I Just got back to NYC after a fantastic week of visiting my family in Palm Springs. My niece, Penelope, turned one and nearly her whole living gene pool on her mother’s side flew out from the east coast. I also got to spend some time with my other awesome niece, Catalina, and my nephew, Desmond, and I learned, that Catalina is still very much in love with math.

On the plane ride out there I started to work on a game to help me practice counting. I know, I know, you’ll say, I should know how to do that, and I do, in most situations I encounter. But I know I can get a lot better, and one area I can definitely improve on is “subitization” which is a form of counting which is instantaneous and almost subliminal. To understand the difference between merely counting and subitizing, consider, the following scenario. You are playing with your niece on the floor, and she picks up a pair of wooden blocks from her basket and drops them in front of you. You smile at her and the two blocks. How cute! They are have carved faces of animals on them. Now in her exuberance to show you her other prodigious gifts, she starts to get up off the ground and puts her weight on the basket, flipping its contents over onto the ground. Now there are lots of blocks. How cute! But how many are there? If you’re like me, or my eldest niece, you would have to count the blocks to know how many there are, it’s not as obvious as when there were just two. Most humans can subitize small quantities, like two, three, or even four without difficulty, but for higher numbers like six, seven, or even eight we are generally quite bad at it and we have to count. When you count you move your eyes over all the objects at least once and keep a running total. When you subitize you “count” in a single glance because the arrangement of objects is as obviously that number of things.

The interesting thing is some people can do much better than almost everyone else. Mathematical savants for example, often subitize quantities of 10 or even 14 with ease. I recently finished a wonderful book, an autobiography actually, called “Born on a Blue Day” by Daniel Tammet, in which Mr. Tammet describes his prodigious abilities to count. He writes that he would spend hours as a child making patterns out of blocks in his room and merely counting how many of this or that shape were present. He now can multiply large numbers together in his head instantly and holds the world’s record (or at least did) for most digits of Pi recited — more than 25,000. Are his mathematical abilities due to his spending so much time counting as a child? Nobody knows, but Mr. Tammet definitely sees a connection.

While I don’t think I will ever have Mr. Tammet’s love for numbers, I am fascinated by them and I do want to count them better. There is some research that says you can improve your subitization, so I thought it would be interesting just to make a sort of practice game for myself that gets harder as I get better. I tried hard to keep it barebones with a simple interface and am very pleased with the results. Try it out and let me know what you think.

After playing with my game for an hour or so, I really did start to see some improvement in my abilities, and I stopped having to count as much, and started just seeing the “sevenness” in the arrangement of dots on the screen. I was subitizing — albeit with occasional errors. I think it might actually be much more important for people learning math to spend a lot of time just seeing collections of things and learning to recognize their number by sight — subitizing! — so that when they think of 7 and 5 they see a collection of seven things and a collection of 5 things combining, not the numeral “7” and the numeral “5” with a cross-hair between them which isn’t nearly as expressive.

March 25, 2011

The number pad on my keyboard doesn’t work here. I want to get the fastest score and these numbers up top are holding me back!@@!

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