With grateful appreciation for the translation bymy dear Brazilian friend and mentor Maria Carmen Gambliel

Date: Thu, 8 Jan 1998 19:48:35 EST

PUTTING 2 + 2 TOGETHER

American professor comes to Brazil to speak about ethnomathematics - which empowers the culture of various cultures - whose premises were formulated by a Brazilian

In the early 1980s, the American professor Daniel C. Orey went to Guatemala to teach Mathematics and English. He was surprised and fascinated by what happened. It was obvious that he saw he had to teach. However he soon realized the extent of what he had to learn in that Central American country.

Daniel told this on his last trip to Brazil, where he worked with Math teachers of the Pueri Domus School, in São Paulo. In 1981, he took a job at the Colégio Americano in Guatemala City. . In the capital city, and in his trips inland, he found out something new: that country's natives, heirs to the famous Mayan civilization, did their most trivial calculations using three Mathematics: the metric, English and Mayan systems.

Daniel is the kind of "gringo", as he likes to say, who is enamored of Mayan, Aztec, and other cultures from all over the world at all times. ("Did you know, he says very excited, that the Aztec calendar has the face of a computer diskette: the very first computer diskette in the history of humanity!").

During his weekends in Guatemala he enjoyed travelling with his friends throughout small villages and cities in the interior of the country. Those were very violent times, and along the Panamerican Freeway, he witnessed plenty of abuse, bodies of Indians massacred in terrible genocide, hardly ever mentioned by the worldwide press.

This was very sad - But this American man of the world loved getting to know those small town markets where one could ask ten tomatoes or for one hand of tomatoes, like and old Mayan would. He also realized that at a Guatemalan tailor's shop you might order fabric by the meter, yard or "barra" - a Mayan measurement unit. ("And in California - Daniel adds ironically - we are used to a single mathematical system. In fact, children in American schools have problem even with the English system, while the Guatemalan Indians do well with three systems".).

But how is this Mayan mathematics? Daniel explains that like in the Aztec system, Mayan mathematics is based on the numbers 5 and 20. One of its characteristics is a set of geometric drawings, of mathematical and mystical meaning.

Cultural Basis - You will be able to learn these things only after gaining the Indians' confidence.

It was after his return to the United States that Daniel became acquainted with Professor Ubiratan D'Ambrosio's ideas.

Nowadays, D'Ambrosio, 64 - professor emeritus at UNICAMP - is, side by side with Paulo Freire, one of the Brazilian masters most well know in the world. In the 1970s, he elaborated the basic premises of a new field of knowledge, ethnomathematics. Professor D'Ambrosio explains ethnomathematics as follows: "We must deals with mathematics from within a cultural system. Well, there are old civilizations everywhere. But the mathematics taught in schools never recognizes this cultural diversity. It has always been the mathematics from the Mediterranean, Greek, Roman, and a little bit of Egyptian. But each culture that has ever flourished in the planet developed a way of measuring or explaining the universe and its methods of quantification. Ethnomathematics, from a historical perspective, seeks to recover these cultural bases.

And the master goes on: In China, if you wanted to talk to a child, you will not bring up only Euclidean, Greek Mathematics, you must talk about the Chinese. If you are among an Amazonian tribe, talking about Euclid and Plato will not help. Their ancestral culture, and not these people, interests them. And how are you going to connect a learning experience for these children with things so absolutely meaningless to them? Tossing out Euclid and Plato on the Indians is to continue the process of colonization.

Summarizing, Professor D'Ambrosio presented his work in the United States and Europe, gave several seminars and Daniel Orey - excited by new ideas and seized by his passion for the multiple cultures in the world - participated in one of them. One of D'Ambrosio's quotes that influenced Daniel the most is "from the pedagogic point of view we recognize that experiences come from a particular culture. And, therefore, these children develop their own means of explaining and understanding things. All of this cannot be overlooked at the moment the children begin school. All learning experience must be based on the child's experience, which is rooted in her cultural base. Ethnomathematics is nothing but this."

The follower - Daniel told D'Ambrosio one of his childhood stories in the United States, when he had a wonderful teacher. "When I was a kid, I had to run and pace a lot in order to learn anything, because I was very hyper and had too much energy. So, my math teacher made me walk in the classroom or in the schoolyard. I talked as I walked with the table of facts in my hands "four times four: sixteen" five times five: twenty-five. It is very important for the children that the teacher understands these needs. However, too many teachers do not acknowledge them, especially math teachers. I always remember my calculus teacher from his back, on the board, and I never got to see his face. We only saw the teacher's face during tests. How could we like math?"

