COMAP 美国大学生数学建模 UMAP journal 2014

Vol.35,Nos.2-32014Table of contentsPublisher's editorialStirring the Pot--The Common Core and All ThatSol garfunkel93Editors noteabout this issue96MCM Modeling forumResults of the 2014 Mathematical Contest in ModelingWilliam p fox97Keep Right to Keep RightYaofeng Zhong, Yunyi Zhang, and xiao zhao.…………11Judges Commentary: The Keep Right PapersKelly black………,,,……139Authors Commentary: The Keep Right PapersMichael tortorella.149Judge's Commentary: The Ben Fusaro AwardJerrold r. Griggs……153Evaluation System for College Coaching LegendsFeng Xiong, Wenchao Ding, and Jingling Li∴157Judges' Commentary: The Coach PapersRobert burks∴181Author's Commentary: The Coach PapersWilliam p fox189Judges'Commentary: The Frank Giordano Award for 2014Marie vanisko ......................................,........................195Our Story with the mcmLibin Wen, Jingyuan Wu, and Cong Wang……………201First Experience with ModelingMatthew Marner, Princep shah dobromir Yordanov, andAmanda beecher.209Model studentsRobert emro215ICM Modeling ForumResults of the 2014 Interdisciplinary Contest in ModelingChris arneyWho Are the 20%?Chen Wang, Mi Gong, and zhen li…………29Judges'Commentary: Measuring Network Influenceand ImpactChris Arney, Kathryn Coronges, and Tina Hartley .... 249Developing an Interdisciplinary Mindset with StudentsThrough the iCmHeidi berger and rick spellerberg………271Publisher 's editorial 93Publisher's editorialStirring The potThe common core and all thatSolomon a. garfunkelExecutive directorCOMAP Inc175 Middlesex Turnpike Suite 3BBed ford MA 01730-1459s.garfunkel@comap.comIntroductionWhen i first started to think seriously about reform in mathematics edu-cation, some 45 years ago, I asked advice from my then mathematics DeptChair at Cornell, Alex Rosenberg. I remember him telling me that he be-lieved that every 20 years or so it is necessary to"stir the pot"so that weare forced to re-think how we teach and re-imagine how children learn40 years ago, I began to work with applications and modeling20 years ago, I was immersed in creating materials that exemplified theNCTM standards; and today, we are all dealing with implementation of theCommon Core. The pot sure as hell is getting stirredBut there is so much noise that it's hard to discern what' s going on andwhat it all means. So here' s my takeThe nctm standards and reactionsIn 1989, I believe that NCTm basically got it right. The standards thatthey wrote emphasized the need to improve the mathematics education ofall students. There was no laundry list of topics to be mastered by a certainage, but rather some key notions of what some have called"mathematicalhabits of mind. " The National Science Foundation (Nsf) quickly fundeda number of projects designed to produce standards-based"curricula atthe elementary, middle, and high school levels. It is interesting to note thatthe progeny of those curricula hold roughly 50% of the elementary market,25% of the middle school market and 5% of the secondary marketThe UMAP Journal 35(2-3)(2014)93-96. C Copyright 2014 by COMAP, Inc. All rights reservedPermission to make digital or hard copies of part or all of this work for personal or classroom useis granted without fee provided that copies are not made or distributed for profit or commercialadvantage and that copies bear this notice. Abstracting with credit is permitted, but copyrightsfor components of this work owned by others than COMAP must be honored To copy otherwise,to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP.94 The UMAP Journal 35.2-3(2014)o what went wrong? Enter the"math wars. Basically a small-butextremely vocal-group of research mathematicians, right-wing politicians,the wealthy, and religious fundamentalists got scared, for a number ofdifferent reasonsThe mathematicians were afraid that in creating curricula designed toserve all students, we would short-change the best and the brightest,potentially losing future Ph. D candidateso For the political right this smacked of federal interference in local controlof education, i.e., a federally-mandated national curriculumFor the wealthy, we were potentially changing the rules in a game thatthey and their children were already winning -so why take the risk?For the fundamentalists, the emphasis on applications and modeling leftthe mathematics classroom open to influencing the hearts and minds oftheir children in a way that solving quadratic equations didntAnd so words like "fuzzy math"were thrown around to make the newcurricula look silly and non -rigorous, and members of this alliance turnedout at every local and statewide school board meeting-and wonThere were many consequences of this turmoil. NCTM rewrote theirstandards in 2000 hoping in vain to placate their critics. NSF redefined itsmission as one primarily--ifnot solely--devoted to research, backing awayfrom 50 years of curriculum reform and implementation But without theNCTM standards to provide