WHY MATHEMATICAL EDUCATORS AND

RESEARCHERS CANNOT IGNORE POLITICAL ISSUES [1]

INTRODUCTION

Political issues deal with government, economics, relations among nations and social classes, people’s welfare and the preservation of natural and cultural resources.

The possibility of final extinction of civilization in Earth is real. Not only through war. We are witnessing an environmental crisis, disruption of the economic system, institutional erosion, mounting social crises in just about every country and, above all, the recurring threat of war. A scenario similar to the disruption of the Roman Empire is before us, with the aggravation that the means of disruption are, nowadays, practically impossible to control.

It is clear that mathematics is well integrated into the technological, industrial, military, economic and political systems and that mathematics has been relying on these systems for the material bases of its continuing progress. It is important to question the role of mathematics and mathematics education in arriving to the perverse behavior of mankind.

After all, the most universal problem -- survival with dignity –- must have something to do with the most universal mode of thought -- mathematics.

I believe that to find the relation between these two universals is an inescapable result of the claim of the universality of mathematics. Consequently, as mathematicians and mathematics educators we have to reflect about our personal role in reversing the situation.

MATHEMATICS, EDUCATION AND CURRICULUM

The nature of mathematical behavior is not yet clearly understood. Although in Classical Philosophy we can notice a concern with the nature of mathematics, only recently the advances of cognitive sciences have probed into the generation of mathematical knowledge. How is mathematics created? How different is mathematical creativity from other forms of creativity?

From the historical viewpoint, there is a need of a complete and structured view of the role of Mathematics in building up our civilization. For this we have to look into the history and geography of human behavior and find new paths in the measure we advance in the search. History is a global view in time and space. It is misleading to see History only as a chronological narrative of events, focused in the narrow geographic limits of a few civilizations which have been successful in a short span of time. The course of the history of mankind, which can not be separated from the natural history of the planet, reveals an increase interdependence which crosses space and time, of cultures and civilizations and of generations.

Education is a strategy created by societies to promote creativity and citizenship. To promote creativity implies helping people to fulfill their potentials and raise to the highest of their capability. To promote citizenship implies showing them their rights and responsibilities in society.

Educational systems throughout history and in every civilization have been focusing on two issues: to transmit values from the past and to promote the future.

In other words, education aims equally at the new (creativity) and the old (societal values). Not irresponsible creativity –- for we do not want our students to become bright scientists creating new weaponry -- neither docile reproduction -- for we do not want our students to accept rules and codes which violate human dignity. This is our challenge as educators, particularly as mathematics educators.

The strategy of educational systems to pursue these goals is the curriculum. Curriculum is usually organized in three strands: objectives, contents and methods. This cartesian organization implies accepting the social aims of educational systems, then identifying contents which may help to reach the goals and developing methods to transmit these contents.

THE POLITICAL DIMENSION OF MATHEMATICS EDUCATION

To agree on objectives is regarded as the political dimension of education. But very rarely has mathematics contents and methodology been examined under this dimension. Some educators and mathematicians claim that contents and methods in mathematics have nothing to do with the political dimension of education.

Even more disturbing is the possibility of offering our children a world convulsed by wars. Since Mathematics is the imprint of the Western thought, it is naïve not to look into a possible role of mathematics in framing a state of mind which tolerates war. Our responsibility as mathematicians and mathematics educators is to offer venues of peace [2].

There is an expectation about our role, as mathematicians and math educators, in the pursuit of peace. The remark below by Anthony Judge, the Director of Communications and Research of the Union of International Associations, express how we, mathematicians, are seen:

"Mathematicians -- having lent the full support of their discipline to the weapons industry supplying the missile delivery systems -- would claim that their subtlest thinking is way beyond the comprehension of those seated around a negotiating table. They have however failed to tackle the challenge of the packing and unpacking of complexity to render it comprehensible without loss of relationships vital to more complex patterns. As with the protagonists in any conflict, they would deny all responsibility for such failures and the manner in which these have reinforced unsustainably simplistic solutions leading to further massacres [3]."

I see my role as an Educator and my discipline, Mathematics, as complementary instruments to fulfill commitments to mankind. In order to make good use of these instruments, I must master them, but I also need to have a critical view of their potentialities and of the risk involved in misusing them. This is my professional commitment.

It is difficult to deny that Mathematics provides an important instrument for social analyses. Western civilization entirely relies on data control and management. Social critics will find it difficult to argue without an understanding of basic mathematics. But, regrettably, the term "basic" has been abusively identified with acritical skill and drilling.

It is an undeniable right of every human being to share all the cultural and natural goods needed to her/his material survival and intellectual enhancement. This is the essence of the Universal Declaration of Human Rights (1948), to which every nation is committed. The educational strand of this important profession on mankind is the World Declaration on Education for All (1990), to which 155 countries are committed. Of course, there are many difficulties in implementing the effectiveness of the United Nations resolutions and mechanisms. But as yet this is the best instrument available that may lead to a planetary civilization, with Peace and dignity for the entire mankind. Regrettably, Mathematics Educators are generally unfamiliar with these documents.

