of school–graduating from high school is critically important for all students’ future success. However, I am pleased that districts are finding even more of our students still in our public school system. The updated data indicate that our use of Statewide Student Identifiers is working as intended. School districts now are highly motivated to communicate with each other to track down students lost in the system to determine their status.”

Each K-12 student in a California public school is entered into the SSID system and assigned an individual, yet non-personally identifiable, number that is maintained throughout the student’s academic career. SSIDs allow for more accurate tracking of how many students are or are not completing their education.

The dropout rates declined among two subgroups of concern in the state’s efforts to close the achievement gap. Among African American students, the revised dropout rate is 36.2 percent, down 5.4 percent from the 41.6 percent reported in July. Among Latino students, the dropout rate is now 27.4 percent, down 2.9 percent from the July report.

Students counted as dropouts include students who are known dropouts and students considered “lost transfers,” or students who indicated they were transferring to another school but then were not reported as enrolled anywhere else. The revised rates show 3,000 fewer students reported as known dropouts and 14,000 fewer students reported as lost transfers.

The revised rates also include an update on the number of students who are neither graduates nor dropouts, now at 10.8 percent. The latter group consists of students who completed or withdrew from school, such as students who transferred to a private school, left the state, took the General Educational Development Test (GED) to earn a California High School Equivalency Certificate, or became a “completer,” such as a special education student who received a certificate of completion or other credential in lieu of a diploma. Each student, whether they graduated, withdrew from, or completed school is assigned one of 28 “withdrawal codes.”

The 2006-07 dropout rate cannot be compared to the prior year’s dropout rate of 13 percent because the numbers are based on different information. Before SSIDs, dropout rates were derived using only aggregate data of enrollment and dropouts collected annually through the California Basic Educational Data System. Now, individual student-level data allow districts and the state to collect and report what becomes of students who leave school…

SSIDs will eventually be tracked through the California Longitudinal Pupil Achievement Data System, or CALPADS, which will maintain longitudinal, individual student-level data including student demographics, program participation, grade level, enrollment, course enrollment and completion, discipline, state assessment, teacher assignment, and other data required to meet state and federal reporting requirements. CALPADS is scheduled to be fully implemented with all districts in the 2009-10 school year. Until student-identifier data are collected over four years, CDE will still be reporting an estimated four-year graduation rate and a derived four-year dropout rate…

Senate Bill 1453, authored by former state Senator Dede Alpert, was signed into law in September 2002 to require the assignment of SSIDs. Local educational agencies have completed assigning all California kindergarten through grade twelve public school students a SSID. To download state-, county-, district-, and school-level dropout data, please visit CDE’s DataQuest at http://dq.cde.ca.gov/dataquest/  Downloadable data files will be uploaded in about two weeks and will be available at http://www.cde.ca.gov/ds/sd/cb/studentdatafiles.asp

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ARTICLES & ANNOUNCEMENTS (NATIONAL FOCUS)

(1) Top 14 Science Questions Facing America: Responses from John McCain and Barack Obama

Source: Science Debate 2008
URL: http://www.sciencedebate2008.com/

U.S. Presidential Candidates John McCain and Barack Obama have both submitted responses to questions posed by Science Debate 2008 on the following topics: innovation, climate change, energy, education, national security, pandemics and biosecurity, genetics, stem cells, ocean health, water, space, scientific integrity, research, and health.

The candidates’ responses appear side by side on the Web site above.
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Note 1: All candidates for Congress on the ballot in November 2008 are being invited to let voters know where they stand on health and research by filling out a brief questionnaire. Visit http://www.yourcandidatesyourhealth.org/ to search for candidate responses. http://www.yourcandidatesyourhealth.org/presidential.php contains the responses of presidential candidates McCain and Obama.

Note 2: For a summary of John McCain’s and Barack Obama’s education platforms, see Education Week’s “McCain, Obama Spar on Education” at http://www.edweek.org/ew/articles/2008/09/17/04prez_ep.h28.html

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(2) “As Easy as 1, 2, 3: Number Sense Correlates with Test Scores”

Source: The Johns Hopkins University 
URL: http://www.jhu.edu/news/home08/sep08/number_sense.html

Knowing how precisely a high school freshman can estimate the number of objects in a group gives you a good idea how well he has done in math as far back as kindergarten, researchers at The Johns Hopkins University found.

