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0|0|0|||||%27Math Wars%27 end%3F And a Response|alexb||12:36:14|02/04/2005|%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%0D%0A From the Washington Post%2C Tuesday%2C December 21%2C 2004%3B Page A10. See%0D%0Ahttp%3A%2F%2Fwww.washingtonpost.com%2Fwp-dyn%2Farticles%2FA15026-2004Dec20.html%0D%0A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%0D%0AMath Educators Find Common Denominators%0D%0A%0D%0ABy Valerie Strauss%0D%0A%0D%0AConfused by the latest %22good news-bad news%22 headlines about how U.S. %0D%0Astudents compare in math with their peers in foreign lands%3F Wondering %0D%0Awhether the math program at your child%27s school is teaching addition %0D%0Abetter than another program might%3F%0D%0A%0D%0AYou aren%27t alone. Many parents are asking these questions and finding %0D%0Athat%2C when it comes to math%2C the educational landscape in the United %0D%0AStates can be maddeningly complicated.%0D%0A%0D%0AMath programs that give students different ways to answer basic %0D%0Aproblems are beloved by some teachers%2C while others scoff and label %0D%0Athe programs %22fuzzy math.%22 Research reports are issued%2C then debunked %0D%0Aby critics. And the long-running %22math wars%2C%22 pitting traditionalists %0D%0Aagainst reformers%2C are at high pitch.%0D%0A%0D%0AAny large-scale meeting of the minds about the best way to teach the %0D%0Asubject%2C educators and mathematicians say%2C is nowhere near -- in %0D%0Apart%2C because the country is so large and education decisions are %0D%0Alocally driven.%0D%0A%0D%0A%22We have 50 states with 15%2C000 separate independent school %0D%0Adistricts%2C%22 said Gerald Kulm%2C a math professor and researcher at %0D%0ATexas A%26M University. %22Our textbooks and other curriculum materials %0D%0Ahave to suit at least some majority of the people in those districts%2C %0D%0Aand so things get complicated.%22%0D%0A%0D%0AThis month%27s release of international comparisons of math performance %0D%0Ahighlighted the confusion. One study showed that U.S. eighth-graders %0D%0Amade significant gains compared with their counterparts worldwide%2C %0D%0Aclimbing several places -- to 15th out of 45 countries -- since the %0D%0Ainternational math rankings came out nine years ago.%0D%0A%0D%0AYet another recent study suggested the opposite of progress -- that %0D%0A15-year-olds in the United States lag behind their peers in most %0D%0Aother leading industrialized nations in the ability to solve %0D%0Areal-life math problems.%0D%0A%0D%0ASome mathematicians and educators even disagree on whether %0D%0Ainternational comparisons are valid. R. James Milgram%2C a Stanford %0D%0AUniversity mathematician%2C said yes%3B Jeremy Kilpatrick%2C a University %0D%0Aof Georgia professor%2C said different cultures and educational systems %0D%0Askew the results.%0D%0A%0D%0AThere may be some room for hope of a truce in the math wars%2C %0D%0Aaccording to Milgram and Kilpatrick%2C both of whom attended a %22peace %0D%0Asummit%22 designed to see whether common ground could be found.%0D%0A%0D%0ARichard J. Schaar%2C a mathematician and senior vice president of Texas %0D%0AInstruments Inc.%2C wooed the two scholars%2C plus three other figures in %0D%0Amath education%2C to Washington early this month. Also attending was %0D%0AHarvard University Professor Wilfried Schmid%2C who%2C like Milgram%2C %0D%0Acriticizes %22reform%22 math programs for failing to teaching children %0D%0Athe fundamentals.%0D%0A%0D%0AKilpatrick and two other leading math educators at the gathering%2C the %0D%0AUniversity of Michigan%27s Deborah Loewenberg Ball and Joan %0D%0AFerrini-Mundy of Michigan State University%2C hold the view that the %0D%0Areforms are helping students better understand math because they do %0D%0Anot rely on memorizing correct answers.%0D%0A%0D%0ATo the surprise of all%2C there was more agreement than they had %0D%0Aimagined%2C several participants said%2C suggesting that they may be %0D%0Amoving toward a %22centrist position.%22 Among the topics they said they %0D%0Aagreed on%3A%0D%0A%0D%0A%2A Heavy reliance on calculators in the early elementary grades is a bad idea.%0D%0A%0D%0A%2A Elementary school children must have automatic recall of number %0D%0Afacts%2C meaning that%2C yes%2C they have to memorize multiplication tables.%0D%0A%0D%0A%2A Children must master basic algorithms. The meeting participants %0D%0Aspent time defining the word %22algorithm%2C%22 which means a set of rules %0D%0Afor solving a problem in a finite number of steps.%0D%0A%0D%0ASchmid called it %22significant that we do have agreement in this group %0D%0A. . . To me%2C it is an indication that we are moving toward peace in %0D%0Athe math wars.%22%0D%0A%0D%0AParticipants said parents can take these areas of agreement and look %0D%0Afor them in their children%27s math programs. The group plans to %0D%0Acontinue meeting and to issue a report with math education goals%2C %0D%0ASchaar said.%0D%0A%0D%0AThe fact that their discussion centered on such basic understandings %0D%0Arevealed how hardened the sides had become.