It is an unrelinquishable duty to cooperate, with respect and solidarity, with all the human beings, who have the same rights, for the preservation of all these goods. This is the essence of the ethics of diversity: respect for the other (the different); solidarity with the other; cooperation with the other. This leads to quality of life and dignity for the entire mankind.

It is impossible to accept the process of exclusion of large sectors of the population of the World, both in the developed and undeveloped nations. An explanation for this perverse concept of civilization asks for a deep reflection on the colonial period. It is not the case of putting the blame in one or another, neither to attempt to redo the past. But to understand the past is a first step to move into the future. To accept inequity, arrogance and bigotry is irrational and may lead to disaster. Mathematics has everything to do with this state of the world. A new world order is urgently needed. Our hopes for the future depend on learning -- critically! -- the lessons of the past.

We have to look into history and epistemology with a broader view. The denial and exclusion of the cultures of the periphery, so common in the colonial process, still prevails in modern society. The denial of knowledge which affects populations is of the same nature as the denial of knowledge to individuals, particularly children. To propose directions to counteract ingrained practices is the major challenge of educators, particularly of mathematics educators. Large sectors of the population do not have access to full citizenship. Some do not have access to the basic needs for survival. This is the situation in most of the world and occurs even in the most developed and richest nations.

In order to build up a civilization which rejects inequity, arrogance and bigotry, education must give special attention to the redemption of peoples that have been for a long time subordinated and must give priority to the empowerment of the excluded sectors of societies.

The Program Ethnomathematics contributes for restoring cultural dignity and offers the intellectual tools for the exercise of citizenship. It enhances creativity, reinforces cultural self-respect and offers a broad view of mankind. In everyday life, it is a system of knowledge which offer the possibility of a more favorable and harmonious relation in human behavior and between humans and nature [4].

A consequence of this program for a new curriculum is synthesized in my proposal of three strands in curricular organization: Literacy, Matheracy and Technoracy [5].

Literacy. Clearly, reading has a new meaning today. We have to read a movie or a TV program. It is common to listen to a concert with a new reading of Chopin! Also socially, the concept of literacy goes through many changes. Nowadays, "reading" includes also the competency of numeracy, interpretation of graphs, tables and other ways of informing the individual. And also understanding the condensed language of codes. These competencies have much more to do with screens and button than with pencil and paper. There is no way for reverting this trend, the same as there was no successful censorship in preventing people to have access a books in the last 500 years. Getting information through the new media precedes the use of pencil and paper and numeracy is dealt with calculators. But, if dealing with numbers is part of modern literacy, where has mathematics gone?

Matheracy is the capability of drawing conclusions from data, inferring, proposing hypotheses and drawing conclusion. It is a first step towards an intellectual posture, which is almost completely absent in our school systems. Regretably, even conceding that problem solving, modeling and projects can be seen in some mathematics classrooms, the main importance is given to numeracy, or the manipulation of numbers and operations. Matheracy is closer to the way Mathematics was present both in classical Greece and in Indigenous cultures. The concern was not with counting and measuring, but with divination and philosophy. Matheracy, this deeper reflection about man and society, should not be restricted to the elite, as it has been in the past.

Technoracy is the critical familiarity with technology. Of course, the operative aspects of it are, in most of the cases, inaccessible to the lay individual. But the basic ideas behind the technological devices, their possibilities and dangers, the morality supporting the use of technology, are essential questions to be raised among children in a very early age. History show us that ethics and values are intimately related to technological progress.

The three together constitute what is essential for citizenship in a world moving fast into a planetary civilization.

NOTAS

[1] Presented at the Session on "Beyond the Ivory Tower: The Politicization of Mathematics Education Research", Research Presession of the 77th Annual Meeting of the National Council of Teachers of Mathematics, San Francisco, 19-21 April 1999. Most of the contents of this paper is in my paper "Mathematics, History, Ethnomathematics and Education: A comprehensive program", The Mathematics Educator, 9/2, 1999; p. 33-38.

[2] See my paper: Mathematics and peace: Our resposibilities, Zentralblatt für Didaktik der Mathematik/ZDM, Jahrgang 30, Juni 1998, Heft 3; pp. 67-73.

[3] Anthony Judge: And when the bombing stops: challenge to mathematicians", http://www.uia.org/uiadocs/mathbom.htm

[4] See my paper: Ethnomathematics and its First International Congress, Zentralblatt für Didaktik der Mathematik, ZDM 99/2; pp. 50-53.

[5] See my paper: Literacy, Matheracy and Technoracy: A Trivium for Today, Mathematical Thinking and Learning, 1(2), 1999; pp. 131-153.