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## Dominique Vellard

**Minutes of the meeting of the 10th of March 2005, on the works of Dominique Vellard**

Were present : Sophie Desrosiers, Robin Jamet, Agathe Keller, Alain le Mignot, Eric Vandendriessche and Dominique Vellard.

Dominique Vellard started informally by telling us about her story. She was a math teacher at the young women’s school of Bamako ( Mali) in the middle of the 70’s when she first questioned the knowledge that her students possessed. At the time, as it still is very much the case, they tought math in French with French textbooks : every thing was different the context of learning and the people to whom the textbooks where adressed, but everything had to be done like in France. Back in France, she did a masters in mathematic’s teaching (didactic) and then met Françoise Héritier (a famous french anthropologist) who told her about ethnomathematics, which didn’t really exist at the time.

This is how she got involved in an adventure which brought her to do research on the logics of games in Rwanda, mental calculations in the Bambara language ( Mali- the article

Vellard, D. (1988). "Anthropologie et sciences cognitives : une étude des procédures de calcul mental utilisées par une population analphabète." * Intellectica* 2(6) : 169-209

and her PhD describe this field work), then to do field work in Canada with the American-Indian population of the North West. In a conference she met a Mixe activist who was attempting to revive his culture by reviving the Mixe language. The field work done there is presented in

Vellard, D. (1999). Collaborative Reasoning : How a group of speakers Retrieve Collectively the Cognitive Meaning of their Traditional Numeration. *European Conference Cognitive Science (ECCS)*, Istituto Di Psicologica,

All the documents concerning the Mixe field work where lost, remains only a 15 mn film on a VHS tape.

She is now working with a community of saleswomen in Togo. She would not only like to do some field work with them, but also to organize a group of Togoleese students to initiate an ethnomathematical awareness in Togo.

Dominique Vellard’s work is characterised by dialog and collaboration. She prepares her field work with semi-organized dialogues, aiming to share knowledge. Her reflexion rests upon language, and her field work can be seen as an attempt to help isolated and minority communities to recover and preserve their culture by preserving their language. Mathematical culture is but one aspect of a larger, global problem.

Agathe Keller bickers about several aspects of the 1999 article. Dominique Vellard explains that it is a poster. A. Keller asks what is Dominique’s idea of the historicity of computing in base 20. Should we really consider that in the past the Mixe really used a pure base 20, and that all the communities used the same methods ? And how can we be sure that the cognitive process is the same ?

Dominique Vellard explains that her idea was essentially to describe how *collectivally* the (re)discovery of a method of computation was elaborated. For the historical part, she used a collection of texts that her Mixe colleague handed to her, which dated back to 1733, which describes how the Mixe counted. She confronted this with the testimony of one villager. The villager used exactly the same system as the one found in the 1733 record. Dominique Vellard thinks that probably the Mixe that evening really recovered ways of noting and naming numbers that where used longtime back, even at the times of the Maya. Sophie Desrosiers adds that on her own field work she has really seen and established such a continuity : you can find weaving models that run back to préhispanic times still used today in the Andes. She also adds that you do need to study the history to be sure of this, of course.

Agathe Keller asks if Dominique Vellard has noticed in her field work ways of counting with hand, arm or feet. Dominique Vellard explains, because there has been a misunderstanding, that the bits of wood and stone in the Mixe article are used to reproduce Maya notations, and not used to count. Dominique Vellard insists in fact that mental computations are always very abstract (do not use the body). Only once in Zaire did she observe gestures linked to computations.

Sophie Desrosiers tells the story of a French junior high school student, passionate about mathematics, who has develloped his own system of computation which often conflicts with what he is tought by his math teachers : conflicts in mathematical culture do not exist only in Mali or in Mexico.

Eric asks how does one transmit mental computations in Mali : are children left alone to devellop their own systems ? Dominique Vellard explains that she has seen but a limited number of algorithms. People are quick or slow but always use the same system.

Agathe and Sophie ask her questions on her protocol : how many people did she interview in Mali, in Mexico, in what regions, for how long etc. Dominique Vellard explains that she is interested in quality interviews not into quantitative studies. The aim wasn’t to exhaust all possibilities, and Françoise Heritier agreed with that. Sophie Desrosiers replies that quantitative informations provide specific information that can help other people to complete her work, which if not as time goes by cannot be used anymore. Dominique Vellard comes back then on the conditions of her field work in Mali, and her search for a community which would speak pure Babmbara. She once again explains the importance of preserving minority languages and scientific knowledge. Agathe Keller adds an Indian flavor to the question of oppressed minorities and their scientific knowledge : in India these movements are often linked to political parties sometimes left-wing sometimes close to religious activist or to the right. She asks if in Mali, the ethnoscience question of tackling with the issue of the truthful knowledge (or un-truthful knowledge) of the beliefs collected is raised. The discussion then takes off on the benefits of cow urine.

Dominique Vellard comes back to the way reasonings are inscribed into syntaxic, linguistic patterns. She explains that in the eighties in Rwanda and then in Mali she studied the way reasonings where expressed, when playing games especially. She explains that such studies enables one to translate with more accuracy mathematical reasonings. She gives the example of the double negation. In English, French and Bambara it works as an affirmation. Not in Spanish. Agathe Keller asks Alain Le Mignot if this is logic. Alain Le Mignot says it is. Discussion then turns on the frontier between natural languages and mathematical language. Dominique Vellard explains the positive effect of using natural languages to translate mathematical reasoning, rather then using a foreign scholarly language (like French in Mali). Agathe Keller remarks that the question of translations of ideas and concept is a classic of the history of mathematical transmissions.

Eric Vandendriessche comes back to the Mali article, to try to understand what is « experimental anthropology ». For Dominique Vellard, it is semi-organized dialogues. Sophie Desrosiers highlights that the frontier between participative observation, formal interviews and experimentation is often hard to describe. Experimentation is often used at the end of a field work, when you understand a system but some elements are still missing. Then you ask questions or create experiences to fill in the gap.

Eric Vandendriessche is also interested in the question of understanding what values represent. As a teacher he has often realized that students do not always realize what a value they obtain represents in the real world. Alain Le Mignot thinks that this is linked to the school context : students/pupils do not think the concret caracter of what is represented in a problem. Dominique Vellard tells a similar story on Mali ? Togo ? where the transposition of problems linked to work didn’t work with adult students.

Eric Vandendriessche regrets the fact that Stella Baruk who has worked on such subjects is not here.