All About Math Olympics

Mathematical Olympians:Who are they, where are they from,and how did they get where they are?Steve Benson Karen MarrongelleEducation Development Center, Inc. Portland State UniversityNewton MA Portland [email protected] [email protected] MathematicsCompetitions activities!American Mathematics Contest (AMC) 8!AMC 10!AMC 12!American Invitational Mathematical Examination(AIME)!USA Mathematical Olympiad (USAMO)!Mathematical Olympiad Summer Program(MOSP)!International Mathematical Olympiad (IMO)AMC 8 (formerly AJ HSME)!Open to all students up to grade 8(age 14 or under if homeschooled)!45 minutes!25 multiple choice questions!Participants as young as 4th grade (2001)!48% of the 169,654 participants were girls (2001)AMC 10!Open to students in 10th grade or below(under 17.5 years old if homeschooled)!75 minutes!25 multiple choice questions!45% of 107,060 participants were girls (2001)AMC 12 (formerly AHSME)!Open to all high school students enrolled in atleast one course (under 19.5 yrs if homeschooled)!75 minutes!25 multiple choice questions!43% of 154,372 participants were girls (2001)AIME!All students with a score of at least 100 on theAMC 12 or a score in the top 1% on the AMC 10are invited to participate.!intermediate to AMC 10 and 12 and USAMO (intiming and difficulty)!3 hours!15 short response questions!Answers are integers from 0 to 999!21-22% of 9534 students were female (2001)USAMO!Invitational based on AIME and AMC 10 or 12 Includes top scorer from each state!essay exam (problems would challenge mostprofessional mathematicians-theyre not kidding!)proofs required!9 hours in 2 days (3 questions/4.5 hours each day)!10-16% of 262 participants were girls (2001)MOSP Mathematical Olympiad Summer Program!30 students invited (including USAMO finalists +top juniors or younger)!4 weeks prior to IMO!Sessions include new content and problem solving!In 2001, two girls participatedIMOInternational Mathematical Olympiad!Two weeks in J uly (typically)!Actual test is over two days 3 essay questions per day (proof required) 4.5 hours per day Graded by international teamIMO 2001 research question!What aspects of the in-school and out ofschool experiences of IMO caliber studentscan be identified as promising for theencouragement of a broader population ofstudents into sustained and advanced studyof mathematics in secondary school andbeyond?Past Research!Do Olympians fulfill their potential?!What factors helped/hindered thedevelopment of extraordinary talent?!Value of the Olympiad programs?Factors Considered!School achievement!Socio-economic status!Family structure!Gender!Parents perception of intellectResearch Findings!J ames Campbell (1996, 2000)!J ohns Hopkins University Study ofMathematically Precocious Youth!International ResearchResearch Findings!Campbell (1996, 2000)!Surveyed 74 Olympians 84% of sample was Caucasian 16% of his sample was Asian American No African Americans or Latinos/as 2 females4 Most Influential Factors ofOlympians Success!Home Small, affluent families High levels of support from parents!School Most Olympians attended public schools Many learned much math on their own!Olympiad Program: Important stimulant!MentoringIMO-2001 research project!Sent surveys to students invited to take USAMO2001 and their parents!Observed students at MOSP 2001, June 5-J uly 3,Georgetown University Interviewed selectedMOSP participants!Observed IMO participants, J uly 4-14USAMO survey!Surveys sent to 252 USAMO invitees and parents!Types of questions: Biographical (age, family characteristics, schoolexperience, competition experience, extra-curricularactivities, free-time, access to math resources, etc.) Attitudes and beliefs Collaboration and competition Learning and doing mathematics Gender and mathematics achievement!94 students/91 parent(s) returned surveysUSAMO survey:Who are they?!Of the students who returned the survey: 58% were Caucasian, 31% were Asian 15% were female Age on 6/1/01: 13 to 19 (average 16 yr 7 months) 6% were lefthanded 94% lived with two parents Average number of children in family: 2.4 57% were first born child, 20% only child 84% born in USA 37% of fathers, 35% of mothers born outside USA 22%: language other than English spoken in homeUSAMO survey:Who are they?!In what activities are they involved? 65% play a musical instrument 74% of these play piano Practice/perform an average of 5.5 hours per week 56% read 3 or more books a month (96% at least 1) Watch 5-6 hours of television per week Use the computer outside of school 12 hours per week Responses ranged from 1/2 hour to 40 hours per week 50% participate in an athletic activity 25% have a part-time job (an average of 10 hr/wk)USAMO survey:Who are they?!School experience 66% in suburban schools,27% urban,7% rural 69% in public schools, 25% private (6% religious),26% in a magnet school, 3% homeschooled 22% have skipped at least one grade in school 32% enrolled in a gifted/talented program 70% officially recognized as mathematically talented byage 10 (39% by age 8, 6% age 13 or older)USAMO survey:Who are they?! 94% of fathers, 93% of mothers have college degrees 60% of fathers and 52% of mothers have a graduate degree! What kinds of occupations doparents have?Father: Academic (21%) [math/sci (15%)], Engineer (20%),Doctor/Dentist (13%), Computing (8%), Law (6%)Mother: Homemaker (20%), Teacher/Principal (14%), Acad. (13%) [math/sci (8%)], Computing (8%), Nurse (7%), Dr. (5%)! 