Session Information
24 SES 05.5 A, General Poster Session
General Poster Session
Contribution
Scientists, in general, and researchers and university teachers, in particular, should have precise information and knowledge about the origins of their disciplinary field. This idea reminds us of Aristotle's argument that we understand a subject best when we see it grow from its origins (Metaphysics, Book I, Chapter I, p. 12). Specifically, he said: "seeking first to understand the causes of the entities that surround us .... in the search for their causes, they advanced to that one".
In the case of Mathematics Education, different authors (Kilpatrick, 1998, 2020; Artigue & Blomhøj, 2013; Fiorentini & Lorenzato, 2015) have described how, during the last two centuries, research in this field has focused on analysing what mathematics was developed in schools and how it was taught and what learning (usefulness) resulted from it. Parallel to this scientific development, Kilpatrick (1998) raised the problems inherent in this work; in particular, the constitution of a group of people who identified themselves as researchers in mathematics education and focused their efforts on defining them and instituting their own research methods. During this period, figures such as Augustin Cauchy, responsible for the reorganisation and foundation of the field of mathematical analysis at the beginning of the 19th century, Ulysse Dini, from the University of Pisa, who wrote the first modern treatise on functions of a real variable, or Emile Borel who, from his collection of works on the theory of functions, developed some twenty volumes that gave the international mathematical community access to the most recent developments in research in this field (Artigue, 2020). Belhoste (1998), for his part, states that the constitution and institutionalisation of the mathematical community in countries such as Germany, France and Italy is largely due to the development of educational institutions focused on the teaching of this discipline.
These and many other examples from the scientific literature describe in great detail the origins of the development of the scientific community of mathematics education; however, we have not found any bibliographical evidence on the origins of research in mathematics education through doctoral theses or dissertations in this scientific field.
As we know, doctoral theses have a long history from the Middle Ages to present-day universities, but the recovery of the first European theses on this field of study -their reading and analysis- is a hard and complex exercise in documentary archaeology. Institutional repositories and databases are sources in which to search for doctoral theses and master's theses; some have indexed dissertations (we speak of dissertations, as a general term, with two variants: doctoral theses and master's theses) from more than 200 years ago. Databases in this respect are: the Spanish database Catalog-CISNE, the British Library-Ethos: e-thesis, the German Deustsche Nationalbibliothek or the Belgian Dial. UCLovaine. Other European dissertation databases are more recent, dating from the mid-20th century, such as the French TEL-These en ligne or the Dutch NARCIS.
For all these reasons, the present study focuses on identifying and analysing the origins of university research in Mathematics Education. Following a documentary archaeology exercise, a total of 23 European doctoral and master's theses in the field of mathematics education, defended more than one hundred years ago (1854-1917), have been located. They are thus centuries-old dissertations and indicative of the origins of university research in this field. In this way, this work is a first step towards understanding and illuminating the field of mathematics education from its beginnings and, by extension, as a study of the history of science geographically limited to Europe.
Method
The study of documentary sources allows the use of different approaches, depending on the objective, the questions posed or the nature of the documentary sources. In this case, we have used what is known as "documentary archaeology", i.e., the analysis of documents extracted from historical records. In the field of archaeology, such studies aim to demonstrate to archaeologists that the historical record, far from being a finite body of specialised information, is in fact a rich treasure trove of new insights into the past (Beaudry, 1988; Saldanha, 2020; City of Alexandria, 2022). It is also a descriptive-exploratory-retrospective study that analyses a total of 23 dissertations that could be called the pioneering European university works in Mathematics Education. These works have been located in four European databases: the Spanish database Catalog-CISNE, the British Library-Ethos: e-thesis, the German Deustsche Nationalbibliothek or the Belgian Dial.UCLovaine. Through successive advanced computer searches in the various databases indicated, the time span 1800-1922 was established. The keywords entered interchangeably were: dissertation, thesis, education, mathematics, arithmetic, geometry. However, the validation of the retrieved document as a "pioneering European thesis in mathematics education" requires a detailed, quasi-craftsmanlike tracing. Since we have only been able to operate with secondary sources (the reference of the thesis contained in a database), access to the thesis itself (primary source) has only been possible in some cases where these had been digitised. The methodological procedure followed is that proposed by documentary archaeology in the following phases: - Selecting the site: European Education. - Conducting research: about Centennial dissertations in mathematics education. - Excavating the site: in European databases on theses and masters. Search sequences. High concern about the validity of primary and secondary sources. - Cleaning and cataloguing artifacts (dissertations): cleaning of retrieved documents, cataloguing dissertations in Excel database, analyzing data and interpreting. - Reporting the results: Treatment of the information obtained (i. e. this poster). The following indicators have been analysed: year of defence, conceptual analysis of the title, author, language, keywords and the producing university.
