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2012 CIE Mathcomp / Mathfun

Resources by age that improve upon the standard curriculum for encouraging problem solving and a love of mathematics.

David Cordeiro

on 1 June 2012

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Transcript of 2012 CIE Mathcomp / Mathfun

We would never ask a child to practice scales on an instrument for 10 years without ever hearing a symphony.
But most US students are given only a linear and uninspiring path through mathematics
And yet we ask students to learn

a sequence of formulas

without inspiration

without challenge

without context

without rigor
And these students

are only one bad




from giving up.
Picture mathematics as a tree
With a narrow trunk to be climbed
Before reaching the thousands of disciplines and wonders on the frontier
What's at stake?
"Nowadays...the only physical frontiers are space and the bottom of the ocean, so fortitude and wanderlust aren’t enough to blaze your own trail. If you want the freedom to build your own future and pursue your dreams, then your best bet is to learn how to solve problems you’ve never seen before."

- Richard Rusczyk
Elementary Years
The Middle School Years
The High School Years
Hedonic Well-Being
Eudaimonic Well-Being
The pleasure that comes with, say, a good meal, an entertaining movie or an important win for one's sports team—a feeling called "hedonic well-being" -- tends to be short-term and fleeting.
Happiness is a ball after which we run wherever it rolls, and we push it with our feet when it stops.

- Johann Wolfgang von Goethe
Eudaimonia (Ancient Greek: εὐδαιμονία; Greek pronunciation: [evðaimoˈnia])—is a Greek word commonly translated as happiness, however "human flourishing" is a more accurate translation.[1]. Etymologically, it consists of the word "eu" ("good") and "daimōn" ("spirit").

In classical Greek, eudaimonia was used as a term for the highest human good, and so it became the aim of practical philosophy, including ethics and political philosophy, to consider what it really is and how it can be achieved.
“Math is at the crux of who gets paid,” said Ed Koc, director of research at NACE. “If you have those skills, you are an extremely valuable asset. We don’t generate enough people like that in this country.”

“It’s a tech-driven world, and demand [for engineers] is only going to grow,” said Farnoosh Torabi, employment expert and Quicken blog editor. “You can’t say that about many fields, especially in a recession.”

There are far fewer people graduating with math-based majors, compared to their liberal-arts counterparts, which is why they are paid at such a premium. The fields of engineering and computer science each make up about 4% of all college graduates, while social science and history each comprise 16%, Koc noted.

As a result, salaries for graduates who studied fields like social work command tiny paychecks, somewhere in the vicinity of $29,000. English, foreign language and communications majors make about $35,000, Koc said.

“It’s a supply and demand issue,” he added. “So few grads offer math skills, and those who can are rewarded.”
It could be that people with high eudaimonic well-being are good at reappraising situations and using the brain more actively to see the positives, Dr. van Reekum says. They may think, "This event is difficult but I can do it," she says. Rather than running away from a difficult situation, they see it as challenging.

The two types of well-being aren't necessarily at odds, and there is overlap. Striving to live a meaningful life or to do good work should bring about feelings of happiness, of course. But people who primarily seek extrinsic rewards, such as money or status, often aren't as happy, says Richard Ryan, professor of psychology, psychiatry and education at the University of Rochester.
Everyone is a Born Problem Solver
Problem Solving as Play
Today’s frontiers are intellectual, not physical. The heroes of your generation won’t have titles before their names, like General or President. They’ll have titles after their names, like PhD and CEO. They’ll earn those titles, and the freedom that can come with them, with their minds.

The action is out on the intellectual frontier, so that’s where you want to be. How do you get there? Is getting A’s in all your classes enough? Of course not, and it hasn’t been for a long time, not even if you plow through the regular curriculum twice as fast as everyone else.

