### Reinvention

Back in second grade, I was dissatisfied with the algorithm we were being taught for doing subtraction. So I “invented” my own

– 185

5 is bigger than 3, so we subtract them in the opposite order (5–3=2) and take the tens-complement (8) of the result. As usual, we borrow from the 6 (which becomes a 5) and we repeat: 8–5=3 and take the tens-complement (7). Finally 2–1=1, so the answer is 178.

While only slightly different from the conventional algorithm, I felt this one to be an improvement because I never had to know how to subtract from numbers larger than 10 (*e.g.* who cares what 13–5 is?).

I haven’t thought much about this little juvenile act of rebellion until a couple of months ago, when I was going over my daughter’s 3^{rd} grade math homework with her. She was doing similar subtraction problems. But, in keeping with the times, she was charged with *explaining* her methods for arriving at the answer.

Imagine my surprise when she explained her method to me. It was exactly the same “unconventional” algorithm that I had used when I was her age. It was not what the teacher had taught; she had figured it out on her own.

[Her method was the same, but her accuracy was not the greatest. So I taught her the other trick that I learned in that era: check your work by doing arithmetic *modulo 9*: 178=1+7+8= 7 mod 9, 185=1+8+5=5 mod 9. So 178+185=5+7=12=1+2 = 3 mod 9, which agrees with 363=3+6+3=3 mod 9.]

Now, I don’t know what this has to do with Larry Summers’ remarks on the dearth of women in the Hard Sciences (at least in this country). My personal experience echoes that of the AIP Study. An alarmingly large majority of the women who arrived at Harvard the year I did, intending to major in Physics, had decided by sophomore year to do something else. As a consequence, it was unsurprising that, by the time I started graduate school, there was only one woman in an entering class of 28. Sean Carroll takes on the thankless task of confronting Summers hypotheses with the data. I’m afraid I can’t muster the energy.

I’m much too busy trying to nurture that spark of creativity in my daughter, hoping that, a decade from now, she doesn’t face the stark choice that my classmates at Harvard/Radcliffe faced a generation ago.

Posted by distler at February 23, 2005 4:28 PM
## Re: Reinvention

I am surprised you don’t mention another Harvard man’s approach to a similar problem.