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History, Philosophy, and Sociology of Mathematical Education in Teachers Training: a Research Program

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History, Philosophy, and Sociology of Mathematical Education in Teachers Training: a Research Program History, philosophy, and sociology of mathematical education in teachers training: a research program Antonio Miguel Universidade Estadual de Campinas Abstract We present and discuss in this article some features of a research program whose central object of investigation is the way in which the recent fields of history, philosophy, and sociology of mathematical education could take part in a critical and qualified manner in the initial and continuing training of teachers in this area. For that, we endorse the viewpoint that the courses for mathematics teacher education should be based on a conception of specificity through which a new pedagogical project could be established. In such project those new fields of investigation would participate, in an organic and clarifying way, in the constitution of multidimensional problematizations of school practices, in which mathematics would be involved, and that would be guided by academic investigations about the issues that currently challenge teachers in the critical work of incorporation, resignification, production, and transmission of mathematical culture in the context of the school institution. Keywords Mathematical school education - Teacher education - Basic education. Contact: Antonio Miguel Rua Jader Passos, 374 – c.37 13091513 – Campinas – SP e-mail: [email protected] Introduction knowledge, leading them to conceive society itself, in its totality, as the result of a social In the last years much has been said, construction (Crespi & Fornari, 2000, p. 9-16). both in Brazil and in other countries, about the The independent constitution of sociology of critical and formative potentialities of an organic science as an academic field, in its turn, seems participation of the history of education in the to have occurred in the 1930s in the U.S.A., the school mathematics education, and consequently work of Robert Merton having exerted a decisive also in the training of mathematics teachers influence for such autonomous constitution of (Fauvel; van Maanen, 2000; Miguel; Miorim, the sociology of science, seeing that around 2002, 2004; Miguel, 2001; Miorim; Miguel, 1945 “Merton had already created an approach 2001, 2002; Miguel; Brito, 1996; Katz; in which he identified science as a social Michalowicz, 2004). In a less emphatic tone, institution with its own ethos” (Barnes, 1980, p. there has also been talk about the critical and 12). Finally, the expression sociology of formative potentialities of the philosophy of mathematics seems to have been used for the mathematics for such formation (Bkouche, 1997; first time in the 1940s, more precisely in a paper Bicudo, 1999, 2003; Ernest, 1991, 1994, 1995; by mathematics historian Dirk J. Struik published Garnica, 1999; Jesus, 2002; Miguel, 2003, in 1942 in the Science and Society journal 2004b; Steiner, 1987; Vianna, 2004). Now, under the title On the sociology of mathematics. although there is a fair amount of discussion Since then, social, cultural, or sociocultural these days concerning the sociocultural and approaches to mathematics began to be more political dimensions both of mathematics and of common. Among them, we can highlight: The mathematics education — discussions that have cultural basis of mathematics by Raymond Wilder been taking place above all inside movements in 1950; the works by David Bloor — such as A born in the 1980s, such as those of naturalistic approach to mathematics, ethnomathematics, of critical mathematics Negotiation in logical and mathematical education, and of mathematics education and thought, and Can there be an alternative society (D’Ambrosio, 1990, 2001; Knijnik, 2002; mathematics? — which began to be published in Frankenstein; Powell, 1997; Barton, 1999; the 1970s; and the more recent work by Sal Ferreira, 1990; Gerdes, 1991; Skovsmose, 2001) Restivo, which started to appear in the 1990s, — we cannot identify any written production from which we can mention the article The so- about the equally critical and formative role that cial roots of pure mathematics1 . It is also from could be played by the so-called sociology of the 1970s the suggestive Sociology of mathematics in the education of mathematics Mathematics and Mathematicians by J. Fang and teachers. K. P. Takayama (Fang; Takayama, 1975). Although discussions about the relationships between thought and society have The emergent research fields in surfaced at least since the late Renascence, the history, philosophy, and sociology has only constituted itself as an sociology of mathematics autonomous and scientific area of knowledge in education the 19th century with the appearance of the Comtean positivism. The