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Boys and girls
Time, space and media: venue decisions
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By Maria Droujkova
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. There are many math woes out there: math anxiety, severe math illiteracy in the child and adult population, disproportional refusal of females to choose math-rich careers, and lack of gifted math support for students. It is futile to address any of these problems directly through tweaking math curricula or having better tests. I see roots of these and other math problems in inadequate social practices and in poorly developed supporting social networks. To paraphrase Shirky's definition of the internet communities, people don't love one another enough in the context of mathematics. What tiny part of the social media is devoted to math is largely confined to school work or aimed at "math geeks" - neither type inviting casual participation. The shift toward authoring, personally significant creative projects, and collaboration within communities that categorizes so much of what the "digital native" generation finds valuable barely started in mathematics. When was the last time your children were invited to create their own math content, other than cookie cutter exercises?
Math Clubs, Circles or Salons work as local cells of a global network, connecting young people and their families to meaningful and significant social mathematical practices. Decisions of math club founders about content, demographics, competition vs. collaboration, and venue determine social practices supported by the club. In this essay, I provide a brief overview of existing math club types, and talk about exciting new directions of the math club movement for the next five to ten years. Since the topic is a subject to controversial opinions, I would like to invite everyone to comment, add your math club information, and express your side of the story here.
National Association of Math Circles
for community resources.
You can ask your math club questions in the
Natural Math Q&A community
Decision about content are probably the most dramatic and thorny for newly formed clubs, or for parents seeking math clubs for their kids. You can investigate consequences of content choices by watching math club videos, reading descriptions, or trying different club options with the kids. Do not discard the very idea of math clubs just because a particular type did not fit! As a child, I loved problem-solving circles, but they are not a good fit for my daughter, who likes to focus on projects and authoring.
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).
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 fresh cool topic to the attention of your 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. You 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 clubs mix some features of the above types. You 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. Your decision about the type of the club strongly depends on your target audience.
Math competitions involve comparing speed, depth, or comprehensiveness of math work among several people. Traditionally, European competitions are more depth-oriented, and Asian and North American competitions are more speed-oriented. The vast majority of math competitions involve solving closed-ended (known answers) problems, however, there are also essay, project and software competitions. There are individual and team math competitions.
Some math clubs are completely devoted to preparing teams or individuals for particular competitions. The biggest plus of the competition framework 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. Beyond the age of ten or so, they also attract significantly more males than females.
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. Team competitions, where members collaborate within the team but compete with other teams, are a hybrid example.
Discussing ages of gifted children is always tricky. With the understanding that your child may be of several emotional and intellectual ages at once, and that math club dynamics will depend more on individuals than on demographic averages, I will discuss a few major factors about each math club age tier.
Baby and toddler
clubs are still rare, but growing. They are a lot of fun, especially for first-time parents, learning smart parenting techniques from each other and from veterans. For a baby and toddler math club, you can use either models similar to playgroups, play museums, Little Gyms or Montessori (working station, equipment, manipulative rooms), or Kindermusic, baby swimming, and baby yoga (activity-based). I view baby and toddler math clubs as parent social groups and think tanks. It is a way for a few friends or like-minded strangers to play together and brainstorm on enriching their kids' environment with mathematics. While gifted babies and toddlers may have adult-size attention spans, the focus of their attention is rarely predictable or manageable. That's why toddler math clubs are planned very loosely and openly, and focused on parents working with their own kids, rather than kids working with each other or the club leader.
clubs, with kids ages three to five, are still very much devoted to open play. There are tremendous attention, interest and ability differences among kids this age. You can't yet assume literacy, any interest in question and answer format, or in fact any desire to communicate with people outside their families. Strong pathways into mathematics, for this age, are hands-on art or construction projects, roleplaying, and games in general. Parents often comment on huge differences between home and group behavior of their children. Because of this, parents will do well to be actively involved or at least observing math clubs, following up on activities at home, and then sharing results in email groups and face-to-face "show and tell" activities. Capturing past activities and displaying them for kids to see and to build on is crucial at this developmental stage, because this way kids can work at higher intellectual levels, unhindered by memory and attention limitations (REF Reggio Emilia).
