12 - 8 = 4

I'd had a few e-mail exchanges with a student about tutoring. Our original schedule didn't fit her schedule, but as more tutors came on board and the schedule was changed she let me know she was coming in. That she did. The tutor did the best he could, what with two other students also being there.

She was having problems converting values between number systems. (It is possible to teach students to convert from decimal to binary in their head. I've done it. They've even done the conversion with negative numbers which seems impossible until you learn the trick. I'm shading the truth a bit. The students do the conversion by having each student act as a binary digit. Each student performs a subtraction and passes the remainder on to the next student representing the next smaller digit. I've wandered afield - back to the narrative.)

All that conversion requires is that the student be able to recognize which of two numbers is bigger (most get that), be able to multiply and subtract. Having spent a long time among technical people I was taken aback when the student needed to use her fingers to calculate the result of subtracting 8 from 12.

I thought she was a joking. Then I saw that she had no feel for numbers: when asked "how many times 4,096 went into 49,000" I expected that she's say "a little more than 12." I never expected her to say, "I dunno" and then start guessing.

Hoo-boy we're in trouble here. She said she didn't like math, I replied that part of the reason that the country was in the financial mess it's in might be attributable to people quite literally being unable to do the math on their mortgage commitment. Her answer was something I never have expected. "Oh, I'd only get a fixed rate mortgage.

Take home message? Maybe a heuristic is an adequate substitution for knowledge. Even so, seeing a college student use their fingers to perform simple math still upsets me. (One exception: computer science students learning once again how to use indexes which begin at zero instead of one.)