What? A journalist who wants to teach new math at the National Institute of Pedagogy? . . . I might have learned a lot about the sociopolitical climate of Colombia had I been in on the discussions in Bogota which resulted in my being able to teach a third-year class of teachers in training at the national institute.
For me, it was enough that the arrangements had been made, that one of the math department faculty members was willing to translate and was fluent in Spanish and English, and that the head of the department would be sitting in on the lesson.
There were about 25 students and five members of the faculty on hand for the session.
I started off by explaining that I knew they did not teach negative numbers to children in the elementary grades, but that many teachers of new math, particularly in the United States did include negative as well as positive numbers in their lessons.
I further explained that I didn't teach these numbers by rules and memorization, but by concepts and number relationships.
I was, of course, doing this teaching so that I could gain entry not only to the institute, but more deeply into the whys and wherefores of current schooling trends in Colombia. And because so very many Colombian professors have studied in the US, generally working toward advanced degrees, there is less dependence on memory work and drills than in many other Latin American countries.
My class was made up of university-level students, some of whom had already done some teaching in village schools. They were quick to voice their thoughts and to make the lesson something besides a lecture.
At the same time, their resistance to the introduction of negative numbers -- backed up, I must add, by their professors -- was real, and i wondered how I might break through that resistance.
Suddenly I realized I was in South (and not North) America. And so i drew a circle which I called Earth, then drew an equator which they willingly let me label 0 degrees (zero). Then I said, "Suppose we impose a grid or graph on this globe; where's Colombia?"
Ah, Colombia is partly on 0 degrees, but much of it lies south of the equator , definitely in the "negative" zone.
The next morning, with many of those in attendance who had been watching the day before, I taught the lesson i had taught at the institute to a group of 40 fifth-graders in the institute's demonstration school.
The head of the institute's math department had been frank -- he thought my lesson very interesting and that I had used clever ways to get the concept of negative numbers across -- but nevertheless he doubted the young children could really get the concept.
Of course, the children were quick to catch on to negative 1 as a companion number to positive 1, and we were soon able to play a game involving coordinates on a full graph using both positive and negative numbers.
It was the reaction of the teachers and school administrators, though, which was even more interesting than the clevernes and adaptability of the Colombian children.
While much of the school system still has lingering traces of the old French memory system, there is an enormous amount of free thinking, and the kind of teaching that encourages the children to think for themselves.
Even though the demonstration school is a public school and serves a nearby neighborhood, the pupils are selected, and I was assured that "many of the best" teachers are on its staff.
And even though every single public school in the nation is expected to use the same syllabus, the same curriculum, and the same textbooks, this demonstration school is free to try new ideas.
Several teachers went out of their way to assure me that most of the country schools just limped along with almost no materials, and with teachers who had not had any college courses and were graduates of weak secondary schools.
Also, I was urged to understand that education is tied closely to socioeconomic changes and that the present mood of the natin is toward technological and industrial development. And that this, in part, is responsible for the high priority given education in the federal budget (nearly 20 percent); a figure I was told was almost twice that of neighboring Ecuador and Venezuela.
I met, too, with several members of the mathematics faculty at the National University -- all of whom had done graduate work in the US at such institutions as the universities of Maryland, Montana, wyoming, and Chicago.
"What did they see as the coming No. 1 academic problem in Colombia?"
Teaching how to teach was the universal answer.
As one mathematician with a doctorate from the University of Chicago explained: "We only know how to present material -- to lecture, if you will. We don't know how to teach those students who need to be taught. The memorizers have been the only ones who have stayed in school. But now must educate a nation and we don't really know how to teach."
This was confirmed in several conversations with education officials, and also with the executive director of the Fulbright Commission, Francisco Calvo, and by a textbook publisher and consultant to the Education Ministry, Gaston de Bedout.
Dr. Calvo, who also teaches at the national pedagogical institute, explained that the original teacher training program in Colombia was patterned after the French normal school concept but that today there is less French influence and more Ameican.
