A MathCircle is where a group of young people get together and work on some interesting Math-related topics introduced by a mentor.
The topics are sometimes problems like you find on ArtOfProblemSolving.com or Math Competitions [ vis AMC Sample Questions ]. They can cover quirky topics that aren’t normally seen in the school curriculum, such as Catalan Numbers.
The idea sounds geeky, and is un-apologetically so, yet has the potential to engage students who might be bored with the traditional material. It preps interested students for careers in science / finance / medicine / engineering and helps the school do well in math and science competitions. Math Circle meets can also be a lot of fun.
Question : “Why do we need more math.. we already do that in school, right?”
Answer : “yeah..but you don’t learn enough Tennis in PE class to become a club player, and you don’t get enough Instrument practice in Music class to get into music school .. you really need to train, to play in an ensemble and have dedicated practice for that.”
MathCircle takes the same approach of intensive practice which you find in Basketball practice, Dance club, Swim meet or musical instrument group … except focused on math-related skills.
Practice with Duration + Intensity
One important aspect that both Math problem solving and programming share is the sustained concentration on one task – in my opinion we have gone too far in the direction of byte size chunks of learning. Sometimes you need to chew on things for a while.
We can look at how Basketball and Music are learnt, and apply what works to math. Training sessions often last for 2 hours, and this is accepted as a social norm – it is well understood it takes time to get into the zone.. repeat the basics, introduce a new skill, practice it, and integrate and perfect it over time thru a range of scenarios.
Its also not about the one or two elite players – the whole team improves and transfer skills around and offer peer-support thru the shared activity. It can help develop individual qualities that are useful for success in other areas of life, namely ‘character’.
MathCircle is something most parents haven’t heard of .. but teaching young people how to program is an easy sell – it has had a lot of positive marketing over the last year or so, and its a clear pathway to a good salary.
I also think that writing small programs is a great way to introduce and discover math ideas .. its tactile, interactive, hands on, iterative, experimental. Your also working with the real concepts – a lot of educational apps and games seem to win in terms of engaging and entertaining, but lose in terms of conveying deeper ideas. When your making a program you are really tinkering under the hood with the engine, not just zooming around the racetrack. So a MathCircle with an emphasis on making your own programs to investigate math topics, and using tools like Geogebra, might work really well.
A MathCircle which has a code-things-up emphasis, we could call a MathCodeCircle.
Here are some topics that might be covered in such a MathCodeCircle :
- find prime number factors, use for solving lcm/gcf problems
- pong game variant – balls bounce around and collide
- adding waves together – beats, square waves
- simulate jumpy stock prices, compare with compound interest
- planets orbiting / solar system simulator
- circle inversion using GeoGebra
Some links if your interested :
- What is a Math Circle
- Circle In a Box – how to build and run a Math Circle
- MathCircles – Washington University vid
- San Francisco MathCircle – vid
- Introduction to Programming – Khan Academy