Ages five to ten
can get into serious enough problem solving and more involved projects or unit studies. Some kids in this age group are able and willing to work with purely symbolic, formal systems. This presents a temptation for club leaders to simply offer formal math activities designed for older students. Such straightforward acceleration is rarely appropriate: even kids capable of abstraction develop stronger math sense from working with pictures, hands-on experiences, and rich math stories. Games, especially group games, and collaborative events such as found math show-and-tell also strengthen friendships within clubs.
can be expected to have more developed interests and preferences for activities. While younger math clubs can easily spend all their time in free exploration and "topic hopping," the clear sense of purpose and significance, as well as strong connections with topics of interest to kids make for stronger tween math clubs. This is the age of more serious applied math projects, and more involved problem-solving competitions. Kids are maturing, and want to take on the world and try their hands at serious, meaningful tasks.
math clubs are tricky! While little kids are happy to explore and play, and tweens to work on projects or competitions, older teens need a stronger sense of community, and a solid meaning of the math club in their overall life path. Professional orientation, affiliation of clubs with particular universities or large tech companies teens consider for the immediate future, invited guests from academia and industry, social outreach and volunteering such as helping to run a club for an impoverished neighborhood, and contribution of club activities to CV are some examples of club meanings for teens. A club without such grown-up meaning structures will experience the "fountain of youth" effect, with its membership getting younger with each new recruiting wave. Also, around the age of twelve many girls fall off the fast math track and withdraw from math-rich activities - an effect some math club leaders are able to reverse by concerted efforts.
face-to-face math clubs are rare, with adults participating largely for the sake of their kids. There are exceptions, such as the Hollywood math club for TV writers where they discuss
math in movies and cartoons
, book study clubs for meaty reads like "Godel, Escher, Bach," or meet-ups for Sudoku, origami and other math-rich events. Adults are much more likely to meet virtually through blogs, wikis, nings, email groups, webinar platforms and virtual environments, such as the
Math 2.0 interest group
Boys and girls
Please keep in mind that similar to the age differences, you can expect individual differences to be stronger than "statistical" gender differences. These considerations are more important for larger math clubs with unpredictable attendance. Small clubs with constant memberships will do better by tailoring their activities to individual members, rather than statistical demographics.
Most math clubs are co-ed, though you see segregated clubs happen spontaneously, and all-girl clubs planned that way. There are strong arguments, backed by studies, that girls benefit academically from all-female environment in their teen years. However, there are strong social benefits for boys and girls becoming friends and working partners, rather than only meeting in the context of romantic involvement. In co-ed clubs, leaders have to pay attention to typical "gender pitfalls" plaguing many group activities, such as the tendency of adults to call more on boys than on girls and give boys longer time to answer questions, or the tendency of kids to always self-select boys as group spokespersons.
"No dark sarcasm in the classroom!" (Pink Floyd) applies to all kids in math clubs, but girls can be more sensitive to even casual and joking put-downs and snark. Again, while networking is important for all kids, you will probably see more girls quickly exchanging emails and connecting through math clubs socially, or coming to keep their friends company - the features club leaders have to mind while recruiting. Boys are less likely than girls to be engaged by stories or general discussions, or writing tasks of any sort. Pre-teen girls also have stronger fine motor skills than boys, so clubs that are heavy on crafts such as weaving or origami may be frustrating for the boys. On the other hand, boys have stronger visual-spatial skills and, typically, stronger interest in math tasks relying on such skills such as mapping.
At the end of the day, the only thing that matters is how club members help one another understand and create mathematics. Gender statistics can only provide very general guidelines for helping club members be productive and comfortable.
Some math clubs have the express purpose to "prepare our best young minds for their future roles as mathematics leaders." Typically, sessions in such circles are lead by mathematicians or math graduate students, who view child members as mathematicians in training, with a strong support from parents who belong to intellectually similar circles. This opportunity for participation in real math academic communities can be exhilarating emotionally, and stimulating intellectually. Kids who don't see themselves as future mathematicians, on the other hand, need enrichment opportunities, cures for math anxiety, and multiple strong ways to connect mathematics to the rest of the human culture. This is the same dilemma that exists in music or sports. Some children want the experience for general self-development, community and health benefits, while others seek it as their future profession.
Club members are faced with tough, value-laden decisions here. Does mathematics provide its own meaning for activities, or is the meaning derived from building better bridges or making more beautiful fractal wallpapers? Can kids hyper-focus on their chosen profession early in their life? How can we deal with exclusivity and the consequent elitism of early deep specialization? How can clubs "for poets" - not for future mathematicians specifically - assure depth and intellectual honesty of their math activities? Do we assume strong parental math support, and if so, what about dreams of making math communities grow through recruiting outside of "already mathy" families?
