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November 19, 2006
Sensory styles for doing arithmetic
I recently bought Brain Age for my Nintendo DS. One of the tasks in the game is to solve arithmetic expressions as fast as you can. The expressions are all drawn from the basic addition, subtraction and multiplication facts. They are parenthesis-free and contain no more than two numbers. For some reason, this task seems particularly addictive to me--probably because I do it at a decent speed. Karolina and I got to talking about how our respective brains actually crunch the numbers during the task.
My preferred sensory style is visual. I do know people who are much more strongly visual than me, but I suppose I screw up the least when working visually. When solving a simple math problem--say 8-5 = ?--I 'see' the 3 next to the equals sign. Karolina has more of an auditory preference. She has to sound out the equation in her head ("eight minus five equals?") to get the answer. When equations appear rapidly on a screen, it is evidently a visual task. This is why I was clocking slightly faster times than her. Conversely, I expect that if somebody shot these questions at me verbally, I'd be slightly slower than Karolina.
We've seen and heard simple addition, multiplication and subtraction facts enough times that working them out is practically automatic. I tried to model exactly what happens in my visual head as I work out addition and subtraction for any pair of two digit numbers. I have a 10x10 grid of numbers burned into my head.
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When I want to perform a subtraction, say 79-26, I start at 79 in the grid. Then I move 6 up and 2 left. For three digit numbers I imagine a 10x10x10 cube. For four digit numbers, I'd probably just use a calculator! Addition works the same way, except I go right and down instead of left and up. This is why there is no significant difference between the speeds at which I do addition and subtraction. A few of my friends I have asked claim to be significantly slower at subtraction than addition because they know the addition facts much better than the subtraction facts. If somebody gave them a subtraction, they convert it into an equivalent addition fact (9-5 = ? becomes ?+5 = 9) because they can just 'look those up' inside their heads that much faster.
I'd be curious about how other readers do arithmetic in their head. I was once speaking with someone, who said that they count on fingers in their head. Like my grid above, they always saw a pair of disembodied hands and they counted fingers on those as necessary. Some claim that it is essential to quit finger counting to get good at math. The good thing about doing finger counting in your head though, instead of with your hands, is that you can have more than two hands! You can store temporary results and carry values on as many hands as you need, making them, in effect, like registers on a CPU.
Admittedly, thinking about your own mental arithmetic style is just the kind of navel gazing that happens only after you stop needing to do math frequently in your head. If you're in grade school though and you really think about it (and play hopelessly nerdy games like Brain Age on the Nintendo DS I am sure you own), you can really kick some math butt.
Posted by Vishy at November 19, 2006 11:55 AM