Good “number sense” at age 14 correlates with higher scores on standardized math tests throughout a child’s life, and weaker “number sense” at 14 predicts lower scores on standardized tests, says Justin Halberda, assistant professor of psychological and brain sciences in the university’s Krieger School of Arts and Sciences.

“We discovered that a child’s ability to quickly estimate how many things are in a group significantly correlates with that child’s performance in school math for every single year, reaching all the way back to when he or she was in kindergarten,” Halberda said.

Halberda teamed up on the research with colleagues Michele Mazzocco, professor of psychiatry and behavioral sciences at Johns Hopkins and Lisa Feigenson, Johns Hopkins assistant professor of psychological and brain sciences.

Though people often think of mathematics as a pinnacle intellectual achievement of humankind, research reveals that some intuition about numbers, counting, and mathematical ability is basic to almost all animals. For example, creatures that gather or hunt for food keep track of the approximate number of food items they procure in order to return to the places where they get the most sustenance. Humans share this very basic “number sense,” allowing them, at a glance, to estimate the number of people in a subway car or bus, Halberda says.

The Johns Hopkins team wondered whether this basic, seemingly innate number sense had any bearing on the formal mathematics that people learn in school. So the researchers asked 64 14-year-olds to look at flashing groups of yellow and blue dots on a computer screen and estimate which dots were more numerous. Though most of the children easily arrived at the correct answer when there were (for example) only 10 blue dots and 25 yellow ones, some had difficulty when the number of dots in each set was closer together. Those results helped the researchers ascertain the accuracy of each child’s individual “number sense.”

They then examined the teenagers’ record of performance in school math all the way back through kindergarten, and found that students who exhibited more acute number sense had performed at a higher level in mathematics than those who showed weaker number sense, even controlling for general intelligence and other factors.

“What this seems to mean is that the very basic number sense that we humans share with animals is related to the formal mathematics that we learn in school,” Halberda concludes. “The number sense we share with the animals and the formal math we learn in school may interact and inform each other throughout our lives.”

Though the team found this strong correlation between number sense and scholastic math achievement, Halberda cautions against concluding that success or failure in mathematics is genetically determined and, therefore, immutable.

“There are many factors that might affect a person’s performance in school mathematics,” Halberda says, “What is exciting in our result is that success in formal mathematics and simple math intuitions appear to be related.”

Future directions for research include investigating the trainability of one’s number sense and seeing how early help in number sense could affect later formal math learning.

Funding for this research was provided by the National Institutes of Health.

Watch a Video of the Study Task:
In this video clip (http://tinyurl.com/52y6ah), entitled “Spots Before Their Eyes,” you will see three students taking the numerical acuity assessment. Each trial involves a very brief flash of blue and yellow dots. For each flash, the students are deciding whether there are more blue or more yellow dots. The full assessment lasts ten minutes. From the students performance, the researchers are able to determine the acuity of their “number sense” and then correlate it with school math performance.

Test Your Approximate Number Sense:  Follow this link to an interactive test available on The New York Timeswebsite: http://tinyurl.com/5jxs9k

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Related Articles:

(a) “How One’s ‘Number Sense’ Helps with Mathematics” by Rob Stein

Source: Washington Post – 8 September 2008
URL: http://www.washingtonpost.com/wp-dyn/content/story/2008/09/07/ST2008090701940.html

(b) “Gut Instinct’s Surprising Role in Math” by Natalie Angier

Source: The New York Times – 16 September 2008
URL: http://www.nytimes.com/2008/09/16/science/16angi.html?em

Excerpt:

Given the antiquity and ubiquity of the nonverbal number sense, the researchers were impressed by how widely it varied in acuity. There were kids with fine powers of discrimination, able to distinguish ratios on the order of 9 blue dots for every 10 yellows, Dr. Feigenson said. “Others performed at a level comparable to a 9-month-old,” barely able to tell if five yellows outgunned three blues. Comparing the acuity scores with other test results that Dr. Mazzocco had collected from the students over the past 10 years, the researchers found a robust correlation between dot-spotting prowess at age 14 and strong performance on a raft of standardized math tests from kindergarten onward. “We can’t draw causal arrows one way or another,” Dr. Feigenson said, “but your evolutionarily endowed sense of approximation is related to how good you are at formal math.”

The researchers caution that they have no idea yet how the two number systems interact. Brain imaging studies have traced the approximate number sense to a specific neural structure called the intraparietal sulcus, which also helps assess features like an object’s magnitude and distance. Symbolic math, by contrast, operates along a more widely distributed circuitry, activating many of the prefrontal regions of the brain that we associate with being human. Somewhere, local and global must be hooked up to a party line.

Other open questions include how malleable our inborn number sense may be, whether it can be improved with training, and whether those improvements would pay off in a greater appetite and aptitude for math. If children start training with the flashing dot game at age 4, will they be supernumerate by middle school?…

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(3) New Study Shows the Unintended Consequences of Moving More Pupils Into Eighth Grade Algebra and Other Advanced Math Classes

Source:  The Brookings Institution
URL: http://tinyurl.com/4xnjah 
URL: http://www.brookings.edu/reports/2008/0922_education_loveless.aspx
URL (Report): http://tinyurl.com/3mcvv6 

A new report from the Brown Center on Education Policy at the Brookings Institution finds that the nation’s push to challenge more students by placing them in advanced math classes in eighth grade has had unintended and damaging consequences, as some 120,000 middle-schoolers are now struggling in advanced classes for which they are woefully unprepared.

“The ‘democratization of algebra’ sounds like a worthy goal–it certainly stems from good intentions,” says Tom Loveless, the Brown Center’s director and author of the new study, which is being released as an advance excerpt of the 2008 Brown Center Report on American Education. But, he adds, “when a large number of students who don’t even know basic arithmetic are placed in classes with students several grade levels ahead of them, the result is false democratization. That’s bad for the misplaced students, and it’s bad for their well-prepared classmates too.”

Algebra in eighth grade was once reserved for mathematically gifted students. But a campaign to extend algebra to many more eighth graders, which began in the 1990s on the grounds that greater equity and future opportunities require broader access to algebra, has had considerable success: The proportion of eighth graders taking algebra nearly doubled from 1990 to 2007, reaching 31 percent, and today more U.S. eighth graders take algebra than any other math course. Until now, however, no empirical evidence has existed to demonstrate whether the push for universal eighth- grade algebra is a good idea, particularly for students who have weak math skills.

The new Brown Center study tackles this question by examining rarely used research data from the National Assessment of Educational Progress (NAEP). Unlike most NAEP data, these restricted- use files allow investigators who have obtained a license to drill down and examine student-level information on a nationally representative sample of 160,000 eighth graders.

The results are sobering. Between 2000 and 2005, as enrollment in advanced math classes rose among eighth-graders and enrollment in basic math declined, there was a significant jump in the percentage of very low scoring students in advanced courses. Among students in the bottom 10 percent nationally on the NAEP math test, enrollment in advanced math classes rose from 8.0 percent in 2000 to 28.6 percent in 2005. The percentage of low achievers enrolled in basic courses fell from 73.7 to 46.3 percent.

During the same period, students in the 10th percentile and below more than doubled as a proportion of those in advanced classes, the study finds, rising from 3 percent in 2000 to 7.8 percent in 2005. That might at first glance seem to be a trivial percentage, but it adds up to a significant number of students–about 120,000 nationwide.

Indeed, Loveless, himself a former public school teacher, notes that having even two children performing significantly below grade level in a class poses problems for classroom instructors, who may water down instruction as a result. That can be bad news for the well-prepared classmates of misplaced students. “Well prepared students need a real algebra class, not a fake one teaching elementary school mathematics,” the report says.

The Brown Center study illustrates just how far “misplaced” students lag behind their peers in advanced math classes. Despite being enrolled in Algebra I, Geometry, and Algebra II, misplaced eighth graders have NAEP scores well below average for fourth graders…

The study also gives detailed information about the characteristics of these misplaced students, their families, and their schools. It finds that they are disproportionately black and Hispanic; have parents whose own education is below the national average; come from low-income households; attend large urban schools with predominantly low socioeconomic status populations; and have math teachers with less experience and mathematics training than the typical teacher of advanced math students in eighth grade.