direction, we were left without guidance onhow to proceed with reform of math educationNCLB and High-Stakes TestingEnter No Child Left Behind(NClB)and the mandated state-wide highstakes tests from grade 3 onward in mathematics and language arts. Effectively nclb created 50 different sets of standards and the tests to assessthem. As you can imagine, the tests are widely disparate in quality, anda satisfactory performance in one state may be woefully inadequate in an-other. But nClB says nothing about what should be on the tests, how hardthe tests should be, or what should be used as cutoff scores. Those are leftup to the individual states to determine. and to be fair, it's a messCCSSM: Higher Expectations--and risksEnter the Common Core State Standards for Mathematics(CCSSM). Thelogic of the Common Core rationale is simple and admittedly compellingWe have a standards/testing Tower of Babel; it makes no sense. We needone common set of standards to teach to and to hold students(and teachers)accountablePublisher s editorial 95The devil, however, is in the details. The current version of the ccssmis, i believe destined to disadvantage the already-disadvantaged For themost part it does obeisance to those who worry most about where our nextgeneration of STEMresearchers and workers will come from. In the name ofraising expectations, it runs the risk of being irrelevant to the vast majorityof students taking math today. The promise of the nctm standards wasmath for all. CCSSM threatens to deliver math for the fewOstensibly, the Common Core is a creature of the states; but its standardswere certainly created in concert with administration education policy andstrongly influenced by large private foundations, as well as publishers andtest-makersAnd these standards, too, have their set opponentso educators who worry that the topic lists grade by grade are simply designed as an escalator to calculuso teachers and teacher unions who see the coming assessment of teacherperformance-based in part on student performance-as an attack ontenure and a weapon to be used against teacherso the same right-wing politicians who fear federal control of education;anthose who fear the undueinfluence of the aforementioned large corporateinterests(publishers, test-makers), as well as that of private and publicfoundationsall of this is confounded by the fact that to the general public, the commonCore is synonymous with thehigh-stakes tests being designed to assess them. Thesetests will roll out this vear and next. The results will likely be horrific, withpredictions of failure rates in excess of 70%. This fact, the general cost ofthe assessments, and the factors mentioned above put the broader issue ofacceptance of the ccssm at great riskWe are not in a raceIn some ways this is a shame. There is promise here. CCSSM needs tobe viewed as a living document one that can be adapted as needed to servethe broad student population. If we can back away from our obsessionwith high-stakes testing then we could use common standards to producecommon assessments which we could then use to diagnose student needsin order to improve learning--not to punish students, teachers, or schoolsForty years ago, we feared the Russians, 20 years ago the Japanese, andtoday the Chinese. Mathematics education is not a horse race. It is notabout ensuring that our best are better than their best. It is about ensuringthat every student has the opportunity to learn as much mathematics-anas much of how they can use that mathematicsas possible. That is a potworth stirring96 The UMAP Journal 35. 2-3(2014)About the authorSolomon garfunkel is the founder and executive director of comapand Executive Publisher of this JournalHe served on the mathematics faculties of Cornell University and theUniversity of Connecticut at Storrs but he has dedicated the last 35 yearsto research and development efforts in mathematics education He wasproject director for the Undergraduate Mathematics and Its Applications(UMAP)and the High School Mathematics and Its Applications(HiMAP)Projects funded by NSe, and directed three telecourse projects, includingAgainst All Odds: Inside Statistics and In Simplest Terms: College Algebra, for theAnnenberg/CPB Project. He has been the Executive Director of COMAPInc. since its inception in 1980Dr. Garfunkel was the project director and host for the video series ForAll Practical Purposes Introduction to Contemporary Mathematics. He was theCo-Principal Investigator on the ARISE Project, and Co-Principal Investigator of the CourseMap, ResourceMap, and WorkMap projects. In 2003,Dr. Garfunkel was Chair of the National Academy of Sciences and Mathematical Sciences education Board Committee on the Preparation of highSchool TeachersEditor's noteabout This issueThis year we had almost 8,000 teams in the mcm and ICM contestscombined the 19 Outstanding papers ran to more than 500 manuscriptpages. Editing and publishing all the Outstanding