%0D%0A%0D%0AControversy over a National Science Foundation-funded program%2C %0D%0AEveryday Mathematics%2C developed at the University of Chicago%2C tells %0D%0Athe tale.%0D%0A%0D%0AThe program is being used in many schools across the country%2C %0D%0Aincluding Annandale Terrace Elementary School. On a recent day at the %0D%0ANorthern Virginia school%2C teacher Abigale Braun presented this %0D%0Aproblem for 21 second-graders to solve%3A 15%2B5%2B9%3D__. Then she asked %0D%0Athem how they got their answers.%0D%0A%0D%0ADennis Segovia-Ramirez said he put 15 plus 5 together to make 20 and %0D%0Athen added 9. Sarah Velegaleti said she knew 5%2B9 was 14 and just %0D%0Aadded 15. Laila Elahi put down 15 tally marks on her white board%2C %0D%0Athen 5%2C then 9%2C and added them all up.%0D%0A%0D%0ABraun praised them%2C telling them that there was no single correct %0D%0Amethod and that it was important for them to figure out the way that %0D%0Aworked best for them. She said that in computational skills%2C her %0D%0Asecond-graders are far ahead of students using other math programs. %0D%0AHer school%27s principal%2C Christina Dickens%2C said the University of %0D%0AChicago program helped children improve on standardized tests.%0D%0A%0D%0AAt the opposite end of the country%2C however%2C Milgram and other math %0D%0Aeducators have persuaded the California legislature not to allow %0D%0Aschool systems to use the University of Chicago program without a %0D%0Aspecial waiver.%0D%0A%0D%0AThe critics believe that it does not teach basic math rules and leads %0D%0Ato computational incompetence. They prefer more traditional %0D%0Aapproaches such as Harcourt Achieve%27s Saxon math program.%0D%0A%0D%0AIn an effort to help bring clarity to the math wars%2C the Mathematical %0D%0ASciences Education Board of the National Academy of Sciences reviewed %0D%0A147 studies done on the effectiveness of 19 math programs used in %0D%0Aschools today. The conclusion%2C released this summer%3A Not one study %0D%0Ahad been carried out well enough to prove a program%27s effectiveness.%0D%0A%0D%0A%22Don%27t believe a thing said to you associated with the phrase %0D%0A%27research shows%2C%27 %22 said W. Stephen Wilson%2C a Johns Hopkins %0D%0AUniversity mathematics professor.%0D%0A%0D%0AThere are programs successful in some schools%2C but there isn%27t a %0D%0Asingle best one%2C according to experts%2C who emphasize it often comes %0D%0Adown to teachers%3A how well they understand math and how much they %0D%0Ahave been taught about the program their school is using.%0D%0A%0D%0A%22All the program can do in the best case is be correct%2C efficient and %0D%0Aaccessible. Then it is up to the teacher%2C%22 Schmid said.%0D%0A%0D%0A-------------------------------%0D%0AA RESPONSE FROM MICHAEL PAUL GOLDENBERG ... Submitted letter to the %0D%0APost Editor.%0D%0A%0D%0AAs a mathematics educator%2C I read with puzzlement Valerie Strauss%27 %0D%0Apiece suggesting that there is peace on the horizon in the Math Wars%3A %0D%0Aone need not read between the lines here if one knows the subject%2C %0D%0Aits recent history and the players.%0D%0A%0D%0AFor those not so informed%2C please don%27t be fooled. Note well that the %0D%0Aagreed-upon positions cited all appear to be compromises%2Fconcessions %0D%0Afrom the reform end %28not that Professors Kilpatrcik%2C Ball%2C %0D%0AFerrini-Mundy or NCTM itself ever advocated for HEAVY calculator use %0D%0Ain early elementary%2C or against knowing algorithms or knowing number %0D%0Afacts%29.%0D%0A%0D%0ANote%2C too%2C the utter lack of anything that vaguely looks like a %0D%0Aconcession or compromise from Professors Milgram or Schmid. Zip. %0D%0ANothing. Nada. Instead%2C we get more criticism of progressive %0D%0Amathematics teaching methods and texts%2C and advocacy for so-called %0D%0A%22teacher-proof%22 materials like Saxon math%2C possibly the textbook %0D%0Aseries least representative of what mathematicians themselves %0D%0Aactually do and think about.  The real goal of the anti-reformers %0D%0Acouldn%27t be more clear%3A banning creative programs like Everyday Math %0D%0Aat any cost%2C as they%27ve already been able to do in California.%0D%0A%0D%0AWhy is what emerged from this %22summit%22 a Roadmap For Peace%3F If it %0D%0Areally represented the current position of NCTM%2C it would be a %0D%0Adocument of surrender. If this is a peace plan%2C I%27ll take another %0D%0Ahalf century of war%2C thank you very much. As will%2C in fact%2C the %0D%0Aentrenched foes of progressive reform until they wipe out any and all %0D%0Acreativity and vitality in mathematics classrooms for the vast%2C vast %0D%0Amajority of American kids.%0D%0A%0D%0AMichael Paul Goldenberg -- mikegold%40umich.edu%0D%0A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%2A%0D%0A
1|1|0|||||RE%3A %27Math Wars%27 end%3F And a Response|Ionut||08:21:35|08/19/2009|%09Find the area of the ring between two concentric circles%2C if the chord of the bigger circle that is tangent to the smaller one has the length of 2009. %0D%0A%0D%0AMy Solution valentin_cons%40yahoo.com.%0D%0A%0D%0AImagine the interior circle as small a point%3B therefore the tangent would be the diameter for the big circle. Therefore the area of the ring is %CF%80%282009%2F2%29%C2%B2.