94% of participant families earn over $55,000 National median income $50,000 65% earn $100,000 or more (nationwide: 15%)USAMO survey:Who are they?! Major influences in choosing to pursue mathematics >3/4 identified parents (68 moms and 50 dads) Over 146 teachers specifically identified(many mentioned all my teachers)! What sorts of resources do they usually utilize most? 33% utilize friends/math team members most 21% consult a teacher, coach, or mentor most 20% consult general mathematics books most 19% consult problem solving books first! 1/3 have read journals for mathematical content Quantum, Math Horizons, Scientific American, MAA journals, etc.USAMO survey:Who are they?!76% of the students were on a math team Average team size was 20 students Among all members of all teams, 28% were girls"teams of female respondents were 41% girls " 72% of teams boy:girl ratio of at least 2:1 52% of students considered selves top team member 96% considered selves in top 2 or 3!Mathematics students prefer to do or learn about abstract mathematics (not necessarily related to contests): 35% sample contest problems: 33% exposition of topics related to contests: 15% applied mathematics not necessarily related to contests: 10%Attitudes about competition!58% prefer individual contests, 33% prefer teamcontests, 9% had no preference!Which of the following aspects of mathematicalcompetitions are important to you?Competition with others/desire to win: 80%Challenging myself:98%Problem solving:90%Meeting other students who like math:76%Getting exposed to new curriculum:67%Collaborating with others:61%More attitudes about competition!Which of the following is more important? winning mathematics competitions: 23% solving challenging mathematics problems: 76%!Why do you participate in math competitions(Why do you believe your child participates)?Reasons for competing student parentWinning awards/scholarships 78 66My parents make me 11 8To make parents/teacher(s)/mentor(s) proud 29 28My friends do 18 20Challenge myself, do mathematics, etc. 95 97Other 15 15More attitudes about competition!45% sometimes have trouble sleeping beforecompetitions!If they dont do as well as they expect, 20% dont worry about it 72% are disappointed for a time (a few hours to 2-3days for most),then get over it 4% are so disappointed they cant think about anythingelse for several days!3% say theyve always done at least as well asthey expectedA survey question! Rank the following in the order in which they match howyou would finish the following sentence (1= mostimportant factor): I am good at mathematics because I was born with natural ability. I work hard. Ive been given unique opportunities and/or assistance from others.55% of students: natural ability most important factor81% of parents predicted their child would say that natural ability was the most important factor26% of students said unique opportunities most important7% of parents predicted opportunities most importantAnother survey question!I sometimesfeel guilty because I dont have to domuch work and still get good grades in my mathclasses. 23% of parents predicted their child would stronglyagree or somewhat agree with the statement 35% of students strongly or somewhat agreed with thestatementAnother survey question! Some people believe that mathematics is a humaninvention created to ask and answer questions about theworld around us and is therefore dependent on the needsand interests of a given culture. Others believe thatmathematics is discovered, claiming that if there were lifeon Mars, then Martian mathematics would be the same asEarth mathematics.Check the statement below that bestdescribes your opinion.Statement %parent %studentAll mathematics is discovered 22 29Most discovered, some invented 42 43Discovered and invented in equal amounts 20 16Most invented, some discovered 10 7All mathematics is invented 6 5Summary!School-related factors contributing toOlympians success Participation in math clubs/teams Participation in MOP and other summerprograms Encouragement and support of teachers/mentors Identification of giftedness/talent at a young age Access to mathematical resourcesWhat can you do?!Continue to support/encourage students!Math clubs/teams with a problem-solvingfocus!Involvement with national competitions AMC (www.unl.edu/amc) MATHCOUNTS (www.mathcounts.org)!Library purchasing mathematics books andjournalsOther mathematics competitions!Mathcounts (middle school)!Mandlebrot Competition!American Regions Math League (ARML)!University sponsored high school contests!International Mathematical Talent Search!Westinghouse Talent SearchConclusions/Suggestions!Summer programs for kids who areinterested in mathematics but who are notthe highest achievers!Funding for math clubs/teams andencouragement of female and minorityparticipationRecommended Resources!Mathematical Olympiads - Problems andSolutions from Around the World (MAA) Titu Andreescu & Zuming Feng!The Contest Problem Book I - VI (MAA) Various authors!Hungarian Problem Book I - III (MAA) Various authors