Abstract:
Besides presenting some experiences conducted with oral history in mathematics teaching (focusing on teacher formation courses), this text also proposes practical possibilities for classroom practice. Examples of several natures are shown, particularly relating to topics associated with the history of mathematics education. We believe that history, seen as a potent aid in the building of knowledge and because of the richness and diversity of the elements involved in a historiographic operation, enables problematization of some fundamental circumstances which lead us, both teachers and students, to become what we are. Therefore, these historiographic practices, together with oral history, are essential aids in teaching and learning processes (in general and, particularly, in mathematics) when transposed to the educational scenario in a promising and instigating manner. The examples shown must be understood as possibilities for action which trigger perspectives so that each reader, with their own interests, conceptions, and curricular demands, may adapt, transform, and transcend these suggestions, thus creating their own sequences and didactic scripts so as to include history, oral history, and history of mathematics education in teaching and learning processes.
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Notes
- 1.
It is the Universidade Estadual de Campinas (UNICAMP), a public academic institution in the state of São Paulo.
- 2.
It is important to point out that the focus of these activities is always on the study and use of the history of school mathematics, that is, in the ways in which mathematics is revealed in teaching and learning situations, whether in formal instances (such as schools) or not. This is not a study focused on what has been called the history of mathematics.
- 3.
In short, in Brazil, education is divided into several stages of schooling: basic education is composed of early childhood education (optional), elementary school (compulsory), and secondary school (seen as a right of all citizens). Early childhood education is the first stage of basic education, and its main purpose is the development of children up to 6 years of age. Elementary school is compulsory for children between the ages 6 and 14. It lasts 9 years. Secondary school lasts 3 years and is compulsory for those wishing to have university education (higher education). To have access to the higher education, students must pass a selection exam for a specific course. There are public institutions (free and secular) and private institutions which offer all levels of education, from kindergarten to university. Public universities are of two natures: state universities (managed according to the legislation of each state) and the federal (whose responsibility befalls the federal government), both circumscribed minimum requirements as per federal legislation.
- 4.
In Brazil, two majors are offered for university-level courses in mathematics: bachelor of mathematics (aimed at training mathematicians) and the teaching degree in mathematics (aimed at training mathematics teachers). Extramural courses are offered by public and private institutions and follow specific legislation. UFMG is a federal public institution.
- 5.
Brazil was “discovered” in the year 1500, as a result of the Portuguese great navigations of the sixteenth century. The “colonial” period lasted from the beginning of the sixteenth century (in 1530, Portugal sent its first colonizing expedition to Brazil after the discovery) until 1822, when the first emperor is crowned (Pedro I of Brazil, also known as Pedro IV of Portugal), who declared the independence from Portugal. Pedro I abdicated in 1831, in favor of his son. The Republic was proclaimed in 1889, when the then emperor Pedro II was deposed after a 58-year reign.
- 6.
Grupo Escolar (low-school or graded school) were primary education schools, created in Brazil at the end of the nineteenth century, as a result of a policy aimed at emphasizing the initiatives of the Republic, in detriment of the elitism of the Empire. These were urban schools. New strikingly modern buildings were constructed to house these institutions in order to characterize them as “Temples of Knowledge.” The same structure which created Grupos Escolares also provided for the grouping of students according to educational levels. Thus, each grade was housed in a different room, with a teacher for each room, and a schoolmaster for the whole school (a position created as a result of the educational reform). The time spent in school was strictly controlled, and all school activities were duly logged and assessed. Grupos Escolares were created in the state of São Paulo, but they rapidly spread throughout the country. This type of institutions was extinguished in the 1970s, and the buildings were passed on to municipal governments. Nowadays, early childhood educational institutions occupy such buildings.
- 7.
It should be noted that the children involved in this activity were illiterate; therefore the interviews were conducted and shared orally. For the elaboration of the interview script, which will be dealt with next, the children suggested the questions which were registered and organized by the researcher.
- 8.
A practiced place is not merely an existing space but space which is lived, meaningful to those who use it and move around it.
- 9.
As Grupos Escolares were installed in very large buildings, now very old, they are linked to several stories, many of which are fantastic, ghost stories, which children hear and tell, thus creating an urban-legend atmosphere.
- 10.
“Fundaments of Elementary Mathematics,” a mandatory discipline for obtaining a teaching degree in mathematics at Universidade Estadual Paulista, Campus Rio Claro
- 11.
National Curricular Parameters (Parâmetros Curriculares Nacionais, known as PCN, in the Portuguese abbreviation) are official documents developed by the Ministry of Education (thus at federal level) which contain all national educational legislation for public schools throughout the country. Each state of the federation simultaneously issues Curricular Guidelines, which complement PCN.
- 12.
Transcription, textualization, and letter of assignment of rights are steps in the work with oral history. These steps were discussed in a specific chapter in this book. In short, through transcription interviews (conducted orally) are registered in writing; during textualization the written account is refined in order to gain greater fluency and purge the usual oral language idiosyncrasies. Letters of assignment are documents signed by the interviewees, which give the researcher the right to use the textualization.
- 13.
The title of the discipline is “Brazilian Educational Policy.”
- 14.
