iad58 | Zen and the Laws of 'Rithmetic (Reply)

This article about mathematics in French schools (thank you,

mura_vey!) brought to my mind the winter of 1998, when I was teaching Artificial Intelligence at the University of Limerick (yes, the same Limerick as in ‘There was a Somebody from Somewhere’*). In the final (written) exam there was a problem that involved the evaluation of several simple arithmetic expressons. Here is one of them.

100 + 5 × 3

I took the exams home (that is, to my room in the hostel where I was staying) to mark.

When I first saw the value 315 (as in 100 plus 5, then times 3), I thought it was a technical error, a lapse of attention. Such things happen; I've been known to subtract instead of adding, or to multiply a weight by another.

Then I saw it again. And again. And again, and …

There it was: the greater half of the class didn't know that multiplication ranks higher than addition!

It was a MSc course, too. Some of the students had just got their BSc degrees, others had worked in industry for several years and returned to university because their companies wanted them to have a higher degree. Now Limerick isn't exactly the intellectual capital of the world, but still it's one of the places that Ireland counts on for providing her with engineering potential. And this is second-grade matter!

My mind couldn't hold this, I had to tell someone. I wrote the expression on a strip of paper and ran downstairs.

It was the middle of the afternoon, and most people were out and about. I only found one person in the kitchen, a German girl. I showed her the note and asked her what this amounted to.

Then came the other half of the shock. She said ‘315’.

Upon further inquiry she turned out not to have heard of such a thing as a hierarchy of arithmetic operations. Nor was she dismayed to have been found less than fully informed in this matter. I forget what she was a student of. Something social, I reckon.

I proceeded to the hostel office, where I addressed employee on duty with the same question. The third half of the shock wasn't so shocking; I was getting used to the thought that the planet was ripe for recycling. However, this woman wouldn't put up with her disgrace so easily. After a brief but intense moment of thought she spoke thus: