She laughed and said she would let me in on a secret

It's a beautiful, old, whitewashed colonial building built around a courtyard whose earth is hard packed by the pounding feet of some 750 little girls. Escuela Diez de Agosto (Tenth of August School) has been in continuous operation since 1918, its name proclaiming the date of liberation for this equatorial mountain nation. Were this primary school in the United States, it might be called the "Fourth of July."

I arrived there the morning of Friday, March 20, with a professional translator. I had asked if i might be allowed to teach a class in "mathematics moderna" (new math).

The director of the school went me one better; she gave all the little girls a long recess under the supervision of two teachers and assembled all the other teachers in a meeting room adjacent to her office.

Portraits of former directors, all women, looked down on us -- Maria Angelica Idrovo (1918-21) appeared the most interested in what was going on.

A teacher (in a white smock) and two little girls (also smocked) brought in a green blackboard, and the teachers sat around in a horseshoe on flat metal chairs, notebooks in hand.

The interpreter, accustomed to doing simultaneous translations during interviews, quickly got into the spirit of the occasion. I gave only the briefest of opening remarks and then drew a number line on the board.

-3-2-1

-- 1 -- 2 -- 3

-- / -- / -- / -- /

/ -- / -- / -- / --

I explained that I knew in Ecuador they did not have the children use negative numbers, only positive, but that it was important for children to learn not only how to count, but how numbers were related to each other.

So far so good -- and even the interpreter was keeping up.

Then I asked how far they thought it was on the number line between negative 7 and positive 1. Most answered 6; the director, Nancy Carrion de Parra, answered 8.

After more discussion on the part of the teachers, they turned to the interpreter and asked: "Why does she ask such a question?"

Yet, in a very short time, I was able to flow back and forth along the line and almost all the teachers were giving the relationships.

It is important to understand that these women had never been given such arithmetic to puzzle out. Instead, they are accustomed to being told rules, copying them down, doing repetitive examples, and providing precisely this type of teaching to their classes.

We moved next to a sentence like the following:

(2X?)-2

Here I tried to explain that a story was in progress and that we must look for patterns and meanings.

By now the teachers were in open revolt -- not in an angry manner, but just like any class of 10-year-olds meeting this type of problem for the first time, finding it essential to talk out what they knew and what they didn't know. But because they were teachers and their public school is one of the best in Quito, they were rebelling against teaching methods that were even more alien than the mathematics involved.

We went on to some graph work with more negative and positive numbers. The interpreter and the director and only a handful of the teachers could keep up, yet at the close of the lesson, they asked for an educational message.

What I said to them was quite what the minister of education said to me the next day.

This is a difficult time for teachers around the world, but particularly for teachers in the developing countries. The children are counting with pebbles, yet we must prepare them for the technical world of computers.

Order, rules, punctuality, concentration, and attention to detail are essential, but so is learning to think, and to be problem solvers.

How they nodded their heads! I was not telling these alert teachers anything new. How to prepare their little girls for a technical society, for a place in world trade, for a bilingual world of commerce -- and still not lose the culture and traditions and grace so deep in their history.

I was presented with a pin and a booklet honoring the school; and I wrote about my visit in the guest book, with a translation by the interpreter.

As we walked down the hill after the children had returned to classes, the interpreter asked me why I, as a journalist, had given the mathematics lesson.

I told her I would let her in on a secret -- that I could learn more about how a school operated and how teachers taught and about the problems a school system had by working with some of the teachers than I could by watching dozens of classes all day long.

She laughed, patted my shoulder, and said she would let me in on a secret: that when the teachers had asked her while I was writing in the guest book why I did that teaching, she had told them (and they had agreed) that I was going to learn more about the school and the teaching methods in Ecuador than if I had watched them teach.