“No element of this story is educationally sound,” the report says. “No social benefit can be produced by placing students in classes for which they are unprepared.” It also notes that hundreds of thousands of well-prepared students–“also predominantly black, Hispanic, or poor”–are sitting in the same classrooms as misplaced students and are “equally deserving of a good education.”

The study makes a variety of reform recommendations that would create a more realistic algebra policy, from early intervention and teaching of basic skills to new research that tests the effectiveness of different approaches to math remediation. As things stand, however, the report concludes, the push for universal eighth grade algebra “is creating more problems than it solves.”

“This is not a call to lower expectations for what students can learn,” Loveless emphasizes. “Instead we have to give more students the preparation they need to succeed in algebra. That won’t be achieved by designating an arbitrary grade in which all students are swept into an algebra course, then turning a blind eye to the troubling results.”

For a full copy of the report, visit http://tinyurl.com/3mcvv6

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Related Article:

“Low Performers Found Unready to Take Algebra” by Sean Cavanagh

Source: Education Week – 22 September 2008
URL: http://www.edweek.org/ew/articles/2008/09/24/05dilute_ep.h28.html

This article goes into more detail regarding the study’s results and implications, and includes reactions from Jeremy Kilpatrick (University of Georgia) and Bob Moses (the Algebra Project).

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(4) Titanic Primes Raced to Win $100,000 Research Award

Source: GIMPS (Great Internet Mersenne Prime Search)
URL: http://www.mersenne.org/m45and46.htm and http://www.mersenne.org/prime.htm

Researchers have discovered the two largest known prime numbers, a whopping 12,978,189 and 11,185,272 digits long, as part of a 12 year old world-wide volunteer computing project, the Great Internet Mersenne Prime Search (“GIMPS”). The primes can be written shorthand as 2^43,112,609 – 1 and 2^37,156,667 – 1.

A nearly decade-long competition for a $100,000 award from the Electronic Frontier Foundation ended closely when the larger prime surfaced on a UCLA computer managed by Edson Smith just two weeks before the second prime was found by Hans-Michael Elvenich’s computer in Langenfeld near Cologne, Germany. Both are among the 100,000 computers in GIMPS PrimeNet, a “grass-roots supercomputer” as Science magazine describes it, which has been running continuously since 1996 and performs 29 trillion calculations per second.

“We’re proud be to participants in GIMPS and grateful to the UCLA Mathematics Department for providing computational resources to the project,” said Edson Smith, Computing Manager. Hans-Michael Elvenich, a German electrical engineer and prime number enthusiast, adds, “After four years of searching for a prime on GIMPS, finally a great success!”

“These exciting discoveries are literally at the Internet’s ‘electronic frontier,'” says PrimeNet inventor, Scott Kurowski, a software technologist in San Diego, California. “Developing technologies and methods to apply the incredibly vast power of cooperative research computing is why the Electronic Frontier Foundation set up their grand challenge awards. It’s serious research, but fun and educational, too.”

GIMPS founder George Woltman in Orlando, Florida said, “In addition to congratulating and gratefully acknowledging the vast contributions of our hundreds of thousands of participants over the years, we’re committed to giving $25,000 to charity, $50,000 to UCLA for its part in the discovery, and most of what’s left to other GIMPS prime discoverers.” He adds, “Our research project will soon offer the chance to achieve the next challenge, the $150,000 award for an immensely more difficult 100-million-digit prime. All you need to participate is our free software download, and a lot of patience!”

For more information, see www.mersenne.org

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Related Article:

“UCLA Mathematicians Discover a 13-Million-Digit Prime Number” by Thomas H. Maugh II

Source: Los Angeles Times – 27 September 2008
URL: http://www.latimes.com/news/science/la-sci-prime27-2008sep27,0,2746766.story

…While the prize money is nothing special, the bragging rights for discovering the 46th known Mersenne prime are huge…

“We’re delighted,” said UCLA’s Edson Smith, leader of the effort. “Now we’re looking for the next one, despite the odds,” which are thought to be about one in 150,000 that any number tested will be a Mersenne prime.

Prime numbers are those, like three, seven and 11, that are divisible only by themselves and one. Mersenne primes, named after the 17th century French mathematician Marin Mersenne, who discovered them, take the form 2^p – 1, where p is also a prime number…

The prize will be awarded when the new prime is published, probably next year…