sociology of knowledge To talk about the history, philosophy, and produced its first developments in the 1930s, the sociology of mathematics is, in our view, quite moment when sociologists such as Schütz, Merton, Berger, Luckmann, and Searle 1. All these works have been translated to the Portuguese by the members recognized and began to consider the circularity of the TEM (Theory of Mathematics education) Research Group of the Uni- versidade Nova of Lisbon, Portugal. The reader can find these works in the of the relationship between society and reference (TEM, 1998). different from talking about the history, seems that only in the 1980s it began to be philosophy, and sociology of mathematics constituted as an autonomous field of study. education. Although mathematics, since Antiquity, According to Bicudo (1999, p. 22), the first work has been the object of historical studies2, and with the title of philosophy of mathematics although we have knowledge that histories of education was Eric Blaire’s doctoral thesis, mathematics began to be written since that time, presented to the Institute of Education of the it was only at the end of the 20th century that University of London in December 1981. But it the first studies related to the history of has been mainly thanks to the work developed mathematics education began to appear3. by Paul Ernest, a professor at the School of We know that since Antiquity mathematics Education and Lifelong Learning, University of has been the object of reflections and isolated Exeter, U.K., that this field has been kept in good philosophical studies. According to Fang & development. In fact, Ernest is the editor of the Takayama (1975, p. 33), Philosophia mathematica international electronic journal Philosophy of was the title given by Erhard Weigel to a book he Mathematics Education Journal, which since had published in 1693. To those authors, the 1990 has been publishing and publicizing studies contents of this book, of a certain theological and investigations in this field4. slant, said very little about “philosophized As far as we could ascertain, it was only mathematics or about mathematized philosophy”. in 1998 that a work appeared bringing in its Still according to them, the dubious title of title the expression Sociology of Mathematics Weigel’s work could be translated in two different education. It is the book entitled The Sociology ways: as ‘philosophical mathematics’ or as of Mathematics Education: Mathematical ‘mathematical philosophy’, expressions that would Myths/Pedagogic Texts by Paul Dowling, a nowadays be representative of two different disci- sociologist and professor at the Institute of plines or fields of investigation. The first of them Education of the University of London. — philosophical mathematics — would be a proper In the preface to Dowling’s book, its domain of mathematicians, since such field is editor, Paul Ernest, explains in the following generally seen by that community as being created manner the emergence of this new field of study: by taking as its object of study theories potentially ‘mathematizable’ or ‘formalizable’ in the sense of With its roots in mathematics, psycology and being possibly capable of integrating the field of everyday classroom practice, it might be said mathematics proper. It is in this sense that many that mathematics education is permeated logicians to this day employ the expression 2. Mathematics historians are unanimous in pointing out the fact that philosophy of mathematics, that is, as philosophical histories of arithmetic, geometry, and astronomy have been written at around mathematics. A representative of this conception is 335 B.C. by Eudemo of Rhodes, a member of the Aristotelian school. Because the work The Philosophy of Mathematics published these works were lost, the little information we have about them are due to Proclus, Simplicius, and to Eutocius of Ascalon, commentators of Greek in 1969, in which its editor J. Hintikka compiles mathematics who lived, respectively, in the 5th, 6th, and 6th centuries A.C. several articles about symbolic logics. For Fang & (Miorim; Miguel, 2001, p. 35) 3. In our country, two references must be noted in this respect: (Miorim, Takayama (1975, p. 33), on the other hand, the 1998) and (Valente, 1999). We also note here that from a total of 169 mathematical philosophy could be seen manifestly works published, partially or in full, in Annals of the National and Luso- as a region for philosophers, and would have as its Brazilian Meetings in the History of Mathematics up to 2002, around 20 percent were inscribed in the field of the investigation on the history of object of investigation certain mathematical mathematics education (cf. Miorim; Miguel, 2002, p. 10). At the theories of a speculative nature that would have international level, deserve to be mentioned, amongst others, the works that are being developed
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