I recently discovered the wonderful world of math circles, and the activity has quickly become a favorite of my daughter. I approached the UCLA math circle with the idea of having Paulina do interesting math with other kids equally interested in the subject. I was also looking for a chance to step back from the role of parent/teacher and let her experience collaborative math without having my looking over her shoulder. I got the schedule wrong for the first meeting, but she managed to spend 30 mins working on cool introductory problems. I wanted Paulina to experience the joy of solving problems and working with other people, but I promised myself that I would not force her to return if she did not want to. To my surprise, Paulina said that the circle was fun and that she wanted to keep going. She now has attended five sessions, and she even fell asleep holding her book of problems the night of the second session. It appears that the math circle may provide Paulina with a source of intellectual challenge, excitement, as well as a place to enjoy math with other like-minded kids.
Why do I like the math circle? The answer is that the it approaches the subject very differently from the boring, tradition-bound, mind-numbing torture imposed on kids all across the US. The last few sessions have centered around binary numbers (i.e. base 2). This is a very simple concept for middle and high school kids, but few six, seven, and eight year olds have ever imagined that one could do arithmetic using anything but the decimals. The circle's leader -- a UCLA professor with kids in the circle -- started the afternoon by asking if anybody knew a way to represented numbers in any way other than using decimal notation. A few kids offered interesting, albeit impractical solutions, and one of them said that you could just use as many sticks as needed, counting each once. The instructor then suggested Roman numerals. The kids worked on writing Roman numbers and ended the discussion by figuring out how to correct the following equation by moving just one stick:
II + III = VI.
Clearly, the point of Roman numerals was to teach that numbers can be represented in different ways. As such, binary numbers were introduced, and this is where the teaching got clever. Instead of using powers of two, the instructor wrote the following sequence on the blackboard: 1, 2, 4, 8, 16, 32, 64... Every kid understood that you get the next number by doubling the preceding one. The instructor then asked the kids to imagine that each number represents a weight and to figure out how to balance an object using only those weights, assuming that each weight could be used only once. One way to think about it is to say that you are trying to balance a given weight with counterweights of 1, 2, 4, 8, ... It actually helps to draw a scale and ask the student to draw the counter weights required to balance both sides.
The beautiful thing about the balance / weight metaphor for binary is that it allows very young kids to understand binary without resorting to exponents and other more advanced material, and binary is, in my opinion, a great way to teach the basic principles of arithmetic.
Binary is just one of the topics taught at the UCLA Math Circle. Challenging word problems, principles of algebra, and other "advanced" material are introduced weekly to kids as young as six. The sad part of this is that most of the participants only get to enjoy fun math once a week. If it was up to me, math class would be abolished, and math circles would become the norm.