- Richard Rusczyk
...they see nothing but the rough trunk of the tree that is in front of them.
Math Circles
Hard Problems
Discrete Math
The Calculus Trap
Time for Play
Math Circles
AMC 10
AMC 12
Other Contests
Math Circle
of Math Circles
National Library of Virtual Manipulatives
Computer Science
Biological Mathematics
Dehaene, a mathematician turned cognitive neuropsychologist, beging with the eye-opening discovery that animals...ca perform simple mathematical calculations. He goes on to describe ingenious experiments that show that human infants also have a rudimentary number sense. Dehaene shows that the animal and infant abilities for dealing with small numbers and with approximate calculations persist in human adults and have a strong influence on the way we represent numbers and peform more complex calculations later in life.
American Computational Linguistics Olympiad
Discrete math is essential to college-level mathematics and beyond
Discrete math is the mathematics of computing
Discrete math is very much "real world" mathematics
Discrete math shows up on most middle and high schoool math contests
Discrete math teaches mathematical reasoning and proof techniques
Discrete math is fun

David Patrick
Conventional Education
Monday - Fractions
Tuesday - Fractions
Wednesday - Fractions
Thursday - Fractions
Friday - Quiz on?
Rigorous Education
Monday - Hard Problem
Tuesday - Geometric Approach
Wednesday - Algebraic Approach
Thursday - Physical Approach
Friday - Evaluate and Optimize
Art of Problem Solving
Art of Problem Solving
Art of Problem Solving Introductory Texts
Introduction to Algebra
Introduction to Counting and Probability
Introduction to Geometry
Introduction to Number Theory

Art of Problem Solving Texts
Intermediate Algebra
Intermediate Counting and Probability

A Sampling of Books by Math Circle Speakers
104 Number Theory Problems
Mathematical Olympiads
Problems from the Book
102 Combinatorial Problems

This olympiad is a contest in which high-school students solve linguistic puzzles. In solving the problems, students learn about the diversity and consistency of language, while exercising logic skills. No prior knowledge of linguistics or second languages is necessary. Professionals in linguistics, computational linguistics and language technologies use dozens of languages to create engaging problems that represent cutting edge issues in their fields. The competition has attracted top students to study and work in those same fields. It is truly an opportunity for young people to experience a taste of natural-language processing in the 21st century.
The Purple Comet! Math Meet is a free, on-line, international, team mathematics competition designed for middle and high school students conducted annually since 2003.
In 2010 and 2011 the grand prize went to Math Circle participants.

Amy Chyao of Metroplex Math Circle
Evan O'Dorney of Berkeley Math Circle
The International Mathematical Olympiad is a two day math competition held each summer. Participating countries send teams of up to six students. In addtion there is one team leader, one deputy leader, and observers. Each day participants take a 4.5 hour, 3 question essay exam. The participating countries trade off in hosting the event, which in it's entirety usually lasts 10- 14 days.
The USAMO (United States of America Mathematics Olympiad) provides a means of identifying and encouraging the most creative secondary mathematics students in the country. It serves to indicate the talent of those who may become leaders in the mathematical sciences of the next generation. The USAMO is part of a worldwide system of national mathematics competitions, a movement in which both educators and research mathematicians are engaged in recognizing and celebrating the imagination and resourcefulness of our youth.

The USAMO is a six question, two day, 9 hour essay/proof examination.
The AIME (American Invitational Mathematics Examination) is an intermediate examination between the AMC 10 or AMC 12 and the USAMO. All students who took the AMC 12 and achieved a score of 100 or more out of a possible 150 or were in the top 5% are invited to take the AIME. All students who took the AMC 10 and had a score of 120 or more out of a possible 150, or were in the top 2.5% also qualify for the AIME.
The AMC 10 and 12 are 25 question, 75 minute multiple choice examinations in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts.

The main purpose of the AMC is to spur interest in mathematics and to develop talent through the excitement of solving challenging problems in a timed multiple-choice format. The problems range from the very easy to the extremely difficult.
The USA Mathematical Talent Search (USAMTS) is a free mathematics competition open to all United States middle and high school students.