papers, which we oncedid, is simply not possible any moreHence, as in the past few years, we present in the pages of this Journalonly one Outstanding paper for each of the MCM and ICM problems. Theselection of which papers to publish reflected editorial considerations andwas done blind to the affiliations of the teamsAll 19 Outstanding papers appear in their original form on the 2014MCM-ICM CD-ROM, which also has the press releases for the two conteststhe results, the problems, and some commentaries. Information about or-deringisathttp://www.comapcom/product/cdrom/index.htmlorat(800)72-6627.Results of the 2014 MCM 97MCM Modeling forumResults of the 2014Mathematical Contest in ModelingWilliam p Fox mcm directorDept of Defense AnalvsisNaval postgraduate schoolI University circleMonterey, CA 93943-5000wpfox@nps. eduIntroductionA total of 6, 755 teams of undergraduates from hundreds of institutionsand departments in 18 countries spent a weekend in February working onapplied mathematics problems in the 30th Mathematical Contest in Mod-eling(cm)The 2014 MCM began at 8: 00 P.M. EST on Thursday, February 6, andended at 8: 00 P.M. eSt on Monday February 10. during that time teamsof up to three undergraduates researched, modeled, and submitted a So-lution to one of two open-ended modeling problems. Students registeredobtained contest materials, downloaded the problems and data, and en-tered completion data through comap's mCm Website. After a weekendof hard work, solution papers were sent to ComaP on monday. Two ofthe top papers appear in this issue of The UMAP Journal, together withcommentariesIn addition to this special issue of The UMAP Journal, COMAP offers asupplementary 2014 MCM-ICM CD-ROM containing the press releases forthe two contests, the results, the problems, unabridged versions of the Out-standing papers, and judges' commentaries. Information about ordering isathttp://www.comapcom/product/?idx=1418orat(800)772-6627The UMAP Journal 35(2-3)(2014)97-110. Copyright 2014 by COMAP, Inc. All rights reservedPermission to make digital or hard copies of part or all of this work for personal or classroom useis granted without fee provided that copies are not made or distributed for profit or commercialadvantage and that copies bear this notice. Abstracting with credit is permitted, but copyrightsfor components of this work owned by others than COmaP must be honored To copy otherwise,to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP98 The UMAP Journal 35. 2-3 (2014)Results and winning papers from the first 29 contests were published inspecial issues of Mathematical Modeling (1985-1987) and The UMaP Journal1985-2013). The 1994 volume of Tools for Teaching, commemorating thetenth anniversary of the contest, contains the 20 problems used in the first10 years of the contest and an Outstanding paper for each year. That volumeand the special MCM issues of the Journal for the last few years are availablefrom COMAP. The 1994 volume is also available on Comap's special mod-eling resource CD-Rom. Also available is The mcm at 21 CD-ROM, whichcontains the 20 problems from the second 10 years of the contest, an outstanding paper from each year, and advice from advisors of Outstandingteams. These CD-ROMs can be ordered from comap athttp://www.comap.com/product/cdrom/index.htm1This year, the two mcm problems represented significant challengese ProblemA, The Keep-Right-Except-To-Pass-Rule, " asked teams to buildand analyze a mathematical model to analyze the performance of thisrule in light and in heavy traffic Is thisrule effectivein promoting greaterthroughput? If not, teams were to suggest and analyze alternatives thatmight promote greater throughput, safety, and/or other factors that theydeemed importanto Problem b, College Coaching Legends, "asked teams to build a math-ematical model to identify the best all-time college coach " male or female, in any sport, over the past century. Teams were to clearly articulatetheir metrics for assessment, and to discuss how their model can be ap-plied across both genders and across all sports. Teams also had to preparea 1-2-page article intended for Sports Illustrated explaining their reason-ing and results, including a nontechnical explanation of their model thatsports fans will understandCOMAP also sponsors:The MCM/ICM Media Contest(see p. 109)The Interdisciplinary Contest in Modeling(icmr, which runs concurrently with the MCM and next year again will offer a modeling probleminvolving network science together with the choice of a second probleminvolving human-environment interactons. Results of this years icmare on the comap website athttp://www.comap.com/undergraduate/contestsThe contest report, an Outstanding paper, and commentaries appear inthis issuee High School Mathematical Contest in Modeling (hiMCM), whichoffers high school students a modeling opportunity similar to the mCmFurther details are athttp://www.comap.com/highschool/contests