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A math circle is an extracurricular activity intended to enrich students' understanding of mathematics. The concept of math circle came into being in the erstwhile USSR and Bulgaria, around 1907, with the very successful mission to "discover future mathematicians and scientists and to train them from the earliest possible age". [1]
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.[ citation needed ] 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. Two features all math circles have in common are (1) that they are composed of students who want to be there - either like math, or want to like math, and (2) that they give students a social context in which to enjoy mathematics. [2]
Mathematical enrichment activities in the United States have been around since sometime before 1977, in the form of residential summer programs, math contests, and local school-based programs. [3] The concept of a math circle, on the other hand, with its emphasis on convening professional mathematicians and secondary school students regularly to solve problems, appeared in the U.S. in 1994 with Robert and Ellen Kaplan at Harvard University. [3] This form of mathematical outreach made its way to the U.S. most directly from the former Soviet Union and present-day Russia and Bulgaria. [3] They first appeared in the Soviet Union during the 1930s; they have existed in Bulgaria since sometime before 1907. [3] The tradition arrived in the U.S. with émigrés who had received their inspiration from math circles as teenagers. [3] 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. [3] These days, math circles frequently partner with other mathematical education organizations, such as CYFEMAT: The International Network of Math Circles and Festivals, the Julia Robinson Mathematics Festival, [4] and the Mandelbrot Competition. [5]
Decisions about content are difficult for newly forming math circles and clubs, or for parents seeking groups for their children.
'Project-based clubs may spend a few meetings building origami, developing a math trail in their town, or programming a math-like computer game together. Math-rich projects may be artistic, exploratory, applied to sciences, executable (software-based), business-oriented, or directed at fundamental 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 webinars 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.
'Guided exploration circles use self-discovery and the Socratic method to probe deep questions. Robert & Ellen Kaplan, in their book Out of the Labyrinth: Setting Mathematics Free, [6] make a case for this format describing the non-profit Cambridge/Boston Math Circle they founded in 1994 at the Harvard University. The book describes the classroom, organizational and practical issues the Kaplans faced in founding their Math Circle. The meetings encourage a free discussion of ideas; while the content is mathematically rigorous, the atmosphere is friendly and relaxed. The philosophy of the teachers is, "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). Children are encouraged to ask exploratory questions. Are there numbers between numbers? What's geometry like with no parallel lines? Can you tile a square with squares all of the different sizes?
Research mathematicians and connecting students with them can be a focus of math circles. Students in these circles appreciate and start to attain a very special way of thinking in research mathematics, such as generalizing problems, continue asking deeper questions, seeing similarities across different examples and so on. [7]
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.[ citation needed ]
Most circles and clubs mix some features of the above types. For example, the Metroplex Math Circle, [8] Arnold & Marsden Mathematical Olympiad Circle (AMMOC) [9] have a combination of problem-solving and research, and the New York Math Circle [10] is some combination of a problem-solving circle and a topic-centered club, with vestiges of a research circle.
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.[ citation needed ]
Math competitions involve comparing speed, depth, or accuracy of math work among several people or groups. Traditionally, European competitions are more depth-oriented, and Asian and North American competitions are more speed-oriented, especially for younger children. The vast majority of math competitions involve solving closed ended (known answers) problems, however, there are also essay, project and software competitions. As with all tests requiring limited time, the problems focus more on the empirical accuracy and foundations of mathematics work rather than an extension of basic knowledge. More often than not, competition differs entirely from curricular mathematics in requiring creativity in elementary applications—so that although there may be closed answers, it takes significant extension of mathematical creativity in order to successfully achieve the ends.
For people like Robert and Ellen Kaplan, competition carries with it a negative connotation and corollary of greed for victory rather than an appreciation of mathematics. However, those who run math circles centering mostly on competition rather than seminars and lessons attest that this is a large assumption. Rather, participants grow in their appreciation of math via math competitions such as the AMC, AIME, USAMO, and ARML.
Some math circles are completely devoted to preparing teams or individuals for particular competitions. The biggest plus of the competition framework for a circle organizer is the ready-made set of well-defined goals. The competition provides a time and task management structure, and easily defined progress tracking. This is also the biggest minus of competition-based mathematics, because defining goals and dealing with complexity and chaos are important in all real-world endeavors. Competitive math circles attract students who are already strong and confident in mathematics, but also welcome those who wish to engage in the mathematics competitive world. Beyond the age of ten or so, they also attract significantly more males than females, and in some countries, their racial composition is disproportionate to the country's demographic.
Collaborative math clubs are more suitable for kids who are anxious about mathematics, need "math therapy" because of painful past experiences, or want to have more casual and artistic relationships with mathematics. A playgroup or a coop that does several activities together, including a math club, usually chooses collaborative or hybrid models that are more likely to accommodate all members already in the group.
Most math circles and clubs combine some competitive and some collaborative activities. For example, many math circles, while largely centering on competitions, host seasonal tournaments and infuse their competition seminars with fun mathematical lessons.[ citation needed ]
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research- and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves mathematical puzzles and games, often appealing to children and untrained adults and inspiring their further study of the subject.
In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge.
Soviet Student Olympiad was an annual set of contests for students in the USSR. There were two separate multi-round competitions every year: for higher education (universities) and general education. Both competitions had several rounds, and winners from lower rounds would go to the next round. Not only individual members, but teams were awarded too. The main difference between two Olympiads was that the school one had separate threads for every grade, while the university one was for all students.
The Canadian Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research, outreach, scholarship and education in Canada. It serves the national community through the publication of academic journals, community bulletins, and the administration of mathematical competitions.
Named in honor of Benoit Mandelbrot, the Mandelbrot Competition was a mathematics competition founded by Sam Vandervelde, Richard Rusczyk and Sandor Lehoczky that operated from 1990 to 2019. It allowed high school students to compete individually and in four-person teams.
Melanie Matchett Wood is an American mathematician and Professor of Mathematics at Harvard University who was the first woman to qualify for the U.S. International Mathematical Olympiad Team. She completed her PhD in 2009 at Princeton University. Previously, she was Chancellor's Professor of Mathematics at UC Berkeley, Vilas Distinguished Achievement Professor of Mathematics at the University of Wisconsin, and spent 2 years as Szegö Assistant Professor at Stanford University.
Founded in 1920, The National Council of Teachers of Mathematics (NCTM) is a professional organization for schoolteachers of mathematics in the United States. One of its goals is to improve the standards of mathematics in education. NCTM holds annual national and regional conferences for teachers and publishes five journals.
Mathematical Kangaroo is an international mathematics competition in over 77 countries. There are six levels of participation, ranging from grade 1 to grade 12. The competition is held annually on the third Thursday of March. The challenge consists of problems in multiple-choice form that are not standard notebook problems and come from a variety of topics. Besides basic computational skills, they require inspiring ideas, perseverance, creativity and imagination, logical thinking, and other problem-solving strategies. Often there are small stories, intriguing problems, and surprising results, which encourage discussions with friends and family.
Richard Rusczyk is the founder and chief executive officer of Art of Problem Solving Inc. and a co-author of the Art of Problem Solving textbooks. Rusczyk was a national Mathcounts participant in 1985, and he won the USA Math Olympiad (USAMO) in 1989. He is one of the co-creators of the Mandelbrot Competition, and the director of the USA Mathematical Talent Search (USAMTS). He also founded the San Diego Math Circle.
Titu Andreescu is an associate professor of mathematics at the University of Texas at Dallas. He is firmly involved in mathematics contests and olympiads, having been the Director of American Mathematics Competitions, Director of the Mathematical Olympiad Program, Head Coach of the United States International Mathematical Olympiad Team, and Chairman of the United States of America Mathematical Olympiad. He has also authored a large number of books on the topic of problem solving and olympiad-style mathematics.
This article describes the selection process, by country, for entrance into the International Mathematical Olympiad.
In the United States, math wars are debates over modern mathematics education, textbooks and curricula that were triggered by the publication in 1989 of the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM) and subsequent development and widespread adoption of a new generation of mathematics curricula inspired by these standards.
Evan Michael O'Dorney is an American mathematician who is a postdoctoral associate at Carnegie Mellon University. His specialization is number theory. As a home-schooled high school student and college student, he won many contests in mathematics and other subjects, including the 2007 Scripps National Spelling Bee, 2011 Intel Science Talent Search, four International Math Olympiad medals, and three Putnam Fellowships. A 2013 report by the National Research Council called him "as famous for academic excellence as any student can be".
Samuel Kendrick Vandervelde is a mathematician who, along with Sandor Lehoczky and Richard Rusczyk, created the Mandelbrot Competition, and is listed first under "Thanks" in the mathematical textbook The Art of Problem Solving.
Mathematics education in the United States varies considerably from one state to the next, and even within a single state. However, with the adoption of the Common Core Standards in most states and the District of Columbia beginning in 2010, mathematics content across the country has moved into closer agreement for each grade level. The SAT, a standardized university entrance exam, has been reformed to better reflect the contents of the Common Core. However, many students take alternatives to the traditional pathways, including accelerated tracks. As of 2023, twenty-seven states require students to pass three math courses before graduation from high school, while seventeen states and the District of Columbia require four. A typical sequence of secondary-school courses in mathematics reads: Pre-Algebra, Algebra I, Geometry, Algebra II, Pre-calculus, and Calculus or Statistics. However, some students enroll in integrated programs while many complete high school without passing Calculus or Statistics. At the other end, counselors at competitive public or private high schools usually encourage talented and ambitious students to take Calculus regardless of future plans in order to increase their chances of getting admitted to a prestigious university and their parents enroll them in enrichment programs in mathematics.
Modern elementary mathematics is the theory and practice of teaching elementary mathematics according to contemporary research and thinking about learning. This can include pedagogical ideas, mathematics education research frameworks, and curricular material.
Zvezdelina Entcheva Stankova is an American mathematician who is a professor of mathematics at Mills College and a teaching professor at the University of California, Berkeley, the founder of the Berkeley Math Circle, and an expert in the combinatorial enumeration of permutations with forbidden patterns.
Moscow State School 57 is a public school located in the Khamovniki District of Moscow, Russia. The school was founded in 1877 and is best known for its specialized secondary program in mathematics and its alumni.
The Julia Robinson Mathematics Festival (JRMF) is an educational organization that sponsors locally organized mathematics festivals and online webinars targeting K–12 students. The events are designed to introduce students to mathematics in a collaborative and non-competitive forum.
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