As opposed to most mathematics competitions, the USAMTS allows students a full month , or more, to work out their solutions. Carefully written justifications are required for each problem. The problems range in difficulty from being within the reach of most high school students to challenging the best students in the nation. Students may use any materials - books, calculators, computers - but all the work must be their own. The USAMTS is run on the honor system - it is an individual competition, whose competitive role is very secondary.
Mathematical Olympiad Summer Program
The goal of the Mathematical Olympiad Summer Program (MOSP) is:

To provide a mathematics program for a select group of very promising students who have risen to the top on the American Mathematics Competitions.
To broaden students' view of mathematics, and better prepare them for possible participation on our International Mathematical Olympiad (IMO) team.
To provide in depth enrichment in important mathematical topics to stimulate their continuing interest in mathematics and help prepare them for future study of mathematics.
To coach the IMO team, selected on the basis of the USA Mathematical Olympiad and further IMO type testing, to its highest level of performance in the IMO, and to achieve an atmosphere of comradeship and cooperation among the team and other participants which brings about feelings of cooperation and pride.
For an avid student with great skill in mathematics, rushing through the standard curriculum is not the best answer. That student who breezed unchallenged through algebra, geometry, and trigonometry, will breeze through calculus, too. This is not to say that high school students should not learn calculus – they should. But more importantly, the gifted, interested student should be exposed to mathematics outside the core curriculum, because the standard curriculum is not designed for the top students. This is even, if not especially, true for the core calculus curriculum found at most high schools, community colleges, and universities.
Stanford EPGY

Discrete Mathematics - Arthur Benjamin
Secrets of Mental Math - Arthur Benjamin
Joy of Mathematics - Arthur Benjamin
Art and Craft of Problem Solving - Paul Zeitz
Mathematics from the Visual World - Michael Starbird
Change and Motion: Calculus - Michael Starbird
Meaning from Data: Statistics - Michael Starbird
What are the Chances?: Probability - Michael Starbird
Joy of Thinking - Michael Starbird and Ed Burger
Introduction to Number Theory - Ed Burger
Zero to Infinity - Ed Burger
Knot Theory
What is a Math Circle?

Mathematical Circles are a form of education enrichment and outreach that bring mathematicians and mathematical scientists into direct contact with pre-college students. These students, and sometimes their teachers, meet with mathematical professionals in an informal setting, after school or on weekends, to work on interesting problems or topics in mathematics. The goal is to get the students excited about the mathematics, giving them a setting that encourages them to become passionate about mathematics.
History of the American Math Circles Experience

Mathematical enrichment activities in the United States have been around for at least thirty years, in the form of residential summer programs, math contests, and local school-based programs. The concept of a math circle, on the other hand, with its emphasis on convening professional mathematicians and secondary school students on a regular basis to solve problems, has appeared only within the past twelve years.
Math Olympiad
Creative Problem Solving
Math Olympiad Contest Problems
Math Olympiad Contest Problems Volume 2

Mathematical Circles (Russian Experience)

AOPS: Alcumus

Algebra I
Algebra II
William Lowell Putnam Mathematical Competitions
The examination will be constructed to test originality as well as technical competence. It is expected that the contestant will be familiar with the formal theories embodied in undergraduate mathematics. It is assumed that such training, designed for mathematics and physical science majors, will include somewhat more sophisticated mathematical concepts than is the case in minimal courses. Thus the differential equations course is presumed to include some references to qualitative existence theorems and subtleties beyond the routine solution devices. Questions will be included that cut across the bounds of various disciplines, and self-contained questions that do not fit into any of the usual categories may be included. It will be assumed that the contestant has acquired a familiarity with the body of mathematical lore commonly discussed in mathematics clubs or in courses with such titles as “survey of the foundations of mathematics.” It is also expected that the self-contained questions involving elementary concepts from group theory, set theory, graph theory, lattice theory, number theory, and cardinal arithmetic will not be entirely foreign to the contestant’s experience.
Simply put, ARML is the World Series of mathematics competitions. The competition consists of several events, which include a team round, a power question (in which a team solves proof-oriented questions), an individual round, two relay rounds (in which a contestant solves a problem and passes his/her answer to another team member, who uses this answer to solve another problem), and a super relay.
National / International
CIE MathComp
Math Rocks
Math Circle
David Cordeiro
HP Enterprise Services
Enterprise Cloud Services
Unified Communications
Global Compliance
Father of two great sons
School experience:
Parent volunteer for MMC

Founder of the Circle of Circles
21st Century Success: Beyond Math Competitions
Information Theory * Logic * Set Theory * Combinatorics * Graph Theory * Probability * Number Theory * Topology * Computational Geometry * Operations Research * Game Theory
College Admissions
Full transcript