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An interesting exchange took place in the Letters to the Editor section of the Providence Journal. In the first letter, Richard Heath wrote regarding whether algebra should be required in school: "I am 83 and took algebra in public school. I have never used it! I have six children who have never used it." His grandchildren haven't used it either. On October 11, Susan Osberg replied with six questions (e.g. "Have you ever had to sort through the fiscal claims of candidates for public office?"), writing that perhaps generations of the Heath family had used algebra without knowing it. Osberg, president of the Rhode Island Mathematics Teachers Association, finished with: "To answer your question about 'whether the public schools need to teach algebra,' I give you a resounding yes."
--- Mike Breen
"Making Math Lessons as Easy as 1, Pause, 2, Pause ...," by Winnie Hu. The New York Times, 30 September 2010.
Schools in the US have been working hard for decades to improve the math skills of their students. They have done this by adopting new programs, like "new math"” in the 60s, which focused on abstract theories and created a back-to-basics backlash, and "reform math", which focuses on conceptual understanding and problem solving, but doesn't lack its critics. Recently, more and more schools have been adopting a program known as Singapore math, based on the country's success. Singapore students have ranked at or near the top on international math exams since the 1990s.
The innovative program devotes more time to fewer topics, and thus addresses one of the big difficulties in teaching math: all children learn differently. By slowing down the learning process, students get a solid math foundation upon which they can build increasingly complex skills. Even though they start out slow in kindergarten (by spending a week on the numbers 1 and 2 for example) the pace can be increased in fourth and fifth grade, putting children as much as a year ahead of students in other math programs. Bill Jackson, a math coach for the Scarsdale district, says that in Singapore math, the students move through a three-step learning process: concrete, pictorial, and abstract. Most American math programs typically skip the middle steps and lose students in the process, says Jackson. The main criticism of the program, and the main reason some schools have dropped it after a few years, is that it is not easy or cheap to successfully adopt. School board members and parents are also reluctant to adopt a foreign math program. Training teachers can be expensive, and in some cases teachers themselves lacked a sufficiently strong math background to be able to implement the program adequately. But recent suggests that students who are taught Singapore math score higher on standardized tests and it even helps young children develop confidence in their math skills, so it might just be worth the trouble.
--- Adriana Salerno
"In Character with Tom Henderson," by Peter Korn. The Portland Tribune, 23 September 2010.
In this brief and amusing article, Peter Korn interviews mathematician Tom Henderson, an adjunct professor of mathematics at Portland State University in Portland, Oregon, as well as an improv comedian. Henderson is currently raising money for a book he intends to write, Punk Mathematics, using the Kickstarter.com website. (As of this writing, Henderson has raised almost $29,000.) During the interview, Henderson speaks about the affinity between punk and mathematics: punk is "very critical of social norms” while, in mathematics, “you can verify everything for yourself if you spend long enough on a problem. Those two can behave very nicely (together)." When asked about the hardest math problem he has faced, Henderson says a few words about the Goldbach Conjecture, and, at the interviewer's request, finishes with a joke about an engineer, a scientist, and a mathematician. (No, the setting is not a bar but a hotel room that catches on fire.) You can read the interview, and hear Henderson and fellow math aficionado Nick Horton discuss infinity, probability, game theory, and other topics related to mathematics.
--- Claudia Clark
"Sizing Up Consciousness by Its Bits," by Carl Zimmer. The New York Times, 20 September 2010.
Measuring a person's level of consciousness in a manner akin to measuring their blood pressure is a lofty goal, but one that mathematician David Balduzzi and acclaimed neuroscientist Giulio Tononi have begun to move towards. Recently, they wrote a paper entitled "Qualia: The Geometry of Integrated Information," which discusses means of viewing the integrated information generated during a conscious experience as a geometric object whose height indicates the quantity of information or level of consciousness associated to that experience. As Carl Zimmer, the author of the New York Times article explains, information technology distinguishes between the aggregate of many disjoint bits of information such as a photograph formed by many pixels, and the integrated information that results from a network of neurons that can communicate with each other. While our brains work by sharing information from one part with another, this type of shared information is harder to quantify than the many pixels in a photo. Consider for example that "simply linking all the parts in every possible way does not raise phi (the level of consciousness) much." Rather, connecting every neuron to every other neuron in a system creates one giant on/off switch. “It’s either all on, or all off,” says Tononi of such a system.
