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April 2011
Brie Finegold summarizes two blogs this month: dan: less helpful and Observations from Scientific American. "A Phrase I Try to Avoid," 22 April 2011, and "Mathematics v. MTV," by Dan Meyers. dan: less helpful, 18 April 2011. In a recent post, "Mathematics v. MTV", Dan Meyer points out that a poorly written math problem "lacks a compelling, clear premise in its first act, obstacles, conflict, and tension for your classroom heroes to resolve in its second act, and a cathartic resolution in its third act that leads naturally and necessarily to more mathematics in its sequel." As a film enthusiast who became a high school math teacher, Mr. Meyers began using videos of reallife situations as hooks to encourage high school students to problemsolve and develop mathematical skills. Meyers is featured on the April cover of Education Week's Professional Development Sourcebook, where it mentions that he has recently embarked on getting a PhD in curriculum development at Stanford. The cover touts "RealWorld Learning", which Meyers writes is "a phrase I try to avoid." While Meyer has complained that many word problems in textbooks are "pseudocontextual" (convoluted problems which do little to sharpen problemsolving skills), he does not equate the value of mathematics with its use in "real life". Also, Meyer makes clear that his style of teaching does not involve simply adding pizzazz to textbook problems. In his TED talk from May 2010, "Math class needs a makeover", he implores teachers to be less helpful. By this he means that they should not break problems down into parts a), b), and c), but should start with a tantalizing question and allow students to come up with the "steps" by themselves. While his philosophy may not be new, both the Education Week article, as well as his own blog posts have generated many comments amongst readers, some of which are combative. His responses and the ensuing conversations are as interesting as the original articles. "Let's Make a Deal: Revisiting the Monty Hall Problem," by Davide Castelvecchi. Observations: Opinion, arguments and analysis from the editors of Scientific American, 15 April 2011. The solution to the Monty Hall Problem, a probability puzzler named after the host of the 60's game show Let's Make a Deal, has left many people upset and confused even when explained in detail. Here's a slight variation of the problem that was told to me by my professor, Jon McCammond, which I think makes the problem much easier to understand: "A game show host shows you 100 identical doors. Exactly one of these doors has a car behind it while the others all have goats on the other side. You are asked to choose a door that you think has the car behind it. The host proceeds to open all but one of the remaining doors, revealing 98 goats. The host then asks you if you'd like to switch your guess to the last unopened door or stick with your original choice. What should you do?" The original problem uses the number 3 instead of 100 and the number 1 instead of 98. But the rest is the same. With the larger numbers, it seems intuitive to switch doors, and sound logic shows that the same is true with only three doors. But when given a chance to play the game several times, pigeons are more likely to get the answer right than humans according to John Allen Paulos' article "Animal Instincts: Are Creatures Better Than Us at Computation?," from January of this year. Revisiting this problem, Castelvecchi recounts Paulos' response to a probabilitysavvy reader who used subtly flawed reasoning to "prove" that Paulos was wrong in his thinking. Paulos, who acknowledged having to give the reader's argument some thought, handily explained what aspect of the reader's argument was wrong. This hinged on the fact that the game show host will always prefer revealing a goat rather than the car.  Brie Finegold "Q&A: Taking Mathematics to Heart," by Kate Travis. Science, 29 April 2011. When John Wesley Cain took an applied mathematics course in ordinary differential equations during his first semester in graduate school, little did he know that the project he chose to work on would lead to a satisfying career in applied mathematics with an emphasis on cardiac electrophysiology. Cain's work as a member of an interdisciplinary team involves modeling natural cardiac phenomena like heart attacks or arrhythmia"anything that you would like to understand the mechanisms for"and running "mathematical and computerbased simulations... to gain intuition... so I can then... tell [the biomedical engineers], 'These might be the sorts of experiments that you might want to run.'" When Cain started working in this field, he "did have to learn a fair amount of electrophysiology to make sure that I wasn't doing anything too outlandish." Much of that he learned during "roundtable discussions where cardiologists, biomedical engineers, physicists, and mathematicians would sit around a table and discuss the physiology." But for Cain, the rewards have made the hard work worthwhile: "The mathematics is very rich and the physiologyhere is just absolutely no end to the types of questions you can pose about dynamics in cardiac tissue." (Photo courtesy of John W. Cain, associate professor of mathematics and computer science, University of Richmond.)  