It was still dark. Like most parents, mine were eager to spend the better part of their Saturday mornings in bed, except on the mornings when my dad had a yen to hit the trailhead early. At six years old, I was incapable of sleeping in past seven.

It was 1981. Space Ghost took turns with the standard stable of Warner Bros. characters on the giant and brilliantly-lit Curtis Mathis console television that dominated our tiny living room. The volume was turned down very, very low so that the sound wouldn't wake my mother, snoring away on the couch in the next room.

My attention wasn't on the TV screen, but rather on the toy I held clumsily in my hands, the Texas Instruments Little Professor, several ounces of hard yellow plastic skin surrounding high-tech electronic guts. Made to help children drill themselves on arithmetic, the toy spat out problems involving addition, subtraction, multiplication, and division. By then I'd learned the first three operations and begun to master them, but was still befuddled by the fourth.

On that morning I drilled myself with multiplication for a while (I'd only just learned that one), working problem after problem as the Little Professor added points and upped the difficulty of the problems it gave me. I missed a few here and there, but it wasn't long before I bored of that operation and decided to move on to something more challenging.

I'd not yet figured out division. Addition and subtraction were old hat, and multiplication I'd learned by conceiving of it as repeated addition, the only means I then had of computing products of multidigit numbers, being at that time unfamiliar with the formal method of "long" multiplication. But division? Fuhgeddaboutit.

That morning I had a hunch I wanted to follow up on: I suspected that just as subtraction served as an inverse operation to addition, "undoing" what addition did, division must serve as an inverse to multiplication. Thus, for example, if 6 x 8 were 48, a request to divide 48 by 6 would be answered by finding the number of sets of size 6 it would take to comprise all of 48 when unioned together. (I'm sure that I wasn't able to so clearly and succinctly summarize the process at the time, but my recollection of those general thoughts is quite clear, even now, nearly three decades later.)

Simple enough in principle, the details of this inverse operation were hard for me to carry out as soon as the superset had more than a few elements in it. Therefore when I switched the Little Professor over to division mode, the only questions I was able to answer unfailingly at first were those in which the divisor was 1. Nevertheless, my success with these simple problems lent credence to my theory regarding division's nature.

After a good deal of trial and error and after even more practice in the quick computation of products that it took me to "unwind" the multiplication once more to obtain the quotients I sought, I began to get better. Soon I was able to tackle the problems in which 2 appeared as the divisor, counting the number of 2s it took to make up the dividend I was given. Soon after that, 3s posed no problem, and I was on to 4s, 5s, and beyond.

My method was clumsy: it would be a long time before I learned long division, and until that time I'd have to resort to the protracted multiplication through repeated addition, done backwards, in order to solve even reasonably complicated division problems.

But I'd done it. I'd fucking done it: I'd uncovered the mystery of division.

The revelation was too exciting to keep from my mother, and I ran into the room next door to wake her and show off what I'd done. Obviously I can't recall her exact words, but I'm sure they were something along the lines of "that's nice, kid. Show me in a few hours, when normal people are up."

I'd hardly be human had I not felt a jolt of euphoria on making the discovery I'd made for myself, for I believe that much of what makes us human is our desire to seek order and understanding of the world around us. There's no high on Earth like the one that making such a discovery gives.

N'est-ce pas?

## Tuesday, August 25, 2009

### The Little Professor

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## 5 comments:

I don't remember what I had for lunch. How do you remember three decades ago??

Omigod, it's finally happened. I've turned into my mother.

Fabulous entry, Patrick. I really enjoyed the narrative... it's interesting how kids learn math.

I almost think that learning methods like long division are a shame. Sure it's a great tool, but for so many kids the subtle logic behind it can further the idea of some "mystery magic" they believe to be math. And it's so easy to then accept individual facts they learn in math class at face value, without trying to look for some underlying reason or order behind it. So much so, that I think many kids begin to ride on memorized facts throughout their education. Eventually, because math tends to build new ideas off of old ideas, there comes a point in their math studies at which there are too many facts to memorize and keep track of. Since they never strived to understand and digest the ideas behind what they were learning, everything breaks down, and they feel as if they are at an impasse between their own intellect and some unknowable "magic mechanics" behind math. Even though things like long division need to be taught for convenience's sake, I hope modern improvements such as calculators and computers can share more and more of the burden of time efficiency in order to allow teachers to focus on helping kids understand more, and blindly accept less.

Update: I just lost my bidding war for a TI Little Professor on EBay. Bummer.

Even though they were before my time, I grew up with one that used to belong to my siblings. I think we were just about to give it away. If we still have it, I know who to give it to.

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