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Mathematical circles are a form of outreach that bring mathematicians into direct contact with pre-college students. These students, and sometimes their teachers, meet with a mathematician or graduate student 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 they are learning; to give them a setting that encourages them to become passionate about mathematics.<ref name="What is a Math Circle?" group="MSRI Circle in a Box">{{cite web|last=Saul|first=Mark|title=May 17, 2006 letter to NYC math department chairs, quoted in "Circle in a Box"|url=http://www.mathcircles.org/Wiki_WhatIsAMathCircle|work="Circle in a Box" part of the Math Circles Wiki|publisher=MSRI|accessdate=28 May 2011|year=2006}}</ref>
{{Generalize|date=October 2009}}
{{Cleanup-rewrite|date=May 2009}}

Math clubs and math circles, while useful and fun in their own right, are a part of the bigger vision: providing children with ample opportunities to experience mathematics as a rich social practice. Math Clubs, Circles or Salons often work as local cells of a global network, such as National Association of Math Circles.

'''The Math Circle''' is a program of courses founded by Robert & Ellen Kaplan in [[Boston]] in 1994, which is now used by groups in many parts of the [[United States]]. The Kaplans were inspired by educational techniques developed in Russia and Eastern Europe which emphasized group discussion, open-ended problem solving, and interaction with working mathematicians.<ref>http://www.math.utah.edu/%7Eptrapa/powerpoint/MAAmathcircles6.ppt</ref> Math Circle classes are primarily designed for students who enjoy [[mathematics]] and want the added challenge of exciting topics that are normally outside the school [[curriculum]]. Classes are taught in such a way that students are challenged to find their own way through a chosen mathematical topic, and are offered to children as young as five.


==Characteristics==
==Characteristics==


Math circles can have a variety of styles. Some are very informal, with the learning proceeding through games, stories, or hands-on activities. Others are more traditional enrichment classes, but without formal examinations. Some have a strong emphasis on preparing for olympiad competitions; some avoid competition as much as possible. Models can use any combination of these techniques, depending on the audience, the mathematician, and the environment of the circle. Athletes have sports teams through which to deepen their involvement with sports; math circles can play a similar role for kids who like to think. One feature all math circles have in common is that they are composed of students who enjoy learning mathematics, and the circle gives them a social context in which to do so.<ref name="What is a Math Circle?" group="MSRI Circle in a Box">{{cite web|last=Saul|first=Mark|title=May 17, 2006 letter to NYC math department chairs, quoted in "Circle in a Box"|url=http://www.mathcircles.org/Wiki_WhatIsAMathCircle|work="Circle in a Box" part of the Math Circles Wiki|publisher=MSRI|accessdate=28 May 2011|year=2006}}</ref>
Robert & Ellen Kaplan, best-selling authors of [http://www.amazon.com/dp/0195142373/ Nothing That Is] and [http://www.amazon.com/dp/0195176065/ The Art of the Infinite: The Pleasures of Mathematics]. Two acclaimed opinion leaders in mathematics education, Bob & Ellen Kaplan, have written a book published by Oxford entitled ''Out of the Labyrinth: Setting Mathematics Free'', about the non-profit [http://www.themathcircle.org Cambridge/Boston Math Circle] they founded in 1994 in the Harvard University environs. It presents a convincing argument for incorporating the art of guided explorations and self-discovery into math curricula. Along the way, they also describe the classroom, organizational and practical issues they faced in founding their Math Circle.

Its teachers are experienced, committed, and enthusiastic. The classes encourage a free discussion of ideas; while the courses are mathematically rigorous, the atmosphere is friendly and relaxed.

The philosophy of the teachers is simple:

<blockquote>
"What you have been obliged to discover
by yourself leaves a path in your mind
which you can use again when the need
arises." --G. C. Lichtenberg
</blockquote>

Children are encouraged via Socratic method as they ask key exploratory questions. Are there numbers between numbers? What's a geometry like with no parallel lines? A soccer ball is made of pentagons and hexagons, with three edges meeting at each vertex. Why MUST the number of pentagons used be twelve? Can you tile a square with squares all of different sizes?