Expected Outcomes
The documentary archaeology work carried out has allowed us to locate and recover 23 theses that fit the aforementioned characteristics; a meagre number, almost an appendix to the dissertations in the two main disciplines: mathematics and education. Some general conclusions can be drawn from the analysis of these works: - The conceptual analysis of the titles of the academic works determines that, except for four doctoral theses, the focus of university studies revolves around mathematics (its origin and history) or any of its disciplines (arithmetic, geometry, probability, calculus, and measurement). - The author's genre according to his or her own name (Vallejo, Torralbo & Fernández-Cano, 2016). All the theses analysed have been written by men, except the one defended by Eva Sachs (1917), written within the area of Philological Studies, although with a notable connotation with mathematics education. - Eleven of the doctoral dissertations are written in German, seven in Spanish, and the rest in French and English. - The German producing universities are the Universität Erlangen and the Universität Munich, with three and two doctoral theses, respectively, and, in the case of Spain, production is centralised only at the Universidad Central de Madrid, with seven. The Université Catholique de Louvain is also worth mentioning, with a production of two doctoral theses. Finally, it should be noted that given the current state of European databases as highly idiosyncratic, national, and not connected, a work of integration of European databases of doctoral dissertations is proposed as an alternative to the powerful American ProQuest Dissertations attempting to conform a specific and updated database for the field of mathematics education. Other educational disciplines and specialties would be able to develop their own databases of dissertations and other end-of-studies projects.
References
ARTIGUE, M. (2020). El desarrollo de la didáctica de las matemáticas, una mirada internacional. Revista Chilena de Educación Matemática, 12(3), 83-95. ARTIGUE, M. & BLOMHØJ, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM, 45(6), 797-810. BEAUDRY, M. C. (1988). Introduction. In: Documentary archaeology in the New World (pp. 1-3). Cambridge University Press. BELHOSTE, B. (1998). Pour une réévaluation du rôle de l’enseignement dans l’histoire des mathématiques [For a re-evaluation of the role of teaching in the history of mathematics]. Revue d’Histoire des Mathématiques, 4, 289-304. Retrieved from: http://www.numdam.org/article/RhM_1998__4_2_289_0.pdf CITY OF ALEXANDRIA, VA. (2022). Archaeological process. Retrieved from: https://www.alexandriava.gov/archaeology/archaeological-process FIORENTINI, D., & LORENZATO, S. (2015). Investigación en Educación Matemática: recorridos históricos y metodológicos [Research in Mathematics Education: historical and methodological background]. Autores Asociados, LTDA. KILPATRICK, J. (1998). Investigación en educación matemática: su historia y algunos temas de actualidad [Research in mathematics education: its history and some current issues]. In J. Kilpatrick, P. Gómez, & L. Rico, (Eds.), Educación Matemática: Errores y dificultades de los estudiantes. Resolución de problemas. Evaluación Historia [Mathematics Education: Students' errors and difficulties. Problem solving. Evaluation History] (p. 1-18). Una Empresa Docente e Universidad de los Andes. KILPATRICK, J. (2020). History of research in mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (p. 349-354). Springer. SACHS, E. (1917). Die fiinf platonischen Korper. Zur Geschichte der Mathematik und der Elementenlehre Platons und der Pythagoreer. Berlin: Weidmann. SALDANHA, G.S. (2020). Linha Cumeada: an archeology of the epistemological statements of Bibliography in the foundation of Information Science. Encontros Bibli-Revista Eletronica de Biblioteconomia e Ciencia da Informacao, 25, (Especial), 1-16. https://doi.org/10.5007/1518-2924.2020.e73443 VALLEJO, M., TORRALBO, M. & FERNÁNDEZ-CANO, A. (2016). Gender bias in higher education: Spanish doctoral dissertations in mathematics education. Journal of Hispanic Higher Education, 15(3), 205-220. https://doi.org/10.1177/153819271559 Infographics (links to databases consulted): https://www.dnb.de/SharedDocs/Downloads/DE/Professionell/Netzpublikationen/anleitungSucheDissertationen.html https://ucm.on.worldcat.org/advancedsearch?queryString=tesis&databaseList= https://www.bl.uk/ethos-and-theses https://dial.uclouvain.be/memoire/ucl/en/search/site
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