Literacy, Matheracy and Technoracy - The New Trivium for the Era of Technology

Ubiratan d’Ambrosio



In the taped lecture he prepared for ICME 9, Paulo Freire recognised that Mathematics is intertwined with all forms of human behaviour and that there is a mathematical way of being in life. He essentially recognises that his program of Critical Literacy cannot be complete without the recognition that mathematics underlies human and societal behaviour. This goes much beyond the acquisition of mathematical skills.

In this Paulo Freire Memorial Lecture I will discuss, under the inspiration of his ideals, the role of Mathematics in building up a new civilisation which rejects inequity, arrogance and bigotry.

Mathematics, history and education

The nature of mathematical behaviour 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 civilisation. For this we have to look into the history and geography of human behaviour 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 civilisations 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 increasing interdependence that crosses space and time, of cultures and civilisations and of generations.

Education is a strategy created by societies to promote creativity and citizenship. To promote creativity implies helping people to fulfil their potentials and rise 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 civilisation 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.

My role as a mathematics educator

The strategy of educational systems to pursue these goals is the curriculum. Curriculum is usually organised in three strands: objectives, contents and methods. This Cartesian organisation 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.

To agree on objectives is regarded as the political dimension of education. But very rarely have mathematics contents and methodology been examined under this dimension. It is generally accepted that contents and methods in mathematics have nothing to do with the political dimension of education. Since mathematics is the imprint of the Western thought, our responsibility as mathematicians and mathematics educators is a major one.

I see my role as an Educator and my discipline, Mathematics, as complementary instruments to fulfil those commitments. In order to make good use of those 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.

The proposal

It is difficult to deny that Mathematics provides an important instrument for social analyses. Western civilisation entirely relies on data control and management. Social critics can not be proposed without an understanding of basic mathematics. But regrettably the term "basic" has been abusively identified with critical skill and drilling.

The proposal of this paper is a reorganisation of school curricula in three strands: Literacy, Matheracy, and Technoracy.

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

The move towards a new civilisation

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 civilisation, with peace and dignity for the entire mankind. Aren’t these the most fundamental principles to which we subscribe? Regrettably, these documents are short of being unknown to most mathematics educators.

It is an unrelinquishable duty to co-operate, with respect and solidarity, with all the human being, 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; co-operation with the other. This leads to quality of life and dignity for the entire mankind.

Quite unusual as a piece on Mathematics Education, many will say. But if we do not accept, very clearly and unequivocally, our general and global professional commitments subordinated to a global ethics such as the proposed ethics of diversity, it is very difficult to engage in a deeper reflection of our role as mathematics educators.

It is impossible to understand the process of exclusion of large sectors of the population of the world, both in the developed and undeveloped nations, without 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 persist in former paths and styles is irrational and may lead to disaster. Maybe the real threat to humanity are not people looking for aliens coming in UFOs, but are the earthlings nostalgic of a fading order anchored in inequity, arrogance and bigotry. Mathematics has everything to do with this past. A new world order is urgently needed. Our hopes for the future depend on learning – critically! – the lessons of the past.

Ethnomathematics programme in history and epistemology, with its intrinsic pedagogical action, is a proposal motivated by the commitment to fulfil these responsibilities. With the growing trend towards multiculturalism, ethnomathematics is recognised as a valid school practice, which enhances creativity, reinforces cultural self-respect and offers a broad view of mankind. In everyday life, ethnomathematics is increasingly recognised as systems of knowledge, which offer the possibility of a more favourable and harmonious relation in human behaviour and between humans and nature.

As History of Mathematics goes, there is need of a broader historiography. History of Mathematics can hardly be distinguished from the broad history of human behaviour in definite regional contexts, recognising the dynamics of population exchanges. This is a way of identifying the origin of exclusion of populations and entire civilisations through denial of knowledge, which allows for the proposal of corrective measures. By looking into the bodies of knowledge which have been integrated in the syncretic evolution of Mathematics, Ethnomathematics allows for a better understanding of the cultural dynamics under which knowledge is generated. The proposed historiography can be seen as a transdisciplinarian and transcultural approach to the History of Mathematics.

The denial of knowledge that 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.