An example lecture by the Kaplans serves as a convincing demonstration that young children can discover some of the larger truths in mathematics through the Socratic method, on the website for [http://www.msri.org/communications/vmath/VMathVideos/VideoInfo/1913/LV/LaunchVideo?videoid=10751 Mathematical Sciences Research Institute].

==Popularity==
Inspired by the Eastern European problem-discussion approach to math education, '''math circles''' have become something of a phenomenon for top math students around the United States. In particular, the Bay Area, known for producing a large number of qualifiers for the [[United States of America Mathematical Olympiad]], is home to several math circles.

Some, but not all math circles concentrate on [[math competition]] problems, or mathematical [[problem solving]]. Many are focused on teaching students to find and write rigorous solutions ([[mathematical proofs]]) to standard and nonstandard math problems. Some also focus on [[mathematical research]] skills.

Mathematics is our lost native language, state the authors. Math talent is a myth, but the drudgery of most early math education fails to instill the confidence and sense of play which invites further exploration. The subtle Art of teaching is woven throughout the book as the lifelong teachers lend examples for creating an intimate model for guiding young students in their own discovery of complex math. Their approach consists of posing foundational questions to group of students—Are there numbers between numbers? What is Area? -- then guiding a discussion down many paths "propelled by the fun of the chase."


==History==
In early 2007, the Kaplans lectured to teachers and educators at conferences by the American Mathematical Society and Mathematical Association of America.
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. This form of mathematical outreach made its way to the U.S. most directly from Russia and Bulgaria, where it has been a fixture of their mathematical culture for decades. (The first ones appeared in Russia during the 1930’s; they have existed in Bulgaria for a century.) The tradition arrived with emigres who had received their inspiration from math circles as teenagers. Many of them successfully climbed the academic ladder to secure positions within universities, and a few pioneers among
them decided to initiate math circles within their communities to preserve the tradition which had been so pivotal in their own formation as mathematicians.<ref name="History - Circle in a Box" group="MSRI Circle in a Box">{{cite web|last=Vandervelde|first=Sam|title=Circle in a Box|url=http://www.mathcircles.org/node/65|publisher=MSRI|accessdate=28 May 2011|date=January 22|year=2007}}</ref>


==Content Choices==
==Content Choices==
Line 50: Line 25:


==References==
==References==
<references group="MSRI Circle in a Box"/>
{{Reflist}}


==External links==
==External links==
Line 63: Line 38:
* [http://www.ocmathcircle.org/ Orange County (California) Math Circle]
* [http://www.ocmathcircle.org/ Orange County (California) Math Circle]
* [http://comet.lehman.cuny.edu/mathcircle/ Lehman College Math Circle] in the [[Bronx]]
* [http://comet.lehman.cuny.edu/mathcircle/ Lehman College Math Circle] in the [[Bronx]]
* [http://www.metroplexmathcircle.org Metroplex Math Circle] at UT Dallas
* [http://www.fiu.edu/~draghici/mathcircle_files/mathcircle.html Miami Math Circle] at [[Florida International University]]
* [http://www.fiu.edu/~draghici/mathcircle_files/mathcircle.html Miami Math Circle] at [[Florida International University]]
* [http://www.midcitiesmathcircle.org Mid-Cities Math Circle] at UT Arlington
* [http://www.southalabama.edu/mathstat/non-css-mathcircle.shtml Mobile Math Circle] in South Alabama
* [http://www.southalabama.edu/mathstat/non-css-mathcircle.shtml Mobile Math Circle] in South Alabama
* [http://www.castilleja.org/faculty/josh_zucker/bamo/circles/PaloAlto/ Palo Alto (California) Math Circle]
* [http://www.castilleja.org/faculty/josh_zucker/bamo/circles/PaloAlto/ Palo Alto (California) Math Circle]

Revision as of 06:12, 28 May 2011

Mathematical circles are a form of outreach that bring mathematicians into direct contact with pre-college students. These students, and sometimes their teachers, meet with a mathematician or graduate student 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 they are learning; to give them a setting that encourages them to become passionate about mathematics.[MSRI Circle in a Box 1]

