"The N.S.A's Math Problem" is the title of Jonathan Farley's Op-Ed piece in the May 16 2006 *New York Times*. Farley, a mathematician and currently a science fellow at the Center for International Security and Cooperation at Stanford, is an expert on mathematical approaches to the terrorism problem. See Terror Network Theory in this column for February, 2005. This Op-Ed piece delivers a critique of the NSA's data-mining approach, in the light of the current scandal about warrantless Federal retrieval of telephone records. Of course what the NSA is *actually* doing with their retrieved data is unknowable, but Farley makes an educated guess on the basis of published descriptions of what they start with. From what the telephone companies seem to have given the NSA ("complete lists of who called whom") he concludes that the Agency's graph theorists are trying to use "social network analysis" to deduce the structure of terrorist groups from the topology of the set of phone links between their members. Farley explains why "this isn't as helpful as you might imagine." And more fundamentally, he argues that "the National Security Agency's entire spying program seems to be based on a false assumption: that you can work out who might be a terrorist based on calling patterns." Farley recommends instead studying populations by means of "formal concept analysis." In a "concept lattice," a node represents "people who share many of the same characteristics," and links between nodes "indicate that all the members of a certain subgroup ... must also have other attributes." He mentions a successful application of this technique, but cautions that what law enforcement should be doing is "using some common sense and knowledge of terrorists, not playing math games." Void in a golden cage The recently constructed molecular cage, made of 16 gold atoms, has the shape of a truncated tetrahedron. Add a new member to the family of nano-polyhedra concocted by chemists. This one is made of 16 gold atoms arranged to form a truncated tetrahedron: delete the four vertex atoms from the array corresponding to the tetrahedral number 20. The *New York Times* for May 16, 2006 reported the construction, which is described in "Existence of hollow golden cages," by Lai-Shen Wang (Pacific Northwest National Laboratory) and collaborators, in the May 30 *PNAS*. The authors report that this is the first time free-standing metal hollow cages have been detected in the laboratory. In fact their method produced a mixture of the Au_{16} cages with slightly larger ones made of 17 and 18 atoms. They note that these cages are presently empty, but that their calculations suggest that "these hollow golden cages can easily accomodate a guest atom with very little structural distortion to the host cages." In case you want to do this at home, "The gold cluster anions were produced by using a laser vaporization cluster source" and the results were anyalyzed by photoelectron spectroscopy, "using a magnetic-bottle time-of-flight photoelectron analyzer." No name has been coined yet for these miniature gold cages (inside diameter about 6Å or 6^{.}10^{-10}m) akin to the evocative "buckyball" for the Carbon-60 soccer-ball shaped molecules. In fact the *Times*'s take on the story, written by Kenneth Chang, was "16 Golden Atoms in Search of a Catchy Name." Now Math Diplomacy - I Two pieces in the May 19 2006 *Science* report on the current state of the controversy between constructivists and algorithmists over the future of primary and secondary mathematics education in the United States. "Finding Common Ground in the U. S. Math Wars," by Jeffrey Mervis, gives a quick tour of recent history: the post-Sputnik New Math, the 1989 NCTM Standards and how the resulting "huge schism in the community" has been stimying reform efforts. He goes on to describe recent developments, "hopeful signs that the two sides may be ready to call a truce and work together to improve U.S. mathematics education." - Common Ground is an MAA-sponsored initiative, funded by the NSF and Texas Instruments, and headed by Richard Schaar, an applied mathematician and former TI executive. The idea was to get around the impasse by forming a panel of "leading figures from both sides," who could forge a compromise position and get the word out so as "to influence the process by which states develop standards, adopt textbooks and develop ... assessment tools ... ." For the algorithmists Schaar chose James Milgram (Stanford) and Wilfried Schmid (Harvard); for the constructivists, Deborah Ball (Michigan), Joan Ferrini-Mundi (Michigan State) and Jeremy Kilpatrick (Georgia). The panel was first convened in December 2004, with Schaar serving as facilitator; six months later, it issued a short list of principles to guide K-12 math education, including: "the automatic recall of basic facts, the importance of abstract reasoning, the need to require a mastery of key algorithms, and the judicious use of calculators and real-world problems." The panel has recently met to "tackle the topics in greater detail."
- The NCTM has drawn up a list of "curriculum focal points," scheduled to be released publicly next fall. There are three for each grade from K through 8. Frances Fennel, the NCTM president, explains "While a lot of things are important, we're saying to teachers that here are three things you need to zero in on." E.g. in 4th grade, multiplication, fractions and decimals, and the concept of area. Mervis quotes Richard Askey ("an outspoken critic of earlier NCTM standards"): "The idea of coming up with a few topics that should be addressed in K through 8 is a very needed step."
Now Math Diplomacy - II A second, shorter piece in *Science*, also by Mervis, reports the formation of a presidential panel to review the state of math education. The National Mathematics Advisory Panel will be headed by Larry Faulkner, former president of the University of Texas. It has some overlap with the Common Ground committee (Schmid, Ball) and includes other prominent representatives of both factions, like H. H. Wu (UC Berkeley), a longtime campaigner for early and strong basics, and Frances Fennel, the NCTM president. The panel is to concentrate on *algebra* as the weak link in the math education process. As Faulkner puts it: "Algebra is a tremendously important gateway course, but our success rates are not very good." The formation of the National Mathematics Advisory Panel was also reported in the May 15 *New York Times*, in an article by Diana Jean Schemo which begins: "The Bush administration has named a former president of the University of Texas at Austin to lead a national panel to weigh in on the math wars playing out across the country. The politically fraught battle pits a more free-form approach to teaching math against the traditional method that emphasizes rules and formulas to solve number problems." Schemo points out the similarity between the math education debate and "the conflict over how to teach reading - whether by teaching children to recognize words in the context of stories or through more explicit instruction in letters and sounds" and remarks that "the conflicts share many of the same political and philosophical disputes." The panel's final report is due in February 2008. Tony Phillips Stony Brook University tony at math.sunysb.edu |