The Incredible Shrinking Attention Span

There was once a kid I went to elementary school with. He was in the fifth grade while I was in the sixth, but the way our school was arranged, we often had classes together. One day I found myself conversing with this friendly-enough student. I don’t even remember what it was that I was saying, but I was talking directly at him and looking at him. And he was listening to me, looking back at me. I was right in the middle of what I was saying, though, when his face suddenly drew a blank and he simply turned away, no longer paying attention to me. He didn’t intend to slight me, I’m sure, but I was so miffed by this apparent rebuff to one of my rare friendly communication attempts that I never did try to talk with him about anything again. And later, after going over “across the field” to another school and the seventh grade, I never saw him again.

It is easy to take it personally when encountering someone suffering from a deficient attention span. As I went through life and kept encountering examples similar to what I experienced in school that day forty years ago, it dawned on me that one of two things must be true. Either a lot of people had incredibly short attention spans, or I was gifted with an incredibly long one. After reading the late, renowned science fiction writer Robert Heinlein’s critical opinion about the state of education, I am tempted to side with the former possibility over the latter.

In one of his notes, published posthumously, Heinlein claimed that it used to be commonplace for math students to be able to express products of two two-digit numbers by simple mental calculation, without the aid of pencil and paper. Although I could do this as well, I also knew that very few around me could. Whenever I would perform this “trick” for others, people would react as if I were either a genius or a magician. But the technique for doing this is painfully simple. All you have to be able to do mentally is be able to store a four digit number temporarily in memory and then add it to the sum of two four-digit numbers.

For example, take a “difficult” problem:

What is 93 x 67?

By simply breaking down the “paper” multiplication procedures most everyone already knows (using distribution), a quick mental shortcut can be devised:
--------------------------------------------------------------------
A) Multiply the tens together and the units together, then adding them to each other by “merging” them in a 4-digit number:

9x6=54
3x7=21
5421

B) Store “5421” in temporary memory (in your brain, not a calculator). Now reverse the units in the two numbers being multiplied, multiply the digits in each number, add them and then add a zero:

93x67
97, 63
9x7=63, 6x3=18
63+18=81
810

C) Now recall from your memory “5421” and add

5421+810=6231
---------------------------------------------------------------------
The instructions seem much more complicated then the actual procedure which, if drilled anywhere near to the extent that written multiplication is drilled in school, would quickly become much more automatic.

I recently mentioned in a comment to a mathematics educator on his blog what Heinlein wrote and that folks commonly used to have this type of skill, which has been allowed to slide over the years until it now seems like a big mystery. His reply was of skepticism and that a feat like this required a rare ability. But multiplying two two-digits mentally only requires knowing the procedure, a little practice, and something resembling an attention span!

It takes an attention span to be able to listen to another, be it in a speech or in a simple conversation. It takes an attention span to be able to read a novel (or even a short story) and store the story’s pertinent information long enough to be able to recall later in reading without having to flip pages back. And it takes an attention span to be a responsible citizen participating in a representative democracy, in order to not allow last-minute flashy or inflammatory, demagogic media spots to play a decisive factor in one’s voting.

Our educational system needs to recognize the need for exercising and developing students’ abilities to focus on different topics, hold them in concentration for a sufficient time, and then be able to recall salient facts from what they have been thinking about. Without using paper, calculators or computers as crutches. And with our ever-increasing emphasis on obtaining close-to-instant results with our nifty 21st century “thought-saving” gadgets, the trend seems to be going in the wrong direction.