Pedagogy courses are university courses for training teachers to work at elementary education level. In elementary schools, during the first five years of the so-called elementary education, a single teacher is in charge of a classroom and must take care of fundaments—such as literacy in the mother tongue, counting, elementary operations, and introduction to history, geography, health, etc. (TN: equivalent to a Bachelor of Education in most countries).
- 15.
This discipline is called “Mathematical Content, Methodology, and Teaching Practice,” and is offered as part of the program for a major in pedagogy at Universidade Estadual Paulista, Campus Rio Claro, a large public university in the state of São Paulo.
- 16.
Literature dealing with mathematics education refers to those teachers who have a degree in pedagogy (as this major also deals with introduction of mathematics to students, in addition to other content) as “teachers who teach mathematics,” whereas the teachers who hold a specific teaching degree in mathematics are called “mathematics teachers.”
- 17.
This is Universidade Estadual Paulista, Campus Bauru.
- 18.
Video (freely available) of a TED talk (technology, entertainment, design)—Ideas Worth Spreading—by Nigerian writer Chimamanda Adichie, in July 2009. The author narrates situations from which she concludes that reducing several versions to a single one annihilates life. In her particular case, she claims that this homogeneous form of storytelling has limited her view of her own country and her own people. She goes on to say that when she moved to the United States, her roommate could only see her through the socially created stereotypes about something called “Africa” and that several times, she yielded to the temptation of those hegemonic versions and stereotypes linked to a “country” called Africa. In this narrative, Chimamanda examines various beliefs about Africa and shows how she also gave into the temptation of hegemonic versions. The version used by Gonzales and Martins-Salandim has Portuguese subtitles (https://www.ted.com/talks/chimamanda_adichie_the_danger_of_a_single_story/transcript?language=pt-br)
- 19.
In this text, D’Ambrósio discusses aspects of historiography to examine how it is possible to understand and study certain political issues involving mathematics education through a historiographical approach. It is written in Portuguese and has not been translated into English.
- 20.
Miorim and Miguel (2001) discuss the different ways history has been used in studies about mathematics education, establishing three great approaches that the authors call history in mathematics education, history of mathematics education, and history and mathematics education. It is written in Portuguese and has not been translated into English.
- 21.
The text by Gomes and Brito, published in the oldest Brazilian journal of mathematics education, is a study of all the works related to the history of mathematics education presented at the Brazilian Meeting of Graduate Students in Mathematics Education (EBRAPEM). Written in Portuguese not translated
- 22.
Garnica (2013) discusses traditional and alternative conceptions of history and historiographical practice to propose an updated approach to the history of mathematical education. The text, written in Portuguese, has not been translated; however some of its considerations can be found in the chapter the second author contributed for this book.
- 23.
In this text, Martins-Salandim, Souza, and Fernandes discuss methodological aspects of oral history linking such methodology to the research in mathematics education.
- 24.
Narradores de Javé is a Franco-Brazilian film of 2003. It features the small town of Javé which is on the verge of being submerged due to the construction of a dam in the region. The inhabitants of Javé will not be compensated and have not even been notified because they have no proof of ownership of the land they occupy. Aggrieved, the villagers find out that the town could be saved if the historical value of the town could be proven “through scientific documentation.” The villagers then invest all their hopes in the elaboration of a history of the small town, which must be written by the only literate resident—the postman. The memorialistic narrative of each resident is done orally and recorded by the postman. The elaboration process of this “historical work” is slow, as each inhabitant insists on continually altering “some lines” and ensuring that their name is quoted.
- 25.
In this text Mendes (2009) points out some similarities and differences between the history of mathematics and the history of school mathematics. The book is written in Portuguese, and has not been translated into English.
- 26.
Under an arithmetical conception, logarithms are numbers, and teaching them is a consequence of teaching of progressions, sequences of numbers with a specific formation law. Under a geometric conception, the logarithms are seen as values of a function (the logarithmic function), and the focus lies on the variation (functional conception), dealt with mainly from graphical representations. The algebraic-functional conception approaches logarithm from the study of exponents and then defines them as values of a specific function (in teaching, according to this conception, logarithms derive from the study of functions).
- 27.
PIBID is an acronym in Portuguese for Institutional Program for Teaching Scholarships Initiatives (Programa Institucional de Bolsas de Iniciação à Docência). This program, implemented by the federal government, provides scholarships for undergraduate students and elementary and high school teachers who work in partnership with university professors in public schools, in specific teaching and research projects.
- 28.
In Brazil, the completion of an internship in public elementary and high schools (under the supervision of a university professor and the teacher in charge of the classroom in which the internship will be carried out) is compulsory for obtaining a teaching degree in mathematics.
- 29.
More widespread in the past, but still found in very small elementary schools (in rural areas, for instance), multigrade classes are spaces in which students of different levels of schooling (grades) will be taught by the same teacher.
- 30.
Life history is a type of oral history. While doing a life history, individuals narrate their lives, from childhood to the present. Life history is, in this sense, broader narratives than the thematic oral history (another type of oral history) through which the interviewees create a more restricted narrative, talking about some specific moment in their lives.
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Tizzo, V.S., Garnica, A.V.M. (2019). History of Mathematics Education and Oral History: Possibilities for the Classroom. In: Garnica, A. (eds) Oral History and Mathematics Education . History of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-16311-2_5
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