Professor D'Ambrosio explained to his students - Daniel among them - that it is necessary to understand the student in front of you. "But the math taught in the schools ignores the whole history of the child, from her personal experiences to her culture. Well, these pedagogic issues affect not only ethnomathematics, but also education in general, when they relate to the individual's ways of quantifying, comparing, classifying - things that happen spontaneously in the life of a child, from birth. As the child grows, she/he develops all this knowledge. Upon arriving in school, this information is already organized, allowing her/him to deal with her/his environment. The role of the school is to provide the students the tools to improve their ways if dealing with the environment.

Culture and Technology - Daniel was very happy when, around 1981, while in Guatemala, he learned about Paulo Freire's work. Shortly after his return to the U.S., in New Mexico, he met his future master Ubiratan

D'Ambrosio. He found it good and interesting for an American to learn things from a Brazilian. (Let us keep in mind that Daniel, as an universalist, has no feelings of domination.)

"It is good that professor D'Ambrosio can change the ideas of the Americans, because we have many different cultures in the United States. For instance, in Sacramento (where he directs the Center for Teaching and Learning at California State University) we have more than 150 different languages and our schools, which operate in thirty languages, which is feat in itself. The majority of our California schools are bilingual. Ethnomathematics is an excellent tool, because it takes the cultures of Asia, Latin America, Africa and the culture of other places into consideration when we teach mathematics. Daniel tells us about a political situation of interest of ethnomathematics.

"Some ten years ago, as a result of the war in Southeast Asia, a large number of people from Vietnam, Cambodia and other countries entered the United States. Among them were many young students who had learned to do math operations according to the French system, which is different from ours. When in class, in a typical United States school, these students heard their teachers say things like this: "This is wrong, this is not our system." Ethnomathematics is important to show new teachers that new ideas coming from others are neither bad nor good, they are just different."

Daniel Orey and his students at California State University, where he is a Ph.D. in Multicultural Education and Mathematics Education, are conducting research on the impact of "changes in culture and technology" on teaching. He has a homemade example to share. A few years ago, his son - like millions of other boys in the whole world - wanted to learn how to read from the video game adventures of the famous character in Mario Brothers of great following in Brazil. "My son used to come to me with questions on what was written on the screen to help Super

Mario. On the other hand who own neither a Nintendo computer nor Super Mario and we must have and educational plan for them. Nothing is more important than equality of access to knowledge."

Daniel likes to think mathematics by using everyday life objects.

Games and Play - He gathered a group of professors of ColÈgio Pueri Domus in a classroom where they sat on the floor to play with a collection of plastic and metal lids of different sizes and colors. It had nothing in common with old time math classes taught by a cranky teacher with his back to the students, like the one Daniel remembered earlier. It seemed unlikely that in that rooms there were teachers from all over Brazil, to participate in one of the frequent professional development meetings sponsored by Pueri Domus for its 77 associated schools. If you think a meeting of teachers is a sluggish, boring, tedious thing you have not seen it yet. That meeting was so funny, and playful that we could imagine that Daniel Orey and the others were playing on the floor, like boys and girls in Kindergarten.

Even Maria Teresa Búrtolo - a Teréco - professional development coordinator of Pueri Domus, who says she has never got a grasp on math, loved it, was "delighted" with everything.

According to Maria Teresa, Orey likes to work with affordable materials of people's everyday lives, he even likes to work with trash. Using those materials, he searches for the attributes of the objects. "He worked - explains TerÈco - with lids of all sizes and materials, and of all colors. He explored concepts of size, color, materials, thickness, weight and shape. He also explored concepts of classification, serialization, sequencing, set, intersection, and value, besides performing operations involving addition, subtraction, division and multiplication. From that point on, Orey also worked with graphs. Finally, the game of lids created challenges among the teachers. And we began to extract concepts from the proposed problems."

The educator finalized by saying that "If I were a journalist and needed to find a title for Daniel Orey's classes, I would come up with something like this: "Playing with Mathematical Concepts", or "Playing and Learning Math", or "Mathematics Is Not A Can Of Worms".

D'Ambrosio says that "one of the main goals of ethnoculture relies on the teacher's ability to enrapture the student and discover what are her/his interests and curiosity. Furthermore, on the teacher's ability to avoid subjecting the student to his/her speech often conditioned by curricula. Students are curious, creative, restless." Here is where we can find step number one of the learning process.