Apart from assessing models of very small neural systems (such as that of a worm) to measure levels of consciousness, an actual model of the human brain is not very near. But Tononi argues that the theoretical implications of his theory would do a better job explaining transitions in and out of consciousness than some of the current theories. Another approach Tononi is taking in an effort to measure consciousness is to record the brain's reaction to a stimulus provided by a magnetic pulse. The duration of the brain waves that echo varies according to how anesthetized the brain is, indicating that a less conscious individual's brain might have fewer reverberations. More experiments on individuals in various states of sleep and wakefulness will soon be performed, giving a firmer shape to Tononi's theory.
--- Brie Finegold
"Fibbing With Numbers": Review of Proofiness: The Dark Arts of Mathematical Deception by Charles Seife. Reviewed by Steven Strogatz. The New York Times, 19 September 2010.
Proofiness (noun): the art of using bogus mathematical arguments to prove something that you know in your heart is true—even if it is not. The concept is the heart (and the title) of a new book by Charles Seife that explores how politicians and marketers use misleading and even inaccurate numbers to support their cases. Seife’s book looks at the perils of ascribing too much importance to numbers that are derived from sloppy or even nonexistent calculations, including vote counting in the recent Minnesota Senate race, in which the observed errors were larger than the difference in the number of votes. He also provides examples of how cherry picking data and assigning high importance to the average of a data set with extreme outliers have been used to mislead the public. Reviewer Steven Strogatz notes that although several recent books have looked at the deceptive power of numbers, Seife’s Proofiness stands out for its strong examples of the effect of this deception on society.
--- Lisa DeKeukelaere
"After Cracking a Theoretical Bottleneck, a Math Prodigy Arrives at the U. of Chicago," by Paul Basken. The Chronicle of Higher Education, 17 September 2010, page A4.
The Chronicle of Higher Education reports on outstanding mathematician, Ngô Bao Châu, becoming the newest professor of mathematics at the University of Chicago. Châu is famous for proving an important theorem, known as the "fundamental lemma" which is a crucial part of a set of conjectures known as the "Langlands Program." The proof had eluded mathematicians ever since Robert P. Langlands conjectured the theorem in 1969. Langlands himself spent more than ten years trying to prove it without success and a considerable body of subsequent work depended on its validity. Châu’s insight that principles of a seemingly unrelated field of mathematics would help in solving this great mathematical challenge along with four years of working with Langlands at the Institute for Advanced Study in Princeton ultimately led to a proof in 2009.
--- Baldur Hedinsson
"Tutors Made to Measure," by Maggie Jones. The New York Times, 16 September 2010.
Online tutoring sites have been around for a while. But virtual tutors, with a face, a gender, a race, and an emotional response to their students’ progress are a relatively new development. The Wayang Outpost, an online program designed by Beverly Park Woolf and Ivon M. Arroyo, two University of Massachusetts, Amherst, researchers, was originally developed to encourage middle- and high-school girls to embrace mathematics. These virtual tutors, or “affective pedagogical agents,” are designed to read students’ emotional cues, like boredom, frustration, anxiety and nervousness. The students are hooked up to sensors monitoring sweat, pressure placed on the mouse, and fidgeting. A small camera monitors facial expressions. This information is then used to tailor the tutor’s encouragement. And even though these computer-generated tutors are never going to be a perfect replacement for human teachers, as long as they keep students engaged and motivated they are doing plenty.
--- Adriana Salerno
Blog: Math Goes Pop! Stand Up to Questionable Odds, by Matthew Lane. 15 September 2010.
