1	Metro NY MAA Meeting May 6th, 2007 Math Circles Workshop/Discussion Lauren Rose rose@bard.edu Japheth Wood jwood@bard.edu Bard College
2	1. What is a Math Circle? A math enrichment program outside of the school system, usually for middle and school students, often taught by PhD mathematicians. Common in Eastern Europe, relatively new to the US. Classroom or workshop setting, weekly or monthly meetings. The focus is on discovery, not rote learning. Some prepare students for competitions (Berkeley Math Circle), others promote non-competitive math exploration (Boston Math Circle). One goal is to identify and develop math talent, but they could also be used to promote equity and diversity in mathematics.
3	2. Where are Math Circles? Berkeley Math Circle (mathcircle.berkeley.edu) Boston: Bob and Ellen Kaplan’s Math Circle (www.themathcircle.org) Davis (www.math.ucdavis.edu/~Eexploration/mathcircle) Irvine (www.math.uci.edu/~Emathcirc) Lehman College (comet.lehman.cuny.edu/mathcircle) Mobile (gauss.usouthal.edu/~Emathcircle) Palo Alto (www.castilleja.org/faculty/josh_zucker/bamo/circles/PaloAlto) Salt Lake City San Diego (www.sdmathcircle.org) San Jose (www.geometer.org/sjcircle) San Francisco (www.sfmathcircle.org) South Bend (http://riverbendmath.org) Utah (www.math.utah.edu/mathcircle) Waterloo (cemc.math.uwaterloo.ca) Wyoming (uwacadweb.uwyo.edu/UW_MATH_CIRCLE)
4	3. Conferences and Resources AIM: How to Run a Teacher’s Math Circle (June 18-22, 2007) http://www.aimath.org/ARCC/workshops/teacherscircle.html AMS-MAA Special Session on Math Circles and Similar Programs for Students and Teachers (January 2007) http://www.ams.org/amsmtgs/2098_program_ss22.html#title MSRI: Mathematical Circles and Olympiads (December 16-18, 2004) (www.msri.org/calendar/workshops/WorkshopInfo/295/show_workshop) Mathematical Circles: Russian Experience by Dmitri Fomin, Sergey Genkin and Ilia V. Itenberg, AMS, 1996 Solve This: Math Activities for Students and Clubs by James S. Tanton, 2001 Out of the Labyrinth: Setting Mathematics Free by Robert Kaplan and Ellen Kaplan, Oxford University Press, 2006
5	4. Ideas and logistics (Paraphrased from http://www.geometer.org/mathcircles/) Concentrate on problem solving techniques applicable to many areas. Sample topics: symmetry, the pigeon-hole principle, divisibility, counting, probability, graphs, induction, plane geometry. Hand out a set of problems a week before your session. Not too many, but include an easy one and a challenging one. Try not to lecture. Sessions should be as interactive as possible. Score yourself: 1 point per minute you talk; 5 points per minute a student talks; 10 points per minute you argue with a student; 50 points per minute the students argue among themselves. Divide students into groups of 2 - 4 to solve problems. Be encouraging, even about wrong answers. If students don't answer your question immediately, don't just tell them the answer. Give hints, not solutions.
6	5. Goals for this Session To Network with mathematicians and math educators with similar interests. To coordinate the development of Math Circles in the Hudson Valley. To share ideas and experiences as we get started. To share our planning so far, and invite suggestions.
7	6. Group Project How many Friday the 13ths can be in a given year? What is the minimum? The maximum? Get into small groups and work on this problem for 5-10 minutes. Discuss solving strategies with other members of the group. Does working on this problem suggest other problems to you? How might you structure this problem if you were giving it to high school students? To middle school students?
8	7. Sample Problems and Activities Problems of the Week from Kaplan’s Math Circle Is there a last prime? Are there more decimals than fractions? What proportion of the powers of two begin with a "7"? Is n(n-1)+ 41 a prime for every whole number n? Can a polyhedron have an odd no. of faces and sides? Which numbers are the sum of two squares? Which numbers whose digits are all equal are prime?
9	8. Classes for All Ages Riverbend Math Center, South Bend , IN Number Fun (preschool) Join us for a 10-week romp through the world of numbers. Get a jump-start on learning math as we hop on number lines and use other life-size models to add, subtract, multiply, and divide. During our journey, we will search the number line for the world's biggest and smallest numbers, and we will peek between the counting numbers to discover fractions. Polyhedra (1^st- 3 ^rd grade) Have fun with us as we build, classify, and analyze three-dimensional shapes using a variety of materials. We will count vertices, edges, and faces to determine the face vector of each polyhedron. Together, we will uncover many ancient geometry secrets as we investigate what types of face vectors are possible. Alien Mathematics (4^th – 6^th grade) Is 2+2 always equal to 4? How might aliens from another planet do mathematics? We will explore this question by decoding messages from hypothetical aliens who need help with their math homework. Along the way, we will see how the unusual math methods that we encounter are actually used by people on planet Earth. The 4th Dimension (6^th – 9^th grade) Challenge your mathematical imagination as we contemplate the 4th dimension and beyond. We will begin by defining the concept of dimension. As we imagine what life would be like in a world with more than three spatial dimensions, we will learn techniques to work with and visualize objects in higher dimensions. Contemplating the Infinite (9^th – 12^th grade) Journey with us to infinity and beyond. We will prove that infinity is equal to negative one, show that some infinite sets are bigger than others, and pack an infinite plane of points onto the surface of a tiny ball. During our journey, we will confront paradoxes that have tormented mathematical philosophers from Xeno to Cantor.
10	9. Mid-Hudson Math Circle To commence in Fall 2007 Weekend workshops for middle/high school students. Aim for diversity in terms of gender, race and ethnicity. Special sessions for girls, maybe as an afterschool program. Sessions in local libraries for younger students. Invite participation by local college faculty and students Connect with other teachers, educators and professionals in the region Coordinate a network of math enrichment programs in the Hudson Valley.