This is reflected in the teaching of French and English as second languages. French is required for one year, and elective for the rest of a student's time. But English is not only required, but often taken for five years by students at the college level who have already had three or four years of English in secondary school.
When I asked Dr. Calvo about the problem of taking the SAT (Scholastic Aptitude Test) and GRE (Graduate Record Examination) in Spanish, he explained that Colombian students took these exams in English.
Then he proffered a recomendation he feels would be a help to every student who must take these exams in what for them is a second language.
"They should report to the colleges and universities two sets of scores: one score, as is done now, based on how a student scores within the total of those who took the exam, and a second score, on a scale based solely on those who are taking the examination in English, which for them is a foreign language."
For example, let's say that Maria scores 600 out of 800 on the SAT verbal, and this places her in the 70th percentile for all students who took that exam. But let's assume that that 600 is in the 90th percentile of those for whom English is a second language.
Dr. Calvo's plan would be for both scores to be forwarded to all the institutions considering an applicant, providing the admissions office with a truer picture of each student's ability.
Discussions with those felt they had been penalized by the current score-reporting system confirmed wide interest in this possibility.
Everyone with whom I spoke agreed on on aspect of schooling -- standards are going down and not up. Those with children in school who have had children in school over a 20-year span are convinced that the younger teachers are not as good as the older teachers, and that the standard of work is poor.
Yet, Gaston de Bedout, while not disagreeing with that assessment, had harsh words for parents -- particularly those who send their children to the private schools in Colombia.
"They are behind the times," he insisted. "They want the same schooling they had; the same rote examples; the same drills; the same philosophical discussions."
And as others explained, Colombia must meet modern demands, technologically and agriculturally. There are rivers to be harnessed for hydroelectric power. Valleys with rich volcanic soil to be farmed. Minerals to be wrested from a rich earth lode. And a tourist and fishing industry based on miles of stupendous coastline.
As Mr. de Bedout explained, "it wouldn't matter so much how poorly the private schools did their job if they weren't the preparatory schools for the universities. And this is true, not only for students who expect to attend private universities, but those who expect to go on to public universities as well."
A quick look at the statistics: About 13 million children start school in Grade 1; about 7 million go on to secondary school; and fewer than 300,000 enter a university. And the startling figure: Fewer than 100,000 complete their university course. In other words, less than 1 of every 100 pupils who start school in Colombia complete a university degree.
But Mr. de Bedout points out that even with that small number, too many university graduates choke too few professions. The figure he gives is that only 10 percent of the graduates are engaged in work that follows their training.
And the profession that is least desirable? By all accounts, it is education.
But this, too is changing, and there is a growing interest in academic research, in high technology, in advanced engineering, and even in pedagogy. A movement toward more open university opportunities, for example, is growing strong and serving the rural population as well as those cities other than Bogota and Cali.
At the elementary level, 3 of every 10 pupils attend a private school; at the secondary level, this is reversed -- 7 out of 10 attend private schools.
I met several university graduates who had taken their full schooling in the public sector -- "and proud of it," said one delightful mathematics teacher.
But even though the dropuout rate is very large ("a national disgrace"), the emphasis today, and for the next several years, is in the area of quality and not quantity, Mr. de Bedout explains.
"We have not had a curriculum revision since the mid-'40x," and that's our present priority. Following that must be massive retraining of teachers already in place, and improved training at all teacher-training institutes."
And he continued, "The market is changing faster than the study of education. We are failing our people if we do not keep up with the changes, yes, even get ahead of them."
One interesting note about the responsibility that comes with a secondary school education: It's tied in with the national literacy campaign aimed at helping all those over the age of 15 to become literate and to have for their use simple manuals for both agricultural and technical purposes.
Before a student may have a certificate stating that he has completed his secondary school, he must certify, and have it verified by a school authority, that he (or she) has taught a minimum of 15 adults to read and write.