Time, space and media: venue decisions
While less important than "What?" and "Who?" questions, the decisions of "Where?" and "When?" also influence the style of math clubs. Here are a few venue decisions to consider
Face to face (f2f) or online?
Most math clubs probably have a mixture of virtual and f2f activities, with email lists used for announcements, and wikis or blogs to keep past content, photos and other media. Some math clubs meet only online, using webinar platforms or virtual worlds. Besides the obvious benefits such as access to millions of people, as opposed to your local town only, online clubs are easier to record and then share as open educational resources.
Registration or open door?
Clubs that have full open-door policy have to plan activities meaningful for one-time attendees. They can have larger community reach, but are limited in long-term projects or team building. Sometimes such clubs attract large crowds, especially if they are organized by well-known institutions. Open-door clubs typically meet once a month, for a longer period of several hours, with multiple activities organized by several leaders, as well as snack and break time. On the other hand, small, tight groups with constant membership usually meet weekly, and engage in long-term projects such as creating a math art exhibit or participating in a competition as a team.
I would like to encourage communities that don't have any math clubs at all to start with clubs designed to run for just a few weeks, whether as a mini-camp or as weekly short meetings. Such a club can read a math storybook together, or start and finish a unit study, or have a few cycles of problem solving with a small local Math Olympiad event at the end. If members find the experience meaningful, they can decide to continue.
Homes or institutions?
Many math clubs meet in living rooms of their organizers, especially if they are targeting a group of friends. This arrangement avoids room booking hassles, provides a relaxed, informal, grassroots atmosphere, saves the club leader travel time, and allows access to the kitchen and other home amenities. On the other hand, meeting on campus of a famous university or a cool software company supplies a certain glamor, gives access to that organization's administrative infrastructure, and helps with recruiting. The hybrid option is to meet in homes regularly, and to have larger events, such as Math Fairs, at professional institutions.
Day and time of the week.
Most young kids do their best math work in the early morning hours. On the other hand, the majority of teens to best in the afternoons or evenings. Most homeschool math clubs meet on weekday mornings or early afternoons, since families incorporate circle work into their regular learning routines. Math clubs for pre-teens that go to school can meet on weekday afternoons or weekends. However, older teens frequently have responsibilities on weekdays. Club leaders can either choose the day and the time according to the audience they want to attract, or get people together first and work on coordinating schedules - which will probably be among the most demanding math problems the club will ever face!
Snacks are very important for math club success, because food forms communities, and mathematics burns a lot of blood sugar. Fruits and nuts are the best math snacks. Kids typically get hungry in about half an hour of vigorous math activities. Tactile stimulation and background activities make clubs go much smoother. Providing modeling clay, small magnetic construction sets, paper for doodling or wire cleaners take good care of "ants in the pants" and help kids focus on ideas, rather than trying to keep still. For physical and mental health reasons, kids need relatively frequent opportunities to move around, such as short whole body math games (human knots, live mirrors, loose kaboose) the group can play together every half an hour or so.
"Always in motion the future is," claims Yoda, yet here I am with math club trend predictions, based on current development. The biggest changes are coming from social media and the internet. Math clubs are registering for directories, pooling together resources, exchanging activity descriptions, project videos and other social objects, and otherwise forming global support, research and development networks. We will probably see more
global math parties
and other events orchestrated online and conducted locally, such as Pi Day (March the fourteenth, 3/14) or Sofia Kovalevskaya math girl celebration, as well as the Math Fairs. Online math clubs, study groups, and support groups will grow explosively. The rare mentors interested in math and hailing from other communities of practice, such as crocheting, electronics, or digital arts, will be able to meet "the long tail" of like-minded kids online, and together develop activities and other know-how open resources that will serve as models for creating such specialized clubs locally. Grassroots clubs organized by a few like-minded parents or a dedicated teacher will continue to gain online visibility through their blogs, sites and global club networks, even if they don't have the academia publishing infrastructure to promote them.
To summarize, we can expect increasing diversity in styles, types and directions of math clubs in the near future, as well as emergence of multiple support networks. It's a good time to start your own club for your children, or to become active in an existing one.
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