Matt Lane, a graduate student at UCLA, documents some of the meetings of pop culture and math in his blog, Math Goes Pop! Hi goal is to "make mathematics more exciting and less terrifying to a general audience." While some of his entries focus on likely sources of mathematical subjects like Futurama and A Beautiful Mind, he also illuminates less obvious mathematical content present in other media. For example, he discusses the physics of the epic punch delivered to character Scott Pilgrim by Todd Ingram, a punch that would have thrown Michael Cera's character almost 700 ft up in the air. He also questions a graph in Slate magazine that records the possibly diminishing revenue taken in by 3D films. Lane also points out the moments when mathematics takes the spotlight like it did in August due to the proof that the Rubik's cube can always be solved in 20 moves or less.Even a Public Service Announcement for the campaign to Stand Up To Cancer uses a long list of statistics on everything from bowling a perfect game to tripping while texting to highlight the high probability of a the viewer getting cancer in his/her lifetime. While this is an effective strategy for getting the American Cancer Society's point across, Mr. Lane wonders where those other statistics came from, and he follows up to determine their believability. Such a combination of reporting and mathematical insight is characteristic of the entries in Math Goes Pop!
--- Brie Finegold
"Change your math attitude, and daughter's," by Leanna Landsmann. Detroit Free Press, 8 September 2010.
In her weekly column, A+ Advice for Parents, education writer and editor Leanna Landsmann answers parent's questions about their children's education. In this week's column, a mother writes that she has told her seventh-grade daughter that it's OK to get a D in math because she herself did poorly in math--"like most women." She asks Landsmann if her daughter, who "hates math" and wants to be a dress designer, really needs math. Landsmann answers in the affirmative and provides several reasons and resources for this parent. These include reading "The I Hate Mathematics Book" by Marilyn Burns to change her own attitude about math, setting higher expectations for her daughter and getting her extra academic support if needed, using "real-life examples to demonstrate the concepts," teaching her daughter to ask "Is my answer logical?", making use of resources on the web, and having her daughter teach math mini-lessons to her.
--- Claudia Clark
"Bringing the Beauty of Math to Life," by Faiza Elmasry. Voice of America, 3 September 2010.
For this article, Faiza Elmasry interviews Alex Bellos, a reporter with degrees in mathematics and philosophy from Oxford University. "After 20 years as a reporter," Bellos "traveled around the world--and back in time--to uncover fascinating stories of mathematical achievements and to profile people whose lives are intertwined with numbers." Bellos wrote about his adventures in the recently-published book, Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Mathematics. Bellos describes to Elmasry a little of what he learned and a few of the people he met. For instance, he found that cultural attitudes toward mathematics, mathematicians, and mathematical ability vary greatly around the world: in France (but not in the U.K., according to Bellos) it's "quite cool" to be a mathematician, while in India "being good at arithmetic" is "almost seen as a badge of national pride." In Japan, Bellos discussed the pleasures of mathematical games with the creator of the Sudoku puzzles, "spent time with a guru of origami" outside of Tokyo, and met "the world's most numeric chimpanzee." Elmasry finds that Bellos's book does what Bellos intended: proves "that mathematics is not a dry field of learning."
--- Claudia Clark
"Rummaging for a Final Theory," by Zeeya Merali. Scientific American, September 2010, pages 14-17.
In July, mathematicians and physicists met at the Banff International Research Station to discuss unifying gravity and the Standard Model. The Standard Model of particle physics uses a combination of three Lie groups to connect all known elementary particles, electromagnetism, the strong force (that binds atomic nuclei), and the weak force (associated with radioactive decay). Physicists Roberto Percacci and Fabrizio Nesti think a larger Lie group would incorporate gravity into the Standard Model, while Oregon State University mathematician Tevian Dray and physicist Corinne Manogue are using octonions to describe some properties of particles, such as spin. Although the research is just beginning, Dray says that "We are starting to get glimmers of the properties that a final theory must have." Others are not so optimistic, countering that the theory would predict particles whose existence would violate previous experiments.
--- Mike Breen
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