Claudia Clark "Top mathematician chooses to live a modest life away from the limelight," Glynn Goffin, BBC NewsEurope, 28 April 2011. The BBC News video segment provides an update on Grigory Perelman, who solved the Poincaré Conjecture and was named a Fields Medal winner in 2006. Perelman declined the US $1 million award for solving the conjecture, and declined the Fields Medal as well. He lives modestly with his mother in St. Petersburg, and declines to speak with the press and most others. Reporter Goffin speaks with Masha Gessen, author of a biography of Perelman (Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century), to find out the origins of Perelman's talent and motivations. Gessen believes that Perelman's mathematical talents came from his mathematician mother, and the (then) Soviet mathematics education system that was so hospitable to talented and focused math students. When Goffin asked if Perelman's turning down the prize money, offers and accolades was due to his mental condition, Gessen says it's more due to his belief system, that Perelman "doesn't believe that mathematical achievement should be monetized."  Annette Emerson "Tattoo formula uses mathematics to forecast ageing of body art," by Emine Sinmaz. Guardian, 28 April 2011. For the farsighted tattoo aficionado, fluid mechanic Ian Eames has two recommendations: get it big, and get it thick. Those are the designslarge ones with bold linesthat look best in the long term, according to his model of tattoo aging [Ed: We hope it's not too jarring to our readers, but we opted for the nonBritish spelling in this summary.]. Tattoo needles puncture the skin thousands of times a second, depositing a tiny drop of insoluble ink into the dermis with each prick. Eames' work tracks the way this ink diffusesnot across cell walls, but as skin cells divide and die. His model, recently published in Mathematics Today, takes into account the owner's skin type and age, and the size, ink type, location, and exposure to the sun of the tattoo, to predict how body art will fade and blur. The calculations indicate that the details of complex patterns are lost after about 10 years. Eames, a reader at University College London, hopes his work will begin an exploration of skin art's longterm health effects.  Ben Polletta "Colorado's Mesa State College gets new name, with help of math diagram," by Nancy Lofholm. The Denver Post, 27 April 2011. After more than a decade of debate, Mesa State College has finally chosen a new name amenable to students, faculty, and neighbors: Colorado Mesa University. The tool that ended the showdown between eight prospective monikers was a Venn diagram, a mathematical diagram of overlapping circles. Heritage, geographical identification, and brand claritythe three characteristics decided to be most importantwere each assigned to a circle, and the eight names were placed into each of the circles to which they qualified. Only two names fell into the intersection of all three circles: Mesa University of Colorado (later abandoned because of its unfortunate acronym, MUC) and Colorado Mesa University, the winner. From here, politicians in Colorado legislature will shepherd the new, mathematically selected name into law.  Lisa DeKeukelaere "More Megaquakes on the Way? That Depends on Your Statistics," by Richard A. Kerr. Science, vol. 332, 22 April 2011, page 411. Clustered or random? Multiple statisticians have examined the pattern of large earthquakes in the last 110 years and arrived at very different conclusions. Two researchers at the U.S. Geological Survey published a paper in 2005 asserting that megaquakes are clustered in time, based on a series of computer simulations indicating that, if quakes are random, the odds of an earthquake record similar to the one observed is just 2%. A series of large earthquakes in 19501965, as well as the recent quakes in Indonesia, Chile, and Japan, appear to support this theory. Other statisticians argue that such analysis is flawed, however, because the data set is small and the hypothesis is tested against the same data with which it was developed. The USGS researchers note that the events of the next few years may provide an indication of which theory is correct—they estimate the probability of a quake in the next 6 years measuring higher than 9 on the Richter scale to be 63% if quakes are clustered, versus 24% if they are random. See also: "Seismologists in a rumble over quake clusters," by Alexandra Witze. Science News, 7 May 2011, pages 56.  Lisa DeKeukelaere "Using Math To Make Complex Systems Simple," Scott Simon and Keith Devlin, Weekend Edition, NPR, 16 April 2011. April is Mathematics Awareness Month. In light of this year's themeUnraveling Complex SystemsScott Simon asked Weekend Edition Math Guy Keith Devlin to describe, as simply as possible, what complex systems are. Devlin said that such systems occur when there are "a very large number of relatively simple systems, which you can specify using mathematics, interacting together." In such systems "the complexity defies prediction." So "we put a whole bunch of mathematics together"including probability theory, statistics, differential equations, and modern network theoryto "build computer models, and then we simulate what's going to happen. The simulation is never going to tell us what happens, but by playing with that simulationchanging one thing, seeing what happens when one power stations goes off on a grid, seeing what might happen when there's an earthquakewe can come to have a much better overall holistic understanding of what's going to happen so we can design [systems] to minimize the likelihood that things go wrong and to prepare [for] when they do." To those who would say that the stakes are too high to have complex systems, Devlin responds that "if we wanted to avoid those dangers, we'd have to say, well, we won?t have airline networks, we won't have a power grid, we won't have the Internet... It's just the world we live in." Learn more about Mathematics Awareness Month.  