Characteristics

Math circles can have a variety of styles. Some are very informal, with the learning proceeding through games, stories, or hands-on activities. Others are more traditional enrichment classes, but without formal examinations. Some have a strong emphasis on preparing for olympiad competitions; some avoid competition as much as possible. Models can use any combination of these techniques, depending on the audience, the mathematician, and the environment of the circle. Athletes have sports teams through which to deepen their involvement with sports; math circles can play a similar role for kids who like to think. One feature all math circles have in common is that they are composed of students who enjoy learning mathematics, and the circle gives them a social context in which to do so.[MSRI Circle in a Box 1]

History

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. This form of mathematical outreach made its way to the U.S. most directly from Russia and Bulgaria, where it has been a fixture of their mathematical culture for decades. (The first ones appeared in Russia during the 1930’s; they have existed in Bulgaria for a century.) The tradition arrived with emigres who had received their inspiration from math circles as teenagers. Many of them successfully climbed the academic ladder to secure positions within universities, and a few pioneers among them decided to initiate math circles within their communities to preserve the tradition which had been so pivotal in their own formation as mathematicians.[MSRI Circle in a Box 2]

Content Choices

Decision about content are difficult for newly forming math circles and clubs, or for parents seeking groups for their kids.

Project-based clubs may spend a few meetings building origami, developing a math trail in their town, or programming a mathy computer game together. Math-rich projects may be artistic, exploratory, applied to sciences, executable (software-based), business-oriented, or directed at real contributions to local communities. Museums, cultural and business clubs, tech groups, online networks, artists/musicians/actors active in the community, and other individual professionals can make math projects especially real and meaningful. Increasingly, math clubs invite remote participation of active people (authors, community leaders, professionals) through webinar and teleconferencing software.

Problem-solving circles get together to pose and solve interesting, deep, meaningful math problems. Problems considered "good" are easy to pose, challenging to solve, require connections among several concepts and techniques, and lead to significant math ideas. Best problem solving practices include meta-cognition (managing memory and attention), grouping problems by type and conceptual connections (e.g. "river crossing problems"), moving between more general and abstract problems and particular, simpler examples, and collaboration with other club members, with current online communities, and with past mathematicians through the media they contributed to the culture.

Research mathematicians and connecting students with them can be a focus of math circles. Students in these circles appreciate and start to attain the very special way of thinking in research mathematics, such as generalizing problems, continue asking deeper questions, seeing similarities across different examples and so on. [1]

Topic-centered clubs follow math themes, such as clock arithmetic, fractals, or linearity. Club members write and read essays, pose and solve problems, create and study definitions, build interesting example spaces, and investigate applications of their current topic. There are lists of time-tested, classic math club topics, especially rich in connections and accessible to a wide range of abilities. The plus of using a classic topic is the variety of resources available from the past; however, bringing a relatively obscure or new topic to the attention of the club and the global community is very rewarding, as well.

Applied math clubs center on a field other than mathematics, such as math for thespians, computer programming math, or musical math. Such clubs need strong leadership both for the math parts and for the other field part. Such clubs can meet at an artists' studio, at a game design company, at a theater or another authentic professional setting. More examples of fruitful applied math pathways include history, storytelling, art, inventing and tinkering, toy and game design, robotics, origami, and natural sciences.

Most circles and clubs mix some features of the above types. One can expect problem-solving groups to attract kids already strong in math and confident in their math abilities. On the other hand, math anxious kids will be more likely to try project-based or applied clubs. Topic-centered clubs typically work with kids who can all work at about the same level. The decision about the type of the club strongly depends on your target audience.

References

  1. ^ a b Saul, Mark (2006). "May 17, 2006 letter to NYC math department chairs, quoted in "Circle in a Box"". "Circle in a Box" part of the Math Circles Wiki. MSRI. Retrieved 28 May 2011.
  2. ^ Vandervelde, Sam (January 22). "Circle in a Box". MSRI. Retrieved 28 May 2011. {{cite web}}: Check date values in: |date= and |year= / |date= mismatch (help)

Math circles around North America

Other

  1. ^ "Math Circle at ASU Temple".
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