Claudia Clark "This Tech Bubble Is Different," by Ashlee Vance. Bloomberg Businessweek, 14 April 2011. Knowing how to dig through mountains of data is becoming an ever more soughtafter skill. In this article Ashlee Vance talks to mathematicians working in Silicon Valley about how a more datadriven world is opening up doors for number crunchers. With data playing a large role at companies such as Google, Facebook and Groupon, math majors are moving more into marketing, business development, and even sales. One pioneer in the area is "math genius" Jeff Hammelbacher, who was one of the first employees at Facebook. "He assembled a team to build a new class of analytical technology. His crew gathered huge volumes of data, pored over it, and learned much about people's relationships, tendencies, and desires. Facebook has since turned these insights into precision advertising, the foundation of its business." Two years later Hammerbacher left Facebook as he didn't think that his talents were best used in "thinking about how to make people click ads." He went on to cofound Cloudera, a dataanalysis software startup. (Photo of Jeff Hammerbacher courtesy of Cloudera.) Editor's note: See also "The Rise of the Wants, Silicon Valley's Answer to Wall Street's Math Nerds," by Alexis Madrigal, The Atlantic, 15 April 2011.  Baldur Hedinsson "Math Day," by Dontaye Carter. WCTV, 14 April 2011. Valdosta State University mathematics professor Denise Reid worked to get high school girls excited about math during the 16^{th} Annual Sonia Kovalevsky High School Mathematics Day on April 14. The event, held in honor of the first woman to receive a doctorate in mathematics, provided handson activities and examples of reallife applications.  Lisa DeKeukelaere SD teacher joins national push to improve math," by Maureen Magee. San Diego UnionTribune, 2 April 2011. While 73 percent of San Diego fourth graders are proficient in math, only 16 percent of tenth graders are. Osvaldo Soto, a math teacher at San Diego's Patrick Henry High School, believes that high school math classes in San Diego and across the country have been sabotaged by a profusion of shortcuts and tricks, which rob students of the opportunity to understand mathematical concepts. "As we advance kids in math, we provide more supports and hints, cheat sheets and tricks that deny them the opportunity to be puzzled or think for themselves. I try to revive the curiosity in students," says Soto in this article. As one of the nonprofit Math for America's master teachers, Soto is in a position to affect students across San Diego County. A mentor to 25 Math for America fellows in the county, he encourages teaching math "the long way", and requiring students to explain and justify their methods. Math for America San Diego recently received a $1.4 million grant from the NSF, and they're going to need itthe San Diego Unified School District recently raised graduation criteria, requiring students to pass more advanced algebra classes to earn a diploma.  Ben Polletta "P&G Passes On Pringles," reported by Kevin Tibbles. NBC Nightly News, 6 April 2011. In this lighthearted piece, Tibbles reports on Proctor & Gamble's sale of Pringles brand potato chips"an icon of American engineered food"to snack industry leader Diamond Foods. According to Tibbles, P & G has decided to focus on household health and beauty aids like Tide laundry detergent and Crest toothpaste. Diamond Foods bought Pringles for 2.35 billion dollars... but this number is not the only math in this report. One of the most notable characteristics of these potato chips is their appearance. Tibbles has identified the shape, with help from University of Chicago mathematics professor Benson Farb: they are hyperbolic paraboloids.  Claudia Clark Making Math Connections," by Michelle R. Davis, Education Week, 4 April 2011. The verdict is still out on brain cancer, but it seems that cell phones have a definite effect on learning math. The website Education Week recently featured an article on Project KNect, a grantfunded program which incorporates smart phones into science and math classrooms in North Carolina, Ohio, and Virginia. Project KNect students receive smartphones with video, chat, and internet  but not calling or texting  capabilities. They can use their phones, which are closely monitored by their teachers, to contact other students in the project, access online math resources, and to view and create instructional videos. While Drexel University was commissioned to create a series of instructional videos, the vast majority of those now available have been created by students. These include movies, serials, and a music video about polynomials which has spawned thousands of imitators on YouTube. Project KNect students show a higher rate of proficiency in basic math courses like Algebra I and II, but perhaps more importantly they show increased comfort in thinking about and explaining mathematical concepts, and increased confidence in their own mathematical abilities. The key is that students use the system to teach each other, and as one Project KNect teacher puts it, "they're better able to articulate how they get their answers. You never know anything quite as well until you have to teach it."  Ben Polletta "What are the odds? A mathematical look at bowling," by Al Stephenson. The AdvertiserTribune, 3 April 2011. If your bowling skills are on par with mine, rolling above 100 is a stretch. Then you probably haven't given much thought to how many ways one can roll a 292. Turns out there is only one way, by starting a game with 11 strikes and then hitting two pins on the last ball. In this piece Al Stephenson digs into the probabilities of bowling scores and gives a mathematical proof of why I always seem to score a 77; it is the most probable score.  Baldur Hedinsson

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